A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained. <s> BIB001 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> I. Molecular Diffusion.- 1.1. Introduction.- 1.2. Concentration.- 1.3. Flux.- 1.4. Fick's Law.- 1.5. Conservation of Mass.- 1.6. Instantaneous Plane Source.- 1.7. Some Simple Examples.- 1.8. Diffusion of Finite Size Cloud.- 1.9. 'Reflection' at Boundary.- 1.10. Two- and Three-Dimensional Problems.- 1.11. Continuous Sources.- 1.12. Source in Uniform Wind.- Appendix to Chapter I.- Exercises.- References.- II. Statistical Theory of Diffusion and Brownian Motion.- 2.1. Introduction.- 2.2. Dispersion Through Random Movements.- 2.3. Diffusion with Stationary Velocities.- 2.4. Brownian Motion.- 2.5. Dispersion of Brownian Particles.- 2.6. Simple Random Walk Model.- 2.7. Reflecting Barrier.- 2.8. Absorbing Barrier.- 2.9. Connection of Random Walk to Diffusion Equation.- 2.10. Deposition on Vertical Surfaces.- 2.11. Deposition on Horizontal Surfaces.- Exercises.- References.- III. Turbulent Diffusion: Elementary Statistical Theory and Atmospheric Applications.- 3.1. Fundamental Concepts of Turbulence.- 3.2. Field Measurements of Concentration and Dosage.- 3.3. The Statistical Approach to Environmental Diffusion.- 3.4. 'Lagrangian' Properties of Turbulence.- 3.5. Consequences of Taylor's Theorem.- 3.6. The Form of the Particle-Displacement Probability Distribution.- 3.7. Mean Concentration Field of Continuous Sources.- 3.8. Apparent Eddy Diffusivity.- 3.9. Application to Laboratory Experiments.- 3.10. Application to Atmospheric Diffusion.- 3.11. Initial Phase of Continuous Plumes.- 3.12. Atmospheric Cloud Growth far from Concentrated Sources.- 3.13. The Non-Stationary Character of Atmospheric Turbulence.- 3.14. The Hay-Pasquill Method of Cloud-Spread Prediction.- Exercise.- References.- IV. 'Relative' Diffusion and Oceanic Applications.- 4.1. Experimental Basis.- 4.2. Mean Concentration Field in a Frame of Reference Attached to the Center of Gravity.- 4.3. Probability Distributions of Particle Displacements.- 4.4. Kinematics of Particle Movements in a Moving Frame.- 4.5. Phases of Cloud Growth.- 4.6. History of a Concentrated Puff.- 4.7. Initially Finite Size Cloud.- 4.8. Use of the Diffusion Equation.- 4.9. Horizontal Diffusion in the Ocean and Large Lakes.- 4.10. Application to Diffusion of Sewage Plumes.- 4.11. Vertical Diffusion in Lakes and Oceans.- Exercise.- References.- V. Dispersion in Shear Flow.- 5.1. Introduction.- 5.2. Properties of the Planetary Boundary Layer.- 5.3. Particle Displacements in a Wall Layer.- 5.4. Continuous Ground-Level Line Source.- 5.5. Flux and Eddy Diffusivity.- 5.6. Comparison with Experiment.- 5.7. Continuous Point Source at Ground Level.- 5.8. Use of the Diffusion Equation.- 5.9. Elevated Sources.- 5.10. Longitudinal Dispersion in Shear Flow.- 5.11. Shear-Augmented Diffusion in a Channel.- 5.12. Dispersion in Natural Streams.- 5.13. Shear-Augmented Dispersion in Unlimited Parallel Flow.- 5.14. Diffusion in Skewed Shear Flow.- References.- VI. Effects of Density Differences on Environmental Diffusion.- 6.1. Introduction.- 6.2. Fundamental Equations.- 6.3. Approximate Forms of the Equations.- 6.4. Equations for Turbulent Flow.- 6.5. Turbulent Energy Equation.- 6.6. Diffusion Floors and Ceilings.- 6.7. Diffusion in a Continuously Stratified Fluid.- 6.8. Velocity Autocorrelation and Particle Spread in Stratified Fluid Model.- 6.9. Bodily Motion of Buoyant and Heavy Plumes.- 6.10. Dynamics of a Line Thermal.- 6.11. Similarity Theory.- 6.12. Bent-Over Chimney Plumes.- 6.13. Theory of Buoyancy Dominated Plumes in a Neutral Atmosphere.- 6.14. Comparison with Observation.- 6.15. Flow Pattern within a Plume.- 6.16. Effect of Atmospheric Stratification.- 6.17. Approximate Arguments for Plumes in Stratified Surroundings.- 6.18. Engineering Assessment of Ground Level Pollution from Buoyancy Dominated Plumes.- 6.19. Effects of Plume Rise on Ground-Level Concentration.- Appendix to Chapter VI.- A6.1. Momentum Plumes.- Exercise.- References.- VII. The Fluctuation Problem in Turbulent Diffusion.- 7.1. Introduction.- 7.2. Probability Distribution of Concentration.- 7.3. The Functional Form of the Probability Distribution.- 7.4. Hazard Assessment on the Basis of Concentration Probabilities.- 7.5. The Variance of Concentration Fluctuations.- 7.6. Self-Similar Fluctuation Intensity Distribution.- 7.7. Fluctuating Plume Model.- References. <s> BIB002 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles. <s> BIB003 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> This monograph discusses selected analytical solutions, semianalytical methods and numerical approaches used to study solute transport in groundwater. It discusses their strengths, pitfalls and application. Comprehensive tables and computer program listings are included in the appendices. <s> BIB004 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Some Mathematical Preliminaries.- Ito Integrals.- The Ito Formula and the Martingale Representation Theorem.- Stochastic Differential Equations.- The Filtering Problem.- Diffusions: Basic Properties.- Other Topics in Diffusion Theory.- Applications to Boundary Value Problems.- Application to Optimal Stopping.- Application to Stochastic Control.