title: George Jung

text: At FCI Danbury in March 1974 during his marijuana trafficking sentence, Jung's cellmate was Carlos Lehder, a young German Colombian man who introduced Jung to the dominant and powerful international drug-trafficking Medellín Cartel; in return, Jung taught Lehder about smuggling. When they were released in 1976, Jung and Lehder smuggled large quantities of cocaine into the United States by joining forces with Pablo Escobar, and they made millions of dollars.


title: George Jung

text: In 1994, Jung was arrested with of cocaine in Topeka, Kansas. He later pleaded guilty to three counts of conspiracy and received a 70-year sentence; his sentence was reduced to nearly 20 years after he testified against his ex-partner Carlos Lehder. Jung was incarcerated at Otisville Federal Prison (Medium Security), in Mount Hope, New York, then was transferred to Federal Correctional Institution, Fort Dix (Low Security), New Jersey, then was transferred to Federal Correctional Institution, La Tuna (Low Security), in Anthony, Texas.


title: George Jung

text: Jung was due to be released in November 2014, but was released early, on June 2, 2014, after nearly 20 years. In 2016, he was jailed for a federal supervision violation, then released from a halfway house in 2017.


title: George Jung

text: In September 2014, Jung contributed to the novel "Heavy" with T. Rafael Cimino, nephew of film director Michael Cimino. "Heavy" is a fictional story about Jung escaping from a Cuban prison and fleeing to Guatemala.


title: George Jung

text: Jung had been suffering from liver and kidney failure and was receiving hospice care when he died on May 5, 2021, at his Weymouth, Massachusetts home.


title: Variance

text: In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by formula_1, formula_2, formula_3, formula_4, or formula_5.


title: Variance

text: An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications is that, unlike the standard deviation, its units differ from the random variable, which is why the standard deviation is more commonly reported as a measure of dispersion once the calculation is finished.


title: Variance

text: There are two distinct concepts that are both called "variance". One, as discussed above, is part of a theoretical probability distribution and is defined by an equation. The other variance is a characteristic of a set of observations. When variance is calculated from observations, those observations are typically measured from a real world system. If all possible observations of the system are present then the calculated variance is called the population variance. Normally, however, only a subset is available, and the variance calculated from this is called the sample variance. The variance calculated from a sample is considered an estimate of the full population variance. There are multiple ways to calculate an estimate of the population variance, as discussed in the section below.


title: Variance

text: The two kinds of variance are closely related. To see how, consider that a theoretical probability distribution can be used as a generator of hypothetical observations. If an infinite number of observations are generated using a distribution, then the sample variance calculated from that infinite set will match the value calculated using the distribution's equation for variance.


title: Variance

text: The term "variance" was first introduced by Ronald Fisher in his 1918 paper "The Correlation Between Relatives on the Supposition of Mendelian Inheritance":


title: Variance

text: The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors, and, therefore, that the variability may be uniformly measured by the standard deviation corresponding to the square root of the mean square error. When there are two independent causes of variability capable of producing in an otherwise uniform population distributions with standard deviations formula_6 and formula_7, it is found that the distribution, when both causes act together, has a standard deviation formula_8. It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance...


title: Variance

text: The variance of a random variable formula_9 is the expected value of the squared deviation from the mean of formula_9, formula_11:


title: Variance

text: This definition encompasses random variables that are generated by processes that are discrete, continuous, neither, or mixed. The variance can also be thought of as the covariance of a random variable with itself:


title: Variance

text: The variance is also equivalent to the second cumulant of a probability distribution that generates formula_9. The variance is typically designated as formula_3, or sometimes as formula_4 or formula_5, or symbolically as formula_18 or simply formula_1 (pronounced "sigma squared"). The expression for the variance can be expanded as follows:


title: Variance

text: In other words, the variance of is equal to the mean of the square of minus the square of the mean of . This equation should not be used for computations using floating point arithmetic, because it suffers from catastrophic cancellation if the two components of the equation are similar in magnitude. For other numerically stable alternatives, see Algorithms for calculating variance.


title: Variance

text: If the generator of random variable formula_9 is discrete with probability mass function formula_22, then


title: Variance

text: The variance of a set of formula_26 equally likely values can be equivalently expressed, without directly referring to the mean, in terms of squared deviations of all pairwise squared distances of points from each other:


title: Variance

text: If the random variable formula_9 has a probability density function formula_33, and formula_34 is the corresponding cumulative distribution function, then


title: Variance

text: The exponential distribution with parameter is a continuous distribution whose probability density function is given by


title: Variance

text: A fair six-sided die can be modeled as a discrete random variable, , with outcomes 1 through 6, each with equal probability 1/6. The expected value of is formula_49 Therefore, the variance of is


title: Variance

text: Conversely, if the variance of a random variable is 0, then it is almost surely a constant. That is, it always has the same value:


title: Variance

text: If a distribution does not have a finite expected value, as is the case for the Cauchy distribution, then the variance cannot be finite either. However, some distributions may not have a finite variance, despite their expected value being finite. An example is a Pareto distribution whose index formula_55 satisfies formula_56


title: Variance

text: The general formula for variance decomposition or the law of total variance is: If formula_9 and formula_58 are two random variables, and the variance of formula_9 exists, then


title: Variance

text: The conditional expectation formula_61 of formula_9 given formula_58, and the conditional variance formula_64 may be understood as follows. Given any particular value "y" of the random variable "Y", there is a conditional expectation formula_65 given the event "Y" = "y". This quantity depends on the particular value "y"; it is a function formula_66. That same function evaluated at the random variable "Y" is the conditional expectation formula_67


title: Variance

text: In particular, if formula_58 is a discrete random variable assuming possible values formula_69 with corresponding probabilities formula_70, then in the formula for total variance, the first term on the right-hand side becomes


title: Variance

text: here formula_78 refers to the Mean of the Squares. In linear regression analysis the corresponding formula is


title: Variance

text: This can also be derived from the additivity of variances, since the total (observed) score is the sum of the predicted score and the error score, where the latter two are uncorrelated.


title: Variance

text: The population variance for a non-negative random variable can be expressed in terms of the cumulative distribution function "F" using


title: Variance

text: This expression can be used to calculate the variance in situations where the CDF, but not the density, can be conveniently expressed.


title: Variance

text: The second moment of a random variable attains the minimum value when taken around the first moment (i.e., mean) of the random variable, i.e. formula_84. Conversely, if a continuous function formula_85 satisfies formula_86 for all random variables "X", then it is necessarily of the form formula_87, where . This also holds in the multidimensional case.


title: Variance

text: Unlike the expected absolute deviation, the variance of a variable has units that are the square of the units of the variable itself. For example, a variable measured in meters will have a variance measured in meters squared. For this reason, describing data sets via their standard deviation or root mean square deviation is often preferred over using the variance. In the dice example the standard deviation is , slightly larger than the expected absolute deviation of 1.5.


title: Variance

text: The standard deviation and the expected absolute deviation can both be used as an indicator of the "spread" of a distribution. The standard deviation is more amenable to algebraic manipulation than the expected absolute deviation, and, together with variance and its generalization covariance, is used frequently in theoretical statistics; however the expected absolute deviation tends to be more robust as it is less sensitive to outliers arising from measurement anomalies or an unduly heavy-tailed distribution.


title: Variance

text: Variance is invariant with respect to changes in a location parameter. That is, if a constant is added to all values of the variable, the variance is unchanged:


title: Variance

text: then they are said to be uncorrelated. It follows immediately from the expression given earlier that if the random variables formula_97 are uncorrelated, then the variance of their sum is equal to the sum of their variances, or, expressed symbolically:


title: Variance

text: Since independent random variables are always uncorrelated (see ), the equation above holds in particular when the random variables formula_101 are independent. Thus, independence is sufficient but not necessary for the variance of the sum to equal the sum of the variances.


title: Variance

text: Define formula_9 as a column vector of formula_26 random variables formula_104, and formula_105 as a column vector of formula_26 scalars formula_107. Therefore, formula_108 is a linear combination of these random variables, where formula_109 denotes the transpose of formula_105. Also let formula_111 be the covariance matrix of formula_9. The variance of formula_113 is then given by:


title: Variance

text: One reason for the use of the variance in preference to other measures of dispersion is that the variance of the sum (or the difference) of uncorrelated random variables is the sum of their variances:


title: Variance

text: This statement is called the Bienaymé formula and was discovered in 1853. It is often made with the stronger condition that the variables are independent, but being uncorrelated suffices. So if all the variables have the same variance σ, then, since division by "n" is a linear transformation, this formula immediately implies that the variance of their mean is


title: Variance

text: That is, the variance of the mean decreases when "n" increases. This formula for the variance of the mean is used in the definition of the standard error of the sample mean, which is used in the central limit theorem.


title: Variance

text: Using the linearity of the expectation operator and the assumption of independence (or uncorrelatedness) of "X" and "Y", this further simplifies as follows:


title: Variance

text: Here, formula_122 is the covariance, which is zero for independent random variables (if it exists). The formula states that the variance of a sum is equal to the sum of all elements in the covariance matrix of the components. The next expression states equivalently that the variance of the sum is the sum of the diagonal of covariance matrix plus two times the sum of its upper triangular elements (or its lower triangular elements); this emphasizes that the covariance matrix is symmetric. This formula is used in the theory of Cronbach's alpha in classical test theory.


