Synopsis.

Moore begins by discussing what capitalism and "free enterprise" mean. Looking back on his happy and prosperous early life, Moore asserts that "if this was capitalism, I loved it... and so did everyone else". Moore states that in the 1950s, the top tax rate was 90% (in his view, this tax rate enabled the U.S. to build dams, bridges, schools and hospitals), most families only had one working parent, union families had free healthcare, college tuition was free, most people had little personal debt and pensions were guaranteed. This prosperity was driven by the manufacturing industry, which benefited from post-war Germany and Japan struggling to recover. He describes President Jimmy Carter's Crisis of Confidence speech as a turning point that led to the election of Ronald Reagan in 1980; Moore calls Reagan a "spokesmodel" for banks and corporations who wanted to remake America to serve their interests.  Moore looks back on his first film, "Roger & Me", about the regional economic impact of General Motors CEO Roger Smith's decision to close several auto plants in his hometown of Flint, Michigan despite large profits. He notes that by the time of the job cuts in Flint, Germany and Japan had rebuilt their automotive industries and were producing better, safer, cleaner, more reliable cars. Moore then returns to the present, showing President George W. Bush enjoying his final year in office as companies announce massive layoffs and the economy starts to collapse.  After seeing the congressional testimony of pilot Chesley "Sully" Sullenberger (who reported that over the course of his career, his salary had been cut by 40 percent and his pension, like most airline pensions, was terminated and replaced by a "PBGC" guarantee worth only pennies on the dollar), Moore notes that pilots being overworked and underpaid did not enter into the media discussion following the crash of Colgan Air Flight 3407. He asserts that capitalism allows people to get away with anything, including making a profit from someone's death. He speaks to the family of a man who worked for Amegy Bank of Texas, which had secretly taken out a life insurance policy on the man with itself as the beneficiary and had then accidentally informed his widow that the bank was receiving a $1.5m payout due to his death of cancer. Moore wonders how the bank's actions can be legal when he himself is prohibited from taking out home insurance on someone else's property.  Moore speaks to Catholic priests and Bishop Thomas Gumbleton, who believes that capitalism is evil and contrary to the teachings of Jesus and the Bible. Moore examines the claim that the tenets of capitalism are compatible with Christianity, arguing that the rich ignore religion when it comes to the poor, sick and disadvantaged. He points to Citigroup's leaked "plutonomy memo", which said that America and other countries were not democracies any more, but were ruled by the wealthy.  Moore reports on the Occupy movement and the 2008 presidential campaign of Democratic Senator Barack Obama, who was demonized as a "socialist". He notes that the smears against Obama did not work, as support for him increased and people become curious about what socialism actually meant. He profiles Wayne County Sheriff Warren Evans, who orders an end to foreclosures; the Miami Low Income Families Fighting Together, who re-occupy foreclosed homes; and workers at Republic Windows and Doors, who organized a sit-down strike after being fired without severance, vacation time, or health care benefits after the company was taken over by Bank of America and JPMorgan Chase.  The film ends with Moore marking Wall Street off as a crime scene, opining that American people live in the richest country on Earth and deserve decent jobs, healthcare, good educations and homes of their own. Moore adds that it is a crime that Americans do not have these things and never will have them as long as the evil of capitalism continues to enrich the few at the expense of the many. He calls for capitalism to be eliminated and replaced with something good for all people: Democracy. Moore concludes that he cannot accomplish this goal this alone and appeals for help from the viewer, ending the film. He quotes Don Regan's line to Ronald Reagan, "... and please, speed it up".

Production.

During the Cannes Film Festival in 2008, Overture Films and Paramount Vantage announced an upcoming project by director Michael Moore, though at the time they were vague about the project's theme. Originally thought to be a follow-up to the 2004 film "Fahrenheit 9/11", it was revealed that Moore's film was to be a documentary about the financial crisis of 2007–2010. In February 2009, he issued an appeal to people who worked for Wall Street or in the financial industry to share firsthand information, requesting, "Be a hero and help me expose the biggest swindle in American history."  Prior to the film's release, Moore partnered with web development company Concentric Sky to develop a companion website for the film.  Footage of President Franklin D. Roosevelt detailing his proposed Second Bill of Rights was believed to be lost. Roosevelt, who had recently recovered from the flu, presented his January 1944 State of the Union address to the public on radio, as a fireside chat from the White House. He asked that newsreel cameras film the last portion of the address, concerning the Second Bill of Rights. This footage was believed lost until it was uncovered in 2008 in South Carolina by Michael Moore while researching for the film. The footage shows Roosevelt's Second Bill of Rights address in its entirety, as well as a shot of the eight rights printed on a sheet of paper.

Release.

Theatrical run.

"Capitalism: A Love Story" premiered at the 66th Venice International Film Festival on September 6, 2009. The film also screened at the Toronto International Film Festival on September 13 and at the New York Film Festival on September 21. On September 23, the film had a limited release at two theaters in New York City and two theaters in Los Angeles, grossing $37,832 in its first day for a $9,458 per theater average. The theater average was considered strong, though it did not beat the record opening of Moore's "Fahrenheit 9/11", which grossed $83,922 at two theaters in one day. Over the weekend of September 25, "Capitalism" grossed $231,964 in the four theaters.  The film had a wide release in 995 theaters in the United States and Canada on October 2, 2009, about a year after the enacting of the Emergency Economic Stabilization Act of 2008, which approved a $700 billion bailout of Wall Street. The film opened in eighth place at the box office on the first weekend of its wide release, grossing $4,447,378. The final domestic total was $14,363,397, making it the 16th highest grossing documentary in history (2014).

Critical reception.

Review aggregator website Rotten Tomatoes reported an approval rating of 75% based on 185 reviews, with an average score of 6.71 out of 10. The site's critics' consensus reads: "Love him or hate him, "Capitalism" captures Michael Moore in his muckraking element -- with all the Moore-centric showmanship that entails." Metacritic, which assigns a weighted average rating out of 100 to mainstream critics' reviews, reported an average score of 61 out of 100 based on 35 reviews, indicating "generally favorable reviews".  Deborah Young, writing for the trade paper "The Hollywood Reporter", wrote of "Capitalism: A Love Story", "Although it's less focused than "Sicko" or "Fahrenheit 9/11"... because its subject is more abstract, this is a typical Moore oeuvre: funny, often over the top and of dubious documentation, but with strongly made points that leave viewers much to ponder and debate after they walk out of the theater." Young acknowledged Moore's simplification of the topic and added, "But here his talent is evident in creating two hours of engrossing cinema by contrasting a fast-moving montage of '50s archive images extolling free enterprise with the economic disaster of the present." The critic noted whom the documentary targeted: "Though it blames all political parties, including the Democrats, for caving in with the bailout, the film is careful to spare President Barack Obama, who remains a symbol of hope for justice."  Leslie Felperin of the trade paper "Variety" wrote, "Pic's target is less capitalism qua capitalism than the banking industry, which Moore skewers ruthlessly, explaining last year's economic meltdown in terms a sixth-grader could understand. That said, there's still plenty here to annoy right-wingers, as well as those who, however much they agree with Moore's politics, just can't stomach his oversimplification, on-the-nose sentimentality and goofball japery." Felperin said that the documentary was similarly structured to Moore's previous documentaries, ""Capitalism" skips around considerably, laying down a mix of reportage, interviews and polemic." Felperin observed Moore's prominent role in his own documentary, believing it to be justified with relevance to crises in the automobile industry that Moore's family personally encountered. The critic complained that Moore strove "to manipulate viewers' emotions with shots of crying children and tearjerking musical choices", believing that the documentary worked better when the director let the topic unfold through various accounts.  Upon the film's February 2010 UK release, "The Times" said the film "showcases Moore at his undeniably powerful best and his exploitative, manipulative worst":  The film is brilliantly researched, both with regard to the labyrinthine web of connections between the world of finance and the corridors of power and the wittily used archive footage. Interviews with Senate insiders and financial experts are informative, and there’s an amusing sequence in which he quizzes a selection of priests and bishops who opine that capitalism is "evil" and was not, in fact, the preferred economic model of Our Lord. Then Moore goes and spoils it all by hauling out his trusty bullhorn for a series of lame stunts. Like the complacent clown prince of agitprop, Moore hectors Wall Street doormen and security guards, while the company bosses remain in their fortress made of money, blissfully unaware of the fat man making a scene on the street far below...But for all his cheap tactics, Moore mounts a persuasive case that something is rotten in the current economic system.

Topical accuracy.

The Associated Press's national business columnist Rachel Beck reviewed the accuracy of three points made in "Capitalism":  The Association of Advanced Life Underwriting issued a statement that Moore "mischaracterized" Corporate Owned Life Insurance (COLI), stating that the issues were addressed by Congress in the 1990s and again in 2006. The AALU further states that corporate-owned life insurance is taken out only on highly compensated employees, only with their knowledge and consent and that COLI finances employee benefits and protects jobs and that employees pay nothing for COLI but receive substantial benefits.  Upon the film's February 2010 theatrical release in the United Kingdom, film critic Mark Kermode, appearing on "The Culture Show", asked the BBC's business editor Robert Peston whether Moore's "crusading" had been based on a misrepresentation of American capitalism.

Religious subject matter.

Religion expert Anthony Stevens-Arroyo stated that the film should be considered "a special kind of Catholic achievement" and asked whether Michael Moore should be named "Catholic of the Year" for raising the serious issues in the context of Catholic social teaching, and for presenting "Catholic currents of social justice" in the film.

Awards and honors.