- Application to Mathematical Finance. <s> BIB005 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Preface 1. Models for diffusion Part I. Fundamentals of Diffusion: 2. Diffusion in dilute solutions 3. Diffusion in concentrated solutions 4. Dispersion Part II. Diffusion Coefficients: 5. Values of diffusion coefficients 6. Diffusion of interacting species 7. Multicomponent diffusion Part III. Mass Transfer: 8. Fundamentals of mass transfer 9. Theories of mass transfer 10. Absorption 11. Absorption in biology and medicine 12. Differential distillation 13. Staged distillation 14. Extraction 15. Absorption Part IV. Diffusion Coupled with other Processes: 16. General questions and heterogeneous chemical reactions 17. Homogeneous chemical reactions 18. Membranes 19. Controlled release and related phenomena 20. Heat transfer 21. Simultaneous heat and mass transfer Problems Subject index Materials index. <s> BIB006 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Capacity for information in biological molecules is traditionally thought to reside in the primary sequence of proteins and RNA, recorded in the DNA. With the exception of some RNA molecules, proteins, if not structural, carry their information in binding sites for substrates of reactions, or in binding sites for control molecules. Some proteins bind to complex carbohydrates in a carbohydrate-specific fashion, including enzymes, lectins and antibodies. These carbohydrates, assembled by sequential glycosyl transferases, also carry biological information, the other side of which is a binding protein that recognizes a specific sugar monosaccharides, sequence, anomerity, linkage, ring size, branching and substitution. It is the latter 7 parameters, however, that give carbohydrates a very large potential for information-carrying capacity in a short sequence. An exponentially growing body of knowledge exists in this aspect of carbohydrate function. <s> BIB007 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Abstract Analytical solutions are provided for the two- and three-dimensional advection–diffusion equation with spatially variable velocity and diffusion coefficients. We assume that the velocity component is proportional to the distance and that the diffusion coefficient is proportional to the square of the corresponding velocity component. There is a simple transformation which reduces the spatially variable equation to a constant coefficient problem for which there are available a large number of known analytical solutions for general initial and boundary conditions. These solutions are also solutions to the spatially variable advection–diffusion equation. The special form of the spatial coefficients has practical relevance and for divergent free flow represent corner or straining flow. Unlike many other analytical solutions, we use the transformation to obtain solutions of the spatially variable coefficient advection–diffusion equation in two and three dimensions. The analytical solutions, which are simple to evaluate, can be used to validate numerical models for solving the advection–diffusion equation with spatially variable coefficients. For numerical schemes which cannot handle flow stagnation points, we provide analytical solution to the spatially variable coefficient advection–diffusion equation for two-dimensional corner flow which contains an impermeable flow boundary. The impermeable flow boundary coincides with a streamline along which the fluid velocity is finite but the concentration vanishes. This example is useful for validating numerical schemes designed to predict transport around a curved boundary. <s> BIB008 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> I Basic Concepts and Discretizations.- II Time Integration Methods.- III Advection-Diffusion Discretizations.- IV Splitting Methods.- V Stabilized Explicit Runge-Kutta Methods. <s> BIB009 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Recent developments in the application of micro- and nanosystems for drug administration include a diverse range of new materials and methods. New approaches include the on-demand activation of molecular interactions, novel diffusion-controlled delivery devices, nanostructured 'smart' surfaces and materials, and prospects for coupling drug delivery to sensors and implants. Micro- and nanotechnologies are enabling the design of novel methods such as radio-frequency addressing of individual molecules or the suppression of immune response to a release device. Current challenges include the need to balance the small scale of the devices with the quantities of drugs that are clinically necessary, the requirement for more stable sensor platforms, and the development of methods to evaluate these new materials and devices for safety and efficacy. <s> BIB010 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> In this paper, the problem of communicating using chemical messages propagating using Brownian motion, rather than electromagnetic messages propagating as waves in free space or along a wire, is considered. This problem is motivated by nanotechnological and biotechnological applications, where the energy cost of electromagnetic communication might be prohibitive. Models are given for communication using particles that propagate with Brownian motion, and achievable capacity results are given. Under conservative assumptions, it is shown that rates exceeding one bit per particle are achievable. <s> BIB011 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Molecular communication is engineered biological communication that allows biological devices to communicate through chemical signals. Since biological devices are made of biological materials and are not amenable to traditional communication means (e.g., electromagnetic waves), molecular