Related papers: Interaction Residues and Localized Spectral Defect…
Spectral properties of Toeplitz operators and their finite truncations have long been central in operator theory. In the finite dimensional, non-normal setting, the spectrum is notoriously unstable under perturbations. Random perturbations…
We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a…
Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical…
Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling…
We introduce a particle-based framework inspired by smoothed particle hydrodynamics (SPH) to simulate the dynamics of a continuous field of coupled phase oscillators. This methodology discretizes the spatial domain into particles and…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We…
Quasiparticle interference (QPI) in spectroscopic imaging scanning tunneling microscopy provides a powerful method to detect orbital band structures and orbital ordering patterns in transition metal oxides. We use the $T$-matrix formalism…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
We apply spatial dynamical-systems techniques to prove that certain spatiotemporal patterns in reversible reaction-diffusion equations undergo snaking bifurcations. That is, in a narrow region of parameter space, countably many branches of…
Methods for correcting residual energy errors of configuration interaction (CI) calculations of molecules and other electronic systems are discussed based on the assumption that the energy defect can be mapped onto atomic regions. The…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
The mechanism determining the band alignment of the amorphous/crystalline Si heterostructures is addressed with direct atomistic simulations of the interface performed using a hierarchical combination of various computational schemes…
This article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\R^3$ which is strongly coupled with a Berger plate equation acting only on a flat…
We consider the existence of localized modes corresponding to eigenvalues of the periodic Schr\"{o}dinger operator $-\partial_x^2+ V(x)$ with an interface. The interface is modeled by a jump either in the value or the derivative of $V(x)$…
This work is a numerical study of a transitional shock wave boundary layer interaction (SWBLI). The main goal is to improve our understanding of the well known low-frequency SWBLI unsteadiness and especially the suspected role of triadic…
When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…
The dislocation skin effect exhibits the capacity of topological defects to trap an extensive number of modes in two-dimensional non-Hermitian systems. Similar to the corresponding skin effects caused by system boundaries, this phenomenon…
The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schr\"odinger operators with a $\delta$-potential. These operators arise by replacing…
Heterostructures combining diverse physico-chemical properties are increasingly in demand for a wide range of applications in modern science and technology. However, despite their importance in materials science, accurately determining…