相关论文: Locally optimal configurations for the two-phase t…
We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…
Motivated by recent experimental evidence of charge order in the pseudogap phase of cuprates, we perform a variational analysis of charge-neutral, spin-singlet ordering in metals on the square lattice, using a wavefunction with double…
The duality and other symmetry properties of the effective conductivity sigma_e of the classical two-dimensional isotropic randomly inhomogeneous heterophase systems at arbitrary number of phases N are discussed. A new approach for a…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
Packing of particles in confined environments is a common problem in multiple fields. Here, based on the two-dimensional Hertzian particle model, we study the packing of deformable spherical particles under compression, and reveal the…
In this paper, we consider the well-known following shape optimization problem: $$\lambda_2(\Omega^*)=\min_{\stackrel{|\Omega|=V_0} {\Omega\textrm{ convex}}} \lambda_2(\Omega),$$ where $\lambda_2(\Om)$ denotes the second eigenvalue of the…
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…
We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the…
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…
It has been a widely belief that for a planar convex domain with two coordinate axes of symmetry, the location of maximal norm of gradient of torsion function is either linked to contact points of largest inscribed circle or connected to…
In this article, the small ball probability is obtained for the collision local time of two independent symmetric $\alpha-$stable processes with parameters $\alpha_1,\alpha_2\in(0,2]$ satisfying $\max\{\alpha_1,\alpha_2\}>1$. The proof is…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…
The packing of hard-core particles in contact with their neighbors offers the statically determinate problem which allows analytical investigation of the stress tensor distribution. We construct the stress probability functional and derive…
The lowest drag shape of fixed volume in Stokes flow has been known for some 40 years. It is front-back symmetric and similar to an American football with ends tangent to a cone of 60 degrees. The analogous convex axisymmetric shape of…
We investigate second order conformal perturbation theory for $\mathbb{Z}_2$ orbifolds of conformal field theories in two dimensions. To evaluate the necessary twisted sector correlation functions and their integrals, we map them from the…
We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are…