相关论文: A note on mass-conserving solutions to the coagula…
The classical Feynman-Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing stochastic representations for classical solutions of linear Kolmogorov PDEs. This opens the door for the…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
Fractional cumulative residual entropy (FCRE) is a powerful tool for the analysis of complex systems. Most of the theoretical results and applications related to the FCRE of the lifetime random variable are based on the distribution…
This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean…
We provide a probabilistic representations of the solution of some semilinear hyperbolicand high-order PDEs based on branching diffusions. These representations pave theway for a Monte-Carlo approximation of the solution, thus bypassing the…
We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute the constrained…
In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability density function (PDF). Traditional mesh-based methods are…
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously…
Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the…
In this paper we take a fresh look at the long standing issue of the nature of macroscopic density fluctuations in the grand canonical treatment of the Bose-Einstein condensation (BEC). Exploiting the close analogy between the spherical and…
In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited…
A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS (a.k.a. L-BFGS) method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a…
Fluid-solid reactions exist in many chemical and metallurgical process industries. Several models describe these reactions such as volume reaction model, grain model, random pore model and nucleation model. These models give two nonlinear…
Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…
The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the…
The flux quanta attachment to the electrons creates composite fermions (CFs). The mass, the size and the density of the CF are inconsistent with real material. The sequence of fractional charges which suggest formation of CF agrees with the…
Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…
We present a simple model to account for the rheological behavior observed in recent experiments on micellar gels. The model combines attachment-detachment kinetics with stretching due to shear, and shows well-defined jammed and flowing…