At the Venice Film Festival, Moore won the "Leoncino d'Oro" ("Little Golden Lion") award for his documentary, and he also received the festival's Open Prize. The documentary was also nominated for the festival's Golden Lion award, but lost to "Lebanon". Moore also received a nomination for Best Documentary Screenplay from the Writers Guild of America.

Capitalism: A Love Story is a 2009 American documentary film directed, written by, and starring Michael Moore. The film centers on the late-2000s financial crisis and the recovery stimulus, while putting forward an indictment of the then-current economic order in the United States and of unfettered capitalism in general. Topics covered include Wall Street's "casino mentality", for-profit prisons, Goldman Sachs' influence in Washington, D.C., the poverty-level wages of many workers, the large wave of home foreclosures, corporate-owned life insurance, and the consequences of "runaway greed". The film also features a religious component in which Moore examines whether or not capitalism is a sin and whether Jesus would be a capitalist; this component highlights Moore's belief that evangelical conservatives contradict themselves by supporting free market ideals while professing to be Christians.

O kapitalismu s láskou (v originále : "Capitalism: A Love Story", doslovný překlad "Kapitalismus: Milostný příběh") je americký dokumentární film režírovaný Michaelem Moorem z roku 2009. Film se zaměřuje na finanční krizi a vládní ozdravující stimuly, zatímco předkládá obžalobu současného ekonomického pořádku ve Spojených státech amerických a obecně kapitalismu. Film se věnuje tématům jako je „kasínová mentalita“ Wall Streetu, privátní věznice, vliv Goldman Sachs na Washington, D.C., úroveň chudoby mnoha pilotů aerolinek, životní pojistky na zaměstnance (tzv. „mrtvé rolníky“), velké vlně vypovídání hypoték a propadnutí zástavy nemovitosti.


History of the profession.

According to the Society for Technical Communication (STC), the professions of technical communication and technical writing were first referenced around World War I, when technical documents became a necessity for military purposes. The job title emerged in the US during World War II, although it wasn't until 1951 that the first "Help Wanted: Technical Writer" ad was published. In fact, the title "Technical Writer" wasn't added to the US Bureau of Labor Statistic's Occupational Employment Handbook until 2010. During the 1940s and 50s, technical communicators and writers were hired to produce documentation for the military, often including detailed instructions on new weaponry. Other technical communicators and writers were involved in developing documentation for new technologies that were developed around this time. According to O'Hara:  In the beginning of the profession, most technical writers worked in an office environment with a team of other writers. Like technical writers today, they conducted primary research and met with subject matter experts to ensure that their information was accurate. During World War II, one of the most important characteristics for technical writers was their ability to follow stringent government specifications for documents. After the war, the rise of new technology, such as the computer, allowed technical writers to work in other areas, producing "user manuals, quick reference guides, hardware installation manuals, and cheat sheets." During the time period after the war (1953-1961), technical communicators (including technical writers) became interested in "professionalizing" their field. According to Malone, technical communicators/writers did so by creating professional organizations, cultivating a "specialized body of knowledge" for the profession, imposing ethical standards on technical communicators, initiating a conversation about certifying practitioners in the field, and working to accredit education programs in the field.  The profession has continued to grow—according to O'Hara, the writing/editing profession, including technical writers, experienced a 22% increase in positions between the years 1994 and 2005. Modern day technical writers work in a variety of contexts. Many technical writers work remotely using VPN or communicate with their team via videotelephony platforms such as Skype or Zoom. Other technical writers work in an office, but share content with their team through complex content management systems that store documents online. Technical writers may work on government reports, internal documentation, instructions for technical equipment, embedded help within software or systems, or other technical documents. As technology continues to advance, the array of possibilities for technical writers will continue to expand. Many technical writers are responsible for creating technical documentation for mobile applications or help documentation built within mobile or web applications. They may be responsible for creating content that will only be viewed on a hand-held device; much of their work will never be published in a printed booklet like technical documentation of the past.

Skill set.

In addition to solid research, language, writing, and revision skills, a technical writer may have skills in: A technical writer may apply their skills in the production of non-technical content, for example, writing high-level consumer information. Usually, a technical writer is not a subject-matter expert (SME), but interviews SMEs and conducts the research necessary to write and compile technically accurate content. Technical writers complete both primary and secondary research to fully understand the topic.

Characteristics.

Proficient technical writers have the ability to create, assimilate, and convey technical material in a concise and effective manner. They may specialize in a particular area but must have a good understanding of the products they describe. For example, API writers primarily work on API documents, while other technical writers specialize in electronic commerce, manufacturing, scientific, or medical material.  Technical writers gather information from many sources. Their information sources are usually scattered throughout an organization, which can range from developers to marketing departments.  According to Markel, useful technical documents are measured by eight characteristics: "honesty, clarity, accuracy, comprehensiveness, accessibility, conciseness, professional appearance, and correctness." Technical writers are focused on using their careful research to create effective documents that meet these eight characteristics.

Roles and functions.

To create effective technical documentation, the writer must analyze three elements that comprise the rhetorical situation of a particular project: audience, purpose, and context. These are followed by document design, which determines what the reader sees.

Audience analysis.

Technical writers strive to simplify complex concepts or processes to maximize reader comprehension. The final goal of a particular document is to help readers find what they need, understand what they find, and use what they understand appropriately. To reach this goal, technical writers must understand how their audiences use and read documentation. An audience analysis at the outset of a document project helps define what an audience for a particular document requires.  When analyzing an audience the technical writer typically asks:  Accurate audience analysis provides a set of guidelines that shape document content, design and presentation (online help system, interactive website, manual, etc.), and tone and knowledge level.

Purpose.

A technical writer analyzes the purpose (or function) of a communication to understand what a document must accomplish. Determining if a communication aims to persuade readers to “think or act a certain way, enable them to perform a task, help them understand something, change their attitude,” etc., guides the technical writer on how to format their communication, and the kind of communication they choose (online help system, white paper, proposal, etc.).

Context.

Context is the physical and temporal circumstances in which readers use communication—for example: at their office desks, in a manufacturing plant, during the slow summer months, or in the middle of a company crisis. Understanding the context of a situation tells the technical writer how readers use communication. This knowledge significantly influences how the writer formats communication. For example, if the document is a quick troubleshooting guide to the controls on a small watercraft, the writer may have the pages laminated to increase usable life.

Document design.

Once the above information has been gathered, the document is designed for optimal readability and usability. According to one expert, technical writers use six design strategies to plan and create technical communication: arrangement, emphasis, clarity, conciseness, tone, and ethos.

Qualifications.

Technical writers normally possess a mixture of technical and writing abilities. They typically have a degree or certification in a technical field, but may have one in journalism, business, or other fields. Many technical writers switch from another field, such as journalism—or a technical field such as engineering or science, often after learning important additional skills through technical communications classes.

Methodology (document development life cycle).

To create a technical document, a technical writer must understand the subject, purpose, and audience. They gather information by studying existing material, interviewing SMEs, and often actually using the product. They study the audience to learn their needs and technical understanding level.  A technical publication's development life cycle typically consists of five phases, coordinated with the overall product development plan:  The document development life cycle typically consists of six phases (This changes organization to organization, how they are following). This is similar to the software development life cycle.  Well-written technical documents usually follow formal standards or guidelines. Technical documentation comes in many styles and formats, depending on the medium and subject area. Printed and online documentation may differ in various ways, but still adhere to largely identical guidelines for prose, information structure, and layout. Usually, technical writers follow formatting conventions described in a standard style guide. In the US, technical writers typically use The Associated Press Stylebook or the Chicago Manual of Style (CMS). Many companies have internal corporate style guides that cover specific corporate issues such as logo use, branding, and other aspects of corporate style. The Microsoft Manual of Style for Technical Publications is typical of these.  Engineering projects, particularly defense or aerospace-related projects, often follow national and international documentation standards—such as ATA100 for civil aircraft or S1000D for civil and defense platforms.

Environment.

Technical writers often work as part of a writing or project development team. Typically, the writer finishes a draft and passes it to one or more SMEs who conduct a "technical review" to verify accuracy and completeness. Another writer or editor may perform an "editorial review" that checks conformance to styles, grammar, and readability. This person may request for clarification or make suggestions. In some cases, the writer or others test the document on audience members to make "usability" improvements. A final production typically follows an inspection checklist to ensure the quality and uniformity of the published product.

Career growth.

There is no single standard career path for technical writers, but they may move into project management over other writers. A writer may advance to a senior technical writer position, handling complex projects or a small team of writers and editors. In larger groups, a documentation manager might handle multiple projects and teams.  Technical writers may also gain expertise in a particular technical domain and branch into related forms, such as software quality analysis or business analysis. A technical writer who becomes a subject matter expert in a field may transition from technical writing to work in that field. Technical writers commonly produce training for the technologies they document—including classroom guides and e-learning—and some transition to specialize as professional trainers and instructional designers.  Technical writers with expertise in writing skills can join printed media or electronic media companies, potentially providing an opportunity to make more money or improved working conditions.  The U.S Department of Labor expects technical writer employment to grow 11 percent from 2016 to 2026, slightly faster than the average for all occupations. They expect job opportunities, especially for applicants with technical skills, to be good. The BLS also noted that the expansion of "scientific and technical products" and the need for technical writers to work in "Web-based product support" will drive increasing demand.

Similar titles.

Technical writers can have various job titles, including "technical communicator," "information developer", "technical content developer" or "technical documentation specialist". In the United Kingdom and some other countries, a technical writer is often called a "technical author" or "knowledge author".

