In this paper, the Crank-Nicolson (CN) difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative is studied. The existence of this difference solution is proved ...
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Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal prop...
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Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h ( q ) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h ( 2 ) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H ≈ 0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h ( 2 ) of MF-DFA on the time series, exponent λ of the exponential degree distribution and fractal dimension d B of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈 h ( 2 ) 〉 (from MF-DFA on time series) and 〈 d B 〉 of the converted HVGs for different energy, pressure and volume.
This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The appr...
In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos et al (2007 Proc. Nat. Acad. Sci. USA 104 7746). In this fractal network model, there is a parameter ...
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In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconformin...
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In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconforming methods and one conforming *** they produce eigenvalues which are smaller than their exact counterparts.
In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. ...
In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of a time variable and a negative power function of an α-stable random variable. The effect o...
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The ordered patterns formed bymicrophase-separated block copolymer systems demonstrate periodic symmetry,and all periodic structures belong to one of 230 space *** on this fact,a strategy of estimating the initial val...
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The ordered patterns formed bymicrophase-separated block copolymer systems demonstrate periodic symmetry,and all periodic structures belong to one of 230 space *** on this fact,a strategy of estimating the initial values of self-consistent field theory to discover ordered patterns of block copolymers is *** particular,the initial period of the computational box is estimated by the Landau-Brazovskii model as *** planting the strategy into the whole-space discrete method,several new metastable patterns are discovered in diblock copolymers.
By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in...
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By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in *** is due to one polynomial degree less in y direction for the first component of velocity,which is a Qk+1,k polynomial of x and *** this manuscript,we will show by supercloseness of the divergence free element that the order of convergence is truly k+1,for both velocity and *** special solutions(if the interpolation is also divergence-free),a two-order supercloseness is shown to *** tests are provided confirming the accuracy of the theory.
We investigate high-fidelity quantum driving in a nonlinear two-level system and find that nonlinear atomic interaction can break the speed limit of the linear model. We show that repulsive atomic interaction can decr...
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We investigate high-fidelity quantum driving in a nonlinear two-level system and find that nonlinear atomic interaction can break the speed limit of the linear model. We show that repulsive atomic interaction can decrease the minimal time requested for reaching target state even to zero, while attractive atomic interaction tends to increase the minimal time. There exists a critical attractive interaction beyond which the target state cannot be reached with high fidelity. Possible experimental observation of the nonlinear effects using a Bose-Einstein condensate in an accelerating optical lattice is discussed.
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