title: Variance

text: So if the variables have equal variance "σ" and the average correlation of distinct variables is "ρ", then the variance of their mean is


title: Variance

text: This implies that the variance of the mean increases with the average of the correlations. In other words, additional correlated observations are not as effective as additional independent observations at reducing the uncertainty of the mean. Moreover, if the variables have unit variance, for example if they are standardized, then this simplifies to


title: Variance

text: This formula is used in the Spearman–Brown prediction formula of classical test theory. This converges to "ρ" if "n" goes to infinity, provided that the average correlation remains constant or converges too. So for the variance of the mean of standardized variables with equal correlations or converging average correlation we have


title: Variance

text: Therefore, the variance of the mean of a large number of standardized variables is approximately equal to their average correlation. This makes clear that the sample mean of correlated variables does not generally converge to the population mean, even though the law of large numbers states that the sample mean will converge for independent variables.


title: Variance

text: There are cases when a sample is taken without knowing, in advance, how many observations will be acceptable according to some criterion. In such cases, the sample size is a random variable whose variation adds to the variation of , such that,


title: Variance

text: If has a Poisson distribution, then formula_127 with estimator = . So, the estimator of formula_128 becomes formula_129 giving formula_130


title: Variance

text: The scaling property and the Bienaymé formula, along with the property of the covariance jointly imply that


title: Variance

text: This implies that in a weighted sum of variables, the variable with the largest weight will have a disproportionally large weight in the variance of the total. For example, if "X" and "Y" are uncorrelated and the weight of "X" is two times the weight of "Y", then the weight of the variance of "X" will be four times the weight of the variance of "Y".


title: Variance

text: In general, if two variables are statistically dependent, then the variance of their product is given by:


title: Variance

text: The delta method uses second-order Taylor expansions to approximate the variance of a function of one or more random variables: see Taylor expansions for the moments of functions of random variables. For example, the approximate variance of a function of one variable is given by


title: Variance

text: Real-world observations such as the measurements of yesterday's rain throughout the day typically cannot be complete sets of all possible observations that could be made. As such, the variance calculated from the finite set will in general not match the variance that would have been calculated from the full population of possible observations. This means that one estimates the mean and variance from a limited set of observations by using an estimator equation. The estimator is a function of the sample of "n" observations drawn without observational bias from the whole population of potential observations. In this example that sample would be the set of actual measurements of yesterday's rainfall from available rain gauges within the geography of interest.


title: Variance

text: The simplest estimators for population mean and population variance are simply the mean and variance of the sample, the sample mean and (uncorrected) sample variance – these are consistent estimators (they converge to the correct value as the number of samples increases), but can be improved. Estimating the population variance by taking the sample's variance is close to optimal in general, but can be improved in two ways. Most simply, the sample variance is computed as an average of squared deviations about the (sample) mean, by dividing by "n." However, using values other than "n" improves the estimator in various ways. Four common values for the denominator are "n," "n" − 1, "n" + 1, and "n" − 1.5: "n" is the simplest (population variance of the sample), "n" − 1 eliminates bias, "n" + 1 minimizes mean squared error for the normal distribution, and "n" − 1.5 mostly eliminates bias in unbiased estimation of standard deviation for the normal distribution.


title: Variance

text: Firstly, if the true population mean is unknown, then the sample variance (which uses the sample mean in place of the true mean) is a biased estimator: it underestimates the variance by a factor of ("n" − 1) / "n"; correcting by this factor (dividing by "n" − 1 instead of "n") is called "Bessel's correction". The resulting estimator is unbiased, and is called the (corrected) sample variance or unbiased sample variance. For example, when "n" = 1 the variance of a single observation about the sample mean (itself) is obviously zero regardless of the population variance. If the mean is determined in some other way than from the same samples used to estimate the variance then this bias does not arise and the variance can safely be estimated as that of the samples about the (independently known) mean.


title: Variance

text: Secondly, the sample variance does not generally minimize mean squared error between sample variance and population variance. Correcting for bias often makes this worse: one can always choose a scale factor that performs better than the corrected sample variance, though the optimal scale factor depends on the excess kurtosis of the population (see mean squared error: variance), and introduces bias. This always consists of scaling down the unbiased estimator (dividing by a number larger than "n" − 1), and is a simple example of a shrinkage estimator: one "shrinks" the unbiased estimator towards zero. For the normal distribution, dividing by "n" + 1 (instead of "n" − 1 or "n") minimizes mean squared error. The resulting estimator is biased, however, and is known as the biased sample variation.


title: Variance

text: The population variance matches the variance of the generating probability distribution. In this sense, the concept of population can be extended to continuous random variables with infinite populations.


title: Variance

text: In many practical situations, the true variance of a population is not known "a priori" and must be computed somehow. When dealing with extremely large populations, it is not possible to count every object in the population, so the computation must be performed on a sample of the population. Sample variance can also be applied to the estimation of the variance of a continuous distribution from a sample of that distribution.


title: Variance

text: We take a sample with replacement of "n" values "Y", ..., "Y" from the population, where "n" < "N", and estimate the variance on the basis of this sample. Directly taking the variance of the sample data gives the average of the squared deviations:


title: Variance

text: Since the "Y" are selected randomly, both formula_142 and formula_145 are random variables. Their expected values can be evaluated by averaging over the ensemble of all possible samples {"Y"} of size "n" from the population. For formula_145 this gives:


title: Variance

text: Hence formula_145 gives an estimate of the population variance that is biased by a factor of formula_149. For this reason, formula_145 is referred to as the "biased sample variance".


title: Variance

text: Either estimator may be simply referred to as the "sample variance" when the version can be determined by context. The same proof is also applicable for samples taken from a continuous probability distribution.


title: Variance

text: The use of the term "n" − 1 is called Bessel's correction, and it is also used in sample covariance and the sample standard deviation (the square root of variance). The square root is a concave function and thus introduces negative bias (by Jensen's inequality), which depends on the distribution, and thus the corrected sample standard deviation (using Bessel's correction) is biased. The unbiased estimation of standard deviation is a technically involved problem, though for the normal distribution using the term "n" − 1.5 yields an almost unbiased estimator.


title: Variance

text: The unbiased sample variance is a U-statistic for the function "ƒ"("y", "y") = ("y" − "y")/2, meaning that it is obtained by averaging a 2-sample statistic over 2-element subsets of the population.


title: Variance

text: Being a function of random variables, the sample variance is itself a random variable, and it is natural to study its distribution. In the case that "Y" are independent observations from a normal distribution, Cochran's theorem shows that "S" follows a scaled chi-squared distribution (see also: asymptotic properties):


title: Variance

text: If the "Y" are independent and identically distributed, but not necessarily normally distributed, then


title: Variance

text: If the conditions of the law of large numbers hold for the squared observations, "S" is a consistent estimator of "σ". One can see indeed that the variance of the estimator tends asymptotically to zero. An asymptotically equivalent formula was given in Kenney and Keeping (1951:164), Rose and Smith (2002:264), and Weisstein (n.d.).


title: Variance

text: Samuelson's inequality is a result that states bounds on the values that individual observations in a sample can take, given that the sample mean and (biased) variance have been calculated. Values must lie within the limits formula_157


title: Variance

text: where "y" is the maximum of the sample, "A" is the arithmetic mean, "H" is the harmonic mean of the sample and formula_159 is the (biased) variance of the sample.


title: Variance

text: The F-test of equality of variances and the chi square tests are adequate when the sample is normally distributed. Non-normality makes testing for the equality of two or more variances more difficult.


title: Variance

text: Several non parametric tests have been proposed: these include the Barton–David–Ansari–Freund–Siegel–Tukey test, the Capon test, Mood test, the Klotz test and the Sukhatme test. The Sukhatme test applies to two variances and requires that both medians be known and equal to zero. The Mood, Klotz, Capon and Barton–David–Ansari–Freund–Siegel–Tukey tests also apply to two variances. They allow the median to be unknown but do require that the two medians are equal.


title: Variance

text: The Lehmann test is a parametric test of two variances. Of this test there are several variants known. Other tests of the equality of variances include the Box test, the Box–Anderson test and the Moses test.


title: Variance

text: Resampling methods, which include the bootstrap and the jackknife, may be used to test the equality of variances.


title: Variance

text: The variance of a probability distribution is analogous to the moment of inertia in classical mechanics of a corresponding mass distribution along a line, with respect to rotation about its center of mass. It is because of this analogy that such things as the variance are called "moments" of probability distributions. The covariance matrix is related to the moment of inertia tensor for multivariate distributions. The moment of inertia of a cloud of "n" points with a covariance matrix of formula_111 is given by


title: Variance

text: This difference between moment of inertia in physics and in statistics is clear for points that are gathered along a line. Suppose many points are close to the "x" axis and distributed along it. The covariance matrix might look like


title: Variance

text: That is, there is the most variance in the "x" direction. Physicists would consider this to have a low moment "about" the "x" axis so the moment-of-inertia tensor is


title: Variance

text: The "semivariance" is calculated in the same manner as the variance but only those observations that fall below the mean are included in the calculation:formula_166It is also described as a specific measure in different fields of application. For skewed distributions, the semivariance can provide additional information that a variance does not.


title: Variance

text: If formula_167 is a scalar complex-valued random variable, with values in formula_168 then its variance is formula_169 where formula_170 is the complex conjugate of formula_171 This variance is a real scalar.


title: Variance

text: If formula_9 is a vector-valued random variable, with values in formula_173 and thought of as a column vector, then a natural generalization of variance is formula_174 where formula_175 and formula_176 is the transpose of formula_177 and so is a row vector. The result is a positive semi-definite square matrix, commonly referred to as the variance-covariance matrix (or simply as the "covariance matrix").


title: Variance

text: If formula_9 is a vector- and complex-valued random variable, with values in formula_179 then the covariance matrix is formula_180 where formula_181 is the conjugate transpose of formula_182 This matrix is also positive semi-definite and square.