A technical writer is a professional information communicator whose task is to transfer information (knowledge) between two or more parties, through any medium that best facilitates the transfer and comprehension of the information. Technical writers research and create information through a variety of delivery media (electronic, printed, audio-visual and even touch). Example types of information include online help, manuals, white papers, design specifications, project plans and software test plans. With the rise of e-learning, technical writers are increasingly becoming involved with creating online training material.

Šnorchl, také dýchací trubice je součást potápěčského vybavení a patří do takzvaného ABC (šnorchl, maska, ploutve). Šnorchl umožňuje při plavání na hladině držet hlavu pod vodou a přitom normálně dýchat.


Selectivity.

Sodium channels are highly selective for the transport of ions across cell membranes. The high selectivity with respect to the sodium ion is achieved in many different ways. All involve encapsulation of the sodium ion in a cavity of specific size within a larger molecule.

Voltage-gated sodium channels.

Structure.

Sodium channels consist of large α subunits that associate with proteins, such as β subunits. An α subunit forms the core of the channel and is functional on its own. When the α subunit protein is expressed by a cell, it is able to form channels that conduct Na in a voltage-gated way, even if β subunits or other known modulating proteins are not expressed. When accessory proteins assemble with α subunits, the resulting complex can display altered voltage dependence and cellular localization.  The α-subunit has four repeat domains, labelled I through IV, each containing six membrane-spanning segments, labelled S1 through S6. The highly conserved S4 segment acts as the channel's voltage sensor. The voltage sensitivity of this channel is due to positive amino acids located at every third position. When stimulated by a change in transmembrane voltage, this segment moves toward the extracellular side of the cell membrane, allowing the channel to become permeable to ions. The ions are conducted through a pore, which can be broken into two regions. The more external (i.e., more extracellular) portion of the pore is formed by the "P-loops" (the region between S5 and S6) of the four domains. This region is the most narrow part of the pore and is responsible for its ion selectivity. The inner portion (i.e., more cytoplasmic) of the pore is formed by the combined S5 and S6 segments of the four domains. The region linking domains III and IV is also important for channel function. This region plugs the channel after prolonged activation, inactivating it.

Gating.

Voltage-gated Na channels have three main conformational states: closed, open and inactivated. Forward/back transitions between these states are correspondingly referred to as activation/deactivation (between open and closed, respectively), inactivation/reactivation (between inactivated and open, respectively), and recovery from inactivation/closed-state inactivation (between inactivated and closed, respectively). Closed and inactivated states are ion impermeable.  Before an action potential occurs, the axonal membrane is at its normal resting potential,about -70mv in most human neurons, and Na channels are in their deactivated state, blocked on the extracellular side by their activation gates. In response to an increase of the membrane potential to about -55 mv (in this case, caused by an action potential), the activation gates open, allowing positively charged Na ions to flow into the neuron through the channels, and causing the voltage across the neuronal membrane to increase to +30 mv in human neurons. Because the voltage across the membrane is initially negative, as its voltage increases "to" and "past" zero (from -70 mv at rest to a maximum of +30 mv), it is said to depolarize. This increase in voltage constitutes the rising phase of an action potential.  At the peak of the action potential, when enough Na has entered the neuron and the membrane's potential has become high enough, the Na channels inactivate themselves by closing their inactivation gates. The inactivation gate can be thought of as a "plug" tethered to domains III and IV of the channel's intracellular alpha subunit. Closure of the inactivation gate causes Na flow through the channel to stop, which in turn causes the membrane potential to stop rising. The closing of the inactivation gate creates a refractory period within each individual Na channel. This refractory period eliminates the possibility of an action potential moving in the opposite direction back towards the soma. With its inactivation gate closed, the channel is said to be inactivated. With the Na channel no longer contributing to the membrane potential, the potential decreases back to its resting potential as the neuron repolarizes and subsequently hyperpolarizes itself, and this constitutes the falling phase of an action potential. The refractory period of each channel is therefore vital in propagating the action potential unidirectionally down an axon for proper communication between neurons.  When the membrane's voltage becomes low enough, the inactivation gate reopens and the activation gate closes in a process called deinactivation. With the activation gate closed and the inactivation gate open, the Na channel is once again in its deactivated state, and is ready to participate in another action potential.  When any kind of ion channel does not inactivate itself, it is said to be persistently (or tonically) active. Some kinds of ion channels are naturally persistently active. However, genetic mutations that cause persistent activity in other channels can cause disease by creating excessive activity of certain kinds of neurons. Mutations that interfere with Na channel inactivation can contribute to cardiovascular diseases or epileptic seizures by window currents, which can cause muscle and/or nerve cells to become over-excited.

Modeling the behavior of gates.

The temporal behavior of Na channels can be modeled by a Markovian scheme or by the Hodgkin–Huxley-type formalism. In the former scheme, each channel occupies a distinct state with differential equations describing transitions between states; in the latter, the channels are treated as a population that are affected by three independent gating variables. Each of these variables can attain a value between 1 (fully permeant to ions) and 0 (fully non-permeant), the product of these variables yielding the percentage of conducting channels. The Hodgkin–Huxley model can be shown to be equivalent to a Markovian model.

Impermeability to other ions.

The pore of sodium channels contains a selectivity filter made of negatively charged amino acid residues, which attract the positive Na ion and keep out negatively charged ions such as chloride. The cations flow into a more constricted part of the pore that is 0.3 by 0.5 nm wide, which is just large enough to allow a single Na ion with a water molecule associated to pass through. The larger K ion cannot fit through this area. Ions of different sizes also cannot interact as well with the negatively charged glutamic acid residues that line the pore.

Diversity.

Voltage-gated sodium channels normally consist of an alpha subunit that forms the ion conduction pore and one to two beta subunits that have several functions including modulation of channel gating. Expression of the alpha subunit alone is sufficient to produce a functional channel.

Alpha subunits.

The family of sodium channels has nine known members, with amino acid identity >50% in the trans-membrane segments and extracellular loop regions. A standardized nomenclature for sodium channels is currently used and is maintained by the IUPHAR.  The proteins of these channels are named Na1.1 through Na1.9. The gene names are referred to as SCN1A through SCN11A (the SCN6/7A gene is part of the Na sub-family and has uncertain function). The likely evolutionary relationship between these channels, based on the similarity of their amino acid sequences, is shown in figure 1. The individual sodium channels are distinguished not only by differences in their sequence but also by their kinetics and expression profiles. Some of this data is summarized in table 1, below.

Beta subunits.

Sodium channel beta subunits are type 1 transmembrane glycoproteins with an extracellular N-terminus and a cytoplasmic C-terminus. As members of the Ig superfamily, beta subunits contain a prototypic V-set Ig loop in their extracellular domain. They do not share any homology with their counterparts of calcium and potassium channels. Instead, they are homologous to neural cell adhesion molecules (CAMs) and the large family of L1 CAMs. There are four distinct betas named in order of discovery: SCN1B, SCN2B, SCN3B, SCN4B (table 2). Beta 1 and beta 3 interact with the alpha subunit non-covalently, whereas beta 2 and beta 4 associate with alpha via disulfide bond.

Role of beta subunits as cell adhesion molecules.

In addition to regulating channel gating, sodium channel beta subunits also modulate channel expression and form links to the intracellular cytoskeleton via ankyrin and spectrin. Voltage-gated sodium channels also assemble with a variety of other proteins, such as FHF proteins (Fibroblast growth factor Homologous Factor), calmodulin, cytoskeleton or regulatory kinases, which form a complex with sodium channels, influencing its expression and/or function. Several beta subunits interact with one or more extracellular matrix (ECM) molecules. Contactin, also known as F3 or F11, associates with beta 1 as shown via co-immunoprecipitation. Fibronectin-like (FN-like) repeats of Tenascin-C and Tenascin-R bind with beta 2 in contrast to the Epidermal growth factor-like (EGF-like) repeats that repel beta2. A disintegrin and metalloproteinase (ADAM) 10 sheds beta 2's ectodomain possibly inducing neurite outgrowth. Beta 3 and beta 1 bind to neurofascin at Nodes of Ranvier in developing neurons.

Ligand-gated sodium channels.

Ligand-gated sodium channels are activated by binding of a ligand instead of a change in membrane potential.  They are found, e.g. in the neuromuscular junction as nicotinic receptors, where the ligands are acetylcholine molecules. Most channels of this type are permeable to potassium to some degree as well as to sodium.

Role in action potential.

Voltage-gated sodium channels play an important role in action potentials. If enough channels open when there is a change in the cell's membrane potential, a small but significant number of Na ions will move into the cell down their electrochemical gradient, further depolarizing the cell. Thus, the more Na channels localized in a region of a cell's membrane the faster the action potential will propagate and the more excitable that area of the cell will be. This is an example of a positive feedback loop. The ability of these channels to assume a closed-inactivated state causes the refractory period and is critical for the propagation of action potentials down an axon.  Na channels both open and close more quickly than K channels, producing an influx of positive charge (Na) toward the beginning of the action potential and an efflux (K) toward the end.  Ligand-gated sodium channels, on the other hand, create the change in the membrane potential in the first place, in response to the binding of a ligand to it.

Pharmacologic modulation.

Activators.

The following naturally produced substances persistently activate (open) sodium channels:

Gating modifiers.

The following toxins modify the gating of sodium channels:

pH modulation.

