0028]In one embodiment of the invention, the binder resin is carbonized to be electrically conductive. In another variation of that embodiment, the binder resin is not carbonized thereby acting simply as a solid filler In either of these variations, the binder resin may be present in a first amount such that the gas diffusion layer has a ratio of water vapor free diffusion coefficient to water vapor effective diffusion coefficient greater than 1.5. In another variation, the ratio of the water vapor free diffusion coefficient to the effective diffusion coefficient may be less than or equal to 20. In yet another variation, the ratio of the water vapor free diffusion coefficient to the effective diffusion coefficient is from 3 to 15. In still another variation, the ratio of the water vapor free diffusion coefficient to the effective diffusion coefficient is from 10 to 12. In this context, the water vapor free diffusion coefficient is the diffusion coefficient of the water vapor in the gas mixture ...
GATICA, Y.A.; SALINAS, C. H. and ANANIAS, R.A.. Modeling conventional one-dimensional drying of radiata pine based on the effective diffusion coefficient. Lat. Am. appl. res. [online]. 2011, vol.41, n.2, pp. 183-189. ISSN 0327-0793.. We modeled conventional one-dimensional drying of radiata pine (Pinus radiata) wood using the concept of effective diffusion. The experimentally determined effective diffusion coefficients for the radial and tangential directions were related exponentially to the moisture content. These coefficients were characterized by two parameters that were determined through optimization within the context of an inverse problem. One-dimensional drying experiments were carried out under constant drying 44/36 (°C/°C) in order to determine transitory spatial distributions of moisture and drying curves, which were used then to determine the model parameters and validate the model. The mathematical model consisted of a partial, non-linear, differential equation of the second ...
A new method for determining the gas effective diffusion coefficient in brine-saturated porous rocks was developed on the basis of the radial diffusion model. T...
[email protected] Abstract - We modeled conventional one-dimensional drying of radiata pine (Pinus radiata) wood using the concept of effective diffusion. The experimentally determined effective diffusion coefficients for the radial and tangential directions were related exponentially to the moisture content. These coefficients were characterized by two parameters that were determined through optimization within the context of an inverse problem. One-dimensional drying experiments were carried out under constant drying 44/36 (°C/°C) in order to determine transitory spatial distributions of moisture and drying curves, which were used then to determine the model parameters and validate the model. The mathematical model consisted of a partial, non-linear, differential equation of the second order and was characterized by coefficients that varied exponentially with moisture content; this later was integrated numerically through the finite volume method. Simulations of the transitory distribution ...
In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, ...
Premier atelier de lERC « Reaction-Diffusion Equations, Propagations and Modelling » Journées détude organisées par Henri Berestycki et Jean-Michel Roquejoffre EHESS, 24-25 septembre 2013 Séquence 1: Hiroshi Matano (University of Tokyo) Spreading speed for some two-component reaction-diffusion system In this talk I will discuss the spreading properties of solutions of a prey-predator type reaction-diffusion system. This system belongs to the class of reaction-diffusion systems for which the comparison principle does not hold. For such class of systems, little has been know about the spreading properties of the solutions. Here, by a spreading property, we mean the way the solution propagates when starting from compactly supported initial data. We show that propagation of both the prey and the predator occur with a definite spreading speed. Furthermore, quite intriguingly, the spreading speed of the prey and that of the predator are different in some
Author(s): Digiacomo, Luca; Digman, Michelle A; Gratton, Enrico; Caracciolo, Giulio | Abstract: Fluorescence microscopy and spectroscopy techniques are commonly used to investigate complex and interacting biological systems (e.g. proteins and nanoparticles in living cells), since these techniques can explore intracellular dynamics with high time resolution at the nanoscale. Here we extended one of the Image Correlation Spectroscopy (ICS) methods, i.e. the image Mean Square Displacement, in order to study 2-dimensional diffusive and flow motion in confined systems, whose driving speed is uniformly distributed in a variable angular range. Although these conditions are not deeply investigated in the current literature, they can be commonly found in the intracellular trafficking of nanocarriers, which diffuse in the cytoplasm and/or may move along the cytoskeleton in different directions. The proposed approach could reveal the underlying systems symmetry using methods derived from fluorescence correlation
Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model.
