Related papers: Variational formulation of planar linearized elast…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
We examine some basic physics surrounding regenerative braking and air drag. First, we analyze under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over ``coasting'' where…
In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…
Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the…
This paper presents a kinematic definition of a serialized Stewart platform designed for autonomous in-space assembly called an Assembler. The Assemblers architecture describes problems inherent to the inverse kinematics of over-actuated…
We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed…
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
We present a computational model of thin elastic bilayers that undergo large bending isometric deformations when actuated by non-mechanical stimuli. We propose a discontinuous Galerkin approximation of the variational formulation discussed…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…
We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In this paper, we derive a linearized Kirchhoff model from three dimensional nonlinear elastic energy of plates with incompatible prestrain as its thickness $h$ tends to zero and its elastic energy scales like $h^{\beta}$ with $2<\beta<4.$…
Kinetic traps are a notorious problem in equilibrium statistical mechanics, where temperature quenches ultimately fail to bring the system to low energy configurations. Using multifarious self-assembly as a model system, we introduce a…
In the theory of elasticity, the constraint of compatibility conditions on displacement field is not equivalent to the property of displacement field. The difference may broaden the possibility of solutions to elasticity problems, which…
The self-consistent system of master equations describing the kinetics of a relativistic non-Abelian plasma, influenced by curvature interactions, is formulated. Non-minimal (curvature induced) coupling is shown to modify all the subsystems…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…