Changes in blood and tissue pH accompany physiological and pathophysiological conditions such as exercise, cardiac ischemia, ischemic stroke, and cocaine ingestion. These conditions are known to trigger the symptoms of electrical diseases in patients carrying sodium channel mutations. Protons cause a diverse set of changes to sodium channel gating, which generally lead to decreases in the amplitude of the transient sodium current and increases in the fraction of non-inactivating channels that pass persistent currents. These effects are shared with disease-causing mutants in neuronal, skeletal muscle, and cardiac tissue and may be compounded in mutants that impart greater proton sensitivity to sodium channels, suggesting a role of protons in triggering acute symptoms of electrical disease.

Molecular mechanisms of proton block.

Single channel data from cardiomyocytes have shown that protons can decrease the conductance of individual sodium channels. The sodium channel selectivity filter is composed of a single residue in each of the four pore-loops of the four functional domains. These four residues are known as the DEKA motif. The permeation rate of sodium through the sodium channel is determined by a four carboxylate residues, the EEDD motif, which make up the outer charged ring. The protonation of these carboxylates is one of the main drivers of proton block in sodium channels, although there are other residues that also contribute to pH sensitivity. One such residue is C373 in the cardiac sodium channel which makes it the most pH-sensitive sodium channel among the sodium channels that have been studied to date.

pH modulation of sodium channel gating.

As the cardiac sodium channel is the most pH-sensitive sodium channel, most of what is known is based on this channel. Reduction in extracellular pH has been shown to depolarize the voltage-dependence of activation and inactivation to more positive potentials. This indicates that during activities that decrease the blood pH, such as exercising, the probability of channels activating and inactivating is higher more positive membrane potentials, which can lead to potential adverse effects. The sodium channels expressed in skeletal muscle fibers have evolved into relatively pH-insensitive channels. This has been suggested to be a protective mechanism against potential over- or under-excitability in skeletal muscles, as blood pH levels are highly susceptible to change during movement. Recently, a mixed syndrome mutation that causes periodic paralysis and myotonia in the skeletal sodium channel has been shown to impart pH-sensitivity in this channel, making the gating of this channel similar to that of the cardiac subtype.

pH modulation across the subtypes studied thus far.

The effects of protonation have been characterized in Nav1.1-Nav1.5. Among these channels, Nav1.1-Nav1.3 and Nav1.5 display depolarized voltage-dependence of activation, while activation in Nav1.4 remains insensitive to acidosis. The voltage-dependence of steady-state fast inactivation is unchanged in Nav1.1-Nav1.4, but steady-state fast inactivation in Nav1.5 is depolarized. Hence, among the sodium channels that have been studied so far, Nav1.4 is the least and Nav1.5 is the most proton-sensitive subtypes.

Evolution.

A voltage-gated sodium channel is present in members of the choanoflagellates, thought to be the closest living, unicellular relative of animals. This suggests that an ancestral form of the animal channel was among the many proteins that play central roles in animal life, but which are thought to have evolved before multicellularity. The four-domain animal voltage-gated sodium channel likely evolved from a single-subunit ion channel, which was probably permeable for potassium ions, via a sequence of two duplication events. This model draws support from the fact that subunits I and III (and II and IV) group by similarity, suggesting that a two-channel intermediate generated from the first duplication existed long enough for divergence to occur between its two subunits. After the second duplication, the channel was left with two sets of similar domains. The resulting four-domain channel is thought to have been permeable primarily for calcium, and to have achieved sodium selectivity a number of times independently. After divergence from the invertebrates, the vertebrate lineage underwent two whole-genome duplications (WGDs), yielding a set of four sodium channel gene prologues in the ancestral vertebrate, all of which were retained. After the tetrapod/teleost split, the teleosts likely underwent a third WGD leading to the eight sodium channel prologues expressed in many modern fishes. The modern, ten-paralogue sodium gene complement of mammals is thought to have arisen from a series of parallel and nested duplications involving two of the four paralogues present in the ancestor of all tetrapods.

Sodium channels are integral membrane proteins that form ion channels, conducting sodium ions (Na) through a cell's plasma membrane. They belong to the superfamily of cation channels and can be classified according to the trigger that opens the channel for such ions, i.e. either a voltage-change ("voltage-gated", "voltage-sensitive", or "voltage-dependent" sodium channel; also called "VGSCs" or "Nav channel") or a binding of a substance (a ligand) to the channel (ligand-gated sodium channels).

Edward Cullen, rozený Edward Anthony Masen, je fiktivní postava ze ságy "Stmívání" Stephenie Meyerové. Ve filmech "Stmívání", "Nový měsíc", "Zatmění" a "Rozbřesk" ho ztvárnil Robert Pattinson.


Personal life.

Kristina Mladenovic was born in Saint-Pol-sur-Mer, in the Nord department of France. Her father is Dragan Mladenović, a former Serbian handball player and an Olympic gold medalist for Yugoslavia, and her mother Dženita (née Helić) is a Serbian former volleyball player, of Bosniak origin. They moved to France in 1992 when Dragan was signed by Dunkerque HGL. All became French citizens. Mladenovic has a brother named Luka. She dated Austrian tennis player Dominic Thiem from the middle of 2017 until the couple split up in November 2019.

Tennis career.

Mladenovic started playing juniors in May 2006. In 2007 she became the European Under 14 singles champion. Her biggest junior achievement was at the 2009 Junior French Open girls' singles, where she beat Daria Gavrilova of Russia in two sets in the final. Her highest junior ranking was No. 1, on 8 June 2009. She advanced to both the girls' singles and doubles finals at the 2009 Junior Wimbledon, losing to Noppawan Lertcheewakarn in the singles. In doubles, with partner Silvia Njirić, lost also to Lertcheewakarn, who partnered Sally Peers.  She began playing on the ITF Women's Circuit in September 2007. On the WTA Tour she tried to qualify for Open Gaz de France, but lost her first match to Petra Kvitová. At the 2009 Australian Open, Kristina received a wild card, but was defeated by the No. 14 seed, Patty Schnyder. In July Kristina qualified for the ECM Prague Open but lost in the first round to Zarina Diyas of Kazakhstan.  At the Internationaux de Strasbourg Mladenovic won her first match on the WTA Tour, coming back from 2–5 in the final set to win the tiebreak against Stefanie Vögele.  Mladenovic played for France at the 2011 Hopman Cup, partnering with Nicolas Mahut. France was drawn in the same group as the United States, Great Britain, and Italy. Mladenovic beat Francesca Schiavone and Laura Robson while losing to Bethanie Mattek-Sands in the singles matches. In the mixed doubles she and Mahut won one of their three matches.

2009-2011.

Mladenovic turned professional in 2009, making her grand slam debut at that year's Australian Open. In 2011, she won her first Senior title at a $25,000 tournament in Sutton, defeating Mona Barthel. This was followed by a win in Stockholm the following week, defeating Arantxa Rus in the final.

2012: Breakthrough.

At the start of the year Mladenovic linked up with Biljana Veselinovic but they split just before Wimbledon and since then she had been coached by Thierry Ascione. Mladenovic claimed her first WTA Tour title of any type in Montreal when she and Klaudia Jans-Ignacik won the doubles title at the Rogers Cup. Mladenovic made it through to the third round of the US Open after defeating Pavlyuchenkova. At the Bell Classic in Québec, Mladenovic reached her first WTA semifinal. With Tatjana Malek, Mladenovic won her second WTA doubles title at the Bell Classic. Following her run to the semifinals, Mladenovic entered the top 100 in the rankings for the first time. Mladenovic won the first ever WTA 125s event the Taipei WTA Ladies Open and took the doubles crown as well.

2013: Grand Slam mixed doubles title.

At the Open GDF Suez, a Premier tournament, Mladenovic made the semifinals, including defeating Petra Kvitová. Teaming with Daniel Nestor she made it to the final of the French Open in mixed doubles where they were defeated. However, she and Nestor rebounded at the mixed doubles at Wimbledon capturing her first grand slam title.  At the 2013 US Open, she beat Anabel Medina Garrigues 6–1, 1–6, 6–1 in the first round and then lost to the 23rd seed Jamie Hampton in two sets. Mladenovic partnered up with Daniel Nestor to reach the semifinals of the mixed doubles, where they were defeated by the seventh-seeded team of Max Mirnyi and Andrea Hlaváčková 7–5, 6–7, [12–10].

2014: Continued success.

Mladenovic would start 2014 off strong capturing her second mixed-doubles title at the Australian Open partnering again with Nestor. At the Open GDF Suez, she defeated Australian Open quarterfinalist Simona Halep in the first round. At Roland Garros, she upset Li Na (world No. 2 and 2011 champion) in the first round, her first top-5 win. She continued her strong performance with a three-set win over American Alison Riske in the second round. In the round of 32 she was beaten by eventual semifinalist Andrea Petkovic.  Mladenovic opened her grass-court season in Birmingham, but lost her opening match to Shahar Pe'er of Israel. She then competed in's-Hertogenbosch qualifying, managing to win a round but ultimately falling to CoCo Vandeweghe, who would go on to qualify and win the entire tournament. At Wimbledon, she drew Zarina Diyas in the first round, but fell to the Kazakh in what was a rain delayed straight-set encounter. In the doubles draw, Mladenovic partnered Tímea Babos of Hungary, and reached their first Grand Slam women's doubles final, ultimately losing to Sara Errani and Roberta Vinci in straight sets. She then stunned at the İstanbul Cup the third seed Klára Koukalová, but lost in the semifinals to No. 1 seed Caroline Wozniacki. Her strong run returned her to the top 100, at No. 81. At Baku, she lost in quarterfinals, losing to Francesca Schiavone in a rematch of the İstanbul Cup quarterfinals. She next competed at the Citi Open, where she stunned top seeded Lucie Šafářová, before defeating qualifier Taylor Townsend. She lost to Kurumi Nara in the quarterfinals. After the Citi Open, Mladenovic lost in the final round of qualifying to Yanina Wickmayer in Montréal, and also the first round of qualifying in Cincinnati. She played doubles in Montréal, losing in the first round with partner Tímea Babos.