VV B337 Title: Relationships between several particle-based stochastic reaction-diffusion models. Abstract: Particle-based stochastic reaction-diffusion models have recently been used to study a number of problems in cell biology. These methods are of interest when both noise in the chemical reaction process and the explicit motion of molecules are important. Several different mathematical models have been used, some spatially-continuous and others lattice-based. In the former molecules usually move by Brownian Motion, and may react when approaching each other. For the latter molecules undergo continuous time random-walks, and usually react with fixed probabilities per unit time when located at the same lattice site. As motivation, we will begin with a brief discussion of the types of biological problems we are studying and how we have used stochastic reaction-diffusion models to gain insight into these systems. We will then introduce several of the stochastic reaction-diffusion models, ...
TY - JOUR. T1 - Diffusion-controlled reactions among spherical traps. T2 - Effect of polydispersity in trap size. AU - Miller, C. A.. AU - Torquato, S.. PY - 1989. Y1 - 1989. N2 - We consider determining the steady-state trapping rate k associated with diffusion-controlled reactions among static, spherical traps with a polydispersity in trap size. Both discrete and continuous size distributions are examined. Theoretical methods, such as rigorous bounds and survival-probability theory, as well as computer-simulation techniques, are employed to address this problem. It is found that the trapping rate for the polydisperse system generally increases or decreases (relative to the monodisperse case) depending upon whether the relative interfacial surface area increases or decreases.. AB - We consider determining the steady-state trapping rate k associated with diffusion-controlled reactions among static, spherical traps with a polydispersity in trap size. Both discrete and continuous size ...
The present invention relates to systems and methods for minimizing or eliminating diffusion effects. Diffused regions of a segmented flow of multiple, miscible fluid species may be vented off to a waste channel, and non-diffused regions of fluid may be preferentially pulled off the channel that contains the segmented flow. Multiple fluid samples that are not contaminated via diffusion may be collected for analysis and measurement in a single channel. The systems and methods for minimizing or eliminating diffusion effects may be used to minimize or eliminate diffusion effects in a microfluidic system for monitoring the amplification of DNA molecules and the dissociation behavior of the DNA molecules.
TY - BOOK. T1 - Recent progress on reaction-diffusion systems and viscosity solutions. AU - Du, Yihong. AU - Ishii, Hitoshi. AU - Lin, Wei Yueh. PY - 2009/1/1. Y1 - 2009/1/1. N2 - This book consists of survey and research articles expanding on the theme of the International Conference on Reaction-Diffusion Systems and Viscosity Solutions, held at Providence University, Taiwan, during January 3-6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin ...
The role of di-boron diffusion in evolution of B diffusion profiles has been investigated. We find that boron pair (B[sub s]â€B[sub i]) diffusion can become as important as boron-interstitial pair (B[sub s]â€Si[sub i]) diffusion when both boron concentration and annealing temperature are very high, leading to concentration-dependent B diffusion. Our simulated B diffusion profiles with dramatic shouldering are in excellent agreement with experimental ones reported by Schroer et al. [Appl. Phys. Lett. 74, 3996 (1999)] for high-temperature (≈1200 °C) postimplantion annealing of ultralow-energy (≈500 eV) implanted high-concentration (>10[sup 19] cm[sup -3]) boron in silicon. © 2003 American Institute of Physics ...
TY - JOUR. T1 - Stability of stationary solutions for a scalar non-local reaction-diffusion equation. AU - Frettas, Pedro. PY - 1995/11. Y1 - 1995/11. N2 - The stability of stationary solutions of the non-local reaction-diffusion equation with homogeneous Neumann boundary conditions is studied. Depending on a, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the specific case of a cubic like f, the existence of a Hopf bifurcation is proven. Finally, some related equations are discussed. © 1995 Oxford University Press.. AB - The stability of stationary solutions of the non-local reaction-diffusion equation with homogeneous Neumann boundary conditions is studied. Depending on a, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the ...
This paper is devoted to develop a new matrix scheme for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions. We first transform these equations into equivalent integro partial differential equations (PDEs). Such these integro-PDEs contain both of the initial and boundary conditions and can be solved numerically in a more appropriate manner. Subsequently, all the existing known and unknown functions in the latter equations are approximated by Bernoulli polynomials and operational matrices of differentiation and integration together with the completeness of these polynomials can be used to reduce the integro-PDEs into the associated algebraic generalized Sylvester equations. For solving these algebraic equations, an efficient Krylov subspace iterative method (i.e., BICGSTAB) is implemented. Two numerical examples are given to demonstrate the efficiency, accuracy, and versatility of the proposed method ...
TY - JOUR. T1 - Protein diffusion and long-term adsorption states at charged solid surfaces. AU - Kubiak-Ossowska, Karina. AU - Mulheran, Paul A. PY - 2012/11/6. Y1 - 2012/11/6. N2 - The diffusion pathways of lysozyme adsorbed to a model charged ionic surface are studied using fully atomistic steered molecular dynamics simulation. The simulations start from existing protein adsorption trajectories, where it has been found that one particular residue, Arg128 at the N,C-terminal face, plays a crucial role in anchoring the lysozyme to the surface [ Langmuir 2010 , 26 , 15954 - 15965 ]. We first investigate the desorption pathway for the protein by pulling the Arg128 side chain away from the surface in the normal direction, and its subsequent readsorption, before studying diffusion pathways by pulling the Arg128 side chain parallel to the surface. We find that the orientation of this side chain plays a decisive role in the diffusion process. Initially, it is oriented normal to the surface, aligning ...
PAHs are the reactive toxic chemical compounds which are present as environmental pollutants. These reactive compounds not only diffuse through the membranes of the cell but also partition into the membranes. They react with the DNA of the cell giving rise to toxicity and may cause cancer. To understand the cellular behavior of these foreign compounds, a mathematical model including the reaction-diffusion system and partitioning phenomenon has been developed. In order to reduce the complex structure of the cytoplasm due to the presence of many thin membranes, and to make the model less computationally expensive and numerically treatable, homogenization techniques have been used. The resulting complex system of PDEs generated from the model is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. Then the model was reduced to a system of ODEs, a compartment model (CM). The quantitative analysis of the ...
H. Lekkerkerker (Debye Research Institute, The Netherlands). You described the use of optical tweezers to drag a colloidal particle through a nematic liquid and measure from the velocity the viscosity. Would the measurement of the mean square displacement of a particle fixed in a trap be viable and perhaps allow a more detailed analysis?. H. Gleeson. A measurement of the mean square displacement of the particle would be expected to show anisotropy in the viscosity. However, additional complications might arise from the optical anisotropy of the medium in determining the mean square displacement of the particle in the trap by interferometry of the scattered light. Furthermore, this method provides only a passive measurement of the dynamics within the system. Our measurement evaluates the effective viscosity under flow conditions and is comparable to the theory of Stark & Ventzki (2001) and Stark et al. (2003).. V. Götz (Department of Chemistry, University of York, UK). Is the direction of ...
Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by Adomians decomposition method (ADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.
The sheet-like endoplasmic reticulum (ER) of eukaryotic cells has been found to be riddled with spiral dislocations, known as Terasaki ramps, in the vicinity of which the doubled bilayer membranes which make up ER sheets can be approximately modeled by helicoids. Here we analyze diffusion on a surface with locally helicoidal topological dislocations, and use the results to argue that the Terasaki ramps facilitate a highly efficient transport of water-soluble molecules within the lumen of the endoplasmic reticulum.. ...
A coated substrate and a method of forming a diffusion barrier coating system between a substrate and a MCrAl coating, including a diffusion barrier coating deposited onto at least a portion of a substrate surface, wherein the diffusion barrier coating comprises a nitride, oxide or carbide of one or more transition metals and/or metalloids and a MCrAl coating, wherein M includes a transition metal or a metalloid, deposited on at least a portion of the diffusion barrier coating, wherein the diffusion barrier coating restricts the inward diffusion of aluminum of the MCrAl coating into the substrate.
Covering both basic and advanced thermodynamic and phase principles, as well as providing stability diagrams relevant for diffusion studies, Thermodynamics, Diffusion and the Kirkendall Effect in Solids maximizes reader insights into Ficks laws of diffusion, atomic mechanisms, interdiffusion, intrinsic diffusion, tracer diffusion and the Kirkendall effect. Recent advances in the area of interdiffusion will be introduced, while the many practical examples and large number of illustrations given will serve to aid researches working in this area in learning the practical evaluation of various diffusion parameters from experimental results. With a unique approach to the two main focal points in solid state transformations, energetics (thermodynamics) and kinetics (interdiffusion) are extensively studied and their combined use in practise is discussed. Recent developments in the area of Kirkendall effect, grain boundary diffusion and multicomponent diffusion are also covered extensively. This book ...
We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed to model coat patterns in leopard and jaguar ...
The purpose of this report is to investigate possible enhancement of diffusion rates in ceramic oxides through imposed stress or the presence of grain boundaries. Diffusion rates of impurity cations such as Ni(2+), Co(2+), Zn(2+), or Ca(2+) have been investigated in single crystal MgO subjected to imposed stress and also in bicrystal and polycrystalline MgO. The solute oxides are supplied as either an initial thin surface film, or through continuous deposition from the vapor phase. Diffusion coefficients are determined from concentration profiles obtained with the aid of electron microbeam probe spectroscopy. Diffusion rates of Ni(2+) in directions normal to the tension and compression surfaces of single crystal MgO subjected to fourpoint loading are not, within experimental error, enhanced above normal lattice diffusion rates for loads up to 5000 psi. Diffusion couples have now been sucessfully prepared from MgO subjected to higher compressive loads of up to 15,000 psi and are currently undergoing
I have another question related to the longitudinal diffusion. I would like to monitor the ion concentration change incurred by longitudinal diffusion of specific ion to and from the specific section. If I only had longitudinal diffusion mechanism in this section, I would simply compute this change by taking the difference between ion concentrations at two edges of the section. But, I have some transmembrane ion exchange mechanisms (such as channels, pumps, etc.) in this section as well....How can I see how much ion concentration change is specifically due to the diffusion of ion from one of this sections neighboring sections? Is there any built-in variable that I can access to view the diffusional current ...
Using Embedded-atom-method (EAM) potential, we have performed in detail molecular dynamics studies on a Fe adatom adsorption and diffusion dynamics on three low miller index surfaces, Fe (110), Fe (001), and Fe (111). Our results present that adatom adsorption energies and diffusion barriers on these surfaces have similar monotonic trend: adsorption energies, Ea(110) Ea(001) Ea(111), diffusion barriers, Ed(110) Ed(001) Ed(111). On the Fe (110) surface, adatom simple jump is the main diffusion mechanism with relatively low energy barrier; nevertheless, adatoms exchange with surface atoms play a dominant role in surface diffusion on the Fe (001).
A diffusion barrier layer comprising TiNxBy is disclosed for protection of gate oxide layers in integrated transistors. The diffusion barrier layer can be fabricated by first forming a TiN layer and then incorporating boron into the TiN layer. The diffusion barrier layer can also be fabricated by forming a TiNxBy layer using a TDMAT process including boron. The diffusion barrier layer can also be fabricated by forming a TiNxBy layer using a CVD process. The diffusion barrier layer is of particular utility in conjunction with tungsten or tungsten silicide conductive layers formed by CVD.
Abstract: Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drift or the diffusion coefficient remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes zero when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model ...
TY - JOUR. T1 - Diffusion Coefficient Measurement of Cu in Liquid Sn by Long Capillary Method. AU - Uchida, Y.. AU - Masaki, T.. PY - 2010/9/22. Y1 - 2010/9/22. M3 - Article. JO - 8th Japan-China-Korea Workshop on Microgravity Sciences. JF - 8th Japan-China-Korea Workshop on Microgravity Sciences. ER - ...
TY - JOUR. T1 - Nitric oxide uptake by erythrocytes is primarily limited by extracellular diffusion not membrane resistance. AU - Liu, Xiaoping. AU - Samouilov, Alexandre. AU - Lancaster, Jack R.. AU - Zweier, Jay L.. PY - 2002/7/19. Y1 - 2002/7/19. N2 - The process of NO transfer into erythrocytes (RBCs) is of critical biological importance because it regulates the bioavailability and diffusional distance of endothelial-derived NO. It has been reported that the rate of NO reaction with oxyhemoglobin (Hb) within RBCs is nearly three orders of magnitude slower than that by equal amounts of free oxyhemoglobin. Consistent with early studies on oxygen uptake by RBCs, the process of extracellular diffusion was reported to explain this much lower NO uptake by RBC encapsulated Hb (Liu, X., Miller, M. J., Joshi, M. S., Sadowska-Krowicka, H., Clark, D. A., and Lancaster, J. R., Jr. (1998) J. Biol. Chem. 273, 18709-18713). However, it was subsequently proposed that the RBC membrane provides the main ...
