Related papers: Geometric Properties of the 2-D Peskin Problem

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 consider spectral mixed discontinuous Galerkin finite element discretizations of the Lam\'e system of linear elasticity in polyhedral domains in $\mathbb{R}^3$. In order to resolve possible corner, edge, and corner-edge singularities,…

The drag of an elliptic intruder in a two-dimensional granular environment is numerically studied. The movement parallel to the major axis of the intruder is found to be unstable. The drag law is given by the sum of the yield force and the…

Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…

Shear strain localization refers to the phenomenon of accumulation of material deformation in narrow slip zones. Many materials exhibit strain localization under different spatial and temporal scales, particularly rocks, metals, soils, and…

Achieving real-time physics-based animation that generalizes across diverse 3D shapes and discretizations remains a fundamental challenge. We introduce PhysSkin, a physics-informed framework that addresses this challenge. In the spirit of…

Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list…

We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be…

The injection of a long flexible rod into a two-dimensional domain yields a complex pattern commonly studied through elasticity theory, packing analysis, and fractal geometries. "Loop" is a one-vertex entity that is naturally formed in this…

We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…

Recent progress on the complete set of solutions of two dimensional classical string theory in any curved spacetime is reviewed. When the curvature is smooth the string solutions are deformed folded string solutions as compared to flat…

Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly…

In this article, we prove that solutions to a problem in nonlinear elasticity corresponding to small initial displacements exist globally in the exterior of a nontrapping obstacle. The medium is assumed to be homogeneous, isotropic, and…

We prove that the initial-value problem for the motion of a certain type of elastic body has a solution for all time if the initial data are sufficiently small. The body must fill all of three space, obey a ``neo-Hookean'' stress-strain…

We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state,…

Our previous molecular dynamic simulation studies of simple two-dimensional (2D) systems \cite{matt_big} suggested that both geometrical defects (localized, large-amplitude deviations from hexagonal ordering) and topological defects…

In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…

In this work we consider bubbles that can form spontaneously when a two-dimensional (2D) crystal is transferred to a substrate with gases or liquids trapped at the crystal-substrate interface. The underlying mechanics may be described by a…

We present a global analysis of the geometries that arise in non-compact current algebra (or gauged WZW) coset models of strings and particles propagating in curved space-time. The simplest case is the 2d black hole. In higher dimensions…

Recent neural, physics-based modeling of garment deformations allows faster and visually aesthetic results as opposed to the existing methods. Material-specific parameters are used by the formulation to control the garment inextensibility.…