Double-diffusive convection, in which a fluid is acted upon by two fields (such as temperature and salinity) that affect the density, has been widely studied areas diverse oceans stellar atmospheres. Assuming classical Fickian diffusion for both heat salt, evolution of salinity are governed parabolic advection–diffusion equations. In reality, there small extra terms these equations render hyper...

We analyze a partial differential equation that models the two-slit experiment of quantum mechanics. The state variable is probability density function particle positions. has diffusion term corresponding to random movement particles, and nonlocal advection particles in transverse directionperpendicular their forward movement. model compared Schrodinger experiment. supports ensemble interpretat...

We present a study on the convergence of computation coupled advection-diffusion-reaction equations. In computation, equations with different coefficients and even dissimilar types are assigned in two subdomains, Schwarz iteration is made between when marching from time step to next one. The analysis starts algebraic systems resulting full discretization linear by explicit schemes. Conditions f...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting which the velocity field is Sobolev regular spatial variable. estimate formulated with help of Kantorovich--Rubinstein distances logarithmic cost functions. Second, are extended to fields whose gradients singular integrals $L^1$ functions entailing new well-p...

Abstract Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in form advection–diffusion–reaction equations. The patient-wise parametrization these models, and their validation experimental data has found be difficult, as time sequence measurements are mostly m...

The LiMIT system (Lithium/Metal Infused Trenches) is an innovative plasma-facing component for tokamak divertors, recently proposed at the University of Illinois. Thanks to the coupling of two metals having different Seebeck coefficients, the device is able to generate internal thermoelectric currents as a response to an incoming heat flux from the plasma. One of the two metals is liquid lithiu...

We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type elements. The resulting are continuous in space, or discontinuous time. In a first test run, all methods applied to scalar advection-diffusion model problem. Then, the convergence properties time-discontinuous studied numerical experiments. Advection velocity diffusion coeffic...

Reactive transport modelling of dissolved CO 2 in porous media iii Dedicated to my parents (late) and eldest sister. iv Reactive transport modelling of dissolved CO 2 in porous media v ABSTRACT The geological sequestration of carbon dioxide (CO 2) is seen as one of the options of mitigating the imbalance of greenhouse gas emissions and to avoid global warming. However, leakage of CO 2 from the ...