title: Variance

text: Another generalization of variance for vector-valued random variables formula_9, which results in a scalar value rather than in a matrix, is the generalized variance formula_184, the determinant of the covariance matrix. The generalized variance can be shown to be related to the multidimensional scatter of points around their mean.


title: Variance

text: A different generalization is obtained by considering the Euclidean distance between the random variable and its mean. This results in formula_185 which is the trace of the covariance matrix.


title: Passengers (2016 film)

text: Passengers is a 2016 American science-fiction romance film directed by Morten Tyldum, written by Jon Spaihts and starring Jennifer Lawrence and Chris Pratt. The supporting cast features Michael Sheen, Laurence Fishburne and Andy García. The film follows two passengers on an immense interstellar spacecraft carrying thousands of people to a colony 60 light years from Earth, when the two are awakened 90 years early from their induced hibernation.


title: Passengers (2016 film)

text: The script was written in 2007 by Spaihts, but languished in development hell with multiple actors attached and detached from it over the years until Sony Pictures Entertainment acquired its rights in late 2014. Lawrence, Pratt and Tyldum quickly joined the project, and filming took place from September 2015 to February 2016 in Atlanta. It was produced by Village Roadshow Pictures, Start Motion Pictures, Original Film, LStar Capital, Wanda Pictures and Company Films, and was the last film from Columbia Pictures with the involvement of Village Roadshow Pictures.


title: Passengers (2016 film)

text: "Passengers" premiered at the Regency Village Theater in Los Angeles on December 14, 2016, and was released theatrically in the United States by Columbia Pictures on December 21, 2016, in standard format and RealD 3D. It received mixed reviews, with praise for Lawrence and Pratt's performances, Newman's musical score, and its visual style and production values, but was criticized for its plot and characters. It grossed $304 million worldwide and was nominated for Best Original Score and Best Production Design at the 89th Academy Awards.


title: Passengers (2016 film)

text: The "Avalon", a sleeper ship transporting 5,000 colonists and 258 crew members in hibernation pods, is traveling from Earth to the planet Homestead II, a 120-year journey. After only 30 years, an asteroid collision damages the ship despite its defense systems, causing a malfunction that awakens mechanical engineer James Preston "Jim" 90 years too early.


title: Passengers (2016 film)

text: After a year of isolation, with only an android barman named Arthur for company, Jim grows despondent and contemplates suicide until he notices Aurora Lane, a beautiful young woman inside her pod. He views her video interview file, and is smitten. He considers reviving her for companionship, but struggles with the morality of doing so, knowing it will rob her of her intended life on their destination planet. He eventually causes her pod to awaken her, letting her believe she was also the victim of a malfunction. He asks Arthur not to reveal what he has done. Aurora, devastated at having to live out her life on the ship, unsuccessfully tries to re-enter hibernation. Resigned to the situation, Aurora, a writer and journalist, resumes writing about her experience.


title: Passengers (2016 film)

text: The two slowly grow closer over the next year, and eventually, fall in love. Jim intends to propose to her; but when Arthur hears Jim say there are "no secrets" between him and Aurora, the android reveals the truth of her awakening. Aurora berates, shuns, and even physically attacks Jim. She furiously rejects his apologies and avoids contact with him.


title: Passengers (2016 film)

text: Sometime later, another pod failure awakens Gus Mancuso, a deck chief officer. Using his personal code to access the bridge (which Jim has repeatedly and unsuccessfully tried to force his way into), they discover multiple cascading failures throughout the ship's systems, but the computer doesn't reveal their origin. If the faults are not repaired, the ship will inevitably fail, causing the passengers and crew to perish. While Gus attempts repairs with Jim and Aurora's help, he uncovers the story of Jim awakening Aurora through examining their pods and discusses it with them separately; Gus does not condone Jim's actions but understands, and tells Aurora that a "drowning man" (the suicidal Jim) will grab onto any lifeline, even if it were to put their rescuer in danger. Having generally felt unwell since waking, Gus falls critically ill. The ship's automated medical suite, the Autodoc, reveals that Gus has suffered pansystemic necrosis and that he has only hours to live, which Gus realizes was caused by multiple failures of his hibernation pod. Before dying, Gus gives Jim and Aurora his officer's ID, allowing them to access crew-only areas and try to repair the ship.


title: Passengers (2016 film)

text: Jim and Aurora find a series of hull breaches from the asteroid's penetration two years earlier. The computer module administering the ship's fusion reactor power plant has been critically damaged, causing the cascading malfunctions as the other systems' computing power was diverted to try to maintain it. They replace the damaged module, but when the computer attempts to vent the reactor to extinguish a runaway plasma reaction, the exterior vent fails. Jim is forced to spacewalk and vent the plasma from outside, using the manual controls in the vent tube.


title: Passengers (2016 film)

text: Jim learns that he must remain in the tube, keeping the vent open, while Aurora initiates venting from inside the ship. Revealing her enduring feelings for him, she admits she is terrified of losing him and being left alone. Jim uses a door as an improvised heat shield and survives the venting but is blasted out into space as his tether snaps, and his damaged spacesuit begins losing oxygen. Aurora retrieves a clinically dead Jim from space and manages to resuscitate him in the Autodoc while the "Avalon", its reactor repaired, returns to normal operations.


title: Passengers (2016 film)

text: After burying Gus in space, Jim learns that with Gus' clearance the Autodoc can function as a hibernation pod for one person, and offers to put Aurora back in hibernation for the remainder of the voyage. Realizing she would never see him again, she chooses to remain awake with him. He presents her with the makeshift engagement ring he made earlier, which she accepts.


title: Passengers (2016 film)

text: Eighty-eight years later, the ship's crew is awakened on schedule, shortly before their arrival at Homestead II. In the ship's grand concourse, they discover a huge tree with trailing vines, lush vegetation, flying birds, and a cabin. A recording of Aurora's story describes the wonderful life she and Jim had together on the "Avalon".


title: Passengers (2016 film)

text: Emma Clarke, Chris Edgerly, Matt Corboy, Fred Melamed, and screenwriter Jon Spaihts perform as the voices of the "Avalon", InfoMat, video game, observatory, and Autodoc, respectively.


title: Passengers (2016 film)

text: In Jon Spaihts's original 2007 script, Aurora's surname was Dunn. At one point in the film's development, it was set to star Keanu Reeves and Emily Blunt. Other actors temporarily attached to it included Reese Witherspoon and Rachel McAdams. Brian Kirk was originally set to make his feature directorial debut with Reeves in the lead. On December 5, 2014, it was announced that Sony Pictures Entertainment had won the rights to the film, and in early 2015, Morten Tyldum was chosen to direct. He had always wanted to do a big-scale sci-fi movie, but also stressed the importance of character development over effects.


title: Passengers (2016 film)

text: The final cast was announced between February 2015 and January 2016. Lawrence was paid $20 million against 30% of the profit after the movie broke even. Pratt received $12 million.


title: Passengers (2016 film)

text: Principal photography began on September 15, 2015 at Pinewood Atlanta Studios in Atlanta, with most of it involving the two leads only. Rodrigo Prieto was cinematographer, and Maryann Brandon was film editor. Filming wrapped on February 12, 2016.


title: Passengers (2016 film)

text: Thomas Newman composed the score for "Passengers". Spaihts said that he wrote "Passengers" while listening to Newman's previous scores. Imagine Dragons also recorded the song "Levitate" for the soundtrack, which was released on November 29, 2016. The Chinese theme song for the film is "Light Years Away", composed by G.E.M.; it became the first Chinese music video to surpass 200 million views in September 2019.


title: Passengers (2016 film)

text: At the 2016 CinemaCon, "Passengers" was featured by Sony Pictures chairman Thomas Rothman with Lawrence and Pratt in attendance. A teaser trailer of unfinished footage was shown afterwards. The first official images of the film were released on August 12, 2016.


title: Passengers (2016 film)

text: In August 2015, Sony Pictures Entertainment set the film's release date for December 21, 2016, in the United Kingdom, United States and Canada. It was concurrently released in 3D and RealD 3D formats, with the international rollout running from Christmas to January 12, 2017.


title: Passengers (2016 film)

text: "Passengers" was released on DVD, Blu-ray, and 4K Ultra HD Blu-ray on March 14, 2017, and made available on digital HD from Amazon Video and iTunes on March 7, 2017.


title: Passengers (2016 film)

text: On March 14, 2017, "Passengers: Awakening", a virtual-reality experience based on the film launched for Oculus Rift and HTC Vive.


title: Passengers (2016 film)

text: "Passengers" grossed $100 million in the United States and Canada and $203.1 million in other territories for a worldwide total of $303.1 million, against a net production budget of $110 million. It was the second-highest grossing original live-action Hollywood release of 2016, after "La La Land".


title: Passengers (2016 film)

text: "Passengers" opened alongside "Sing" and "Assassin's Creed", and was initially expected to gross around $50 million from 3,478 theaters over its first six days, although the studio anticipated a more conservative $35 million debut. After making $1.2 million from Tuesday night previews and $4.1 million on its first day, projections for the six-day opening were lowered to $27 million. It went on to gross $15.1 million in its opening weekend (a six-day total of $30 million), finishing third at the box office behind "Rogue One" and "Sing". It became the third-biggest original live-action domestic release of 2016 behind "La La Land" ($149 million) and "Central Intelligence" ($126 million).


title: Passengers (2016 film)

text: On Rotten Tomatoes, the film has an approval rating of 30% based on reviews from 290 critics with an average rating of 5.00/10. The website's critical consensus reads: ""Passengers" proves Chris Pratt and Jennifer Lawrence work well together – and that even their chemistry isn't enough to overcome a fatally flawed story." On Metacritic, the film has a weighted average score of 41 out of 100, based on 48 reviews, indicating "mixed or average reviews". Audiences polled by CinemaScore gave the film an average grade of "B" on an A+ to F scale, while PostTrak reported filmgoers gave it a 77% overall positive score.