2015: Top 30 and first Grand Slam quarterfinal in singles.

Mladenovic began the year losing in the second round of the Australian Open to Bethanie Mattek-Sands. She, along with Daniel Nestor, reached the final of the mixed doubles event. She lost in the second round of the Diamond Games in Antwerp to Lucie Šafářová.  She reached the semifinals of Marrakesh, losing to her doubles partner Tímea Babos. She reached the singles final in Strasbourg, her first ever WTA Tour singles final, where she lost to Samantha Stosur. Her strong showing at both tournaments ensured her entry into the top 50 of the WTA singles rankings.  At the French Open, Mladenovic once again stunned a top-10 player in her opening match by defeating world No. 6, Eugenie Bouchard of Canada. She advanced to the third round with a victory over Danka Kovinić but lost to Belgian Alison Van Uytvanck in straight sets while fighting for a spot in the last 16.  At the Topshelf Open, Mladenovic lost to eventual finalist and good friend Belinda Bencic, despite having match point opportunities. At the Aegon Classic, she beat Eugenie Bouchard again 3–6, 6–4, 6–0, and then once again stunned a top-10 player by defeating world No. 3, Simona Halep, 2–6, 6–0, 7–6.  At the US Open, she reached the quarterfinals with wins over Svetlana Kuznetsova, Bojana Jovanovski, lucky loser Daria Kasatkina and Ekaterina Makarova before losing to eventual finalist Roberta Vinci in the quarterfinals, and entered the top 30 of the WTA singles rankings for the first time in her career.

2016: French Open women's doubles champion.

In May, Mladenovic reached the singles semifinals of the Internationaux de Strasbourg, but lost to Mirjana Lučić-Baroni.  At the French Open, Mladenovic won her first round match against the 2010 French Open singles champion Francesca Schiavone, and defeated her former doubles partner Tímea Babos in the second. She lost in the third round to world No. 1 and defending champion, Serena Williams, 4–6, 6–7, after she had a set point at 9–8 in the tiebreak. Mladenovic won the women's doubles event partnering Caroline Garcia, beating Ekaterina Makarova and Elena Vesnina in the final. It was the first Grand Slam women's doubles crown for Garcia and Mladenovic and they became the first all-French pair to win the French Open women's doubles title since Gail Chanfreau and Françoise Dürr in 1971.  In June, Mladenovic reached her second career WTA Tour singles final at the Rosmalen Grass Court Championships. She lost her final match to CoCo Vandeweghe, 5–7, 5–7.  Mladenovic participated in the women's singles, women's doubles and mixed-doubles events of the London Summer Olympics. In the women's singles, she was defeated in the second round by Madison Keys. In the women's doubles event, Mladenovic partnered countrywoman Caroline Garcia, with whom she had won the French Open in June. Despite being seeded No. 2, they lost in the first round. Mladenovic (she was paired with Pierre-Hugues Herbert and they were seeded No. 2) also lost in the first round of the mixed-doubles event. At the US Open singles event, Mladenovic cleared the first round before falling to Anastasia Pavlyuchenkova in the second. In doubles, Mladenovic (partnered with Garcia) reached the final, where the French team was defeated by Bethanie Mattek-Sands and Lucie Šafářová. This allowed Garcia and Mladenovic to qualify for the WTA Finals, becoming the second doubles team yet to do so.  Mladenovic moved on to the Asian swing, starting at the Korea Open. Seeded No. 4, Mladenovic had a surprise loss against Sara Sorribes Tormo, the 139th player in the world. Next, at the Wuhan Open, she faced world No. 1, Angelique Kerber in the second round. Kerber won the match, although Mladenovic captured the first set. In doubles, Mladenovic partnered with Garcia again, and the team was seeded No. 1. Despite this, the Frenchwomen lost their opening match against Christina McHale and Peng Shuai. In Beijing, Mladenovic defeated Jelena Jankovic in the first round, before coming across 8th seed Madison Keys. Keys won in straight sets. In doubles, Mladenovic and Garcia, once again the No. 1 seeds, made their way to the final, in which they faced Mattek-Sands and Šafářová, in a rematch of the US Open final a few weeks earlier. Mattek-Sands and Šafářová won the final 6–4, 6–4.  Mladenovic had success in singles at the Hong Kong Tennis Open. An unseeded player, she reached the semifinals after defeating doubles rival Mattek-Sands in the quarterfinals. She passed No. 8 seed Daria Gavrilova to reach her second singles final of the year. She was defeated by former No. 1, Caroline Wozniacki, in the final.  Shortly before heading into the WTA Doubles Finals, Mladenovic and Caroline Garcia received the WTA Award for Best Doubles Team of the Year. During the WTA Finals, the Frenchwomen defeated Julia Görges and Karolína Plíšková in the quarterfinals, but fell to Mattek-Sands and Šafářová in the semifinals.  During the 2016 Fed Cup final between France and the Czech Republic, Mladenovic lost the first rubber narrowly against Karolína Plíšková 3–6, 6–4, 14–16, a match that lasted 3 hours and 48 minutes. She later played doubles with Garcia in the fifth and decisive rubber against Plíšková and Barbora Strýcová, which they lost 5–7, 5–7, enabling the Czechs to win the Fed Cup for the fifth time in six years.  In December, Garcia and Mladenovic were named the doubles ITF World Champions of 2016. Mladenovic ended the year ranked No. 42 in singles, and tied No. 2 in doubles (with Garcia).

2017: First WTA Tour singles title, top-10 singles debut.

Mladenovic began the year by playing at the Hopman Cup alongside Richard Gasquet. The pair won their first tie against Germany's Andrea Petkovic and Alexander Zverev 2–1 (Mladenovic lost her singles match against Petkovic), and their second tie against Great Britain's Daniel Evans and Heather Watson 3–0. In France's third Group A tie against Switzerland which would decide which team would enter the final, Mladenovic (following Gasquet's defeat to Roger Federer) defeated Belinda Bencic and triumphed with Gasquet against the Swiss pair in mixed doubles, winning the tie 2-1. In the final, Mladenovic and Gasquet faced Americans Jack Sock and CoCo Vandeweghe. Although Gasquet won his singles match and Mladenovic lost hers, the French duo won the decisive mixed-doubles match, meaning that France were the 2017 Hopman Cup champions.  Mladenovic had a disappointing run at the Australian Open in singles, losing in the first round to Ana Konjuh. However, in doubles, Mladenovic, reuniting with partner Caroline Garcia, reached the semifinals of the event, where they lost to Andrea Hlaváčková and Peng Shuai.  At the St. Petersburg Ladies Trophy, Mladenovic won her first round match against Elise Mertens before upsetting reigning Australian Open finalist Venus Williams to reach the quarterfinals. She continued her fabulous form against No. 6 seed and defending champion Roberta Vinci, defeating the Italian veteran in straight sets. In the semifinals, the Frenchwoman defeated rising player Natalia Vikhlyantseva to reach the first WTA Premier singles final of her career. In a tense final, Mladenovic defeated Yulia Putintseva, 6–2, 6–7, 6–4 to win the first WTA Tour singles title of her career. Mladenovic became the first Frenchwoman to win a WTA Premier singles title since Marion Bartoli in June 2011. In addition, Mladenovic competed in doubles with Daria Gavrilova; this was the first time Mladenovic played with someone other than Garcia in over a year. The pair were defeated in the semifinals.  In the Fed Cup World Group quarterfinals against Switzerland, Mladenovic won her first singles match against Belinda Bencic. However, she then lost to Timea Bacsinszky in her next singles match. France lost the tie 1-4, resulting in France needing to win the Fed Cup World Group Play-off tie to earn the right to play in the 2018 World Group.  At Dubai, at the first Premier-5 event of the season, Mladenovic defeated Kateřina Siniaková in the first round before defeating world No. 3, Karolína Plíšková, 6–2, 6–4 in the second round. She then lost to Wang Qiang in the third round. Mladenovic's good form continued at the Mexican Open, where she stormed past Varvara Lepchenko before winning a marathon match against Heather Watson to reach the quarterfinals, in which she defeated Kirsten Flipkens. Mladenovic then won her semifinal encounter with Christina McHale, reaching her second WTA Tour singles final of 2017. Though she did end up losing to Lesia Tsurenko in the final, her success in February allowed Mladenovic to reach a career-high WTA singles ranking of No. 26. Moreover, Mladenovic was nominated for February's "WTA Shot of the Month, WTA Breakthrough Player of the Month," and "WTA Player of the Month" (winning the "WTA Breakthrough Player of the Month)".  Prior to the BNP Paribas Open, Mladenovic announced that her doubles partnership with Caroline Garcia would end for Garcia wanted to focus on her singles career. Mladenovic instead competed with Svetlana Kuznetsova in the doubles draw of Indian Wells. Meanwhile, in singles, the Frenchwoman received a bye into the second round, being seeded No. 28. She had a strong opening, defeating Annika Beck of Germany. In the third round, Mladenovic continued her newfound success by defeating world No. 4, Simona Halep, in straight sets, setting up an encounter with Lauren Davis, which she won in straight sets as well, reaching her first career WTA Premier Mandatory singles quarterfinals. Mladenovic continued to shine, defeating Caroline Wozniacki 3–6, 7–6, 6–2 (Mladenovic had never beaten Wozniacki in three previous encounters) before losing to eventual champion Elena Vesnina in the semifinals. Her good performance at the BNP Paribas Open enabled Mladenovic to attain a career-high WTA singles ranking of No. 18, and she became the No. 1 Frenchwoman once again (passing Caroline Garcia). She also had success with Kuznetsova in the doubles, knocking out the fifth-seeded pair of Andrea Hlaváčková and Peng Shuai in the second round before losing in the quarterfinals.  At the Miami Open, Mladenovic lost her opening singles match to the Romanian qualifier Patricia Maria Țig. In doubles, playing again with Kuznetsova, she faced Hlaváčková and Peng in the quarterfinals, in a repeat of their Indian Wells encounter. This time, Hlaváčková and Peng won the match, and Mladenovic missed the opportunity to become doubles world No. 1.  At the Porsche Tennis Grand Prix, Mladenovic defeated top-seed Angelique Kerber in the second round and three-time champion Maria Sharapova (who was playing her first WTA tournament after serving a 15-month suspension for failing a drug test) in the semifinals to reach her third WTA Tour singles final of the year. Against German wildcard Laura Siegemund (who was playing in her hometown), Mladenovic led 4–1 in the final set tiebreak but ended losing the match 1–6, 6–2, 6–7.  Mladenovic, seeded No. 14, reached her first career WTA Premier Mandatory singles final at the Mutua Madrid Open by defeating her doubles partner Svetlana Kuznetsova in the semifinals. In the final, she lost to third seeded Simona Halep in three sets. On 15 May (the day after the Madrid final), Mladenovic reached a career-high WTA singles ranking of No. 14. Seeded No. 13, Mladenovic lost her singles first round match against Julia Görges at the Internazionali BNL d'Italia.  At her home Grand Slam, the French Open, she won her first-round match in a tight three sets against American Jennifer Brady to advance to the second round where she faced the 2012 finalist Sara Errani whom she defeated in straight sets to advance to the third round at the tournament once again where she had another close match against last years quarterfinalist Shelby Rogers. She then advanced to the fourth round, her best showing at this tournament, and defeated the defending champion Garbiñe Muguruza in three sets to advance to her second quarterfinal of a Grand Slam tournament in her career but then lost to Timea Bacsinszky.  Since then however she has had a difficult second half of the season. At Wimbledon, she lost in the singles second round, sustaining a right knee injury in the process. Over the next four months, she struggled to get back into shape again and suffered a loss of confidence. This caused Mladenovic to lose all twelve of her remaining singles matches of 2018 after winning her first-round singles match at the Citi Open (she won only two sets in those twelve singles matches) at various hard-court tournaments (including the US Open) in North America, Asia and Europe. Arguably her worst moment came at the Pan Pacific Open, where she suffered a double bagel defeat in the first round against Wang Qiang.  However, due to a consistent first half of the season which saw Mladenovic being constantly in the top 8 of the Race to the WTA Finals, she eventually broke into the top-ten of the WTA singles rankings for the first time in her career (at No. 10) on 23 October 2017, at the start of the WTA Finals. And because of big results in that half of the season, Mladenovic called the season'still the best of my career', when opening about her singles slump in the second half of the year.

