Related papers: Topological interface modes in systems with dampin…
This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on…
This paper studies wave localisation in chains of finitely many resonators. There is an extensive theory predicting the existence of localised modes induced by defects in infinitely periodic systems. This work extends these principles to…
We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We…
We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the…
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 $V(x)$…
Let $N$ local decision makers in a sensor network communicate with their neighbors to reach a decision \emph{consensus}. Communication is local, among neighboring sensors only, through noiseless or noisy links. We study the design of the…
In this paper, we study the indirect stability of Timoshenko system with local or global Kelvin-Voigt damping, under fully Dirichlet or mixed boundary conditions. Unlike the results of H. L. Zhao, K. S. Liu, and C. G. Zhang and of X. Tian…
Topological phononic crystals (PCs) are periodic artificial structures which can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies…
Interfaces impede heat flow in micro/nanostructured systems. Conventional theories for interfacial thermal transport were derived based on bulk phonon properties of the materials making up the interface without explicitly considering the…
Chiral edge states can transmit energy along imperfect interfaces in a topologically robust and unidirectional manner when protected by bulk-boundary correspondence. However, in continuum systems, the number of states at an interface can…
Preserving the topology from being inferred by external adversaries has become a paramount security issue for network systems (NSs), and adding random noises to the nodal states provides a promising way. Nevertheless, recent works have…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of…
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…
Hypothesis: Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…
We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and…
We present a microscopic theory of nonlinear damping and dephasing of low-frequency eigenmodes in nano- and micro-mechanical systems. The mechanism of the both effects is scattering of thermally excited vibrational modes off the considered…
Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states…