communication provides a mechanism for biological devices to communicate by transmitting, propagating, and receiving molecules that represent information. In this paper, we explore biological cells and their communication mechanisms for designing and engineering synthetic molecular communication systems. The paper first discusses the characteristics and potential design of communication mechanisms, and then reports our experimental and modeling studies to address physical layer issues of molecular communication. <s> BIB012 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> We obtain compact, exact, analytical expressions for the first-passage-time distribution for a particle diffusing on a planar wedge for special values of the wedge angle. Specifically, we calculate the first-passage-time distribution for the diffusing particle through a planar wedge of angle pi/n, where n is an integer. For the cases n=2 and n odd, we provide an exact closed-form expression to the first-passage-time distribution while for the remaining cases, we provide it in integral form and evaluate numerically using quadratures. We then show that our results are in good agreement with Markovian simulations in the continuum limit. <s> BIB013 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> This article reviews the physical processes responsible for the transport and deposition of particles and their theoretical modeling. Both laminar and turbulent processes are considered, emphasizing the physical understanding of the various transport mechanisms. State-of-the-art computational methods for determining particle motion and deposition are discussed, including stochastic Lagrangian particle tracking and a unified Eulerian advection-diffusion approach. The theory presented includes Brownian and turbulent diffusion, turbophoresis, thermophoresis, inertial impaction, gravitational settling, electrical forces, and the effects of surface roughness and particle interception. The article describes two example applications: the deposition of particles in the human respiratory tract and deposition in gas and steam turbines. <s> BIB014 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Molecular communication is a new paradigm for communication between biological nanomachines over a nano- and microscale range. As biological nanomachines (or nanomachines in short) are too small and simple to communicate through traditional communication mechanisms (e.g., through sending and receiving of radio or infrared signals), molecular communication provides a mechanism for a nanomachine (i.e., a sender) to communicate information by propagating molecules (i.e., information molecules) that represent the information to a nanomachine (i.e., a receiver). This paper describes the design of an in vitro molecular communication system and evaluates various approaches to maximize the probability of information molecules reaching a receiver(s) and the rate of information reaching the receiver(s). The approaches considered in this paper include propagating information molecules (diffusion or directional transport along protein filaments), removing excessive information molecules (natural decay or receiver removal of excessive information molecules), and encoding and decoding approaches (redundant information molecules to represent information and to decode information). Two types of molecular communication systems are considered: a unicast system in which a sender communicates with a single receiver and a broadcast system in which a sender communicates with multiple receivers. Through exploring tradeoffs among the various approaches on the two types of molecular communication systems, this paper identifies promising approaches and shows the feasibility of an in vitro molecular communication system. <s> BIB015 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> In this paper, we consider molecular communication, with information conveyed in the time of release of molecules. These molecules propagate to the transmitter through a fluid medium, propelled by a positive drift velocity and Brownian motion. The main contribution of this paper is the development of a theoretical foundation for such a communication system; specifically, the additive inverse Gaussian noise (AIGN) channel model. In such a channel, the information is corrupted by noise that follows an IG distribution. We show that such a channel model is appropriate for molecular communication in fluid media. Taking advantage of the available literature on the IG distribution, upper and lower bounds on channel capacity are developed, and a maximum likelihood receiver is derived. Results are presented which suggest that this channel does not have a single quality measure analogous to signal-to-noise ratio in the additive white Gaussian noise channel. It is also shown that the use of multiple molecules leads to reduced error rate in a manner akin to diversity order in wireless communications. Finally, some open problems are discussed that arise from the IG channel model. <s> BIB016 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> We aimed to create an autonomous on-chip system that performs targeted delivery of lipid vesicles (liposomes) as nano- or microscale reactors using machinery from biological systems. Reactor-liposomes would be ideal model cargoes to realize biomolecular-motor-based biochemical analysis chips; however, there are no existing systems that enable targeted delivery of cargo-liposomes in an autonomous manner. By