title: Passengers (2016 film)

text: Mick LaSalle of "The San Francisco Chronicle" gave the film 3 out of 4 stars, writing: "Despite the confinement and the limited cast, "Passengers" has moments of intense drama that take the actors to places of extreme feeling." James Dyer of "Empire" gave the film 4 out of 5 stars, saying it was "as surprisingly traditional as it is undeniably effective", and describing it as ""Titanic" amongst the stars" and "a touching, heartfelt tale of loss and love for the "Gravity" generation". Peter Keough of "The Boston Globe" gave it 2.5 out of 4 stars, stating: "Perhaps as a well-written play for a cast of three, "Passengers" might have been first class. Instead, it's just another mediocre thrill ride." Peter Bradshaw of "The Guardian" called the film an "appealing sci-fi romance", but criticized its final act as an "anticlimax", giving it 3 out of 5 stars. Sheri Linden of "The Hollywood Reporter" said it "concocts a sort of "Titanic" in outer space, with dollops of "Sleeping Beauty" and "Gravity" thrown into the high-concept mix." She praised the striking visual design and elegant costumes, but said that the "heavy-handed mix of life-or-death exigencies and feel-good bromides finally feels like a case of more being less."


title: Passengers (2016 film)

text: Rebecca Hawkes of "The Telegraph" described the film as not a romance, but "a creepy ode to manipulation", describing the action as a "central act of violence" that is softened and justified. Andrew Pulver of "The Guardian" called it an "interstellar version of social-media stalking" with "a fantastically creepy start" that, contrary to romantic comedies that managed to "plane down" the nastiness of stalking tactics, presented them in a way where they were "gruesomely inescapable". Alissa Wilkinson of "Vox" called it "a fantasy of Stockholm syndrome, in which the captured eventually identifies with and even loves the captor" and "a really disturbing wish fulfillment fantasy".


title: Passengers (2016 film)

text: Lawrence was initially proud of the film, but agreed with suggestions that it might have benefited from a different edit, starting with her character waking up. Later Lawrence said that Adele had advised her against doing the film and she should have listened. Producer Neal Moritz said he loved the film and thought the script was one of the best he had ever read. He pointed out that it was well received at test screenings, but that shortly before its release the media picked up on one review and "it became a mantra". He "thought it was a really unfair thing because I think it's a beautiful film I couldn't be more proud of."


title: Calvin Harris

text: Adam Richard Wiles (born 17 January 1984), known professionally as Calvin Harris, is a Scottish DJ, record producer, singer, and songwriter. He has released six studio albums and is best known for producing.


title: Calvin Harris

text: His debut studio album, "I Created Disco", was released in June 2007. Its singles "Acceptable in the 80s" and "The Girls" both reached the top 10 in the UK. In 2009, he released second studio album, "Ready for the Weekend", which debuted at number one on the UK Albums Chart and whose lead single, "I'm Not Alone", became his first song to top the UK Singles Chart.


title: Calvin Harris

text: In 2012, Harris rose to international prominence with the release of his third studio album, "18 Months", which topped the UK Albums Chart and became his first album to chart on the US "Billboard" 200, peaking at number 19. All eight of the album's singles reached the top 10 in the UK, breaking the record for the most top 10 songs from one studio album on the UK Singles Chart with eight entries, surpassing Michael Jackson's record. In 2014, he released his fourth studio album, "Motion", which debuted at number two in the UK and number five in the US. In 2017, he released his fifth studio album, "Funk Wav Bounces Vol. 1", which reached the top two in the UK and the US and became his third consecutive number one album on the US Dance/Electronic Albums chart. His sixth studio album "Funk Wav Bounces Vol. 2" (2022) serves as a sequel to his previous release.


title: Calvin Harris

text: In October 2014, Harris became the first artist to place three songs simultaneously on the top 10 of "Billboard" Dance/Electronic Songs chart. He also became the first UK solo artist to reach more than one billion streams on Spotify. Harris has received 18 Brit Award nominations–winning British Producer of the Year and British Single of the Year in 2019, as well as five Grammy nominations, including a win for Best Music Video in 2013. In 2013 he also received a Ivor Novello Award, and was named the Top Dance/Electronic Artist at the 2015 "Billboard" Music Awards. He appeared on Debrett's 2017 list of the most influential people in the United Kingdom. He topped "Forbes" list of the world's highest-paid DJs for six consecutive years from 2013 to 2018 until being dethroned by The Chainsmokers in 2019.


title: Calvin Harris

text: Adam Richard Wiles was born on 17 January 1984 in Dumfries, to English parents, a biochemist father, and housewife mother, who married in their native Oxford before moving to Dumfries. He has an elder sister and brother. Wiles attended Calside Primary School then Dumfries High School, and, after leaving school, he stocked shelves in supermarkets and worked in a local fish processing factory in order to buy DJ gear.


title: Calvin Harris

text: He was first attracted to electronic music in his teens and began recording bedroom demos in 1999. When Harris was 18, he released two songs, "Da Bongos" and "Brighter Days". Both were released as 12-inch club singles and CD-EPs by the label Prima Facie in early 2002 under the name "Stouffer". With these singles to his credit, Harris moved from Scotland to London, hoping to learn from the local music scene. Only one of his songs, "Let Me Know" with vocalist Ayah Marar on the Unabombers' 2004 live-mix CD Electric Soul, Vol. 2, was released during his time in London. With the lack of job opportunities and money, he returned home to Dumfries and began posting homemade solo recordings to his Myspace page. His popularity on the social media website prompted Mark Gillespie, a talent booker for the dance-festival firm Global Gathering who had recently founded his own management firm, to make Harris the company's first signee. Regarding his choice of his stage name, Harris stated that, "My first single was more of a soul track, and I thought Calvin Harris sounded a bit more racially ambiguous. I thought people might not know if I was black or not. After that, I was stuck with it."


title: Calvin Harris

text: Harris signed contracts with Three Six Zero Group (management), EMI (publishing), and Sony BMG (recording) in 2006 after he had been discovered on the social networking website Myspace. Later in 2006, Harris produced a remix of All Saints' single "Rock Steady".


title: Calvin Harris

text: Harris's debut album, "I Created Disco", was released in June 2007. He started working on the album in 2006 after he moved back from living in London to his hometown of Dumfries. All 14 tracks were written, produced, and performed solely by Harris, and all recording and producing for the album took place on an Amiga computer. To promote "I Created Disco", Harris embarked on a tour of the UK, supporting Faithless and Groove Armada. "I Created Disco" was certified gold by the British Phonographic Industry (BPI). It reached number eight on the UK Albums Chart and number 19 on the US Top Electronic Albums.


title: Calvin Harris

text: The album contained uptempo electroclash songs that were influenced by music from the 1980s. The song, "Vegas", was issued on limited edition vinyl. The first wide-release single from the album was released in March 2007. "Acceptable in the 80s", a tribute to the style and culture of the decade, peaked at number ten on the UK Singles Chart, remaining on the chart for 15 weeks. "The Girls", the album's second single, peaked at number three on the UK Singles Chart. The third and final release from the album, "Merrymaking at My Place", peaked at number 43 on the chart.


title: Calvin Harris

text: The same year, Harris caught the attention of Australian pop singer Kylie Minogue after his recordings had been passed on to her by another record producer. This led to him co-writing and producing two songs, "Heart Beat Rock" and "In My Arms", on her 2007 album "X", the latter becoming a top 10 single in the UK. Harris said that working with Minogue was "surreal, but fun" although he admitted to "Mixmag" in 2007 to "needing a few drinks before meeting her". Harris also contributed the song "Off & On" to Róisín Murphy's album "Overpowered", but it was cut from the album. Harris would later give the song to Sophie Ellis-Bextor to record for her 2011 album "Make a Scene". Harris also produced a remix of the second single "4th of July (Fireworks)" from Kelis' album "Flesh Tone". He additionally reworked singles by Jamiroquai, Groove Armada, All Saints, and CSS.


title: Calvin Harris

text: In 2008, Harris collaborated with rapper Dizzee Rascal on his single "Dance wiv Me", producing the track and singing the hook. The single topped the UK Singles Chart for four weeks and was certified platinum by the BPI, selling 600,000 copies. It was shortlisted for the 2008 Popjustice £20 Music Prize. In 2009, it received a Brit Award nomination for British Single and an Ivor Novello Award nomination for Best Contemporary Song. On 18 October 2008, Harris was featured on BBC Radio 1's "Essential Mix" on a two-hour set.


title: Calvin Harris

text: Harris's second album, "Ready for the Weekend", was released in August 2009 and entered at number one on the UK Albums Chart, being certified gold by the BPI within two months of release. Eleven of the fourteen tracks on the album were sung, produced, and written solely by Harris. "I'm Not Alone", released as the album's lead single in April 2009, debuted at number one on the UK Singles Chart. The follow-up single, "Ready for the Weekend", reached number three. The third single, "Flashback", featuring Jordanian singer Ayah Marar reached number eighteen in the UK. During promotion of the album, Harris hosted a series of videos on YouTube titled Jam TV, in which musicians such as Florence Welch, Goldie, and Katy Perry tried to open pots of jam. At the 2010 Brit Awards, Harris received a nomination for Best British Male.


