Two identical chaotic systems of conservative flow are shown to be synchronous by applying periodic pubes at a regular time *** idea is illustrated with a numerical *** is robust against external noise.
Two identical chaotic systems of conservative flow are shown to be synchronous by applying periodic pubes at a regular time *** idea is illustrated with a numerical *** is robust against external noise.
There have been great efforts on the development of higher-order numerical schemes for compressible Euler equations in recent *** traditional test cases proposed thirty years ago mostly target on the strong shock inte...
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There have been great efforts on the development of higher-order numerical schemes for compressible Euler equations in recent *** traditional test cases proposed thirty years ago mostly target on the strong shock interactions,which may not be adequate enough for evaluating the performance of current higher-order *** order to set up a higher standard for the development of new algorithms,in this paper we present a few benchmark cases with severe and complicated wave structures and interactions,which can be used to clearly distinguish different kinds of higher-order *** tests are selected so that the numerical settings are very simple and any higher order scheme can be straightforwardly applied to these *** examples include highly oscillatory solutions and the large density ratio problem in one dimensional *** two dimensions,the cases include hurricane-like solutions;interactions of planar contact discontinuities with asymptotic large Mach number (the composite of entropy wave and vortex sheets);interaction of planar rarefaction waves with transition from continuous flows to the presence of shocks;and other types of interactions of two-dimensional planar *** get good performance on all these cases may push algorithm developer to seek for new methodology in the design of higher-order schemes,and improve the robustness and accuracy of higher-order schemes to a new level of *** order to give reference solutions,the fourth-order gas-kinetic scheme (GKS) will be used to all these benchmark cases,even though the GKS solutions may not be very accurate in some *** main purpose of this paper is to recommend other CFD researchers to try these cases as well,and promote further development of higher-order schemes.
Employing both the Dirac R-matrix and the relativistic distorted wave with independent process and isolated reso- nance approaches, we report resonance enhanced electron impact excitation data （specifically, effectiv...
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Employing both the Dirac R-matrix and the relativistic distorted wave with independent process and isolated reso- nance approaches, we report resonance enhanced electron impact excitation data （specifically, effective collision strengths） among the lowest 41 levels from the n = 3 configurations of Cu XV. The results show that the latter approach can obtain resonance contributions reasonably well for most excitations of Cu XV, though a comparison between the two approaches shows that the close-coupling effects are truly significant for rather weak excitations, especially for two-electron excitations from the 3s3p4 to 3s23p23d configuration. Resonance contributions are significant （more than two orders of magnitude） for many excitations and dramatically influence the line intensity ratios associated with density diagnostics.
The X^3Σg^-,A^'3△u,A^3Σ^u+,1^3Πg,and B^3Σu^-electronic states of oxygen molecule(O2)are calculated by the multiconfiguration self-consisted filed(MRCI)+Q method with the scalar relativistic correction and cor...
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The X^3Σg^-,A^'3△u,A^3Σ^u+,1^3Πg,and B^3Σu^-electronic states of oxygen molecule(O2)are calculated by the multiconfiguration self-consisted filed(MRCI)+Q method with the scalar relativistic correction and core-valence correlation *** obtained spectroscopic constants of the low-lying bound states are in excellent agreement with *** on the accurately calculated structure parameters,the opacities of the oxygen molecule at the temperatures of 1000 K,2000 K,2500 K,and 5000 K under a pressure of 100 atm(1 atm=1.01325×10^5 Pa)and the partition functions between 10 K and 10^4 K are *** is found that with the increase of temperature,the opacities for transitions in a long wavelength range are enlarged because of the larger population on excited electronic states at the higher temperatures.
The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical...
The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.
Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order s...
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Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical *** complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<*** results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208
The magnetisation of heavy holes in III-V semiconductor quantum wells with Rashba spin-orbit coupling （SOC） in an external perpendicular magnetic field is studied theoretically. We concentrate on the effects on the ...
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The magnetisation of heavy holes in III-V semiconductor quantum wells with Rashba spin-orbit coupling （SOC） in an external perpendicular magnetic field is studied theoretically. We concentrate on the effects on the magnetisation induced by the system boundary, the l^ashba SOC and the temperature. It is found that the sawtooth-like de Haas- van Alphen （dHvA） oscillations of the magnetisation will change dramatically in the presence of such three factors. Especially, the effects of the edge states and Rashba SOC on the magnetisation are more evident when the magnetic field is smaller. The oscillation center will shift when the boundary effect is considered and the Rashba SOC will bring beating patterns to the dHvA oscillations. These effects on the dHvA oscillations are preferably observed at low temperatures. With increasing temperature, the dHvA oscillations turn to be blurred and eventually disappear.
In this paper, we consider the solution of the standard linear programming [Lt＇）. A remarkable result in LP claims that all optimal solutions form an optimal face of the underlying polyhedron. In practice, many real...
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In this paper, we consider the solution of the standard linear programming [Lt＇）. A remarkable result in LP claims that all optimal solutions form an optimal face of the underlying polyhedron. In practice, many real-world problems have infinitely many optimal solutions and pursuing the optimal face, not just an optimal vertex, is quite desirable. The face algorithm proposed by Pan [19] targets at the optimal face by iterating from face to face, along an orthogonal projection of the negative objective gradient onto a relevant null space. The algorithm exhibits a favorable numerical performance by comparing the simplex method. In this paper, we further investigate the face algorithm by proposing an improved implementation. In exact arithmetic computation, the new algorithm generates the same sequence as Pan＇s face algorithm, but uses less computational costs per iteration, and enjoys favorable properties for sparse problems.
We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ ...
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We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.
1 Introduction We want to investigate the following boundary value problem:where m>1, n>1, p≥1 and m>p. As for a, the following properties will be assumed: (A.1) a(r)∈C^1 ([0, ∞)) and a(r)&...
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1 Introduction We want to investigate the following boundary value problem:where m>1, n>1, p≥1 and m>p. As for a, the following properties will be assumed: (A.1) a(r)∈C^1 ([0, ∞)) and a(r)>0 for any r∈(0, ∞); (A.2) there exists α>0 such that (r-α)a(r)≥0 for any r∈[0, ∞). The initial value problem corresponding to (1.1) is the following Cauchy problem:
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