2018: Disaster in singles.

Mladenovic started her season at the Brisbane International, where she lost in the first round to the eventual singles finalist Aliaksandra Sasnovich in three sets. In her next tournament, the Sydney International, she retired in second set of her first-round match against the Australian wildcard Ellen Perez due to heat stress. At the Australian Open, Mladenovic's poor form in singles continued, losing her first round match in straight sets to world No. 104, Ana Bogdan from Romania, extending her losing streak in singles to 15 consecutive matches. Opening up about the loss, Mladenovic stated that it was not about injury anymore, that it was just a bad day and that it could not continue like that. Mladenovic turned things around when she won the Australian Open women's doubles with Tímea Babos, thus winning her second career Grand Slam women's doubles title.  Mladenovic next played in St. Petersburg as the defending singles champion. After receiving a first-round bye, Mladenovic showed signs of her top form and confidence which enabled her to reach four WTA Tour singles finals in the first half of 2017 by defeating former top-5 player and 2016 WTA Finals champion Dominika Cibulková in the second round, ending her 15-match losing streak in singles. She then followed up her second round win by beating Kateřina Siniaková in the quarterfinals and Daria Kasatkina in the semifinals (who had beaten the 2018 Australian Open champion Caroline Wozniacki previously), to advance to her first WTA Tour singles final since the Madrid Open last year. In the final she lost to Petra Kvitova in straight sets. Mladenovic won both her singles matches and her doubles match in the Fed Cup World Group quarterfinal tie against Belgium on February 10–11. She lost her singles second round and first round matches in Doha and Dubai respectively.  Mladenovic reached her second WTA singles quarterfinal of the year in Acapulco, where she lost to the defending champion Lesia Tsurenko. In Indian Wells, Mladenovic defeated Samantha Stosur in the second round before losing in the third round to Wang Qiang, who improved their head-to-head to 3-0. In Indian Wells doubles event, Mladenovic partnered Babos and they lost in the semifinals to Ekaterina Makarova and Elena Vesnina. Mladenovic lost her opening singles match in Miami to Petra Martić. Mladenovic lost her singles first-round matches in three (Lugano, Stuttgart and Rome) of her next five tournaments, winning a total of three singles matches in the other two (Fed Cup World Group semifinals and Madrid).  At the French Open, the 29th seeded Mladenovic lost in the singles first round to Andrea Petkovic. Mladenovic and Tímea Babos were the women's doubles top-seeds at that tournament, losing in the quarterfinals to the unseeded Japanese pair of Eri Hozumi and Makoto Ninomiya. On 11 June (the day after the last day of the French Open), Mladenovic's WTA singles ranking fell to world No. 54, compared to world No. 31 two weeks earlier. Mladenovic played her first grass-court tournament of the year in Birmingham, where she lost in the singles second round to the unseeded Magdaléna Rybáriková. Mladenovic and Babos won the Birmingham doubles title, defeating Elise Mertens and Demi Schuurs in the final. The following week in Eastbourne, the unseeded Mladenovic again lost in the singles second round, to the No. 8 seed Ashleigh Barty. The unseeded Mladenovic was defeated in the singles third round of Wimbledon by the no. 25 seed Serena Williams 5–7, 6–7. The top-seeded pair of Mladenovic and Tímea Babos were defeated in the Wimbledon women's doubles quarterfinals.  Mladenovic lost her opening singles matches (both in straight sets) in her next two tournaments, to Tímea Babos and Victoria Azarenka in San Jose and Montreal respectively. Mladenovic registered her first top-10 singles win of 2018 in Cincinnati when she defeated Julia Görges 6–4, 3-2, retired in the first round (Görges was forced to retire from their match because of a calf injury).

2019: No. 1 in Doubles.

Kristina Mladenovic and Tímea Babos were the defending champions at the Australian Open. They lost in the final to Samantha Stosur and Zhang Shuai.  In Dubai, Mladenovic defeated world No.1 Naomi Osaka in the second round. She then lost her next match to Carla Suárez Navarro.  In April, Mladenovic played for France in the Fed Cup semifinals. She lost her match against Simona Halep. Then in the deciding doubles rubber, Mladenovic and Garcia defeated Halep and Niculescu.  Mladenovic and Babos made the final of the 2019 French Open and in the process, Mladenovic became the number one doubles player in the world. In the final, they defeated Duan Yingying and Zheng Saisai and won their third Grand Slam title.  Mladenovic reached the second round of the Wimbledon singles, but lost to Petra Kvitová.  At the US Open she won her first round match against three-time Grandslam-Champion and 14th seed Angelique Kerber.  At the Fed Cup final against Australia, Mladenovic was essential in France winning their first title since 2003, winning all three of her rubbers. First, she defeated Ajla Tomljanović 6–1, 6–1, and then upset world No. 1 Ashleigh Barty in three sets, 2–6, 6–4, 7–6. Then, Mladenovic and Garcia defeated Barty and Samantha Stosur in the decisive doubles rubber 6–4, 6–3.

Playing style.

Mladenovic employs an all-court playing style, using variety along with her baseline play to win points. Her forehand is the stronger wing, and is hit both flatly and with topspin. Her backhand is a solid shot, and she is capable of hitting her two-hander consistently and can earn winners from it, but she does also tend to use the backhand slice a lot to change the pace of the rally. She possesses a powerful serve, and her height of 1.84 m (6 ft 1⁄2 in) means that she is able to nail first serves accurately with a lot of aces. However, her second serve is a lot weaker and she can serve a lot of double faults in a match. Her doubles success in recent years means she has developed a very good net game as well and she frequently approaches the net to finish off points. She uses her volleys, along with her backhand slice and drop shots, to create a lot of variety in her game. Her movement around the court is very good, considering her height and her footwork, but this can be exposed as a weakness when she needs to recover.

Apparel and equipment.

Mladenovic wears Adidas clothing and uses Wilson rackets.

Kristina "Kiki" Mladenovic (; / Kristina "Kiki" Mladenović, ; born 14 May 1993) is a French professional tennis player. Mladenovic has won one singles and twenty-one doubles titles on the WTA Tour, as well as four singles and seven doubles titles on the ITF Women's Circuit. On 23 October 2017, she reached her highest WTA singles ranking of world No. 10. On 10 June 2019, she peaked at No. 1 in the WTA doubles rankings.

