相关论文: A nonlinear least squares method for the inverse d…

In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…

In recent years, much attention has been paid to the study of forward and inverse problems for the Rayleigh-Stokes equation in connection with the importance of this equation for applications. This equation plays an important role, in…

It is well known that for a large class of coagulation kernels, Smoluchowski coagulation equations have particular power law solutions which yield a constant flux of mass along all scales of the system. In this paper, we prove that for some…

Particle-stabilized emulsions are commonly used in various industrial applications. These emulsions can present in different forms, such as Pickering emulsions or bijels, which can be distinguished by their different topologies and…

A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical…

We conduct numerical experiments to investigate the spatial clustering of particles and bubbles in simulations of homogeneous and isotropic turbulence. Varying the Stokes parameter and the densities, striking differences in the clustering…

We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…

In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…

The Smoluchowski equation with a time dependent sink term is solved exactly. In this method by knowing the probability distribution at the origin P(0,s), one may derive the probability distribution at all positions i.e., P(x,s). Further the…

We study the solutions of the Smoluchowski coagulation equation with a regularisation term which removes clusters from the system when their mass exceeds a specified cut-off size, M. We focus primarily on collision kernels which would…

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$…

We study the Euler scheme for scalar non-autonomous stochastic differential equations, whose diffusion coefficient is not globally Lipschitz but a fractional power of a globally Lipschitz function. We analyse the strong error and establish…

To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are…

In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…

In this paper, we consider a class of nonsmooth sum-of-ratios fractional optimization problems with block structure. This model class is ubiquitous and encompasses several important nonsmooth optimization problems in the literature. We…

Let $\varphi_{n,K}$ denote the largest angle in all the triangles with vertices among the $n$ points selected at random in a compact convex subset $K$ of $\mathbb{R}^d$ with nonempty interior, where $d\ge2$. It is shown that the…

We consider the following fractional prescribed curvature problem $$(-\Delta)^s u= K(y)u^{2^*_s-1},\ \ u>0,\ \ y\in \mathbb{R}^N,\qquad (0.1)$$ where $s\in(0,\frac{1}{2})$ for $N=3$, $s\in(0,1)$ for $N\geqslant4$ and $2^*_s=\frac{2N}{N-2s}$…

Let $K_n$ denote the number of types of a sample of size $n$ taken from an exchangeable coalescent process ($\Xi$-coalescent) with mutation. A distributional recursion for the sequence $(K_n)_{n\in{\mathbb N}}$ is derived. If the coalescent…

Pulvirenti and Toscani introduced an equation which extends the Kac caricature of a Maxwellian gas to inelastic particles. We show that the probability distribution, solution of the relative Cauchy problem, converges weakly to a probability…

We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities \alpha(n,m) of mass n and mass m particles grow more slowly than…