相关论文: Periodic body-and-bar frameworks

We study a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a configuration that can mimic…

We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…

Shape-morphing metamaterials enable adaptive structures capable of complex functional deformations, with applications ranging from reconfigurable structures and soft robotics to medical devices. However, their design remains challenging due…

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…

Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…

We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent…

We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights…

Periodic control systems used in spacecrafts and automotives are usually period-driven and can be decomposed into different modes with each mode representing a system state observed from outside. Such systems may also involve intensive…

The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of…

Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with…

A large family of periodic planar non-linear bimode metamaterials are constructed from rigid bars and pivots. They are affine materials in the sense that their macroscopic deformations are only affine deformations: at large distances any…

The fully coupled dynamic interaction problem of the free surface of an incompressible fluid and a rigid body beneath it, in an inviscid, irrotational framework and in the absence of surface tension, is considered. Evolution equations of…

A rigorous homogenization theory of metamaterials -- artificial periodic structures judiciously designed to control the propagation of electromagnetic waves -- is developed. All coarse-grained fields are unambiguously defined and effective…

Solid materials are commonly classified as crystalline or amorphous based on the presence or absence of long-range order.Metal-organic frameworks (MOFs), like other solids,also display markedly different properties and functions in these…

Metamaterial homogenization is often based on implicit assumptions inspired to natural material models. Retrieved effective permittivity and permeability, however, are often non-physical, especially near the array resonances, of most…

Modeling the atomic structure of amorphous materials has long been a critical challenge in materials science. Recent advances in monolayer amorphous materials enable direct observation of their atomic structures, paving the way for a better…

This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…

To each discrete translationally periodic bar-joint framework $\C$ in $\bR^d$ we associate a matrix-valued function $\Phi_\C(z)$ defined on the d-torus. The rigid unit mode spectrum $\Omega(\C)$ of $\C$ is defined in terms of the…

A bar framework determined by a finite graph $G$ and configuration $\bf p$ in $d$ space is universally rigid if it is rigid in any ${\mathbb R}^D \supset {\mathbb R}^d$. We provide a characterization of universally rigidity for any graph…