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Non-Hermitian systems exploiting the synergy between gain and loss have recently become the focus of interest to discover novel physical phenomena. The spatial symmetry breaking in such systems allows tailoring the wave propagation at will.…
The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian…
Recently many methods have been proposed to create the vector fields, due to the academic interest and a variety of attractive applications such as for particle acceleration, optical trapping, particle manipulation, and fluorescence…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
We introduce a novel method for directional-field design on meshes, enabling users to specify singularities at any location on a mesh. Our method uses a piecewise power-linear representation for phase and scale, offering precise control…
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
Torse-forming vector fields are generalizations of some important vector fields. In this paper, we present some techniques to transform a proper torse-forming vector field into its special cases. Concrete examples are given.
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
We have recently developed an algorithm for vector field visualization with oriented streamlines, able to depict the flow directions everywhere in a dense vector field and the sense of the local orientations. The algorithm has useful…
The Doppler effect of light was implemented by interference with a reference wave to infer linear velocities in early manifestations, and more recently lateral and angular velocities with scalar phase structured light. A consequence of the…
We propose a general design strategy based on genetic optimization to realize asymmetric reflectivity in periodic and non-periodic planar structures containing dielectric and gain-loss layers. By means of an optimization algorithm, it is…
We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator…
We present a novel diffusion-based framework for synthesizing 2D vector fields from sparse, coherent inputs (i.e., streamlines) while maintaining physical plausibility. Our method employs a conditional denoising diffusion probabilistic…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
This paper extends the capabilities of the harmonic potential field (HPF) approach to planning. The extension covers the situation where the workspace of a robot cannot be segmented into geometrical subregions where each region has an…
This paper introduces a novel method to extend the Helmholtz Decomposition to n-dimensional sufficiently smooth and fast decaying vector fields. The rotation is described by a superposition of n(n-1)/2 rotations within the coordinate…
A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential. The transition is related to depinning of…
We propose and demonstrate a novel method for generating propagation-invariant spatially-stationary fields in a controllable manner. Our method relies on producing incoherent mixtures of plane waves using planar primary sources that are…
In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(\alpha,\beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the…
Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is known about a local slowdown of the twist; we show…