We study the restriction estimates in a class of conical singular space X = C(Y) = (0, ∞)r × Y with the metric g = dr2 + r2h, where the cross section Y is a compact (n − 1)-dimensional closed Riemannian manifold...
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The local number variance σ2(R) associated with a spherical sampling window of radius R enables a classification of many-particle systems in d-dimensional Euclidean space Rd according to the degree to which large-sca...
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The local number variance σ2(R) associated with a spherical sampling window of radius R enables a classification of many-particle systems in d-dimensional Euclidean space Rd according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To more completely characterize density fluctuations, we carry out an extensive study of higher-order moments or cumulants, including the skewness γ1(R), excess kurtosis γ2(R) and the corresponding probability distribution function P[N(R)] of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. To carry out this comprehensive program, we derive new theoretical results that apply to general point processes and conduct high-precision numerical studies. Specifically, we derive explicit closed-form integral expressions for γ1(R) and γ2(R) that encode structural information up to three-body and four-body correlation functions, respectively. We also derive rigorous bounds on γ1(R), γ2(R) and P[N(R)] for general point processes and corresponding exact results for general packings of identical spheres. High-quality simulation data for γ1(R), γ2(R) and P[N(R)] are generated for each model. We also ascertain the proximity of P[N(R)] to the normal distribution via a novel Gaussian "distance" metric l2(R). Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes such that γ1(R) ∼ l2(R) ∼ R-(d+1)/2 and γ2(R) ∼ R-(d+1) for large R. The convergence to a CLT is slower for standard nonhyperuniform models and slowest for the "antihyperuniform" model studied here. We prove that one-dimensional hyperuniform systems of class I or any d-dimensional lattice cannot obey a CLT. Remarkably, we discovered that the gamma distribution provides a good approximation to P[N(R)] for
Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a...
Analyzing atomically resolved images is a time-consuming process requiring solid experience and substantial human intervention. In addition, the acquired images contain a large amount of information such as crystal st...
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A common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme [J. Chem. Phys. 88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Be...
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We study finite-size effects on the convergence time in a continuous-opinion dynamics model. In the model, each individual's opinion is represented by a real number on a finite interval, e.g., [0;1], and a uniform...
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The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-fie...
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Moist convection is a physical process where the latent heat released by condensation acts as a buoyancy source that can enhance or even trigger an overturning convective instability. Since the saturation temperature ...
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The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural supp...
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In a systematic study of shock wave propagating in crystalline polyethylenes using molecular dynamics method and the electron force field (eFF) potential, we show that microscopic structure of shock front is significa...
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In a systematic study of shock wave propagating in crystalline polyethylenes using molecular dynamics method and the electron force field (eFF) potential, we show that microscopic structure of shock front is significantly affected by the anisotropy of long carbon chain and the bond breaking and recombination dynamics. However, macroscopic properties measured in Hugoniot experiments, such as compression ratio and shock velocity, are not sensitive to carbon chain anisotropy and bond dynamics. Our work also display that hydrogen molecules are formed when the piston speed is in the region between 10 km/s and 30 km/s. However, carbon-hydrogen pair distribution function does not display an indication of carbon-hydrogen phase segregation.
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