相关论文: Recovering the normal form of an elasticity tensor
Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…
A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
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…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…
A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input…
Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
Given an ideal triangulation of a connected 3-manifold with non-empty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject…
Quite a few future high precision space missions for testing Special and General Relativity will use optical resonators which are used for laser frequency stabilization. These devices are used for carrying out tests of the isotropy of light…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
We present the details for the covariant renormalization of the stress tensor for vacuum tensor perturbations at the level of the effective action, adopting Hadamard regularization techniques to isolate short distance divergences and gauge…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
We derive the membrane elastic stress and torque tensors using the standard Helfrich model and a direct variational method in which the edges of a membrane are infinitesimally translated and rotated. We give simple expressions of the stress…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…