The results of numerical simulations of random-force-driven Navier-Stokes turbulence designed to test predictions of the renormalization group theory of turbulence are presented. By specially choosing the random force...
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It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Nav...
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It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.
In some applications, the accuracy of the numerical solution of an elliptic problem needs to be increased only in certain parts of the domain. In this paper, local refinement is introduced for an overlapping additive ...
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In some applications, the accuracy of the numerical solution of an elliptic problem needs to be increased only in certain parts of the domain. In this paper, local refinement is introduced for an overlapping additive Schwarz algorithm for the p-version finite element method. Both uniform and variable degree refinements are considered. The resulting algorithm is highly parallel and scalable. In two and three dimensions, we prove an optimal bound for the condition number of the iteration operator under certain hypotheses on the refinement region. This bound is independent of the degree p, the number of subdomains N(r) and the mesh size H. In the general two dimensional case, we prove an almost optimal bound with polylogarithmic growth in p.
In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in with finite Hausdorff and fractal dimensions.
In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in with finite Hausdorff and fractal dimensions.
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function ty...
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.
In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） wi...
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In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.
Carbon sulfide cation(CS^+) plays a dominant role in some astrophysical atmosphere environments. In this work, the rovibrational transition lines are computed for the lowest three electronic states, in which the inter...
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Carbon sulfide cation(CS^+) plays a dominant role in some astrophysical atmosphere environments. In this work, the rovibrational transition lines are computed for the lowest three electronic states, in which the internally contracted multireference configuration interaction approach(MRCI) with Davison size-extensivity correction(+Q) is employed to calculate the potential curves and dipole moments, and then the vibrational energies and spectroscopic constants are extracted. The Frank–Condon factors are calculated for the bands of X^2^+Σ^+–A^2Π and X^2Σ^+–B^2Σ^+systems, and the band of X^2Σ^+–A^2Π is in good agreement with the available experimental results. Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated. The opacities of the CS^+ molecule are computed at different temperatures under the pressure of 100 atms. It is found that as temperature increases, the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.
Several formulae for the O + −O momentum transfer collision frequency are currently in use in aeronomical calculations. Recent experimental determinations of the collision frequency, from radar and optical observation...
Several formulae for the O + −O momentum transfer collision frequency are currently in use in aeronomical calculations. Recent experimental determinations of the collision frequency, from radar and optical observations of the ionosphere and thermosphere, are in disagreement. A mathematical model of the plasmasphere is used to investigate the effects on F -region behaviour of variations in the collision frequency. It is found that variations of the order of 30% from the Stubbe theoretical formula for the collision frequency are unlikely to have significant consequences. But the greater changes to the formula that have been suggested recently cause large departures in the density and height of the F 2-peak ionisation.
Quad-curl equations with Navier type boundary conditions are studied in this *** order reduced formulations equivalent to the model problems are presented,and finite element discretizations are *** convergence rates a...
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Quad-curl equations with Navier type boundary conditions are studied in this *** order reduced formulations equivalent to the model problems are presented,and finite element discretizations are *** convergence rates are proved.
Published experimental data on ion composition in the topside ionosphere are examined. For certain features (the light ion trough, the high-latitude trough, the high-latitude hole and the mid-latitude total ion concen...
Published experimental data on ion composition in the topside ionosphere are examined. For certain features (the light ion trough, the high-latitude trough, the high-latitude hole and the mid-latitude total ion concentration trough) it is pointed out that the number of major ions present may be 3 or more. Transport equations derived by Schunk and co-workers are extended to include the case of three major ions in the topside ionosphere. Specific calculations are made for the O + , H + and He + ions and the behaviour of the diffusion coefficients is discussed. From a model of the high-latitude ionization hole, described by Heelis et al. , representative concentration and temperature profiles are obtained. These profiles are used to demonstrate further the behaviour of the ion diffusion coefficients.
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