exploiting biomolecular-motor-based motility and DNA hybridization, we demonstrate that single-stranded DNA (ssDNA)-labeled microtubules (MTs), gliding on kinesin-coated surfaces, acted as cargo transporters and that ssDNA-labeled cargo-liposomes were loaded/unloaded onto/from gliding MTs without bursting at loading reservoirs/micropatterned unloading sites specified by DNA base sequences. Our results contribute to the development of an alternative strategy to pressure-driven or electrokinetic flow-based microfluidic devices. <s> BIB017 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Molecular communication has been recently proposed for interconnected nano-scale devices as an alternative to classical communication paradigms such as electromagnetic waves, acoustic or optical communication. In this novel approach, the information is encoded as molecules that are transported between nano-scale devices within different distances. For short distances (nm-mm ranges) there exist molecular motors and calcium signaling techniques to realize the communication. For long distances (mm-m ranges), pheromones are used to transport information. In this work, the medium-range is explored to cover distances from ?m to mm and a molecular network architecture is proposed to realize the communication between nano-machines that can be deployed over different (short, medium and long) distances. In addition, two new communication techniques, flagellated bacteria and catalytic nanomotors, are proposed to cover the medium-range. Both techniques are based on the transport of DNA encoded information between emitters and receivers by means of a physical carrier. Finally, a qualitative comparison of both communication techniques is carried out and some future research topics are pointed out. <s> BIB018 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Abstract In this paper, we investigated approaches to form a self-organizing microtubule network. Microtubules are protein filaments naturally occurring in the aqueous environment of cells. A microtubule network connects multiple nano- or micro-scale objects (i.e., nanomachines). In the paper, we propose two approaches to form an in vitro microtubule network in a self-organizing manner. The first approach utilizes polymerization and depolymerization of microtubules. The second approach utilizes molecular motors to reorganize a microtubule network. In addition, we conducted preliminary in vitro experiments to investigate the feasibility of the proposed approaches. In the preliminary experiments, we observed that a few sender and receiver nanomachines were interconnected with the first approach, and that distinct topologies of microtubules were reorganized with the second approach. <s> BIB019 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Nanotechnology is enabling the development of devices in a scale ranging from one to a few hundred nanometers, known as nanomachines. How these nanomachines will communicate is still an open debate. Molecular communication is a promising paradigm that has been proposed to implement nanonetworks, i.e., the interconnection of nanomachines. Recent studies have attempted to model the physical channel of molecular communication, mainly from a communication or information-theoretical point of view. In this work, we focus on the diffusion-based molecular communication, whose physical channel is governed by Fick's laws of diffusion. We characterize the molecular channel following two complementary approaches: first, we obtain the channel impulse response, transfer function and group delay; second, we propose a pulse-based modulation scheme and we obtain analytical expressions for the most relevant performance evaluation metrics, which we also validate by simulation. Finally, we compare the scalability of these metrics with their equivalents in a wireless electromagnetic channel. We consider that these results provide interesting insights which may serve designers as a guide to implement future molecular nanonetworks. <s> BIB020 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Abstract As the field of molecular communication continues to grow, numerous solutions have been proposed to enable communication between nanomachines. Amongst these solutions, bacteria communication nanonetworks has been proposed as a promising approach for molecular communication. This is driven by a number of attractive properties found in bacteria, which includes biased motility toward the destination through chemotaxis process, as well as the ability of bacteria to transfer genetic information between each other using conjugation. Bacterial conjugation is a major mechanism for Lateral Gene Transfer (LGT) that enables information transfer among bacteria. In this paper, we propose an opportunistic routing process in bacteria communication network using these two properties. The paper presents the simulation work to analyze the performance of message delivery for three different topology shapes, which includes grid, hexagon, and T-shape topologies. The aim of simulating on different shape topologies is to determine the impact that conjugation will have to improve message delivery. In all topologies, the use of conjugation helped improve the reliability of message delivery to the destination point. The paper will analyze various commonly used metrics used in communication networks, such as the average delay, the number of messages, as well as the distribution of messages and their originating node. The conjugation process