In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with Dirichlet boundary *** revisit the scattering result below ground state i...
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In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with Dirichlet boundary *** revisit the scattering result below ground state in Killip-Visan-Zhang[The focusing cubic NLS on exterior domains in three ***,1,146-180(2016)]by utilizing the method of Dodson and Murphy[A new proof of scattering below the ground state for the 3d radial focusing cubic ***.,145,4859-4867(2017)]and the dispersive estimate in Ivanovici and Lebeau[Dispersion for the wave and the Schr?dinger equations outside strictly convex obstacles and ***.,355,774-779(2017)],which avoids using the concentration *** conquer the difficulty of the boundary in the focusing case by establishing a local smoothing effect of the *** on this effect and the interaction Morawetz estimates,we prove that the solution decays at a large time interval,which meets the scattering criterion.
Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming *** optical metasurfaces,for example,the localized modes of individual meta-units govern the wavefront shape o...
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Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming *** optical metasurfaces,for example,the localized modes of individual meta-units govern the wavefront shape over a broad bandwidth,while nonlocal lattice modes extended over many unit cells support high quality-factor ***,we experimentally demonstrate nonlocal dielectric metasurfaces in the near-infrared that offer both spatial and spectral control of light,realizing metalenses focusing light exclusively over a narrowband resonance while leaving off-resonant frequencies *** devices attain this functionality by supporting a quasi-bound state in the continuum encoded with a spatially varying geometric *** leverage this capability to experimentally realize a versatile platform for multispectral wavefront shaping where a stack of metasurfaces,each supporting multiple independently controlled quasi-bound states in the continuum,molds the optical wavefront distinctively at multiple wavelengths and yet stay transparent over the rest of the *** a platform is scalable to the visible for applications in augmented reality and transparent displays.
We consider the trajectory planning of a 6-Degree-of-Freedom (DOF) robot manipulator using computer algebra, with controlling the orientation of the end-effector. As a first step towards the objective, we present a so...
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This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given...
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This paper discusses the trajectory planning of a robot manipulator with computer algebra. In the operation of robot manipulators, it is important to make the trajectory of the end effector so that it does not collide...
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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.
We propose a method for solving the speech direction estimation problem by computer algebra. The method is based on the function approximation using the minimax polynomial. The minimax polynomial is obtained by an ite...
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The effect of ablation on the nonlinear spike growth of single-mode ablative Rayleigh–Taylor instability(RTI)is studied by two-dimensional numerical *** is shown that the ablation can reduce the quasi-constant veloci...
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The effect of ablation on the nonlinear spike growth of single-mode ablative Rayleigh–Taylor instability(RTI)is studied by two-dimensional numerical *** is shown that the ablation can reduce the quasi-constant velocity and significantly suppress the reacceleration of the spike in the nonlinear *** is also shown that the spike growth can affect the ablation-generated vorticity inside the bubble,which further affects the nonlinear bubble *** vorticity evolution is found to be correlated with the mixing width(i.e.,the sum of the bubble and spike growths)for a given wave number and ablation *** considering the effects of mass ablation and vorticity,an analytical model for the nonlinear bubble and spike growth of single-mode ablative RTI is developed in this *** is found that the nonlinear growth of the mixing width,induced by the single mode,is dominated by the bubble growth for small-scale ablative RTI,whereas it is dominated by the spike growth for classical RTI.
We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained o...
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We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.
The advancement of single-cell RNA-sequencing (scRNA-seq) technologies allow us to study the individual level cell-type-specific gene expression networks by direct inference of genes’ conditional independence structu...
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