title: Calvin Harris

text: On 8 February 2010, "You Used to Hold Me" was released as the fourth and final single from the album. It peaked at number 27 on the UK Singles Chart. The song marked the last time Harris regularly sang on his records, opting to focus more on music production while having guest singers provide the vocals for him. The same year, shortly after his "Ready for the Weekend tour" wrapped up, Harris parted ways with members of his band in which he served as lead vocalist and made the decision to stop doing live shows. In an interview with "Billboard", Harris said that, "I thought I'd exhausted every avenue [on the two albums] and it takes a long time to make me sound good, which is why I stopped singing live as well. I'd like to think of someone who's better-looking, a better singer, better dancer to be the frontperson for the song." He also released several remixes, including remixes of Shakira's "She Wolf", Katy Perry's "Waking Up in Vegas", Mr Hudson's "Supernova" (featuring Kanye West), and Mika's "We Are Golden".


title: Calvin Harris

text: Harris also produced Dizzee Rascal's next single titled "Holiday", which topped the UK Singles Chart in August 2009. Harris made a guest appearance as vocalist on Tiësto's song "Century" on the Dutch producer's album, "Kaleidoscope". Harris also produced and mixed The Ting Tings' single "Hands" which was released on 18 August 2010. The song was originally set to become the first single of the duo's second studio album, but they cancelled the album plans and the song was included as a bonus track on the deluxe edition of "Sounds from Nowheresville". On 14 November 2009, Harris invaded the stage of the ITV talent competition "The X Factor" during a live performance by Irish contestants John and Edward Grimes, holding a pineapple on his head. He later apologised on Twitter.


title: Calvin Harris

text: Harris claimed that Chris Brown's "Yeah 3x", released in October 2010, plagiarised his 2009 single "I'm Not Alone". After considering similarities between the two songs, Harris was subsequently added to the songwriting credits on the single and the "F.A.M.E." album. Harris was also featured on Kylie Minogue's eleventh studio album, "Aphrodite", collaborating the track "Too Much".


title: Calvin Harris

text: In 2011, Harris toured as a support act for the European leg of Barbadian singer Rihanna's Loud Tour. Rihanna was quoted as saying, "Calvin is the perfect fit for the Loud Tour. He is going to bring something unique and fun for the fans." Harris played the 2011 Mardi Gras Party in Sydney on 5 March. Harris was also featured on LMFAO's album "Sorry for Party Rocking," appearing on the track "Reminds Me of You", which is based on Harris's own song "Awooga". Harris produced Tinchy Stryder's second single, "Off the Record", from his fourth studio album, "Full Tank." The track had its premiere on 15 September 2011 and was released in the UK on 6 November 2011.


title: Calvin Harris

text: Harris released the single "Bounce", the first single from his upcoming album, a collaboration with Kelis that debuted at number two on the UK Singles Chart in June 2011. "Feel So Close", the second single from the album, was released in August 2011 and also reached number two in the United Kingdom. "Feel So Close" became his first solo entry on the "Billboard" Hot 100 in the US, peaking at number 12. He performed at the 2011 Jingle Bell Ball concert and was announced as one of the headline acts at a number of Southern Hemisphere 2011/2012 new year music festivals.


title: Calvin Harris

text: Following a stint as the support act on the Australian leg of Rihanna's tour, Harris produced Rihanna's songs "We Found Love" and "Where Have You Been". The former was included on Harris's upcoming album "18 Months" and premiered on Capital FM radio in the UK on 22 September 2011. "We Found Love" topped the charts in 27 countries worldwide, including the UK where it became Harris's third UK number one, peaked in the top 10 in 30 countries, and broke many records worldwide. Topping the "Billboard" Hot 100 for 10 non-consecutive weeks, it was Harris's first US number one and was also Rihanna's longest-running US number one and the longest-running number one of 2011. "We Found Love" was later ranked number 24 on the list of the all-time top 100 songs on the "Billboard "Hot 100. In 2013, "We Found Love" was placed at number three on "Billboard"s top 10 dance-pop collaborations of all time.


title: Calvin Harris

text: Harris co-wrote and co-produced the bonus track "One Life" for R&B singer Mary J. Blige's album "My Life II... The Journey Continues" (2011). He also worked with the pop band Scissor Sisters on the single "Only the Horses" from their fourth studio album, "Magic Hour". He wrote and produced Cheryl Cole's single "Call My Name", the lead single from her third album "A Million Lights". He also produced a remix of Florence and the Machine's "Spectrum" titled "Spectrum (Say My Name)". The song was released as the album's fifth single on 5 July 2012. It was serviced to radio in the UK on 2 July 2012. It became the group's first single to peak at number one on the UK Singles Chart.


title: Calvin Harris

text: "Let's Go" featuring Ne-Yo, the third single from the album, was released in April 2012 and reached number two in the UK Singles Chart. It was his second US "Billboard" Hot 100 appearance as a main artist, charting at number 17. The song received a nomination for Best Dance Recording at the 55th Grammy Awards which was held in February 2013. The album's fourth single "We'll Be Coming Back" was released in July 2012. Featuring rapper Example, it peaked at number two in the UK. The fifth single, "Sweet Nothing", features Florence Welch of Florence and the Machine and was released on 14 October 2012. It peaked at number one on the UK Singles Chart and at number 10 on the US "Billboard" Hot 100. The song received a nomination for Best Dance Recording at the 56th Grammy Awards.


title: Calvin Harris

text: His third studio album, "18 Months", was released on 29 October 2012. Harris eventually made UK chart history by becoming the first artist to attain eight top-10 singles from one studio album, breaking the record previously set by Michael Jackson. In March 2017, the record was surpassed once again by Ed Sheeran, after his album "÷" spawned 10 top-10 songs on the UK chart. "18 Months" received a nomination for Best Dance/Electronica Album at the 56th Grammy Awards. Harris was also nominated for Best British Male Solo Artist at the 2013 Brit Awards in February.


title: Calvin Harris

text: Harris was the house DJ at the 2012 MTV Video Music Awards held at the Staples Center, Los Angeles, where he won Best Electronic Video for "Feel So Close" and Video of the Year alongside Rihanna for "We Found Love". Harris performed as part of the post-race concert of the 2013 Formula One Bahrain Grand Prix in April 2013. At the 2013 Ivor Novello Awards held at the Grosvenor House Hotel, London in May, Harris received the British Academy's Ivor Novello Award for Songwriter of the Year, with Harris calling it "easily the greatest achievement of my entire life". In 2012, Harris made statements explaining why he wanted to stop singing on tracks stating, "I want each track as good as it can possibly be, which usually means me not singing on it."


title: Calvin Harris

text: On 7 October 2013, Harris and Swedish DJ Alesso released a collaborative single with synthpop duo Hurts called "Under Control" as the first single from his fourth album. The song debuted at number one in the UK. Later that month, Harris remixed The Killers' song "When You Were Young" for the deluxe edition of their greatest hits album "Direct Hits". He unveiled the full six-minute version through "Rolling Stone" and told the magazine: "It was a real honour to be asked to remix one of my favourite modern bands, and it was an exciting challenge for me to update this classic track for the dance-floor in a tasteful and respectful way".


title: Calvin Harris

text: On 14 March 2014, Harris's song "Summer" premiered on the UK's Capital FM. The track which was released as the album's second single debuted at number one on the UK Singles Chart, becoming Harris's sixth UK number-one single. It also became Harris's highest-charting solo single on the US "Billboard" Hot 100, peaking at number seven. "Summer" was Spotify's most-streamed track of 2014 with over 200 million streams. Harris also produced the single "I Will Never Let You Down" for British singer Rita Ora. On 18 May 2014, the song debuted at number one on the UK Singles Chart, two weeks after his song "Summer" debuted at the top of the charts.


title: Calvin Harris

text: In April 2014, Harris performed on the main stage of Coachella Festival. His set attracted the second largest crowd in the festival's history, topped only by the 2012 set of Dr. Dre and Snoop Dogg which featured a hologram of Tupac Shakur. That year, he was also a headline act at several prominent music festivals, including Lollapalooza, Austin City Limits Music Festival, the iTunes Festival in London, Electric Daisy Carnival, and the iHeartRadio Music Festival.


title: Calvin Harris

text: The third single, "Blame", was a collaboration with vocalist John Newman. It was released in September 2014 to positive reviews from music critics and debuted at number one on the UK Singles Chart, giving Harris his third consecutive UK number-one single (and his seventh solo single overall). After the release of the song, Harris became the first British solo artist to reach more than a billion streams on Spotify. Later that month, Harris uploaded an instrumental track called "C.U.B.A." to SoundCloud. "Outside", the fourth single from the album, featuring Ellie Goulding, was released in October 2014. It marked the second collaboration between Harris and Goulding, following the internationally successful single "I Need Your Love" from 2013. The instrumental track "Slow Acid" was released as a promotional single from the album on 14 October 2014.


title: Calvin Harris

text: His fourth album, "Motion", was released on 4 November 2014. It includes the previously released singles "Under Control", "Summer", "Blame", and "Outside". Another track from the album, "Pray to God", featuring rock band trio Haim, was released on 11 February 2015. At the 2015 Brit Awards, "Summer" was nominated for Best British Single and British Artist Video of the Year. At the 2015 Glamour Awards in London on 2 June, Harris was named "Glamour" UK's Man of the Year. He was also ranked 6th on "Billboard"s Top 30 EDM Power Players. The same month, he was part of the main stage line-up at the Electric Daisy Carnival held in Las Vegas.


title: Calvin Harris

text: On 17 July 2015, Harris and London-based production trio Disciples released the single "How Deep Is Your Love". The song peaked at number two on the UK Singles Chart, giving Harris his 19th top-10 entry in the UK. It peaked at number one on the ARIA Charts, giving Harris his first chart-topper in Australia. The song peaked at number three on the Hot Dance/Electronic Songs in the US and marked Harris's eighth top-10 entry since the chart's launch, making it the most of any act. In September, Harris was featured on Dillon Francis's EP "This Mixtape Is Fire", collaborating on a Moombahton-style track entitled "What's Your Name". At the 2016 Brit Awards, Harris received three nominations: Best British Male Solo Artist, "How Deep Is Your Love" for British Single of the Year, and Best British Video.


