相关论文: Backward Uniqueness for a PDE Fluid-Structure Inte…

We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the fluid, and a thick layer which sits on top of the thin structural…

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the…

We study the features of a radial Stokes flow due to a submerged jet directed toward a liquid-air interface. The presence of surface-active impurities confers to the interface an in-plane elasticity that resists the incident flow. Both…

The structural and thermodynamic properties of fluids whose molecules interact via potentials with a hard-core plus a square well, a square shoulder, and a second square well, are considered. Those properties are derived by using a…

Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…

We present the results of an experimental and numerical investigation of a turbulent flow over a backward-facing step in a channel. Experimental data are visualized using a Particle Image Velocimetry (PIV) device. As a mathematical model we…

We study the interaction between incompressible viscous fluids and multilayered elastic structures in a 3D/2D/3D framework, where a 3D fluid interacts with a 2D thin elastic layer, coupled to a 3D thick elastic solid. The system is driven…

The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing…

These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…

A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor…

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…

The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…

The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…

We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational…

In this paper backward stochastic differential equations with interaction (shorter BSDEs with interaction) are introduced. Far to our knowledge, this type of equation is not seen in the literature before. Existence and uniqueness result for…

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…

This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…

We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics…