Related papers: Interaction Residues and Localized Spectral Defect…
This paper investigates residue maps and their spanning properties for singular algebraic curves, with particular emphasis on three interconnected themes: the \emph{scheme--theoretic residue span}, the \emph{residue--balancing principle},…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescoping energy residuals" in particular. We prove new results…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
We investigate the localization transition for a simple model of interface which interacts with an inhomonegeous defect plane. The interface is modeled by the graph of a function $\phi: \mathbb Z^2 \to \mathbb Z$,and the disorder is given…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
We initiate the study of intersecting surface operators/defects in four-dimensional quantum field theories (QFTs). We characterize these defects by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom localized at a…
Robotic systems with redundant degrees of freedom can achieve the same task outcome using multiple configurations, resulting in solution sets that form manifolds in the configuration space. Existing approaches typically exploit such…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
Shape had been intuitively recognized to play a dominant role in determining the global motion patterns of bio-molecular assemblies. However, it is not clear exactly how shape determines the motion patterns. What about the local…
The non-Hermitian skin effect is fundamentally characterized by its sensitivity to boundary conditions, reflected in changes to the energy spectrum and boundary-localized eigenstates. Here, we demonstrate that a spatially inhomogeneous…
Using first principles, classical potentials, and elasticity theory, we investigated the structure of a semiconductor/semiconductor interface with a high lattice mismatch, SiC/Si(001). Among several tested possible configurations, a…
Non-topological defects such as grain boundaries abound in pattern forming systems, arising from local variations of pattern properties such as amplitude, wavelength, orientation, etc. We introduce the idea of treating such non-topological…
We present a projection-based numerical integration technique to deal with embedded interface in finite element (FE) framework. The element cut by an embedded interface is denoted as a cut cell. We recognize elemental matrices of a cut cell…
Applied work under interference typically models outcomes as functions of own treatment and a low-dimensional exposure mapping of others' treatments, even when that mapping may be misspecified. We ask what policy object such exposure-based…
In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation…
We study the intensity spatial correlation function of optical speckle patterns above a disordered dielectric medium in the multiple scattering regime. The intensity distributions are recorded by scanning near-field optical microscopy…
Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in…
Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…
To accurately analyze structures, soil-structure interaction effects must be taken into account. One approach is to create a complete finite element model of the full system wherein the soil is represented as a semi-infinite domain. This…