Deep-Learning-based Variational Monte Carlo (DL-VMC) has recently emerged as a highly accurate approach for finding approximate solutions to the many-electron Schrödinger equation. Despite its favorable scaling w...
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A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained conformational dynamics. Constrained by the fluctuation-dissipa...
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The presence of large amounts of data in hyperspectral images makes it very difficult to perform further tractable analyses. Here, we present a method of analyzing real hyperspectral data by dimensionality reduction u...
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The presence of large amounts of data in hyperspectral images makes it very difficult to perform further tractable analyses. Here, we present a method of analyzing real hyperspectral data by dimensionality reduction using diffusion maps. Diffusion maps interpret the eigenfunctions of Markov matrices as a system of coordinates on the original data set in order to obtain an efficient representation of data geometric descriptions. A neural network clustering theory, Fuzzy ART, is further applied to the reduced data to form clusters of the potential minerals. Experimental results on a subset of hyperspectral core imager data show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals in core samples.
Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we...
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This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which have been proposed to describe the dynamics of a variety of large s...
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In heavy-fermion compounds, the dual character of f electrons underlies their rich and often exotic properties like fragile heavy quasipartilces, variety of magnetic orders and unconventional superconductivity. 5f-ele...
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This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear s...
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The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the me...
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The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much l
A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-ord...
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