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1 oborated by a theoretical model based on the diffusion equation.
2 in layers by the one-dimensional generalized diffusion equation.
3 redicted by solving a 1-dimensional reaction-diffusion equation.
4  TRBDF2 method is employed for the advection-diffusion equation.
5 m solution of the two-dimensional convection-diffusion equation.
6  We report that vesicle movement follows the diffusion equation.
7 l distribution is governed by the force-free diffusion equation.
8 mulations based on a one-dimensional exciton diffusion equation.
9 l is shown to be a solution of a generalized diffusion equation.
10 g approach allowed by an exact quantum-state-diffusion equation.
11 d glutamate can be described with a reaction-diffusion equation.
12 and biofilm, respectively, and the advection-diffusion equation.
13 a geometric basis for solving the stationary diffusion equation.
14 = 2 via a monotone flow governed by the fast diffusion equation.
15 culated using the analytical solution of the diffusion equation.
16 (deterministic) PDE, which we call a fitness-diffusion equation.
17  tube compared with the prediction using the diffusion equation.
18 d in some cases do not appear to satisfy the diffusion equation.
19 uous range (0,1) were found from the forward diffusion equation.
20 d from the vesicle using a three-dimensional diffusion equation.
21 s in the efficient solution of the continuum diffusion equation.
22 ments are modeled with a convective reaction-diffusion equation.
23 ion of transport, which consists of singular diffusion equations.
24 an external signal into a series of reaction-diffusion equations.
25  automatically generate a system of reaction-diffusion equations.
26 ifferential equations, for example, reaction-diffusion equations.
27 algorithms and algorithms for integration of diffusion equations.
28 signal each other via traditional growth and diffusion equations.
29 vant for other systems described by reaction-diffusion equations.
30 modules are implemented in terms of reaction-diffusion equations.
31 bryos can be described by nonlinear reaction-diffusion equations.
32 ed-order (DO) space-time fractional reaction-diffusion equations.
33 he model comprises a system of four reaction-diffusion equations.
34 ome models treat motility using an advection diffusion equation (ADE).
35 ite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the sour
36              The approximation is based on a diffusion equation and is valid when N exp(-u/s) >> 1, w
37          For this, we numerically invert the diffusion equation and thereby obtain the diffusivity an
38 e theoretical calculations based on the heat diffusion equations and experimental measurements based
39 tion of coupled Navier-Stokes and convection-diffusion equations and experiments using fluorescence r
40 the complete system of differential reaction diffusion equations and fitting the theoretical pH distr
41 llent agreement with theory involving linear diffusion equations and the experimentally determined Ne
42  in the brain was simulated by the advection-diffusion equations and was numerically solved in COMSOL
43 water in the Phase Chip is modeled using the diffusion equation, and good agreement between experimen
44 re knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical te
45 verse first power of the distance, following diffusion equations, and describes the flat rotation cur
46                                     Reaction-diffusion equations are the cornerstone of modeling bioc
47                    Numerical solution of the diffusion equation, as well as ab initio calculations, s
48 ss by numerical solution of the Smoluchowski diffusion equation, as well as by coarse-grained Brownia
49                            We use a reaction-diffusion equation based model of tumour growth to inves
50 Most of the proposed models rely on reaction-diffusion equations, but their formulation and applicabi
51  generalized the standard two-state reaction-diffusion equations by 1), accounting for the parallel a
52                            Then, a long-time diffusion equation can be derived analytically from the
53 ple radiative boundary condition on the heat diffusion equation cannot adequately describe interfacia
54 on model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poiss
55  jet hydrodynamics and associated convective-diffusion equation, coupled to a first-order surface pro
56  of the coupled system of nonlinear reaction-diffusion equations, defined inside the cell and on the
57         At the extracellular level, reaction diffusion equations describe nutrient concentrations ove
58         At the extracellular level, reaction-diffusion equations describe the chemical dynamics (nutr
59  The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia an
60 built to model a radially symmetric reaction-diffusion equation describing the activity of immuno-PET
61                     Using rho, we modified a diffusion equation describing the change of chloride ion
62                             From the optical diffusion equation describing the propagation and genera
63  presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be red
64 elds, characterized by a system of advection-diffusion equations, designed to replicate the character
65                                    Advection-diffusion equation determined the mixing dynamics.
66 nalysis of the data using the unsteady-state diffusion equation, enabled estimation of the permeabili
67 l is based on an approximate solution of the diffusion equation for both aqueous and organic diffusio
68                                  The forward diffusion equation for gene frequency dynamics is solved
69 he two-state proteins, obtained by solving a diffusion equation for motion on the free energy profile
70 ntitatively with analytical solutions of the diffusion equation for simple geometries.
71  length-sensing mechanism in which advection-diffusion equations for bidirectional motor transport ar
72 ent a complete solution to the FRAP reaction-diffusion equations for either single or multiple indepe
73                The numerical solution of the diffusion equations for substrate generation-tip collect
74 hematical model that involves taxis-reaction-diffusion equations for the critical components in the i
75 ) for the cell species coupled with reaction-diffusion equations for the substrate components.
76 the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous m
77                         A system of reaction-diffusion equations has been developed to track the conc
78 m for scalar mixing by solving the advection-diffusion equation in a quantum computational fluid dyna
79 mpling rate is calculated using the Einstein diffusion equation in conjunction with an experimentally
80 rflow was determined by solving the unsteady diffusion equation in the air-phase.
