Related papers: New links between PDE's and Voronoi patterns
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
In this article, we develop a new approach to functional quantization, which consists in discretizing only a finite subset of the Karhunen-Lo\`eve coordinates of a continuous Gaussian semimartingale $X$. Using filtration enlargement…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
This course explains how the usual mean field evolution partial differential equations (PDEs) in Statistical Physics - such as the Vlasov-Poisson system, the vorticity formulation of the two-dimensional Euler equation for incompressible…
A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction…
A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed p-adic fields.…
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity…
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
Poisson Voronoi tessellations have been used in modeling many types of systems across different sciences, from geography and astronomy to telecommunications. The existing literature on the statistical properties of Poisson Voronoi cells is…
We provide a self-contained analysis, based entirely on pde methods, of the exponentially long time behavior of solutions to linear uniformly parabolic equations which are small perturbations of a transport equation with vector field having…
In this paper, we propose simple numerical algorithms for partial differential equations (PDEs) defined on closed, smooth surfaces (or curves). In particular, we consider PDEs that originate from variational principles defined on the…
Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent,…
Dengue is a vector-borne viral disease increasing dramatically over the past years due to improvement in human mobility. The movement of host individuals between and within the patches are captured via a residence-time matrix. A system of…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary conforming Delaunay meshes provide good approximation of the…