Related papers: Stability under lamination and polycrystalline eff…
We propose an experimentally relevant scheme to create stable solitons in a three-dimensional Bose-Einstein condensate confined by a one-dimensional optical lattice, using temporal modulation of the scattering length (through ac magnetic…
Relations between components of the effective tensors of composites that hold regardless of composite's microstructure are called exact relations. Relations between components of the effective tensors of all laminates are called lamination…
We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity…
We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination…
We investigate the existence and stability of three-dimensional (3D) solitons supported by cylindrical Bessel lattices (BLs) in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the…
We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local…
In the framework of the perturbation theory an expression suitable for calculation of the effective conductivity of 3-D inhomogeneous metals in uniform magnetic field $H$ is derived. For polycrystals of metals with closed Fermi surfaces in…
The paper gathers and unifies mechanical stability conditions for all symmetry classes of 3D and 2D materials under arbitrary load. The methodology is based on the spectral decomposition of the fourth-order stiffness tensors mapped to…
We analyze the electrostatic stability of insulating surfaces in the framework of the bulk modern theory of polarization. We show that heuristic arguments based on a fully ionic limit find formal justification at the microscopic level, even…
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying…
We present a first-principles study of a coherent relationship between the optimized geometry and conductance of a three-aluminum-atom wire during its elongation process. Our simulation employs the most definite model including…
This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.
This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part I, we formulate and motivate three stability problems: 1.…
In this article, we present an analysis of the stability of optical lattices. Starting with the study of an unstable optical lattice, we establish a necessary and sufficient condition for intrinsic phase stability, and discuss two practical…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Assemblies of circular inclusions with spiraling laminate structure inside them are studied, such as spirals with inner inclusions, spirals with shells, assemblies of "wheels" - structures from laminates with radially dependent volume…
We prove stability for a class of heterogeneous catalysis models in the $L_p$-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a…
Algebraic expressions are found for the effective conductivities of some infinite tessellations composed of conducting square, triangular, or hexagonal tiles. A tessellation is further characterized by the number N of different colors…
The existence and stability of solitons in Bose-Einstein condensates with attractive inter-atomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic…
The main objective of this paper is to study the regularity and stability for solutions to the conductivity problems with degenerate coefficients in the presence of two rigid conductors, as one conductor keeps motionless and another…