Diffusion in lipid membranes is an essential component of many cellular process and fluorescence a method of choice to study membrane dynamics. The goal of this work was to directly compare two common fluorescence methods, line-scanning fluorescence correlation spectroscopy and single-particle tracking, to observe the diffusion of a fluorescent lipophilic dye, DiD, in a complex five-component mitochondria-like solid-supported lipid bilayer. We measured diffusion coefficients of \(D_{\text{FCS}} \sim\) 3 \(μ\text{m}^2\cdot\text{s}^{-1}\) and \(D_{\text{SPT}} \sim\) 2 \( μ\text{m}^2\cdot\text{s}^{-1}\), respectively. These comparable, yet statistically different values are used to highlight the main message of the paper, namely that the two considered methods give access to distinctly different dynamic ranges: \(D \gtrsim\) 1 \(μ\text{m}^2\cdot\text{s}^{-1}\) for FCS and \(D \lesssim\) 5 \(μ\text{m}^2\cdot\text{s}^{-1}\) for SPT (with standard imaging conditions). In the context of membrane diffusion,
Confocal or multi-photon laser scanning microscopes are convenient tools to perform FRAP diffusion measurements. Despite its popularity, accurate FRAP remains often challenging since current methods are either limited to relatively large bleach regions or can be complicated for non-specialists. In order to bring reliable quantitative FRAP measurements to the broad community of laser scanning microscopy users, here we have revised FRAP theory and present a new pixel based FRAP method relying on the photo bleaching of rectangular regions of any size and aspect ratio. The method allows for fast and straightforward quantitative diffusion measurements due to a closed-form expression for the recovery process utilizing all available spatial and temporal data. After a detailed validation, its versatility is demonstrated by diffusion studies in heterogeneous biopolymer mixtures.. ©2010 Optical Society of America. Full Article , PDF Article ...
Molecular diffusion, often called simply diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration, but it is important to note that diffusion also occurs when there is no concentration gradient. The result of diffusion is a gradual mixing of material. In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing.. Diffusive equilibrium is reached when the concentrations of the diffusing substance in the two compartments becomes equal.. Consider two systems; S1 and S2 at the same temperature and capable of exchanging particles. If there is a change in the potential energy of a system; for example μ1>μ2 (μ is Chemical potential) an ...
Abstract The VAPEX analytical model is extended to cover situations when diffusion coefficients are dependent on concentration due to the extreme viscosity reduction with solvent dissolution into bitumen. The new analytical model covers such situati
Managing an invasive species is particularly challenging as little is generally known about the species biological characteristics in its new habitat. In practice, removal of individuals often starts before the species is studied to provide the information that will later improve control. Therefore, the locations and the amount of control have to be determined in the face of great uncertainty about the species characteristics and with a limited amount of resources. We propose framing spatial control as a linear programming optimization problem. This formulation, paired with a discrete reaction-diffusion model, permits calculation of an optimal control strategy that minimizes the remaining number of invaders for a fixed cost or that minimizes the control cost for containment or protecting specific areas from invasion. We propose computing the optimal strategy for a range of possible model parameters, representing current uncertainty on the possible invasion scenarios. Then, a best strategy can be
The purpose of our study was to determine the incidence, causes, and reversibility of leukoencephalopathies demonstrating confluent areas of restricted diffusion on magnetic resonant imaging (DWI+LE). We hypothesized DWI+LE would have a low incidence, and be primarily caused by toxic exposures. We performed a logic sentence based search of the Yale-New Haven MRI database to select for reports indicating restricted diffusion within the cerebral white matter. We examined patients neuroimaging studies and medical record. We identified a total of 35 cases of DWI+LE, which resulted in an overall incidence of 0.2% over the five-year period queried. The medical conditions associated with DWI+LE were as follows: toxic exposure (7), hypoxia with concurrent trauma (7), hypoxia with concurrent toxic exposure (4), hypoxia with concurrent metabolic derangements (4), seizure with concurrent metabolic derangements (2), metabolic derangements (2), antiepileptic therapy (2), hypoxia (1), trauma (1), and unknown (5). The
The diffusive arrival of transcription factors at the promoter sites on DNA sets a lower bound on how accurately a cell can regulate its protein levels. Using results from the literature on diffusion-influenced reactions, we derive an analytical expression for the lower bound on the precision of transcriptional regulation. In our theory, transcription factors can perform multiple rounds of one-dimensional (1D) diffusion along the DNA and 3D diffusion in the cytoplasm before binding to the promoter. Comparing our expression for the lower bound on the precision against results from Greens function reaction dynamics simulations shows that the theory is highly accurate under biologically relevant conditions. Our results demonstrate that, to an excellent approximation, the promoter switches between the transcription-factor bound and unbound state in a Markovian fashion. This remains true even in the presence of sliding, i.e., with 1D diffusion along the DNA. This has two important implications: (1)
In a previous study [21], a class of efficient semi-implicit schemes was developed for stiff reaction-diffusion systems. This method which treats linear diffusion terms exactly and nonlinear reaction terms implicitly has excellent stability properties, and its second-order version, with a name IIF2, is linearly unconditionally stable. In this paper, we present another linearly unconditionally stable method that approximates both diffusions and reactions implicitly using a second order Crank-Nicholson scheme. The nonlinear system resulted from the implicit approximation at each time step is solved using a multi-grid method. We compare this method (CN-MG) with IIF2 for their accuracy and efficiency. Numerical simulations demonstrate that both methods are accurate and robust with convergence using even very large size of time steps. IIF2 is found to be more accurate for systems with large diffusion while CN-MG is more efficient when the number of spatial grid points is large.
