Related papers: Anchored Peskin Problem
Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…
We consider a model for the evolution of an interface in a heterogeneous environment governed by a parabolic equation. The heterogeneity is introduced as obstacles exerting a localized dry friction. Our main result establishes the emergence…
In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the…
We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equations that accounts for both…
As a main result of the paper, we construct and justify an asymptotic approximation of Green's function in a domain with many small inclusions. Periodicity of the array of inclusions is not required. We start with an analysis of the…
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
Motivated to understand the behavior of biological filaments interacting with membranes of various types, we study a theoretical model for the shape and thermodynamics of intrinsically-helical filaments bound to curved membranes. We show…
We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the Fluctuating Immersed Boundary (FIB) approach that treats a solute as discrete Lagrangian particles that…
State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
We focus on a highly nonlinear evolutionary abstract PDE system describing volume processes coupled with surfaces processes in thermoviscoelasticity, featuring the quasi-static momentum balance, the equation for the unidirectional evolution…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general…
Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate in the velocity. However, almost no rigorous theoretical…
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs are coupled through a…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…