It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution ...
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It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.
By molecular dynamics simulations employing an embedded atom method potential, we have investigated structural transformations in single crystal A1 caused by uniaxial strain loading along the [001], [011] and [111] di...
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By molecular dynamics simulations employing an embedded atom method potential, we have investigated structural transformations in single crystal A1 caused by uniaxial strain loading along the [001], [011] and [111] directions. We find that the structural transition is strongly dependent on the crystal orientations. The entire structure phase transition only occurs when loading along the [001] direction, and the increased amplitude of temperature for [001] loading is evidently lower than that for other orientations. The morphology evolutions of the structural transition for [011] and [111] loadings are analysed in detail. The results indicate that only 20% of atoms transit to the hcp phase for [011] and [111] loadings, and the appearance of the hcp phase is due to the partial dislocation moving forward on {lll}fcc family. For [011] loading, the hcp phase grows to form laminar morphology in four planes, which belong to the {111}fcc family; while for [111] loading, the hcp phase grows into a laminar structure in three planes, which belong to the {111}fcc family except for the （111） plane. In addition, the phase transition is evaluated by using the radial distribution functions.
The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was ...
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The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.
We investigate the dynamics of two interacting electrons confined in a quantum dot molecule under the influence of cosine squared electric fields. The conditions for two-electron localization in the same quantum dot a...
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We investigate the dynamics of two interacting electrons confined in a quantum dot molecule under the influence of cosine squared electric fields. The conditions for two-electron localization in the same quantum dot are analytically derived within the frame of the Floquet formalism. The analytical results are compared to numerical results obtained from the solution of the time-dependent Schtdinger equation.
In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionalit...
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We formulate truncated singular value decompositions of entire convolutional neural networks. We demonstrate the computed left and right singular vectors are useful in identifying which images the convolutional neural...
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We report the determination of the Landé gJ factor and Zeeman coefficients for the ground-state of 171Yb+, relevant to microwave quantum frequency standards (QFSs). The gJ factor is obtained by using two independ...
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We report the determination of the Landé gJ factor and Zeeman coefficients for the ground-state of 171Yb+, relevant to microwave quantum frequency standards (QFSs). The gJ factor is obtained by using two independent methods, the multiconfiguration Dirac-Hartree-Fock and multireference configuration-interaction methods, yielding a consistent value of 2.002615(70). The first- and second-order Zeeman coefficients are determined as 14010.78(49)Hz/µT and 31.0869(22)mHz/µT2, respectively, based on the calculated gJ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the 171Yb+ microwave QFSs. The results reported in this work also offer potential for improved constraints on variations in fundamental constants through frequency comparisons and advancing trapped-ion quantum computers based on the ground-state hyperfine splitting of 171Yb+.
In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional *** interface may be arbitrary smooth *** is shown that the error estima...
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In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional *** interface may be arbitrary smooth *** is shown that the error estimates in L;-norm for the solution and the flux are O（h;|log h|）and O(h|log h|;),*** numerical experiments,the successive substitution iterative methods are used to solve the LDG *** results verify the efficiency and accuracy of the method.
A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically ge...
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A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.
Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain com...
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