title: Calvin Harris

text: Harris released a new single titled "This Is What You Came For", which features Rihanna, on 29 April 2016. The single debuted at number two on the UK Singles Chart. It peaked at number three on the US "Billboard" Hot 100, becoming Harris's second top five song. It also reached number one on the US Hot Dance/Electronic Songs, became Harris's tenth number one on sister chart Dance/Mix Show Airplay and his fourth chart-topper on the Hot Dance Club Songs Chart. It topped the charts in Australia, Canada, and the Republic of Ireland and peaked within the top ten of the charts in Germany, Ireland, New Zealand and Switzerland.


title: Calvin Harris

text: On 24 June 2016, Harris released a collaboration with Dizzee Rascal, titled "Hype". On 8 July 2016, John Newman released the track "Olé", which was produced by Harris. On 16 September 2016, Harris released "My Way", where he also performed vocals for the song.


title: Calvin Harris

text: On 21 February 2017, he announced the song "Slide", his collaboration with American singer-songwriter Frank Ocean and hip hop group Migos. The song was released on 25 February 2017. Harris released a collaboration with Young Thug, Ariana Grande, and Pharrell Williams titled "Heatstroke" on 31 March 2017. In May, he announced that his forthcoming fifth studio album, "Funk Wav Bounces Vol. 1", would be released on 30 June 2017. The album featured appearances from the likes of Travis Scott, Kehlani, Future, Katy Perry, Big Sean, John Legend, Khalid, Schoolboy Q, DRAM, Nicki Minaj, Lil Yachty, Jessie Reyez, PartyNextDoor and Snoop Dogg.


title: Calvin Harris

text: On 8 February 2018, Harris collaborated with PartyNextDoor to release a dancehall-influenced house track titled "Nuh Ready Nuh Ready". On 6 April 2018, he released "One Kiss" with Dua Lipa. On 17 August 2018, the next single "Promises" was released with Sam Smith. The music video for the song was released on 4 September and honours the LGBTQ community with references to the ball scene and voguing. In November 2018, he released "I Found You", a collaboration with Benny Blanco. The song features his first time singing on a track since his 2016 single "My Way". It peaked at number 29 in the UK. On 22 October 2018, Harris collaborated with Normani on the two track EP Normani x Calvin Harris. He topped Forbes' Highest-Paid DJs of 2018, becoming his sixth consecutive year to top the list (2013–2018).


title: Calvin Harris

text: His next single "Giant", a collaboration with English singer Rag'n'Bone Man was released in January 2019, peaking in the top 10 in several countries, including at number 2 in the UK. That year, mega-club Ushuaïa Ibiza booked Harris for a weekly Friday DJ residency for six weeks in August and September 2019.


title: Calvin Harris

text: In 2020, Harris went on "rediscover the way he originally began producing music 22 years ago" and released two EPs, "Love Regenerator 1" and "Love Regenerator 2", under his "Love Regenerator" alias. The third EP "Love Regenerator 3" was released on 13 March 2020.


title: Calvin Harris

text: On 22 August 2020, Harris announced his new song called, "Over Now" with Canadian singer The Weeknd. The song was released on 28 August 2020.


title: Calvin Harris

text: On 21 May 2021, Harris announced the song "By Your Side" featuring Tom Grennan. The song was released on 4 June 2021.


title: Calvin Harris

text: On 3 March 2022, Harris hinted at the release of his sixth album, "Funk Wav Bounces Vol. 2", on his Twitter. The lead single "Potion", featuring Dua Lipa and Young Thug, was released on 27 May.


title: Calvin Harris

text: On 29 June 2022, Harris announced that "Funk Wav Bounces Vol. 2" would be released on 5 August 2022. The album contains features from Charlie Puth, Swae Lee, Pusha T, Normani, Halsey, Tinashe, and Justin Timberlake, among others.


title: Calvin Harris

text: Harris announced the second single, "New Money", which features vocals from 21 Savage. The song was released on 1 July 2022. On 6 July 2022, Harris announced that his third single, "Stay with Me", featuring Halsey, Justin Timberlake, and Pharrell, would be released on 15 July 2022.


title: Calvin Harris

text: The fourth single, "New to You", was announced by Harris. It was set to be released on 29 July 2022. It features American singers Normani and Tinashe, and rapper Offset.


title: Calvin Harris

text: Following his professed disinterest in the genre of EDM in late 2016, Harris transitioned to funk on his fifth studio album "Funk Wav Bounces Vol. 1".


title: Calvin Harris

text: In 2008, the artwork of Harris's debut album "I Created Disco" was featured as part of a multicoloured iPod nano campaign on TV and in print in the US. In 2009, Harris teamed up with Coca-Cola for their 'Open Happiness' advertising campaign in the UK. Harris wrote and produced an exclusive track for the brand called 'Yeah Yeah Yeah, La La La' which was featured on TV, digital, outdoor and on-pack promotional activity and was offered on 'Coke Zone' website for free download. The same year, Harris's song "Colours" was featured in Kia Motors's hamster television advertisement for the Kia Soul EV.


title: Calvin Harris

text: In 2012, Harris was featured in the Pepsi Max commercial for their football campaign. Titled "crowd surfing", the advert showed Harris on the DJ deck playing his single "Let's Go" to the crowd of partygoers alongside star footballers Lionel Messi, Didier Drogba, Fernando Torres, Frank Lampard, Sergio Agüero and Jack Wilshere. In 2013, Harris teamed up with Sol Republic to create their first studio-tuned, professional-calibre headphones. The partnership involved designing a customised look for the headphones and redesigning its drivers to Harris's specifications.


title: Calvin Harris

text: On 17 December 2014, Harris was announced as the new face of Emporio Armani for its men's underwear line for the Spring/Summer 2015 season. He was also named the worldwide testimonial of the Emporio Armani eyewear and watch collection. The black and white campaign was shot in Los Angeles by photographer Boo George. Harris returned as the face of the brand underwear line, eyewear and watch line for their Emporio Armani Fall/Winter 2015/2016 campaign. The images, shot by Lachlan Bailey, were released in July 2015.


title: Calvin Harris

text: In March 2010, Harris launched his own vanity label, Fly Eye Records. Most of the label's releases belong to the EDM genre. In 2014, the label formed a partnership with Sony/ATV Music Publishing. Later that year, Harris was appointed as the head of the artists and repertoire team at the dance label Deconstruction Records.


title: Calvin Harris

text: In early 2012, Harris signed an exclusive DJ residency deal with Wynn Las Vegas which included gigs at three of the luxury resort's avenues: Encore Beach Club, Surrender and XS Nightclub. In February 2013, Harris signed as the first exclusive resident DJ with the Abu Dhabi-owned hospitality company Hakkasan Group in Las Vegas. The 20-month residency saw him play 46 dates at MGM Grand's Hakkasan nightclub, as well as 22 additional gigs at the MGM Grand's Wet Republic. In January 2015, he extended his partnership with the Hakkasan group for three more years, which includes residencies at three of the group's Las Vegas venues (Hakkasan nightclub, Wet Republic and Omnia Nightclub at Caesars Palace). Harris also serves as the Group's music consultant for its restaurants, nightclubs and hotels.


title: Calvin Harris

text: On 30 March 2015, Harris was announced as a co-owner, along with various other music artists, in the music streaming service Tidal. The service specialises in lossless audio and high definition music videos. Rapper Jay Z acquired the parent company of Tidal, Aspiro, in the first quarter of 2015. Including Beyoncé and Jay Z, 16 artist stakeholders (such as Kanye West, Beyoncé, Madonna, Chris Martin and Nicki Minaj) co-own Tidal, with the majority owning a 3% equity stake. The idea of having a completely artist-owned streaming service was created by those involved to adapt to the increased demand for streaming within the current music industry and to rival other streaming services such as Spotify, which have been criticised for their low payout of royalties.


title: Calvin Harris

text: In September 2007, Harris performed in the charity event "Wasted Youth" in aid of the Campaign Against Living Miserably at KOKO nightclub in Camden Town, London. The event aimed to draw attention to the issue of youth suicide among men in the UK and to raise awareness and money for the charity. In 2008, he supported Shelter's campaign "Hometime Scotland" which pledges to end homelessness and bad housing in Scotland. In 2010, Harris performed live in The War Child's post-Brit Awards show (alongside La Roux and Kasabian) which took place at the Shepherd's Bush Empire, London. The event raised funds and public awareness on children affected by violence in war zones.


title: Calvin Harris

text: In February 2012, Harris teamed up with several other artists (including Rihanna and Coldplay) to perform at a charity concert with all proceeds from the show going to the Children's Orthopaedic Center at the Children's Hospital Los Angeles. In November 2012, Harris contributed several songs to Tiësto's compilation album "Dance (RED) Save Lives" in collaboration with anti-AIDS charity Product Red which was aimed at creating awareness on the fight for an AIDS Free Generation. Harris participated in a global live stream of the Stereosonic music festival in Melbourne, Australia which took place on World AIDS Day on 1 December 2012. The proceeds from both the album and the event were donated for the cause.