Kristina Mladenovicová,, (* 14. května 1993 Saint-Pol-sur-Mer) je francouzská profesionální tenistka srbského původu, vítězka čtyř Grand Slamů v ženské čtyřhře a dvou z mixu, rovněž tak čtyřhry na Turnaji mistryň 2018 i 2019. V letech 2019–2020 byla světovou jedničkou ve čtyřhře, kterou se poprvé stala jako druhá Francouzka a čtyřicátá druhá hráčka od zavedení klasifikace v září 1984. Ve třech obdobích na čele strávila osm týdnů.


Terminology.

Physicist Murray Gell-Mann coined the word "quark" in its present sense. It originally comes from the phrase "Three quarks for Muster Mark" in "Finnegans Wake" by James Joyce. On June 27, 1978, Gell-Mann wrote a private letter to the editor of the "Oxford English Dictionary", in which he related that he had been influenced by Joyce's words: "The allusion to three quarks seemed perfect." (Originally, only three quarks had been discovered.)  The three kinds of charge in QCD (as opposed to one in quantum electrodynamics or QED) are usually referred to as "color charge" by loose analogy to the three kinds of color (red, green and blue) perceived by humans. Other than this nomenclature, the quantum parameter "color" is completely unrelated to the everyday, familiar phenomenon of color.  The force between quarks is known as the colour force (or color force ) or strong interaction, and is responsible for the strong nuclear force.  Since the theory of electric charge is dubbed "electrodynamics", the Greek word χρῶμα "chroma" "color" is applied to the theory of color charge, "chromodynamics".

History.

With the invention of bubble chambers and spark chambers in the 1950s, experimental particle physics discovered a large and ever-growing number of particles called hadrons. It seemed that such a large number of particles could not all be fundamental. First, the particles were classified by charge and isospin by Eugene Wigner and Werner Heisenberg; then, in 1953–56, according to strangeness by Murray Gell-Mann and Kazuhiko Nishijima (see Gell-Mann–Nishijima formula). To gain greater insight, the hadrons were sorted into groups having similar properties and masses using the "eightfold way", invented in 1961 by Gell-Mann and Yuval Ne'eman. Gell-Mann and George Zweig, correcting an earlier approach of Shoichi Sakata, went on to propose in 1963 that the structure of the groups could be explained by the existence of three flavors of smaller particles inside the hadrons: the quarks.  Perhaps the first remark that quarks should possess an additional quantum number was made as a short footnote in the preprint of Boris Struminsky in connection with the Ω hyperon being composed of three strange quarks with parallel spins (this situation was peculiar, because since quarks are fermions, such a combination is forbidden by the Pauli exclusion principle): Boris Struminsky was a PhD student of Nikolay Bogolyubov. The problem considered in this preprint was suggested by Nikolay Bogolyubov, who advised Boris Struminsky in this research. In the beginning of 1965, Nikolay Bogolyubov, Boris Struminsky and Albert Tavkhelidze wrote a preprint with a more detailed discussion of the additional quark quantum degree of freedom. This work was also presented by Albert Tavkhelidze without obtaining consent of his collaborators for doing so at an international conference in Trieste (Italy), in May 1965.  A similar mysterious situation was with the Δ baryon; in the quark model, it is composed of three up quarks with parallel spins. In 1964–65, Greenberg and Han–Nambu independently resolved the problem by proposing that quarks possess an additional SU(3) gauge degree of freedom, later called color charge. Han and Nambu noted that quarks might interact via an octet of vector gauge bosons: the gluons.  Since free quark searches consistently failed to turn up any evidence for the new particles, and because an elementary particle back then was "defined" as a particle which could be separated and isolated, Gell-Mann often said that quarks were merely convenient mathematical constructs, not real particles. The meaning of this statement was usually clear in context: He meant quarks are confined, but he also was implying that the strong interactions could probably not be fully described by quantum field theory.  Richard Feynman argued that high energy experiments showed quarks are real particles: he called them "partons" (since they were parts of hadrons). By particles, Feynman meant objects which travel along paths, elementary particles in a field theory.  The difference between Feynman's and Gell-Mann's approaches reflected a deep split in the theoretical physics community. Feynman thought the quarks have a distribution of position or momentum, like any other particle, and he (correctly) believed that the diffusion of parton momentum explained diffractive scattering. Although Gell-Mann believed that certain quark charges could be localized, he was open to the possibility that the quarks themselves could not be localized because space and time break down. This was the more radical approach of S-matrix theory.  James Bjorken proposed that pointlike partons would imply certain relations in deep inelastic scattering of electrons and protons, which were verified in experiments at SLAC in 1969. This led physicists to abandon the S-matrix approach for the strong interactions.  In 1973 the concept of color as the source of a "strong field" was developed into the theory of QCD by physicists Harald Fritzsch and Heinrich Leutwyler, together with physicist Murray Gell-Mann. In particular, they employed the general field theory developed in 1954 by Chen Ning Yang and Robert Mills (see Yang–Mills theory), in which the carrier particles of a force can themselves radiate further carrier particles. (This is different from QED, where the photons that carry the electromagnetic force do not radiate further photons.)  The discovery of asymptotic freedom in the strong interactions by David Gross, David Politzer and Frank Wilczek allowed physicists to make precise predictions of the results of many high energy experiments using the quantum field theory technique of perturbation theory. Evidence of gluons was discovered in three-jet events at PETRA in 1979. These experiments became more and more precise, culminating in the verification of perturbative QCD at the level of a few percent at the LEP in CERN.  The other side of asymptotic freedom is confinement. Since the force between color charges does not decrease with distance, it is believed that quarks and gluons can never be liberated from hadrons. This aspect of the theory is verified within lattice QCD computations, but is not mathematically proven. One of the Millennium Prize Problems announced by the Clay Mathematics Institute requires a claimant to produce such a proof. Other aspects of non-perturbative QCD are the exploration of phases of quark matter, including the quark–gluon plasma.  The relation between the short-distance particle limit and the confining long-distance limit is one of the topics recently explored using string theory, the modern form of S-matrix theory.

Theory.

Some definitions.

Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations. These can be  QCD is a non-abelian gauge theory (or Yang–Mills theory) of the SU(3) gauge group obtained by taking the color charge to define a local symmetry.  Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks.  There are additional global symmetries whose definitions require the notion of chirality, discrimination between left and right-handed. If the spin of a particle has a positive projection on its direction of motion then it is called left-handed; otherwise, it is right-handed. Chirality and handedness are not the same, but become approximately equivalent at high energies.

Additional remarks: duality.

As mentioned, "asymptotic freedom" means that at large energy – this corresponds also to "short distances" – there is practically no interaction between the particles. This is in contrast – more precisely one would say "dual"– to what one is used to, since usually one connects the absence of interactions with "large" distances. However, as already mentioned in the original paper of Franz Wegner, a solid state theorist who introduced 1971 simple gauge invariant lattice models, the high-temperature behaviour of the "original model", e.g. the strong decay of correlations at large distances, corresponds to the low-temperature behaviour of the (usually ordered!) "dual model", namely the asymptotic decay of non-trivial correlations, e.g. short-range deviations from almost perfect arrangements, for short distances. Here, in contrast to Wegner, we have only the dual model, which is that one described in this article.

Symmetry groups.

The color group SU(3) corresponds to the local symmetry whose gauging gives rise to QCD. The electric charge labels a representation of the local symmetry group U(1) which is gauged to give QED: this is an abelian group. If one considers a version of QCD with "N" flavors of massless quarks, then there is a global (chiral) flavor symmetry group SU("N") × SU("N") × U(1) × U(1). The chiral symmetry is spontaneously broken by the QCD vacuum to the vector (L+R) SU("N") with the formation of a chiral condensate. The vector symmetry, U(1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry U(1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an anomaly. Gluon field configurations called instantons are closely related to this anomaly.  There are two different types of SU(3) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry which rotates different flavors of quarks to each other, or "flavor SU(3)". Flavor SU(3) is an approximate symmetry of the vacuum of QCD, and is not a fundamental symmetry at all. It is an accidental consequence of the small mass of the three lightest quarks.  In the QCD vacuum there are vacuum condensates of all the quarks whose mass is less than the QCD scale. This includes the up and down quarks, and to a lesser extent the strange quark, but not any of the others. The vacuum is symmetric under SU(2) isospin rotations of up and down, and to a lesser extent under rotations of up, down and strange, or full flavor group SU(3), and the observed particles make isospin and SU(3) multiplets.  The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate string description of QCD.

Lagrangian.

The dynamics of the quarks and gluons are controlled by the quantum chromodynamics Lagrangian. The gauge invariant QCD Lagrangian is  where formula_1 is the quark field, a dynamical function of spacetime, in the fundamental representation of the SU(3) gauge group, indexed by formula_2; formula_3 is the gauge covariant derivative; the γ are Dirac matrices connecting the spinor representation to the vector representation of the Lorentz group.  The symbol formula_4 represents the gauge invariant gluon field strength tensor, analogous to the electromagnetic field strength tensor, "F", in quantum electrodynamics. It is given by:  where formula_6 are the gluon fields, dynamical functions of spacetime, in the adjoint representation of the SU(3) gauge group, indexed by "a", "b"...; and "f" are the structure constants of SU(3). Note that the rules to move-up or pull-down the "a", "b", or "c" indices are "trivial", (+,..., +), so that "f" = "f" = "f" whereas for the "μ" or "ν" indices one has the non-trivial "relativistic" rules corresponding to the metric signature (+ − − −).  The variables "m" and "g" correspond to the quark mass and coupling of the theory, respectively, which are subject to renormalization.  An important theoretical concept is the "Wilson loop" (named after Kenneth G. Wilson). In lattice QCD, the final term of the above Lagrangian is discretized via Wilson loops, and more generally the behavior of Wilson loops can distinguish confined and deconfined phases.