is most beneficial in complexed shaped topologies, where the directionality from the source to the destination is a number of hops apart, as represented in the T-shape topology. <s> BIB021 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Molecular Communication (MC) is a communication paradigm based on the exchange of molecules. The implicit biocompatibility and nanoscale feasibility of MC make it a promising communication technology for nanonetworks. This paper provides a closed-form expression for the information capacity of an MC system based on the free diffusion of molecules, which is of primary importance to understand the performance of the MC paradigm. Unlike previous contributions, the provided capacity expression is independent from any coding scheme and takes into account the two main effects of the diffusion channel: the memory and the molecular noise. For this, the diffusion is decomposed into two processes, namely, the Fick's diffusion and the particle location displacement, which are analyzed as a cascade of two separate systems. The Fick's diffusion captures solely the channel memory, while the particle location displacement isolates the molecular noise. The MC capacity expression is obtained by combining the two systems as function of the diffusion coefficient, the temperature, the transmitter-receiver distance, the bandwidth of the transmitted signal, and the average transmitted power. Numerical results show that a few kilobits per second can be reached within a distance range of tenth of micrometer and for an average transmitted power around 1 pW. <s> BIB022 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Communication via diffusion is an effective and energy efficient method for transmitting information in nanonetworks. However, the histogram of the molecules hitting at the receiver has a long tail. The molecules constituting this long tail significantly decrease the data rate since the selection of a high symbol duration becomes mandatory to have acceptable bit error rates. In this paper, a novel signal shaping technique for nanonetworking is proposed. This technique aims to decrease the variance of the hitting times via special so-called “destroyer molecules”. This system is inspired by the neuromuscular junction in biology, in which Acetylcholinesterase molecules are used to clean the channel for further transmissions. We consider a molecular communication channel where a tunnel composed of destroyer molecules exist between the communicating pair. Simulation results show that the inclusion of such destroyer molecules decrease both the mean and the variance of the hitting time distribution, allowing better time-responsiveness and higher data rate for the communication via diffusion system. <s> BIB023 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Abstract Advancements in nanotechnology have promised the building of nanomachines capable of carrying out simple tasks. Final goals of using these nanomachines in applications such as monitoring body tissues, drug delivery or other complicated applications need them to do complex tasks. A feasible way to have them cooperate and do complex tasks is to interconnect them by building a nanonetwork. As nanomachines can only carry out simple tasks, nanonetworks bring up new issues in networking and communication. There have been many papers addressing solutions for communication challenges in nanonetworks and analysing their characteristics. At this stage, going towards higher goals needs a comprehensive look at the literature and state of the art in the field. In this paper, we present an inclusive look at issues introduced and analysed in nanonetworks. We focus on two methods which provide properties needed in nanonetworks efficiently, namely communication via microtubules and physical contact. <s> BIB024 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> We investigate the influences of the diffusion coefficients for heat and salt in the deep ocean upon the stability of the Atlantic thermohaline circulation through a parameter space investigation that employs the GFDL Modular Ocean Model (MOM). The ocean general circulation model is configured to represent an idealized Atlantic basin and steadily (including an annual cycle) forced under the assumption of mixed boundary conditions. The impact on the results of the use of mixed boundary conditions is examined through additional sensitivity experiments to demonstrate that this choice of boundary conditions does not affect the main conclusions. The two primary sets of the experiments that we describe consist of sensitivity analyses for both horizontal and vertical diffusion coefficients; Bryan-Lewis type diffusion coefficient profiles are applied in such a way that one diffusion coefficient profile is varied while the other diffusion coefficient profile is fixed. We are thereby able to demonstrate that the choice of the horizontal diffusion coefficient plays a crucial role in determining the stability of the thermohaline circulation which is such that the thermohaline circulation exhibits very intense oscillations on a multi-millennium timescale when the horizontal diffusion coefficient of the deep ocean is set to a sufficiently small value. We demonstrate that the critical value required to realize an oscillatory solution of the thermohaline circulation lies well within the range of observed large-scale ocean diffusion coefficients, whereas the value of vertical diffusion coefficients affect not the bifurcation structure