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By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear…
Electronic metadevices leveraging sub-wavelength metallic features have shown great potential for high-frequency switching. Theoretical analysis based on a one-dimensional (1D) model indicates that reducing the size of subwavelength…
Intuition dictates that a very long, very thin cavity (e.g., a fiber optic cable) could perhaps be modeled as an approximately one dimensional system. In this paper we rigorously explore the validity of such intuition from the perspective…
We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultra-cold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the…
In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…
We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be expressed as diagonal system with a perturbation which is small enough. Moreover we show that the diagonal terms are contained in…
In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of traveling-wave solutions…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane…
The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy…
The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe non-periodic structured waveguides. It was shown that for the studied…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points.…
Low-loss optical communication requires light sources at 1.5um wavelengths. Experiments showed without much theoretical guidance that InAs/GaAs quantum dots (QDs) may be tuned to such wavelengths by adjusting the In fraction in an…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
We present a continuum formulation of a (d+1)-dimensional directed line interacting with sparse potentials (i.e. d-dimensional potentials defined only at discrete longitudinal locations.) An iterative solution for the partition function is…
In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…