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Based on the generalized non-Markovian equations obtained earlier for a nonequilibrium one-particle distribution function and potential part of the averaged enthalpy density [Markiv B.B., Omelyan I.P, Tokarchuk M.V., Condens. Matter Phys.,…
In this work we give a proof of the mean-field limit for $\lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows…
Over the past fifteen years, the theory of Wasserstein gradient flows of convex (or, more generally, semiconvex) energies has led to advances in several areas of partial differential equations and analysis. In this work, we extend the…
Dynamic density functionals (DDFs) are popular tools for studying the dynamical evolution of inhomogeneous polymer systems. Here, we present a systematic evaluation of a set of diffusive DDF theories by comparing their predictions with data…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…
Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…
Discrete Ginzburg-Landau (DGL) equations with non-local nonlinearities have been established as significant inherently discrete models in numerous physical contexts, similar to their counterparts with local nonlinear terms. We study two…
Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and…
We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the well-posedness, continuation criteria and smoothness of…
In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
The goal of this paper is to discuss some of the results in [31] and [32] and expand upon the work there by proving a global weak existence result as well as a first bubbling analysis in finite time. In addition, an alternative local…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
This paper extends the multiscale modeling framework introduced in Part I (Deng and Ha, Physica D: Nonlinear Phenomena 483 (2025) 134951) for sea-ice floe dynamics with non-rotating floes to the case with rotational floes and nonlinear…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…