scholarly journals Fast solutions for the first-passage distribution of diffusion models with space-time-dependent drift functions and time-dependent boundaries

2021 ◽  
Vol 105 ◽  
pp. 102613
Author(s):  
Udo Boehm ◽  
Sonja Cox ◽  
Gregor Gantner ◽  
Rob Stevenson
Keyword(s):  
Space Time ◽  
Diffusion Models ◽  
Time Dependent ◽  
First Passage

scholarly journals Fast Solutions for the First-Passage Distribution of Diffusion Models with Space-Time-Dependent Drift Functions and Time-Dependent Boundaries

2021 ◽  
Author(s):  
Udo Boehm ◽  
Sonja Cox ◽  
Gregor Gantner ◽  
Rob Stevenson
Keyword(s):  
First Passage Time ◽  
Numerical Algorithms ◽  
Planck Equation ◽  
Passage Time ◽  
Space Time ◽  
Diffusion Models ◽  
Time Dependent ◽  
First Passage ◽  
Theoretical Evaluation ◽  
Wide Range

Diffusion models with constant boundaries and constant drift function have been successfully applied to model phenomena in a wide range of areas in psychology. In recent years, more complex models with time-dependent boundaries and space time-dependent drift functions have gained popularity. One obstacle to the empirical and theoretical evaluation of these models is the lack of simple and efficient numerical algorithms for computing their first-passage time distributions. In the present work we use a known series expansion for the first-passage time distribution for models with constant drift function and constant boundaries to simplify the Fokker-Planck equation for models with time dependent boundaries and space-time-dependent drift functions. We show how a simple Crank--Nicolson scheme can be used to efficiently solve the simplified equation.

scholarly journals A martingale analysis of first passage times of time-dependent Wiener diffusion models

2017 ◽  
Vol 77 ◽  
pp. 94-110 ◽  
Author(s):  
Vaibhav Srivastava ◽  
Samuel F. Feng ◽  
Jonathan D. Cohen ◽  
Naomi Ehrich Leonard ◽  
Amitai Shenhav
Keyword(s):  
Diffusion Models ◽  
First Passage Times ◽  
Time Dependent ◽  
First Passage ◽  
Passage Times

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

scholarly journals A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis

2020 ◽  
Vol 9 (1) ◽  
pp. 201-222 ◽  
Author(s):  
Usha Shankar ◽  
Neminath B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Brownian Motion ◽  
Joule Heating ◽  
Concentration Field ◽  
Double Diffusion ◽  
Diffusion Models ◽  
Time Dependent ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Casson Nanofluid ◽  
Highly Nonlinear

AbstractPresent research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

scholarly journals Evolution of a domain wall in expanding universe: inflation and after it

2018 ◽  
Vol 191 ◽  
pp. 08004
Author(s):  
A.D. Dolgov ◽  
S.I. Godunov ◽  
A.S. Rudenko
Keyword(s):  
Domain Wall ◽  
Hubble Parameter ◽  
Domain Walls ◽  
Flat Space ◽  
Space Time ◽  
Time Dependent ◽  
Expanding Universe ◽  
Large Size ◽  
Dependent Parameter ◽  
Thick Domain Walls

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.

A local radial basis function differential quadrature semi-discretisation technique for the simulation of time-dependent reaction-diffusion problems

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ram Jiwari ◽  
Alf Gerisch
Keyword(s):  
Meshless Method ◽  
Order Of Convergence ◽  
Method Of Lines ◽  
Reaction Diffusion ◽  
Diffusion Models ◽  
Second Order ◽  
Differential Quadrature ◽  
Time Dependent ◽  
Content Type ◽  
Radial Basis

Purpose This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time. Design/methodology/approach In a method of lines setting, a meshless method for their discretization in space is proposed. This discretization is based on a DQ approach, and RBFs are used as test functions. A local approach is followed where only selected RBFs feature in the computation of a particular DQ weight. Findings The proposed method is applied on four reaction-diffusion models: Huxley’s equation, a linear reaction-diffusion system, the Gray–Scott model and the two-dimensional Brusselator model. The method captured the various patterns of the models similar to available in literature. The method shows second order of convergence in space variables and works reliably and efficiently for the problems. Originality/value The originality lies in the following facts: A meshless method is proposed for reaction-diffusion models based on local RBFs; the proposed scheme is able to capture patterns of the models for big time T; the scheme has second order of convergence in both time and space variables and Nuemann boundary conditions are easy to implement in this scheme.

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