81                    By solving the convection-diffusion equation in the frame of the moving rod, it wa
82 t, and stable numerical routine to solve the diffusion equation in the steady-state and time-domain f
83 e review the properties of the extended flow-diffusion equation in tumor tissue.
84 The kinetic theory is based on a generalized diffusion equation in which the driving force for motion
85 +, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium.
86 s using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids,
87 numerical model consisting of a 3D advection/diffusion equation, including uptake/release reactions b
88 ared with values predicted using the optical diffusion equation incorporating 1) biexponential decay,
89 tal solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic s
90  obtained from the solution of a generalized diffusion equation incorporating an effective Langmuir a
91  was also modeled via a modified form of the diffusion equation inside an evaporating droplet that to
92 nsport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption requi
93                                  The forward diffusion equation is thus solved for all gene frequenci
94  mathematical model comprised of 23 reaction-diffusion equations is used to simulate the biochemical
95                                          The diffusion equation method of global minimization is appl
96                                 We solve the diffusion equation numerically on various static curved
97 ompared with the solutions of the adsorption-diffusion equation of the channel for determining the ad
98 gnitude and a scheme for handling convection-diffusion equations of interest in electrochemical and s
99  have built a system of interacting reaction diffusion equations of the Fisher-Kolmogorov-Petrovskii-
100 of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell
101 fusive transport have focused on solving the diffusion equation on curved surfaces, for which it is n
102  through the embryo is well described by the diffusion equation on the relevant length and time scale
103  formulate and solve rather general reaction-diffusion equations on general surfaces without having t
104 w to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple w
105 including the Butler-Volmer (BV), Nernst and diffusion equations on the backbone of neural networks f
106 sional framework is constructed on the drift-diffusion equations, Poisson's equation, and wave propag
107                     In these cases, reaction-diffusion equations provide a valuable tool to learn how
108  be shown to rigorously satisfy the extended diffusion equation provided one correctly defines the ti
109 genation is obtained by solving the reaction-diffusion equation; radiotherapy kills tumor cells accor
110 ch solves the Schrodinger, Poisson and drift-diffusion equations self-consistently.
111 cellent quantitative agreement with the full diffusion equation solutions demonstrating that the two
112 ion at dendritic spines by means of reaction-diffusion equations solved on spine-like geometries.
113        We use a system of Reaction-Advection-Diffusion equations solved with a stabilized finite elem
114 lly expensive numerical solution of reaction-diffusion equations, such approximations proved useful i
115 dependent drug penetration by the 1D general diffusion equation that accounts for spatial variations
116                   We formulate a generalized diffusion equation that includes these various pushing a
117 n be described by an inhomogeneous advection diffusion equation that is free of all parameters.
118 ed tumor model is based on a set of reaction-diffusion equations that describe the spatio-temporal ev
119 ses, we constructed models based on reaction-diffusion equations that fit well with the experimental
120 utions have been identified for the reaction-diffusion equations that govern FRAP, there has been no
121 is described by a coupled system of reaction-diffusion equations that-assuming spherical radial symme
122 on, the Schrodinger equation, the convection-diffusion equation, the anisotropic conductivity equatio
123 ttering solution, when incorporated into the diffusion equation, the kinetic parameters failed to lik
124                    By solving the full drift-diffusion equations, the existence of high-injection eff
125 e was calculated numerically, by solving the diffusion equation through a Legendre polynomial expansi
126                                 We apply the diffusion equation to a case study of Kruger National Pa
127  model, we parameterize and solve a reaction-diffusion equation to determine hydrolysis rates consist
128  solution of the uncoupled steady convective-diffusion equation to determine the concentration field
129 efore used the corresponding solution to the diffusion equation to estimate an apparent diffusion coe
130 the bidomain equations along with the photon diffusion equation to study the excitation and emission
131 quential-step schemes consisting of reaction-diffusion equations to compare to each other and to expe
132                      The model uses reaction-diffusion equations to describe 3(') phosphoinositide si
133                              We use reaction-diffusion equations to model the invasion of a species w
134 of primary energy metabolism within reaction-diffusion equations to predict local glucose, oxygen, an
135 vel, the PINNs permit the solution of the 2D diffusion equation under cylindrical geometry incorporat
136                         Anisotropic reaction-diffusion equations, using diffusion coefficients determ
137                                          The diffusion equation was used to model the propagation of
138 ncepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for
139                   Using a system of reaction-diffusion equations, we study diffusion of VEGF, binding
140 educes the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equation
141                                    Mesoscale diffusion equations were then formulated upon a new two-
142 it optimal control model based on a reaction-diffusion equation which includes an Holling II type fun
143 system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dyna
144  solute transport by the classical advection-diffusion equation, which could lead to systematic error
145                                     The flow-diffusion equation, which describes the relation between
146 aditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffu
147 0 and 1 were found by appeal to the backward diffusion equation, while those in the continuous range
148                                  Solving the diffusion equation whose parameters are derived from the
149 be well described by a model that combined a diffusion equation with a competitive Michaelis-Menten e
150 e resolve this paradox and derive a modified diffusion equation with finite speed.
151 ted at the macroscopic level by an advection-diffusion equation with memory (ADEM) whose parameters a

 
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