but the period of the millennial timescale oscillation. <s> BIB025 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> Within the domain of molecular communications, researchers mimic the techniques in nature to come up with alternative communication methods for collaborating nanomachines. This letter investigates the channel transfer function for molecular communications via diffusion. In nature, information-carrying molecules are generally absorbed by the target node via receptors. Using the concentration function, without considering the absorption process, as the channel transfer function implicitly assumes that the receiver node does not affect the system. In this letter, we propose a solid analytical formulation and analyze the signal metrics (attenuation and propagation delay) for molecular communication via diffusion channel with an absorbing receiver in a 3-D environment. The proposed model and the formulation match well with the simulations without any normalization. <s> BIB026 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> B. Channel and Propagation <s> This paper presents a method for shaping the transmit pulse of a molecular signal such that the diffusion channel's response is a sharp pulse. The impulse response of a diffusion channel is typically characterised as having an infinitely long transient response. This can cause severe inter-symbol-interference, and reduce the achievable reliable bit rate. We achieve the desired chemical channel response by poisoning the channel with a secondary compound, such that it chemically cancels aspects of the primary information signal. We use two independent methods to show that the chemical concentration of the information signal should be ∝ δ(t) and that of the poison signal should be ∝ t-3/2. <s> BIB027
For microscale molecular communication, many different propagation schemes are possible for transporting information particles. They are: diffusion based propagation BIB012 - BIB022 , flow assisted propagation BIB016 , active transport using molecular motors and cytoskeletal filaments BIB017 , bacterial assisted propagation BIB018 - BIB021 , kinesin molecular motors moving over immobilized microtubule (MT) tracks BIB015 , BIB019 . We describe each propagation method in details over the next few subsections. 1) Free Diffusion: Diffusion, also known as Brownian motion, refers to the random motion of a particle as it collides with other molecules in its vicinity. Through this random motion, the information-carrying particles can propagate from the transmitter to the receiver by using the thermal energy that is already present in the channel environment. Therefore, no source of external energy is required for diffusion based propagation. There are many examples of this class of propagation in biology. An example is the neurotransmitter molecules Acetylcholine (ACh) emitted from nerve cell to neuromascular junction for muscle cells to receive motor actions BIB023 . When muscles in a specific part of the body need to be contracted, the nerve cells in that region send a signal to the muscle tissue through these junctions to trigger the contraction [5] . Another example is DNA binding molecules (e.g., repressors) propagating over a DNA segment to search for a binding site BIB003 . Diffusion can be accurately simulated using Monte Carlo simulation  . In particular, the motion of the information particles is considered for a discrete time period of duration ∆t. Given some initial position (x 0 , y 0 , z 0 ) at time t = 0, for any integer k > 0, the motion of the particles is given by the sequence of coordinates (x i , y i , z i ) for i = 1, 2, . . . , k. Each coordinate (x i , y i , z i ) represents the position of the particle at the end of time t = i∆t, where where ∆x i , ∆y i , ∆z i , D and N (µ, σ 2 ) are the particle's displacements at each component over each time interval ∆t, the diffusion coefficient, and the normal distribution with mean µ and the variance σ 2 . The diffusion movement in these equations is a Martingale process, where subsequent motions are unrelated to previous motions and positions of particles BIB005 . Alternatively diffusion can be simulated via the following method: where ∆r is the particle's total displacement over each time interval of ∆t, and both θ i and φ i define the angle of displacement in 3-dimensional space over the time interval ∆t. Furthermore, over each time interval of ∆t, the particle's displacement ∆r is given by The angle θ i is an independent, identically distributed (iid) random variable for all i, uniformly distributed on [0, 2π], and the angle φ i is also an iid random variable given by φ i = arccos(1 − 2U ), where U is a uniformly distributed random variable over [0, 1]. The comparative sizes between the propagating molecule S m and the molecules of the fluid S fluid affect the diffusion coefficient  . For a given particle and fluidic channel environment, D is given by where k B = 1.38 · 10 −23 J/K is the Boltzman constant, T is the temperature (in K), η is the dynamic viscosity of the fluid, and R H is the hydraulic radius (also known as Stoke's radius) of the information particle. For most application it can be assumed that D is the same throughout the medium, and that collisions with the boundaries are elastic. Moreover, it can be assume particles do not get stuck to the walls of the channel environment. Example values of D in µm 2 /s in water at 25 • C are obtained from  and listed in Table I . 