Related papers: On a class of forced active scalar equations with …
Active suspensions, which consist of suspended self-propelling particles such as swimming microorganisms, often exhibit non-trivial transport properties. Continuum models are frequently employed to elucidate phenomena in active suspensions,…
Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
We discuss the lateral dynamics of two active force dipoles, which interact with each other via hydrodynamic interactions in a thin fluid layer that is active and chiral. The fluid layer is modeled as a two-dimensional (2D) compressible…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
We introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic…
Electrohydrodynamics is crucial in many nanofluidic and biotechnological applications. In such small scales, the complexity due to the coupling of fluid dynamics with the dynamics of ions is increased by the relevance of thermal…
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
The study of Mayer's cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE non-physical behavior at condensed states of fluids. In particular, a general equation of state is derived…
We derive the hydrodynamic equations of motion for a fluid of active particles described by under- damped Langevin equations that reduce to the Active-Brownian-Particle model, in the overdamped limit. The contraction into the hydrodynamic…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
We consider a 2D model of an autophoretic particle in which the particle has a circular shape and emits/absorbs a solute that diffuses and is advected by the suspending fluid. Beyond a certain emission/absorption rate (characterized by a…
We study the periodical solutions of a Poisson-gradient PDEs system with bounded nonlinearity. Section 1 introduces the basic spaces and functionals. Section 2 studies the weak differential of a function and establishes an inequality.…