Theoretically describing feature learning in neural networks is crucial for understanding their expressive power and inductive biases, motivating various approaches. Some approaches describe network behavior after tra...
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Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purp...
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In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly s...
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In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly singular kernel arising in the theory of linear viscoelas-ticity. The novel OSC method is used for the spatial discretization, and ADI Crank-Nicolson-type method combined with the second order fractional quadrature rule are considered for thetemporal component. The stability of proposed scheme is rigourously established, and nearlyoptimal order error estimate is also derived. Numerical experiments are conducted to supportthe predicted convergence rates and also exhibit expected super-convergence phenomena.
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 this paper, we investigate the dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules through a stimulated Raman adiabatic passage aided by Feshbach resonance. We ana...
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In this paper, we investigate the dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules through a stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions where the dynamical instability appears and find that such instability in the Bose-Fermi mixture system is caused not only by bosonic interparticle interactions but also by Pauli blocking terms, which is different from the scenario of a pure bosonic system where instability is induced by nonlinear interparticle collisions. Taking a 40K-87Rb mixture as an example, we give the unstable regions numerically.
Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipol...
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Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.
We systematically investigate the influence of atomic potentials on the above-threshold ionization （ATI） spectra in one-dimensional （1D） cases and compare them with the three-dimensional （3D） case by numerically...
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We systematically investigate the influence of atomic potentials on the above-threshold ionization （ATI） spectra in one-dimensional （1D） cases and compare them with the three-dimensional （3D） case by numerically solving the time-dependent Schrrdinger equation. It is found that the direct ionization plateau and the rescattering plateau of the ATI spectrum in the 3D case can be well reproduced by the 1D ATI spectra calculated from the supersolid-core potential and the soft-core potential, respectively. By analyzing the factors that affect the yield of the ATI spectrum, we propose a modified-potential with which we can reproduce the overall 3D ATI spectrum. In addition, the influence of the incident laser intensities and frequencies on the ATI spectra calculated from the proposed modified potential is studied.
Based on the relativistic multichannel theory, a non-isolated resonance approach has been developed to calculate the cross sections of dielectronic recombination on He+ for △n=1 and 2 transitions. A first order appro...
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Based on the relativistic multichannel theory, a non-isolated resonance approach has been developed to calculate the cross sections of dielectronic recombination on He+ for △n=1 and 2 transitions. A first order approximation is adopted for the radiative process. The convolved cross sections for the n≤3 states in both transitions are in good agreement with those of the observations. It is shown that the l-dependence of the field ionization and the radiative decay during the time-of-flight affect significantly the measurement of the cross sections near the initial state of the field ionization.
It is presented in this paper that the new design and its analysis of finite difference domain decomposition algorithms for the two-dimensional heat equation, and the numerical results have shown the stability and acc...
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It is presented in this paper that the new design and its analysis of finite difference domain decomposition algorithms for the two-dimensional heat equation, and the numerical results have shown the stability and accuracy of the algorithms, where SauFyev asymmetric schemes have been used at the interface points. The Algorithm II in this paper has further extended those developed by Dawson and the others, Zhang and Shen.
This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than...
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This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].
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