We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error syste...
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We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.
In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optima...
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In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts： The first part is about integration of the state over the whole time interval, the second part refers to final-time state, and the third part is a regularization term about the control. We discretize the state and co-state by piecewise linear continuous functions, while the control is approximated by piecewise constant functions. Pointwise inequality function constraints on the control are considered, and optimal a L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...
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Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time ***, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
It becomes increasingly clear that non-uniform distribution of immiscible fluids in porous rock is particularly relevant to seismic wave dispersion. White proposed a patchy saturation model in 1975, in which spherical...
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It becomes increasingly clear that non-uniform distribution of immiscible fluids in porous rock is particularly relevant to seismic wave dispersion. White proposed a patchy saturation model in 1975, in which spherical gas pockets were located at the center of a liquid saturated cube. For an extremely light and compressible inner gas, the physical properties can be approximated by a vacuum with White＇s model. The model successfully analyzes the dispersion phenomena of a P-wave velocity in gas-water- saturated rocks. In the case of liquid pocket saturation, e.g., an oil-pocket surrounded by a water saturated host matrix, the light fluid-pocket assumption is doubtful, and few works have been reported in White＇s framework. In this work, Poisson＇s ratio, the bulk modulus, and the effective density of a dual-liquid saturated medium are formulated for the heterogeneous porous rocks containing liquid-pockets. The analysis of the difference between the newly derived bulk modulus and that of White＇s model shows that the effects of liquid-pocket saturation do not disappear unless the porosity approaches zero. The inner pocket fluid can no longer be ignored. The improvements of the P-wave velocity predictions are illustrated with two examples taken from experiments, i.e., the P-wave velocity in the sandstone saturated by oil and brine and the P-wave velocity for heavy oils and stones at different temperatures.
The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equati...
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The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.
Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. It is mainly considered as a powerful tool with high flexibility to approximate functions. This paper pro...
Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. It is mainly considered as a powerful tool with high flexibility to approximate functions. This paper proposes a generalized NURBS based approach to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains by using physics-informed neural networks (PINNs). Our approach is based on a posteriori error estimation in which the adjoint problem is solved for the error localization to formulate an error estimator within the framework of neural network. An efficient and easy to implement algorithm is developed to obtain a posteriori error estimate for multiple goal functionals by employing the dual-weighted residual approach, which is followed by the computation of both primal and adjoint solutions using the neural network. The present study shows that such a data-driven model based learning has superior approximation of quantities of interest even with relatively less training data. Moreover, we illustrate the versatility of activation functions in achieving better learning capabilities and improving convergence rates, especially at the early training stage, and also in increasing solutions accuracies. The novel algorithmic developments are substantiated with several numerical test examples. It has been demonstrated that deep neural networks have distinct advantages over shallow neural networks, and the techniques for enhancing convergence have also been reviewed.
This paper theoretically investigates the orbital magnetization of electron-doped （n-type） semiconductor het-erostructures and of hole-doped （p-type） bulk semiconductors, which are respectively described by a two-...
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This paper theoretically investigates the orbital magnetization of electron-doped （n-type） semiconductor het-erostructures and of hole-doped （p-type） bulk semiconductors, which are respectively described by a two-dimensional electron/hole Hamiltonian with both the included Rashba spin-orbit coupling and Zeeman splitting terms. It is the Zeeman splitting, rather than the Rashba spin-orbit coupling, that destroys the time-reversal symmetry of the semiconductor systems and results in nontrivial orbital magnetization. The results show that the magnitude of the orbital magnetization per hole and the Hall conductance in the p-type bulk semiconductors are about 10^-2-10^-1 effective Bohr magneton and 10^-1-1 e^2/h, respectively. However, the orbital magnetization per electron and the Hall conductance in the n-type semiconductor heterostructures are too small to be easily observed in experiment.
In terms of energy efficiency and computational speed, neuromorphic electronics based on nonvolatile memory devices are expected to be one of most promising hardware candidates for future artificial intelligence (AI)....
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In terms of energy efficiency and computational speed, neuromorphic electronics based on nonvolatile memory devices are expected to be one of most promising hardware candidates for future artificial intelligence (AI). However, catastrophic forgetting, networks rapidly overwriting previously learned weights when learning new tasks, remains a pivotal obstacle in either digital or analog AI chips for unleashing the true power of brainlike computing. To address catastrophic forgetting in the context of online memory storage, a complex synapse model (the Benna-Fusi model) was proposed recently [M. K. Benna and S. Fusi, Nat. Neurosci. 19, 1697 (2016)], the synaptic weight and internal variables of which evolve following diffusion dynamics. In this work, by designing a proton transistor with a series of charge-diffusion-controlled storage components, we have experimentally realized the Benna-Fusi artificial complex synapse. Memory consolidation from coupled storage components is revealed by both numerical simulations and experimental observations. Different memory timescales for the complex synapse are engineered by the diffusion length of charge carriers and the capacity and number of coupled storage components. The advantages of the demonstrated complex synapse for both memory capacity and memory consolidation are revealed by neural network simulations of face-familiarity detection. Our experimental realization of the complex synapse suggests a promising approach to enhance memory capacity and to enable continual learning.
We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of un...
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We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.
The reconstruction with minimized dispersion and controllable dissipation(MDCD) optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation.A low dispersion finite...
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The reconstruction with minimized dispersion and controllable dissipation(MDCD) optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation.A low dispersion finite volume scheme based on MDCD reconstruction is proposed which is capable of handling flow discontinuities and resolving a broad range of length *** the proposed scheme is formally second order accurate,the optimized dispersion and dissipation make it very accurate and robust so that the rich flow features encountered in practical engineering applications can be handled properly.A number of test cases are computed to verify the performances of the proposed scheme.
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