In this paper, a sufficient condition is obtained to ensure the stable recovery(ε≠ 0) or exact recovery(ε = 0) of all r-rank matrices X ∈ Rm×nfrom b = A(X) + z via nonconvex Schatten p-minimization for anyδ4...
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In this paper, a sufficient condition is obtained to ensure the stable recovery(ε≠ 0) or exact recovery(ε = 0) of all r-rank matrices X ∈ Rm×nfrom b = A(X) + z via nonconvex Schatten p-minimization for anyδ4r∈ [3～(1/2))2, 1). Moreover, we determine the range of parameter p with any given δ4r∈ [(3～(1/2))/22, 1). In fact, for any given δ4r∈ [3～(1/2))2, 1), p ∈(0, 2(1- δ4r)] suffices for the stable recovery or exact recovery of all r-rank matrices.
This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global we...
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This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method.
We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in...
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We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.
The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighte...
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The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author＇s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ〉1.
In the construction of nine point scheme, both vertex unknowns and cell-centered unknowns are introduced, and the vertex unknowns are usually eliminated by using the interpolation of neighboring cell-centered unknowns...
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In the construction of nine point scheme, both vertex unknowns and cell-centered unknowns are introduced, and the vertex unknowns are usually eliminated by using the interpolation of neighboring cell-centered unknowns, which often leads to lose accuracy. Instead of using interpolation, here we propose a different method of calculating the vertex unknowns of nine point scheme, which are solved independently on a new generated mesh. This new mesh is a Vorono? mesh based on the vertexes of primary mesh and some additional points on the interface. The advantage of this method is that it is particularly suitable for solving diffusion problems with discontinuous coefficients on highly distorted meshes, and it leads to a symmetric positive definite matrix. We prove that the method has first-order convergence on distorted meshes. Numerical experiments show that the method obtains nearly second-order accuracy on distorted meshes.
Understanding the evolution of irradiation-induced defects is of critical importance for the performance estimation of nuclear materials under ***,we systematically investigate the influence of He on the evolution of ...
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Understanding the evolution of irradiation-induced defects is of critical importance for the performance estimation of nuclear materials under ***,we systematically investigate the influence of He on the evolution of Frenkel pairs and collision cascades in tungsten(W)via using the object kinetic Monte Carlo(OKMC)*** findings suggest that the presence of He has significant effect on the evolution of irradiation-induced *** the one hand,the presence of He can facilitate the recombination of vacancies and self-interstitial atoms(SIAs)in *** can be attributed to the formation of immobile He-SIA complexes,which increases the annihilation probability of vacancies and *** the other hand,due to the high stability and low mobility of He-vacancy complexes,the growth of large vacancy clusters in W is kinetically suppressed by He ***,in comparison with the injection of collision cascades and He in sequential way at 1223 K,the average sizes of surviving vacancy clusters in W via simultaneous way are smaller,which is in good agreement with previous experimental *** results advocate that the impurity with low concentration has significant effect on the evolution of irradiation-induced defects in materials,and contributes to our understanding of W performance under irradiation.
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time peri...
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The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray_Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Pressure is an effective and clean way to modify the electronic structures of materials,cause structural phase transitions and even induce the emergence of ***,we predicted several new phases of the Zr XY family at hi...
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Pressure is an effective and clean way to modify the electronic structures of materials,cause structural phase transitions and even induce the emergence of ***,we predicted several new phases of the Zr XY family at high pressures using the crystal structures search method together with first-principle *** particular,the Zr Ge S compound undergoes an isosymmetric phase transition from P4/nmm-I to P4/nmm-II at approximately 82 *** band structures show that all the high-pressure phases are *** these new structures,P4/nmm-II Zr Ge S and P4/mmm Zr Ge Se can be quenched to ambient pressure with superconducting critical temperatures of approximately 8.1 K and 8.0 K,*** study provides a way to tune the structure,electronic properties,and superconducting behavior of topological materials through pressure.
The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a cons...
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The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a conservative spatial interpolation, the time integration methodology with the adapitve time increment and an adaptive computational region method. The advantage of AMR technique is exhibited by numerical examples, including the 1-D C-J detonation and the 2-D implosion ignited from a single point. Results show that AMR can promote the computational efficiency, keeping the accuracy in interesting regions.
Lagrangianmethods arewidely used inmany fields formulti-material compressible flow simulations such as in astrophysics and inertial confinement fusion(ICF),due to their distinguished advantage in capturing material in...
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Lagrangianmethods arewidely used inmany fields formulti-material compressible flow simulations such as in astrophysics and inertial confinement fusion(ICF),due to their distinguished advantage in capturing material interfaces *** some of these applications,multiple internal energy equations such as those for electron,ion and radiation are *** the past decades,several staggeredgrid based Lagrangian schemes have been developed which are designed to solve the internal energy equation *** schemes can be easily extended to solve problems with multiple internal energy *** such schemes are typically not conservative for the total ***,significant progress has been made in developing cell-centered Lagrangian schemes which have several good properties such as conservation for all the conserved variables and easiness for ***,these schemes are commonly designed to solve the Euler equations in the form of the total energy,therefore they cannot be directly applied to the solution of either the single internal energy equation or the multiple internal energy equations without significant *** modifications,if not designed carefully,may lead to the loss of some of the nice properties of the original schemes such as conservation of the total *** this paper,we establish an equivalency relationship between the cell-centered discretizations of the Euler equations in the forms of the total energy and of the internal *** a carefully designed modification in the implementation,the cell-centered Lagrangian scheme can be used to solve the compressible fluid flow with one or multiple internal energy equations and meanwhile it does not lose its total energy conservation *** advantage of this approach is that it can be easily applied to many existing large application codes which are based on the framework of solving multiple internal energy *** two dimensional numerical examp
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