Fields.

Quarks are massive spin- fermions which carry a color charge whose gauging is the content of QCD. Quarks are represented by Dirac fields in the fundamental representation 3 of the gauge group SU(3). They also carry electric charge (either − or +) and participate in weak interactions as part of weak isospin doublets. They carry global quantum numbers including the baryon number, which is for each quark, hypercharge and one of the flavor quantum numbers.  Gluons are spin-1 bosons which also carry color charges, since they lie in the adjoint representation 8 of SU(3). They have no electric charge, do not participate in the weak interactions, and have no flavor. They lie in the singlet representation 1 of all these symmetry groups.  Every quark has its own antiquark. The charge of each antiquark is exactly the opposite of the corresponding quark.

Dynamics.

According to the rules of quantum field theory, and the associated Feynman diagrams, the above theory gives rise to three basic interactions: a quark may emit (or absorb) a gluon, a gluon may emit (or absorb) a gluon, and two gluons may directly interact. This contrasts with QED, in which only the first kind of interaction occurs, since photons have no charge. Diagrams involving Faddeev–Popov ghosts must be considered too (except in the unitarity gauge).

Area law and confinement.

Detailed computations with the above-mentioned Lagrangian show that the effective potential between a quark and its anti-quark in a meson contains a term that increases in proportion to the distance between the quark and anti-quark (formula_7), which represents some kind of "stiffness" of the interaction between the particle and its anti-particle at large distances, similar to the entropic elasticity of a rubber band (see below). This leads to "confinement" of the quarks to the interior of hadrons, i.e. mesons and nucleons, with typical radii "R", corresponding to former "Bag models" of the hadrons The order of magnitude of the "bag radius" is 1 fm (= 10 m). Moreover, the above-mentioned stiffness is quantitatively related to the so-called "area law" behaviour of the expectation value of the Wilson loop product "P" of the ordered coupling constants around a closed loop "W"; i.e. formula_8 is proportional to the "area" enclosed by the loop. For this behaviour the non-abelian behaviour of the gauge group is essential.

Methods.

Further analysis of the content of the theory is complicated. Various techniques have been developed to work with QCD. Some of them are discussed briefly below.

Perturbative QCD.

This approach is based on asymptotic freedom, which allows perturbation theory to be used accurately in experiments performed at very high energies. Although limited in scope, this approach has resulted in the most precise tests of QCD to date.

Lattice QCD.

Among non-perturbative approaches to QCD, the most well established one is lattice QCD. This approach uses a discrete set of spacetime points (called the lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation which is then carried out on supercomputers like the QCDOC which was constructed for precisely this purpose. While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means, in particular into the explicit forces acting between quarks and antiquarks in a meson. However, the numerical sign problem makes it difficult to use lattice methods to study QCD at high density and low temperature (e.g. nuclear matter or the interior of neutron stars).

expansion.

A well-known approximation scheme, the expansion, starts from the idea that the number of colors is infinite, and makes a series of corrections to account for the fact that it is not. Until now, it has been the source of qualitative insight rather than a method for quantitative predictions. Modern variants include the AdS/CFT approach.

Effective theories.

For specific problems effective theories may be written down which give qualitatively correct results in certain limits. In the best of cases, these may then be obtained as systematic expansions in some parameter of the QCD Lagrangian. One such effective field theory is chiral perturbation theory or ChiPT, which is the QCD effective theory at low energies. More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u, d and s quark, which have small mass, it is still a good approximate symmetry. Depending on the number of quarks which are treated as light, one uses either SU(2) ChiPT or SU(3) ChiPT. Other effective theories are heavy quark effective theory (which expands around heavy quark mass near infinity), and soft-collinear effective theory (which expands around large ratios of energy scales). In addition to effective theories, models like the Nambu–Jona-Lasinio model and the chiral model are often used when discussing general features.

QCD sum rules.

Based on an Operator product expansion one can derive sets of relations that connect different observables with each other.

Nambu–Jona-Lasinio model.

In one of his recent works, Kei-Ichi Kondo derived as a low-energy limit of QCD, a theory linked to the Nambu–Jona-Lasinio model since it is basically a particular non-local version of the Polyakov–Nambu–Jona-Lasinio model. The later being in its local version, nothing but the Nambu–Jona-Lasinio model in which one has included the Polyakov loop effect, in order to describe a 'certain confinement'.  The Nambu–Jona-Lasinio model in itself is, among many other things, used because it is a'relatively simple' model of chiral symmetry breaking, phenomenon present up to certain conditions (Chiral limit i.e. massless fermions) in QCD itself. In this model, however, there is no confinement. In particular, the energy of an isolated quark in the physical vacuum turns out well defined and finite.

Experimental tests.

The notion of quark flavors was prompted by the necessity of explaining the properties of hadrons during the development of the quark model. The notion of color was necessitated by the puzzle of the. This has been dealt with in the section on the history of QCD.  The first evidence for quarks as real constituent elements of hadrons was obtained in deep inelastic scattering experiments at SLAC. The first evidence for gluons came in three-jet events at PETRA.  Several good quantitative tests of perturbative QCD exist:  Quantitative tests of non-perturbative QCD are fewer, because the predictions are harder to make. The best is probably the running of the QCD coupling as probed through lattice computations of heavy-quarkonium spectra. There is a recent claim about the mass of the heavy meson B. Other non-perturbative tests are currently at the level of 5% at best. Continuing work on masses and form factors of hadrons and their weak matrix elements are promising candidates for future quantitative tests. The whole subject of quark matter and the quark–gluon plasma is a non-perturbative test bed for QCD which still remains to be properly exploited.  One qualitative prediction of QCD is that there exist composite particles made solely of gluons called glueballs that have not yet been definitively observed experimentally. A definitive observation of a glueball with the properties predicted by QCD would strongly confirm the theory. In principle, if glueballs could be definitively ruled out, this would be a serious experimental blow to QCD. But, as of 2013, scientists are unable to confirm or deny the existence of glueballs definitively, despite the fact that particle accelerators have sufficient energy to generate them.

Cross-relations to condensed matter physics.

There are unexpected cross-relations to condensed matter physics. For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom formula_9 for "i" =1...,N, with the special fixed "random" couplings formula_10 Here the ε and ε quantities can independently and "randomly" take the values ±1, which corresponds to a most-simple gauge transformation formula_11 This means that thermodynamic expectation values of measurable quantities, e.g. of the energy formula_12 are invariant.  However, here the "coupling degrees of freedom" formula_13, which in the QCD correspond to the "gluons", are "frozen" to fixed values (quenching). In contrast, in the QCD they "fluctuate" (annealing), and through the large number of gauge degrees of freedom the entropy plays an important role (see below).  For positive "J" the thermodynamics of the Mattis spin glass corresponds in fact simply to a "ferromagnet in disguise", just because these systems have no "frustration" at all. This term is a basic measure in spin glass theory. Quantitatively it is identical with the loop product formula_14 along a closed loop "W". However, for a Mattis spin glass – in contrast to "genuine" spin glasses – the quantity "P" never becomes negative.  The basic notion "frustration" of the spin-glass is actually similar to the Wilson loop quantity of the QCD. The only difference is again that in the QCD one is dealing with SU(3) matrices, and that one is dealing with a "fluctuating" quantity. Energetically, perfect absence of frustration should be non-favorable and atypical for a spin glass, which means that one should add the loop product to the Hamiltonian, by some kind of term representing a "punishment". In the QCD the Wilson loop is essential for the Lagrangian rightaway.  The relation between the QCD and "disordered magnetic systems" (the spin glasses belong to them) were additionally stressed in a paper by Fradkin, Huberman and Shenker, which also stresses the notion of duality.  A further analogy consists in the already mentioned similarity to polymer physics, where, analogously to Wilson Loops, so-called "entangled nets" appear, which are important for the formation of the entropy-elasticity (force proportional to the length) of a rubber band. The non-abelian character of the SU(3) corresponds thereby to the non-trivial "chemical links", which glue different loop segments together, and "asymptotic freedom" means in the polymer analogy simply the fact that in the short-wave limit, i.e. for formula_15 (where "R" is a characteristic correlation length for the glued loops, corresponding to the above-mentioned "bag radius", while λ is the wavelength of an excitation) any non-trivial correlation vanishes totally, as if the system had crystallized.  There is also a correspondence between confinement in QCD – the fact that the color field is only different from zero in the interior of hadrons – and the behaviour of the usual magnetic field in the theory of type-II superconductors: there the magnetism is confined to the interior of the Abrikosov flux-line lattice, i.e., the London penetration depth "λ" of that theory is analogous to the confinement radius "R" of quantum chromodynamics. Mathematically, this correspondendence is supported by the second term, formula_16 on the r.h.s. of the Lagrangian.

In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called "color". Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.

Kvantová chromodynamika (QCD) je kalibrační teorie interakcí barevných kvarků, antikvarků a gluonů. Kvantová chromodynamika jako teorie silných interakcí vznikla v polovině 70. let. Její platnost byla potvrzena značným množstvím experimentů. Dodnes se však její předpovědi omezují na příklady interakcí na velmi malé vzdálenosti, kde je aplikovatelná poruchová teorie.