Poiseuille flow between parallel plates advects chemical reaction fronts, distorting them and altering their propagation velocities. Analytical solutions of the cubic reaction-diffusion-advection equation resolve the chemical concentration for narrow gaps, wide gaps, and small-amplitude flow. Numerical solutions supply a general description for fluid flow in the direction of propagation of the ...

Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employe...

Time-dependent advection-diffusion equations arise in mathematical models of porous medium flow and transport processes, including petroleum reservoir simulation, environmental modeling, and other applications. In such applications as immiscible displacement of oil by water in a secondary oil recovery process in petroleum industry or a groundwater transport process involving a non-aqueous phase...

A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)(1/3) for a fixed value of branching number n, which is consistent with observations in mammalian...

We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the numerical solution of such optimal control problems. In the discretize-then-optimize approach the optimal control problem is first discretized, using the SUPG met...

Atmospheric air pollution turbulent fluxes can be assumed proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. In this work we present an analytical solution of the three-dimensional steady stat...

In this paper we describe a general purpose, graphics processing unit (GP-GPU)-based approach for solving partial differential equations (PDEs) within advection-reactiondiffusion models. The GP-GPU-based approach provides a platform for solving PDEs in parallel and can thus significantly reduce solution times over traditional CPU implementations. This allows for a more efficient exploration of ...

We consider the advection-diffusion equation φt +Au · ∇φ = ∆φ, φ(0, x) = φ0(x) on R, with u a periodic incompressible flow and A 1 its amplitude. We provide a sharp characterization of all u that optimally enhance dissipation in the sense that for any initial datum φ0 ∈ L(R), p <∞, and any τ > 0, ‖φ(·, τ)‖∞ → 0 as A→∞. Our characterization is expressed in terms of simple geometric and spectral ...

tumor growth has a number of features in common with a physical process known as molecular beam epitaxy (mbe). so using the same equations for tumor growth is sensible. however, tumor substrate unlike mbe is not planar that makes necessary a geometrical treatment of the growth equations. a variety of mathematical models have been proposed to describe tumor growth. the justification for these mo...

Abstract. Reactive transport processes in natural environments often involve many ionic species. The diffusivities of species vary. Since assigning different the advection–diffusion equation leads to charge imbalance, a single diffusivity is usually used for all In this work, we apply Nernst–Planck equation, which resolves unequal an electroneutral manner, model reactive transport. To demonstra...