2) Diffusion with First Hitting: In nature, most of the receptor types remove the information molecules from the environment once they arrive at the receiver  . Therefore, in most of the cases almost all of the molecules contribute to the signal once. If the receptors do not remove molecules from the environment, they have other mechanisms to guarantee that each molecule contributes to the signal only once (e.g., acetylcholinesterase breaks down the molecules in neuromuscular junctions) BIB023 . This process is modeled by first hitting processes and molecules are assumed to be removed from the environment by means of receptors or other mechanisms after first hitting to the absorbing receiver. Asymptotic behavior of first hitting probabilities are given in  as Asymptotic behaviors in BIB024 are determined by only the spatial dimension. For reception process, the nanonetworking literature has mostly considered an absorbing receiver in 1-dimensional (1-D) environment BIB011 or a hypothetical sphere (i.e., the receiver does not affect the process) in a 3-D medium with the ability to measure concentration within BIB022 . First hitting formulations are handy when the receptors, detectors, or sensors detect the information particles by removing them from the environment or transforming them. The first generalized model, in the nanonetworking domain, including first hitting process in 1-D environment was derived in BIB011 as where d and D correspond to distance and the diffusion coefficient, respectively. This equation can be interpreted as the impulse response of the diffusion channel in 1-D environment with an absorbing receiver. To find the probability of hitting to an absorbing receiver until time t, (12) is integrated with respect to time, and obtained where erfc(.) and Φ(.) represent the complementary error function and the standard Gaussian cdf, respectively. Similarly, fraction of hitting molecules to a perfectly absorbing spherical receiver in a 3-D environment is derived in BIB026 with focusing the communication aspects. One can obtain the fraction of hitting molecules until time t by integrating f 3D hit (t) in  with respect to time, which yields similar results with the 1-D case. Hitting rate of molecules to a spherical receiver in a 3-D environment is formulated as where r r denotes the radius of the spherical receiver BIB026 . Note that, there is a positive probability of not hitting to the absorbing boundary for a diffusing particle in a 3-D environment when time goes to infinity. The survival probability depends on the radius of the receiver and the distance. First hitting formulations in a 2-D environment are not elaborated deeply in the nanonetworking domain. In (11), we just have the asymptotic behavior from  . In BIB013 , the analytical expressions are derived for the first hitting time distribution on a planar wedge with special wedge angle values. Authors derived closed form expressions for the wedge angles of π/2 and π/k where k is an odd integer. Although diffusion is advantageous because no external energy is required for propagation, it can be very slow at transporting information particles from the transmitter to the receiver over large separation distances. 3) Flow Assisted Propagation: One way to assist the speed of propagation in pure diffusion is to introduce flow in to the channel environment. The flow is most effective when it is directly in the direction of the transmitter to the receiver. Therefore, the information particles that are released by the transmitter, both diffuse and follow the flow towards the receiver. The flow reduces the random motion of the pure diffusion into a more directed form of propagation. An example of this propagation scheme is found in biology. Certain cells can secrete hormonal substances that propagate using the flow present in the blood stream to distant target cells. Depending on the flow speed, diffusion may be an important part of the this propagation scheme. Therefore, flow assisted propagation can be simulated using Monte Carlo simulations by modifying the equation presented in the previous section. Introducing flow will change Equations (6)-(8) into, where are flow velocities in the x, y, and z directions  . These velocities are a function of time and space because in practice flows can change with respect these variables. There are two main form of propagation at macroscales: diffusion and flow based propagation. In the previous section, we showed that the diffusion and flow based propagation of a single information particle can be simulated using Monte Carlo techniques. At macroscales, instead of a single or few information particles, a large number of particles are used to transfer information. Therefore, a more general formulation, namely the diffusion equations, could be effectively used to model the propagation of chemicals. The diffusion equation allows us to talk about the statistical movements of randomly moving particles. It is important to know that, unlike Monte Carlo simulation equations presented in the previous section, the movement of each individual particle does not follow the diffusion equation. However, many identical particles each obeying the same boundary and initial conditions share some statistical properties and the diffusion equation deals with the average spatial and temporal evolution of these particles. The diffusion equation is given by partial differential equation BIB001 as: where D is the diffusion coefficient, and c is the concentration at a particular spatiotemporal location. Therefore, c is a