Related papers: Convergence Relative to a Microstructure : Propert…
A one-dimensional system of bosons interacting with contact and single-Gaussian forces is studied with an expansion in hyperspherical harmonics. The hyperradial potentials are calculated using the link between the hyperspherical harmonics…
The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…
In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
In [2], the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces $\phi:M^n \to \mathbb{H}^{n+1}$ and a class of conformal metrics on domains of the round sphere $\mathbb{S}^n$. Some of the key…
We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under…
A set of sequences is said to converge simultaneously if there exists an infinite subset $H$ of the index set $\omega$ such that all sequences converge when restricted to $H$. We discuss simultaneous convergence of sequences in the same or…
The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape…
Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
In this paper, we propose an approach for describing wave propagation in finite-size microstructured metamaterials using a reduced relaxed micromorphic model. This method introduces an additional kinematic field with respect to the…
New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, non-Hermitian linear systems. These bounds are given for the case when the Hermitian part of the coefficient matrix is…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial…
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…
Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is…
Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization…
We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements…