Related papers: Using wave packet decompositions to construct func…
We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet influenced by an environment containing a few discrete modes. We obtain two intrinsic energy scales…
We present a new sink particle algorithm developed for the Adaptive Mesh Refinement code RAMSES. Our main addition is the use of a clump finder to identify density peaks and their associated regions (the peak patches). This allows us to…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
Due to the emergence of embedded applications in image and video processing, communication and cryptography, improvement of pictorial information for better human perception like deblurring, denoising in several fields such as satellite…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for best approximation by spaces of shifts in…
Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based…
The use of ultrasonic guided waves to probe the materials/structures for damage continues to increase in popularity for non-destructive evaluation (NDE) and structural health monitoring (SHM). The use of high-frequency waves such as these…
Modern detector manufacturing allows spectral and polarimetric filters to be directly integrated on top of separate detector pixels. This enables the creation of CubeSat-sized spectro-polarimetric instruments that are not much larger than…
Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for partial differential equations (PDEs) work in general geometries, and can have exponential convergence properties for smooth solution…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
The decomposition of polynomials of one vector variable into irreducible modules for the orthogonal group is a crucial result in harmonic analysis which makes use of the Howe duality theorem and leads to the study of spherical harmonics.…
We discuss the design of ``wave packet systems'' that admit strong concentration properties in phase space. We make a connection between this problem and topics in signal processing related to the spectral behavior of spatial and…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on…
We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the…