In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction functions; (ii) convergence results for all weak solutions in the strongest topologies; (iii) new structure and regularity properties for global and trajectory attractors. The obtained results allow investigating the long-time behavior of state functions for the following problems: (a) a model of combustion in porous media; (b) a model of conduction of electrical impulses in nerve axons; (c) a climate energy balance model; (d) a parabolic feedback control problem. ...
Aquatic vegetation has major influence on the local water environment, affecting flow velocities and solute mixing. Extensive research has been conducted on the flow characteristics of vegetated areas, but little is known about solute transport. In this study, Laboratory experiments were carried out to investigate how solute transport is affected by emergent and submerged rigid vegetation. Vegetation greatly reduces the mean velocity, especially within the vegetated region. Near the bottom, the solute concentration is greater in the dense vegetation than in the sparse vegetation. The vertical distribution of the solute concentration decreases rapidly with the relative water depth. Generally, the longitudinal and lateral diffusion coefficients are less affected by denser vegetation, but both coefficients are strongly influenced by the relative water depth (submerged vegetation height). A modified function to estimate the longitudinal diffusion coefficients is proposed under both emergent and submerged
Nutrition All living organisms requires energy. They take in nutrition to produce energy, to grow and repair.. Below is an illustration which shows simple diffusion. Simple diffusion is when molecules travel from a place which has a lot of molecules to a place that either lacks or has low amounts of molecules. They do this by travelling down through the membrane until both places have, more or less equal amounts of molecules. Molecules that travel through the simple diffusion method must be nonpolar and they must be small in size. Below is an illustration which shows facilitated diffusion. Facilitated diffusion is different to simple diffusion because the molecules can not travel directly through the membrane. In order to go from a place which has lots of molecules to a place which lacks or doesnt have many molecule, it needs to use a channel. This channel is named a protein channel and it provides the molecules a way of getting through to the membrane.. Below is an illustration that shows ...
We study the existence and stability of spike clusters for biological reaction-diffusion systems with two small diffusion constants. In particular we consider a consumer chain model and the Gierer-Meinhardt system with a precursor gradient. In a spike cluster the spikes converge to the same limiting point. We will present results on the asymptotic behaviour of the spikes including their shapes, positions, and amplitudes. We will also compute the asymptotic behaviour of the eigenvalues. Such systems and their solutions play an important role in biological modelling to account for the bridging of lengthscales, e.g. between genetic, nuclear, intra cellular, cellular and tissue levels, or for the hierarchy of biological processes, e.g. first a large scale structure appears and then it induces patterns on a smaller scale. This is joint work with Juncheng Wei ...
DAB = liquid phase diffusion coefficient (diffusion coefficient of solution A in solution B). MB = molecular weight of solution B. Φ = correlation factor of solution B. T = absolute temperature. μ = viscosity of solution B. VA = molar volume of solution A. Diffusion can be defined as the mixing of two or more substances or the net motion of a substance from a high concentration to a low concentration region.. The diffusion coefficient can be defined as the ratio of the proportion of the substance represented by the diffusion through the unit concentration gradient per unit area per unit time.. ...
