This paper is concemed with numerical method for a two-dimensional timedependent cubic nonlinear Schr(o)dinger *** approximations are obtained by the Galerkin finite element method in space in conjunction with the bac...
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This paper is concemed with numerical method for a two-dimensional timedependent cubic nonlinear Schr(o)dinger *** approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time,*** prove optimal L2 error estimates for two fully discrete schemes by using elliptic projection ***,a numerical example is provided to verify our theoretical results.
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-cons...
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This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These ...
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We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation. The main idea is to replace the gradient operator ∇ on linear finite element space by G(∇) in the w...
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The chirality-induced spin selectivity (CISS), demonstrated in diverse chiral molecules by numerous experimental and theoretical groups, has been attracting extensive and ongoing interest in recent years. As the secon...
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The chirality-induced spin selectivity (CISS), demonstrated in diverse chiral molecules by numerous experimental and theoretical groups, has been attracting extensive and ongoing interest in recent years. As the secondary structure of DNA, the charge transfer along DNA hairpins has been widely studied for more than two decades, finding that DNA hairpins exhibit spin-related effects as reported in recent experiments. Here, we propose a setup to demonstrate directly the CISS effect in DNA hairpins contacted by two nonmagnetic leads at both ends of the stem. Our results indicate that DNA hairpins present a pronounced CISS effect and the spin polarization could be enhanced by using conducting molecules as the loop. In particular, DNA hairpins exhibit several intriguing features. First, the local spin currents can flow circularly and assemble into a number of vortex clusters when the electron energy locates in the left/right electronic band of the stem. The chirality of vortex clusters in each band is the same and will be reversed by switching the electron energy from the left band to the right one, inducing the sign reversal of the spin polarization. Interestingly, the local spin currents can be greater than the corresponding spin component of the source-drain current. Second, both the conductance and the spin polarization can increase with molecular length as well as dephasing strength, contrary to the physical intuition that the transmission ability of molecular wires should be poorer when suffering from stronger scattering. Third, we unveil the optimal contact configuration of efficient electron transport and that of the CISS effect, which are distinct from each other and can be controlled by dephasing strength. The experimental realization of these results is discussed and the underlying physical mechanism is illustrated.
In this paper, by modifying the smoothness factor of the third-order CWENO scheme, we present the two-parameter CWENO-NZ3 scheme to improve accuracy at critical points. We selected some classical examples for numerica...
In this paper, by modifying the smoothness factor of the third-order CWENO scheme, we present the two-parameter CWENO-NZ3 scheme to improve accuracy at critical points. We selected some classical examples for numerical simulation, such as one-dimensional Sod shock tube, Shock-entropy wave interaction, Riemann problem with strong discontinuity and Rayleigh-Taylor instability problem. Numerically comparing with the classical third-order CWENO schemes, it is found that the improved schemes not only improve accuracy and resolution at the extreme points, but also reduce dissipation.
In this paper, an efficient and high-order accuracy finite difference method is proposed for solving multidimensional nonlinear Burgers' equation. The third-order three stage Runge-Kutta total variation diminishin...
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Fractal and multifractal properties of various systems have been studied extensively. In this paper, first, the multivariate multifractal detrend cross-correlation analysis (MMXDFA) is proposed to investigate the mult...
Fractal and multifractal properties of various systems have been studied extensively. In this paper, first, the multivariate multifractal detrend cross-correlation analysis (MMXDFA) is proposed to investigate the multifractal features in multivariate time series. MMXDFA may produce oscillations in the fluctuation function and spurious cross correlations. In order to overcome these problems, we then propose the multivariate multifractal temporally weighted detrended cross-correlation analysis (MMTWXDFA). In relation to the multivariate detrended cross-correlation analysis and multifractal temporally weighted detrended cross-correlation analysis, an innovation of MMTWXDFA is the application of the signed Manhattan distance to calculate the local detrended covariance function. To evaluate the performance of the MMXDFA and MMTWXDFA methods, we apply them on some artificially generated multivariate series. Several numerical tests demonstrate that both methods can identify their fractality, but MMTWXDFA can detect long-range cross correlations and simultaneously quantify the levels of cross correlation between two multivariate series more accurately.
Balancing domain decomposition by constraints (BDDC) algorithms with adaptive primal constraints are developed in a concise variational framework for the weighted plane wave least-squares (PWLS) discritization of Helm...
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