function of x, y, z, and t, where the first three variables represent a Cartesian coordinate and t represents time. This partial differential equation can be solved using different initial conditions. One of the most useful initial conditions corresponds to a point source release of molecules at the transmitter. Assuming M 0 molecules are released by the point source suddenly at time t = 0, the initial conditions for 1-D, 2-D, and 3-D diffusion can be mathematically represented as where δ(.) is the Dirac delta function defined by: Solving the diffusion equation with these initial conditions we get the solution for 1-D, 2-D, and 3-D diffusion as: c(x, y, z, t) = M 0 (4πDt) −3/2 exp − The diffusion equation can also be solved for other initial conditions BIB003 . Adjusting the boundary conditions may lead to capture concentrations when there is an absorbing structure  . Depending on whether absorption is considered or not, differentiating the capture or free diffusion equation with respect to time yields to impulse response of the diffusion channel BIB026 , BIB020 . Moreover, one can find the peak signal concentration and time, pulse width, and the tractable complex s-domain channel equations using the impulse response function BIB027 . At macroscales molecular diffusion itself can be a very slow propagation mechanism. For example, the diffusion coefficient of water vapor in air is about 0.3 cm 2 /s. Therefore, assuming pure diffusion, on average, in 1 second it propagates about 0.5 cm, in 1 minutes 4 cm, and in 1 hour 30 cm. However, it is possible to speed up the propagation by introducing flow. Other forms of mass transport assist the propagation of particles at macroscales. These include: • Advection -Advection refers to transport with the bulk fluid flow BIB009 . For example, information particles released inside a duct with air flows, are moved by bulk air flows. • Mechanical dispersion -Mechanical dispersion, is the result of (a) variations in the flow pathways taken by different fluid parcels that originate in the nearby locations near one another, or (b) variations in the speed at which fluid travels in different regions BIB004 . For example, information particles moving through liquid flows in porous materials such as soil follow mechanical dispersion because of different paths they could travel. Similarly, in a pipe where there is a liquid flow, at the boundaries the flow speed could be slower than at the center of the pipe. This effect will disperse the information particles in the pipe. • Convection -In thermodynamics convection is the fluid flows generated because of difference in temperature BIB006 . For example, in a room cold air, which is dense, moves downward while warm air moves upright. It must be noted that convection is also used to specify the combined advection-diffusion process in fluid mechanics. However in this survey, convection is the fluid flows created due to temperature differences. • Turbulent flows -Turbulent flows are random movements within a fluidic flow BIB002 . Because this random movement is similar to molecular diffusion, the motion of particles inside turbulent flows are sometimes called turbulent diffusion. This is fundamentally different from the processes which determine molecular diffusion: in turbulent diffusion, it is the random motion of the fluid that does the transport, while in molecular diffusion it is the random motion of the information particles themselves. To indicate this difference in causation, the diffusion coefficient for turbulent diffusion is often referred to as the eddy diffusion coefficient. The value of the eddy diffusion coefficient depends on the properties of the fluid flow, rather than on the properties of the information particles. Most important is the flow velocity. Turbulence is only present at flow velocities above a critical level, and the degree of turbulence is correlated with velocity. More precisely, the presence or absence of turbulence depends on the Reynolds Number, a non-dimensional number which depends on velocity, width of the pipe, and the viscosity of the fluid. In addition, the degree of turbulence depends on the material over which the flow is occurring, so that flow over bumpy surfaces will be more turbulent than flow over a smooth surface. When flow is present, the diffusion equation in BIB010 becomes the advective diffusion equation (also known as convection-diffusion equation or diffusion equation with drift) where v is the velocity vector and it is a function of spatial location and time. The D in (33) can be the diffusion coefficient for pure molecular diffusion or a combine molecular and turbulent diffusion coefficient BIB014 . In BIB010 and BIB018 , it was assumed that the diffusion coefficient is the same in all spatial dimensions. However, it is also possible to derive analytical solutions when the diffusion coefficient is spatially variable BIB008 . For example, in oceans, the diffusivity along the water can be 10 7 larger than the vertical diffusivity BIB025 . The solution for this partial differential equation can be obtained using different initial conditions. For example, assume that the flow is constant and in the direction of positive x axis only. Moreover, assume that the boundaries are infinite with a point source initial condition as in BIB007 . Then the solution of advective diffusion equation becomes where v is the speed in the positive x direction. The advective diffusion equation can be solved for some other initial conditions as well.