title: Calvin Harris

text: Following the 2017 Las Vegas shooting, Harris revealed on his Instagram that he donated his fees from his show at Omnia Nightclub to the Las Vegas Victims fund. Later that year, Harris donated $20,000 to DJ Snake charity campaign to benefit the Rohingyas, people living in Myanmar that have consistently been attacked by the Myanmar government and are being pushed out of their home with nowhere to go. The situation in Myanmar has been deemed "beyond critical" by Amnesty International. In July 2020, Harris donated £20,000 for the Save Our Sub campaign to benefit Glasgow's Sub Club which was at risk of permanent closure after temporarily closing doors on March due to the coronavirus pandemic.


title: Calvin Harris

text: Calvin Harris is one of the highest paid disk jockeys/producers. "Forbes" began reporting on Harris's earnings in 2013, calculating that he earned $46 million between May 2012 and May 2013, for his music, tour and his residency in Las Vegas which placed him as the highest-paid DJ of the year. In 2014, Harris came in at number one on the list again for the second consecutive year with a total of $66 million in annual earnings. In 2015, Harris topped the highest-paid DJs list for a third consecutive year, having earned $66 million over the previous 12 months. On "The Sunday Times" Rich List published in April 2015, Harris was ranked the 30th richest British millionaire in music, with a personal fortune of £70 million ($105 million). In 2018, he made $48.5 million.


title: Calvin Harris

text: Harris dated British singer Rita Ora from 2013 to June 2014. He started dating American model Aarika Wolf in 2014, after Wolf appeared in the music video for his song "Blame". They broke up in 2015. From March 2015 to June 2016, Harris dated American singer Taylor Swift. He and Wolf got back together in 2017, and broke up in 2022. In January 2022, Harris started dating British presenter Vick Hope and in May they got engaged.


title: Calvin Harris

text: Harris stopped drinking alcohol in 2008, stating, "I wasn't an alcoholic or anything like that, but it was clearly affecting what I do." He is a supporter of his hometown football team Queen of the South and Liverpool F.C. Harris considered writing a song to celebrate the team reaching the 2008 Scottish Cup Final, but the idea was scrapped due to the time constraints of recording his 2009 album "Ready for the Weekend". Queen of the South would go on to lose the match 2-3 to Rangers.


title: Capacitor

text: A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.


title: Capacitor

text: The effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit. The capacitor was originally known as a condenser, a term still encountered in a few compound names, such as the "condenser microphone".


title: Capacitor

text: The physical form and construction of practical capacitors vary widely and many types of capacitor are in common use. Most capacitors contain at least two electrical conductors often in the form of metallic plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, sintered bead of metal, or an electrolyte. The nonconducting dielectric acts to increase the capacitor's charge capacity. Materials commonly used as dielectrics include glass, ceramic, plastic film, paper, mica, air, and oxide layers. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, an ideal capacitor does not dissipate energy, although real-life capacitors do dissipate a small amount (see Non-ideal behavior). When an electric potential difference (a voltage) is applied across the terminals of a capacitor, for example when a capacitor is connected across a battery, an electric field develops across the dielectric, causing a net positive charge to collect on one plate and net negative charge to collect on the other plate. No current actually flows through the dielectric. However, there is a flow of charge through the source circuit. If the condition is maintained sufficiently long, the current through the source circuit ceases. If a time-varying voltage is applied across the leads of the capacitor, the source experiences an ongoing current due to the charging and discharging cycles of the capacitor.


title: Capacitor

text: The earliest forms of capacitors were created in the 1740s, when European experimenters discovered that electric charge could be stored in water-filled glass jars that came to be known as Leyden jars. Today, capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems, they stabilize voltage and power flow. The property of energy storage in capacitors was exploited as dynamic memory in early digital computers, and still is in modern DRAM.


title: Capacitor

text: In October 1745, Ewald Georg von Kleist of Pomerania, Germany, found that charge could be stored by connecting a high-voltage electrostatic generator by a wire to a volume of water in a hand-held glass jar. Von Kleist's hand and the water acted as conductors and the jar as a dielectric (although details of the mechanism were incorrectly identified at the time). Von Kleist found that touching the wire resulted in a powerful spark, much more painful than that obtained from an electrostatic machine. The following year, the Dutch physicist Pieter van Musschenbroek invented a similar capacitor, which was named the Leyden jar, after the University of Leiden where he worked. He also was impressed by the power of the shock he received, writing, "I would not take a second shock for the kingdom of France."


title: Capacitor

text: Daniel Gralath was the first to combine several jars in parallel to increase the charge storage capacity. Benjamin Franklin investigated the Leyden jar and came to the conclusion that the charge was stored on the glass, not in the water as others had assumed. He also adopted the term "battery", (denoting the increase of power with a row of similar units as in a battery of cannon), subsequently applied to clusters of electrochemical cells. Leyden jars were later made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between the foils. The earliest unit of capacitance was the jar, equivalent to about 1.11 nanofarads.


title: Capacitor

text: Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of wireless (radio) created a demand for standard capacitors, and the steady move to higher frequencies required capacitors with lower inductance. More compact construction methods began to be used, such as a flexible dielectric sheet (like oiled paper) sandwiched between sheets of metal foil, rolled or folded into a small package.


title: Capacitor

text: Early capacitors were known as "condensers", a term that is still occasionally used today, particularly in high power applications, such as automotive systems. The term was first used for this purpose by Alessandro Volta in 1782, with reference to the device's ability to store a higher density of electric charge than was possible with an isolated conductor. The term became deprecated because of the ambiguous meaning of steam condenser, with "capacitor" becoming the recommended term in the UK from 1926, while the change occurred considerably later in the United States. In other countries, the term condensator has been in common use.


title: Capacitor

text: Since the beginning of the study of electricity, non-conductive materials like glass, porcelain, paper and mica have been used as insulators. Decades later, these materials were also well-suited for use as the dielectric for the first capacitors.


title: Capacitor

text: Paper capacitors, made by sandwiching a strip of impregnated paper between strips of metal and rolling the result into a cylinder, were commonly used in the late 19th century; their manufacture started in 1876, and they were used from the early 20th century as decoupling capacitors in telephony.


title: Capacitor

text: Porcelain was used in the first ceramic capacitors. In the early years of Marconi's wireless transmitting apparatus, porcelain capacitors were used for high voltage and high frequency application in the transmitters. On the receiver side, smaller mica capacitors were used for resonant circuits. Mica capacitors were invented in 1909 by William Dubilier. Prior to World War II, mica was the most common dielectric for capacitors in the United States.


title: Capacitor

text: Charles Pollak (born Karol Pollak), the inventor of the first electrolytic capacitors, found out that the oxide layer on an aluminum anode remained stable in a neutral or alkaline electrolyte, even when the power was switched off. In 1896 he was granted U.S. Patent No. 672,913 for an "Electric liquid capacitor with aluminum electrodes". Solid electrolyte tantalum capacitors were invented by Bell Laboratories in the early 1950s as a miniaturized and more reliable low-voltage support capacitor to complement their newly invented transistor.


title: Capacitor

text: With the development of plastic materials by organic chemists during the Second World War, the capacitor industry began to replace paper with thinner polymer films. One very early development in film capacitors was described in British Patent 587,953 in 1944.


title: Capacitor

text: Electric double-layer capacitors (now supercapacitors) were invented in 1957 when H. Becker developed a "Low voltage electrolytic capacitor with porous carbon electrodes". He believed that the energy was stored as a charge in the carbon pores used in his capacitor as in the pores of the etched foils of electrolytic capacitors. Because the double layer mechanism was not known by him at the time, he wrote in the patent: "It is not known exactly what is taking place in the component if it is used for energy storage, but it leads to an extremely high capacity."


title: Capacitor

text: The metal–oxide–semiconductor capacitor (MOS capacitor) originates from the metal–oxide–semiconductor field-effect transistor (MOSFET) structure, where the MOS capacitor is flanked by two doped regions. The MOSFET structure was invented by Mohamed M. Atalla and Dawon Kahng at Bell Labs in 1959. The MOS capacitor was later widely adopted as a storage capacitor in memory chips, and as the basic building block of the charge-coupled device (CCD) in image sensor technology. In dynamic random-access memory (DRAM), each memory cell typically consists of a MOSFET and MOS capacitor.


title: Capacitor

text: A capacitor consists of two conductors separated by a non-conductive region. The non-conductive region can either be a vacuum or an electrical insulator material known as a dielectric. Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a semiconductor depletion region chemically identical to the conductors. From Coulomb's law a charge on one conductor will exert a force on the charge carriers within the other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity charge will be induced on the surface of the other conductor. The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field.


title: Capacitor

text: An ideal capacitor is characterized by a constant capacitance "C", in farads in the SI system of units, defined as the ratio of the positive or negative charge "Q" on each conductor to the voltage "V" between them:


title: Capacitor

text: A capacitance of one farad (F) means that one coulomb of charge on each conductor causes a voltage of one volt across the device. Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than when the conductors are separated, yielding a larger capacitance.


title: Capacitor

text: In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes:


title: Capacitor

text: In the hydraulic analogy, charge carriers flowing through a wire are analogous to water flowing through a pipe. A capacitor is like a rubber membrane sealed inside a pipe. Water molecules cannot pass through the membrane, but some water can move by stretching the membrane. The pressure differential is analogous to voltage, while the rate of flow is analogous to electric current:


title: Capacitor

text: In a circuit, a capacitor can behave differently at different time instants. However, it is usually easy to think about the short-time limit and long-time limit:


title: Capacitor

text: The simplest model of a capacitor consists of two thin parallel conductive plates each with an area of formula_3 separated by a uniform gap of thickness formula_4 filled with a dielectric with permittivity formula_5. It is assumed the gap formula_4 is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of the capacitor.


