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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 $V(x)$…
It has been shown that a small discontinuity such as an enlargement or a hole on circular waveguides can produce trapped electromagnetic modes with frequencies slightly below the waveguide cutoff. The trapped modes due to multiple…
Disordered pinning models deal with the (de)localization tran- sition of a polymer in interaction with a heterogeneous interface. In this paper, we focus on two models where the inhomogeneities at the interface are not independent but given…
Excitations of disordered systems such as glasses are of fundamental and practical interest but computationally very expensive to solve. Here we introduce a technique for modeling these excitations in an infinite disordered medium with a…
We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T->0, the steady state is dominated by a single configuration…
We consider the resolvent on asymptotically Euclidean warped product manifolds in an appropriate 0-Gevrey class, with trapped sets consisting of only finitely many components. We prove that the high-frequency resolvent is either bounded by…
We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the…
We consider the problem of fully unsupervised learning of grammatical (part-of-speech) categories from unlabeled text. The standard maximum-likelihood hidden Markov model for this task performs poorly, because of its weak inductive bias and…
Motivated by the novel electronic behaviors seen in transition metal oxides, we look for physical insight into disordered, strongly-correlated systems by exploring the atomic limit. In recent work, the atomic limit has provided a useful…
Microscopic description of Raman spectra in nanopowders of nonpolar crystals is accomplished by developing the theory of disorder-induced broadening of optical vibrational eigenmodes. Analytical treatment of this problem is performed, and…
Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their…
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…
The density of states of one-dimensional disordered electron systems with long range Coulomb interaction is studied in the weak pinning limit. The density of states is found to follow a power law with an exponent determined by localization…
Actuating the acoustic resonance modes of a microfluidic device containing suspended particles (e.g., cells) allows for the manipulation of their individual positions. In this work, we investigate how the number of resonance modes $M$…
We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We…
The main limitation in order to exploit spin torque nano-oscillators (STNOs) in various potential applications is their large phase noise. In this work, we demonstrate its efficient reduction by a highly reconfigurable, compact,…
Recent Vision-based Large Language Models~(VisionLLMs) for autonomous driving have seen rapid advancements. However, such promotion is extremely dependent on large-scale high-quality annotated data, which is costly and labor-intensive. To…
We propose a lattice model to study the dynamics of a driven interface in a medium with random pinning forces. For driving forces F smaller than a threshold force F_c the whole interface gets pinned. The depinning transition can be…
We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of…
A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and…