We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline. The statistics are based on consistency constraints that arise within the clustered structure of the g...
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MSC Codes 35Q30, 35Q35, 35Q92We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of Rd, d = 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the ...
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We consider a Gatenby–Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in di...
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This short paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed methodology facilitates the app...
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Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ...
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Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ˜V(k), which can be obtained experimentally from scattering techniques, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability S(t) and effective dynamic dielectric constant ϵe for electromagnetic wave propagation. Moreover, χ˜V(k) has been employed to derive sharp bounds on the fluid permeability k. Given the importance of χ˜V(k), we present here an efficient Fourier-space based computational framework to construct three-dimensional (3D) statistically isotropic two-phase heterogeneous materials corresponding to targeted spectral density functions. In particular, we employ a variety of analytical χ˜V(k) functions that satisfy all known necessary conditions to construct disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions . We show that by tuning the correlations in the system across length scales via the targeted functions, one can generate a rich spectrum of distinct structures within each of the above classes of materials. Importantly, we present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by a power-law autocovariance function χV (r) and contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability S(t) and estimate the fluid permeability k associated with all of the constructed materials directly from the corresponding χ˜V(k) functions. Although it is well established that the long-time asymptotic scaling behavior of S(t) only depends on the functional form of χ˜V(k), with the stealthy hyperuniform and antihyperuniform media respectively
This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admi...
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The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies and distort the resonant-mode e...
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Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for ...
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ISBN:
(数字)9783982633619
Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for acceleration, providing robust GPU-hosted implementations of special functions, such as the modified Bessel function, is crucial for performance. Existing implementations of the modified Bessel function of the second kind rely on CPUs and have limited coverage of the full range of values needed in some applications. In this work, we present a robust implementation of the modified Bessel function of the second kind on GPUs, eliminating the dependence on the CPU host. We cover a range of values commonly used in real applications, providing high accuracy compared to common libraries like the GNU Scientific Library (GSL) when referenced to Mathematica as the authority. Our GPU-accelerated approach also demonstrates a 2.68X performance improvement using a single A100 GPU compared to the GSL on 40-core Intel Cascade Lake CPUs. Our implementation is integrated into ExaGeoStat, the HPC framework for Gaussian process modeling, where the modified Bessel function of the second kind is required by the Matérn covariance function in generating covariance matrices. We accelerate the matrix generation process in ExaGeoStat by up to 12.62X with four A100 GPUs while maintaining almost the same accuracy for modeling and prediction operations using synthetic and real datasets.
An optimal control problem in the space of probability measures, and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value func...
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Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to frac...
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Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ̃V(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ̃V(k)=0 for k∈Ω, i.e., complete suppression of scattering in an “exclusion” region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions
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