In this article we present a system of coupled bulk-surface reaction-diffusion equations on exponentially evolving volumes. Detailed linear stability analysis of the homogeneous steady state is carried out. It turns out that due to the nature of the coupling (linear Robin-type boundary conditions) the characterisation of the dispersion relation in the absence and presence of spatial variation (i.e. diffusion), can be decomposed as a product of the dispersion relation of the bulk and surface models thereby allowing detailed analytical tractability. As a result we state and prove the conditions for diffusion-driven instability for systems of coupled bulk-surface reaction-diffusion equations. Furthermore, we plot explicit evolving parameter spaces for the case of an exponential growth. By selecting parameter values from the parameter spaces, we exhibit pattern formation in the bulk and on the surface in complete agreement with theoretical predictions.. ...
7.7. NUMERICAL METHODS FOR UNSTEADY-STATE MOLECULAR DIFFUSION 7.7A. Introduction Unsteady-state diffusion often occurs in inorganic, organic, and biological solid materials. If the boundary conditions are constant with time ... - Selection from Transport Processes and Separation Process Principles (Includes Unit Operations) Fourth Edition [Book]
Surova Y, Nilsson M, Lampinen B, Lätt J, Hall S, Widner H, van Westen D, Hansson O. Alteration of putaminal fractional anisotropy in Parkinsons disease: a longitudinal diffusion kurtosis imaging study. Neuroradiology. 2018;60 (3) :247-254.
Kilner J, Shen Z, Skinner SJ, 2018, Electrical conductivity and oxygen diffusion behaviour of the (La0.8Sr0.2)0.95CrxFe1-xO3-δ (x=0.3, 0.5 and 0.7) A-site deficient perovskites, Physical Chemistry Chemical Physics, Vol: 20, Pages: 18279-18290, ISSN: 1463-9076 Lanthanum strontium chromite ferrite ((La0.8Sr0.2)0.95CrxFe1−xO3−δ, LSCrF) pellets with 5% A-site deficiency were fabricated and the electrical conductivity and oxygen diffusion behaviour with different Cr substitution levels (x = 0.3, 0.5 and 0.7) were investigated. As the Cr content increased, the electrical conductivity increased and then a maximum value was achieved at x = 0.7. In the oxygen diffusion studies, all the measured materials present good surface exchange rates (,9 × 10−8 cm s−1 at 900 °C) while the bulk diffusivity of the investigated materials decreased as the Cr substitution level increased: at 900 °C the oxygen diffusion coefficients of the LSCrF materials (x = 0.3, 0.5 and 0.7) are 1.1 × 10−10 cm2 s−1, ...
Diffusion Processes. Basic idea:. In its simplest form, diffusion is the transport of a material or chemical by molecular motion. If molecules of a chemical are present in an apparently motionless fluid, they will exhibit microscopic erratic motions due to being randomly struck by other molecules in the fluid. Individual particles or molecules will follow paths sometimes known as random walks.. In such processes, a chemical initially concentrated in one area will disperse. That is, there will be a net transport of that chemical from regions of high concentration to regions of low concentration.. An analogous form of diffusion is called conduction. In this case, heat is the chemical that is transported by molecular motion. As in chemical diffusion, heat migrates from regions of high heat to regions of low heat. The mathematics describing both conduction and diffusion are the same.. What this lab is about:. In this laboratory, students will explore two-dimensional diffusion phenomena by ...
Long-term potentiation (LTP) of excitatory synaptic transmission has long been considered a cellular correlate for learning and memory. Early LTP (eLTP, ,1 hour) had initially been explained either by presynaptic increases in glutamate release or by direct modification of post-synaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) function. Compelling models have more recently proposed that synaptic potentiation can occur by the recruitment of additional post-synaptic AMPARs, sourced either from an intracellular reserve pool by exocytosis or from nearby extra synaptic receptors pre-existing on the neuronal surface. However, the exact mechanism through which synapses can rapidly recruit new AMPARs during eLTP is still unknown. In particular, direct evidence for a pivotal role of AMPAR surface diffusion as a trafficking mechanism in synaptic plasticity is still lacking. Using AMPAR immobilization approaches, we show that interfering with AMPAR surface diffusion ...
We find a continuum of extinction rates of solutions of the Cauchy problem for the fast diffusion equation $u_\tau=\nabla\cdot(u^{m-1}\,\nabla u)$ with $m=m_*:=(n-4)/(n-2)$, here $n|2$ is the space-dimension. The extinction rates depend explicitly on the spatial decay rates of initial data and contain a logarithmic term.