title: Capacitor

text: Since the separation between the plates is uniform over the plate area, the electric field between the plates formula_7 is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area is approximately the same width as the plate separation, formula_4, and assuming formula_4 is small compared to the plate dimensions, it is small enough to be ignored. Therefore, if a charge of formula_10 is placed on one plate and formula_11 on the other plate (the situation for unevenly charged plates is discussed below), the charge on each plate will be spread evenly in a surface charge layer of constant charge density formula_12 coulombs per square meter, on the inside surface of each plate. From Gauss's law the magnitude of the electric field between the plates is formula_13. The voltage(difference) formula_14 between the plates is defined as the line integral of the electric field over a line (in the z-direction) from one plate to another


title: Capacitor

text: Therefore, in a capacitor the highest capacitance is achieved with a high permittivity dielectric material, large plate area, and small separation between the plates.


title: Capacitor

text: Since the area formula_3 of the plates increases with the square of the linear dimensions and the separation formula_4 increases linearly, the capacitance scales with the linear dimension of a capacitor (formula_20), or as the cube root of the volume.


title: Capacitor

text: A parallel plate capacitor can only store a finite amount of energy before dielectric breakdown occurs. The capacitor's dielectric material has a dielectric strength "U" which sets the capacitor's breakdown voltage at . The maximum energy that the capacitor can store is therefore


title: Capacitor

text: The maximum energy is a function of dielectric volume, permittivity, and dielectric strength. Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. In addition, these equations assume that the electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which increase the effective capacitance of the capacitor. This is sometimes called parasitic capacitance. For some simple capacitor geometries this additional capacitance term can be calculated analytically. It becomes negligibly small when the ratios of plate width to separation and length to separation are large.


title: Capacitor

text: where formula_37 is the capacitance for a single plate and formula_35 is the number of interleaved plates.


title: Capacitor

text: As shown to the figure on the right, the interleaved plates can be seen as parallel plates connected to each other. Every pair of adjacent plates acts as a separate capacitor; the number of pairs is always one less than the number of plates, hence the formula_39 multiplier.


title: Capacitor

text: To increase the charge and voltage on a capacitor, work must be done by an external power source to move charge from the negative to the positive plate against the opposing force of the electric field. If the voltage on the capacitor is formula_14, the work formula_41 required to move a small increment of charge formula_42 from the negative to the positive plate is formula_43. The energy is stored in the increased electric field between the plates. The total energy formula_44 stored in a capacitor (expressed in joules) is equal to the total work done in establishing the electric field from an uncharged state.


title: Capacitor

text: where formula_46 is the charge stored in the capacitor, formula_14 is the voltage across the capacitor, and formula_48 is the capacitance. This potential energy will remain in the capacitor until the charge is removed. If charge is allowed to move back from the positive to the negative plate, for example by connecting a circuit with resistance between the plates, the charge moving under the influence of the electric field will do work on the external circuit.


title: Capacitor

text: If the gap between the capacitor plates formula_4 is constant, as in the parallel plate model above, the electric field between the plates will be uniform (neglecting fringing fields) and will have a constant value formula_50. In this case the stored energy can be calculated from the electric field strength


title: Capacitor

text: The last formula above is equal to the energy density per unit volume in the electric field multiplied by the volume of field between the plates, confirming that the energy in the capacitor is stored in its electric field.


title: Capacitor

text: The current "I"("t") through any component in an electric circuit is defined as the rate of flow of a charge "Q"("t") passing through it. Actual charges – electrons – cannot pass through the dielectric layer of a capacitor. Rather, one electron accumulates on the negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the integral of the current as well as proportional to the voltage, as discussed above. As with any antiderivative, a constant of integration is added to represent the initial voltage "V"("t"). This is the integral form of the capacitor equation:


title: Capacitor

text: The dual of the capacitor is the inductor, which stores energy in a magnetic field rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing with the inductance .


title: Capacitor

text: A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage is known as a "charging circuit". If the capacitor is initially uncharged while the switch is open, and the switch is closed at , it follows from Kirchhoff's voltage law that


title: Capacitor

text: At , the voltage across the capacitor is zero and the voltage across the resistor is "V". The initial current is then . With this assumption, solving the differential equation yields


title: Capacitor

text: where is the "time constant" of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially. In the case of a "discharging" capacitor, the capacitor's initial voltage () replaces . The equations become


title: Capacitor

text: Impedance, the vector sum of reactance and resistance, describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. Fourier analysis allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively


title: Capacitor

text: where is the imaginary unit and is the angular frequency of the sinusoidal signal. The phase indicates that the AC voltage lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc.


title: Capacitor

text: Impedance decreases with increasing capacitance and increasing frequency. This implies that a higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude – an AC "short circuit" or AC coupling. Conversely, for very low frequencies, the reactance is high, so that a capacitor is nearly an open circuit in AC analysis – those frequencies have been "filtered out".


title: Capacitor

text: Capacitors are different from resistors and inductors in that the impedance is "inversely" proportional to the defining characteristic; i.e., capacitance.


title: Capacitor

text: A capacitor connected to a sinusoidal voltage source causes a displacement current to flow through it. In the case that the voltage source is "V"cos(ωt), the displacement current can be expressed as:


title: Capacitor

text: At , the capacitor has a maximum (or peak) current whereby . The ratio of peak voltage to peak current is due to capacitive reactance (denoted X).


title: Capacitor

text: X approaches zero as approaches infinity. If X approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies. X approaches infinity as ω approaches zero. If X approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies.


title: Capacitor

text: The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source:


title: Capacitor

text: In this situation, the current is out of phase with the voltage by +π/2 radians or +90 degrees, i.e. the current leads the voltage by 90°.


title: Capacitor

text: When using the Laplace transform in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the domain by:


title: Capacitor

text: In practice, capacitors deviate from the ideal capacitor equation in several aspects. Some of these, such as leakage current and parasitic effects are linear, or can be analyzed as nearly linear, and can be accounted for by adding virtual components to the equivalent circuit of an ideal capacitor. The usual methods of network analysis can then be applied. In other cases, such as with breakdown voltage, the effect is non-linear and ordinary (normal, e.g., linear) network analysis cannot be used, the effect must be considered separately. Yet another group of artifacts may exist, including temperature dependence, that may be linear but invalidates the assumption in the analysis that capacitance is a constant. Finally, combined parasitic effects such as inherent inductance, resistance, or dielectric losses can exhibit non-uniform behavior at varying frequencies of operation.


title: Capacitor

text: Above a particular electric field strength, known as the dielectric strength "E", the dielectric in a capacitor becomes conductive. The voltage at which this occurs is called the breakdown voltage of the device, and is given by the product of the dielectric strength and the separation between the conductors,


title: Capacitor

text: The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage. Due to the scaling of capacitance and breakdown voltage with dielectric thickness, all capacitors made with a particular dielectric have approximately equal maximum energy density, to the extent that the dielectric dominates their volume.


title: Capacitor

text: For air dielectric capacitors the breakdown field strength is of the order 2–5 MV/m (or kV/mm); for mica the breakdown is 100–300 MV/m; for oil, 15–25 MV/m; it can be much less when other materials are used for the dielectric. The dielectric is used in very thin layers and so absolute breakdown voltage of capacitors is limited. Typical ratings for capacitors used for general electronics applications range from a few volts to 1 kV. As the voltage increases, the dielectric must be thicker, making high-voltage capacitors larger per capacitance than those rated for lower voltages.


title: Capacitor

text: The breakdown voltage is critically affected by factors such as the geometry of the capacitor conductive parts; sharp edges or points increase the electric field strength at that point and can lead to a local breakdown. Once this starts to happen, the breakdown quickly tracks through the dielectric until it reaches the opposite plate, leaving carbon behind and causing a short (or relatively low resistance) circuit. The results can be explosive, as the short in the capacitor draws current from the surrounding circuitry and dissipates the energy. However, in capacitors with particular dielectrics and thin metal electrodes shorts are not formed after breakdown. It happens because a metal melts or evaporates in a breakdown vicinity, isolating it from the rest of the capacitor.


title: Capacitor

text: The usual breakdown route is that the field strength becomes large enough to pull electrons in the dielectric from their atoms thus causing conduction. Other scenarios are possible, such as impurities in the dielectric, and, if the dielectric is of a crystalline nature, imperfections in the crystal structure can result in an avalanche breakdown as seen in semi-conductor devices. Breakdown voltage is also affected by pressure, humidity and temperature.


title: Capacitor

text: An ideal capacitor only stores and releases electrical energy, without dissipation. In practice, all capacitors have imperfections within the capacitor's materials that permit leakage current, and represent resistance. This is specified as the "equivalent series resistance" (ESR) of the device. It add a real-valued component to the impedance:


title: Capacitor

text: As frequency approaches infinity, the capacitive impedance (reactance) approaches zero and the ESR becomes significant. As the reactance becomes negligible, power dissipation approaches "P" = "V" /"R".


title: Capacitor

text: Similarly to ESR, the capacitor's leads add "equivalent series inductance" (ESL) to the component. This is usually significant only at relatively high frequencies. As inductive reactance is positive and increases with frequency, capacitance is canceled by inductance above a certain frequency. High-frequency engineering involves accounting for the inductance of all connections and components.


title: Capacitor

text: If the conductors are separated by a material with a small conductivity rather than a perfect dielectric, then a small leakage current flows directly between them. The capacitor therefore has a finite parallel resistance, and slowly discharges over time, which may vary greatly depending on the capacitor material and quality.


title: Capacitor

text: The quality factor (or "Q") of a capacitor is the ratio of its reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the capacitor, the closer it approaches the behavior of an ideal capacitor.


title: Capacitor

text: where formula_72 is angular frequency, formula_48 is the capacitance, formula_74 is the capacitive reactance, and formula_75 is the equivalent series resistance (ESR) of the capacitor.