相关论文: Selection theory of free dendritic growth in a pot…
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut theorem for boundary regions, applied recently to develop a "bit-thread" interpretation of…
In this work, we propose a new semi-Lagrangian (SL) finite difference scheme for nonlinear advection-diffusion problems. To ensure conservation, which is fundamental for achieving physically consistent solutions, the governing equations are…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
We show, in this report, how a population balance model differential equation describing batch crystal growth from solution can be solved in closed form for the case of diffusion limited growth with and without modeling the effects of…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…
The diffusional growth of wetting droplets on the boundary wall of a semi-infinite system is considered in different regions of a first-order wetting phase diagram. In a quasistationary approximation of the concentration field, a general…
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…
We consider a class of parametric Schr\"odinger equations driven by the fractional $p$-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth. By using variational methods and…
The pattern selection problem in binary-mixture convection in an extended channel with a lateral through-flow is presented. The through-flow breaks left--right parity and changes pattern dynamics dramatically. The problem is studied based…
It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
Under the condition of nonuniformly bounded growth, %nonuniform exponential dichotomy spectrum for nonautonomous linear system is proposed the relationship of the nonuniform exponential dichotomy spectrum and the other two classical…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
A statistical theory of two-dimensional Laplacian growths is formulated from first-principles. First the area enclosed by the growing surface is mapped conformally to the interior of the unit circle, generating a set of dynamically evolving…
We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…
The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Can standard continuous-time generative models represent distributions whose support is an extremely sparse, globally constrained discrete set? We study this question using completed Sudoku grids as a controlled testbed, treating them as a…
We perform an exhaustive study of the simplest, nontrivial problem in advection-diffusion -- a finite absorber of arbitrary cross section in a steady two-dimensional potential flow of concentrated fluid. This classical problem has been…