We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equ...
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We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.
Conventional dialysate recycling methods struggle to effectively remove creatinine, urea, and other minor contaminants. This study explores mixed matrix membrane adsorbers (MMMAs) as a novel approach to address these ...
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Making informed economic decisions based on agricultural data is challenging without proper crop management. Data has become the single most important part of modern farming, and its rapid evolution is a major contrib...
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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 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.
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.
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonhar...
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In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see (3]). In the case of an orthonormal basis, our estimate reduces to Kadec' optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian [4] for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter) actually holds for a large class of wavelet Riesz bases.
The novel constructive EHands protocol defines a universal set of quantum operations for multivariable polynomial transformations on quantum processors by introducing four basic subcircuits—multiplication, addition, ...
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In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional *** interface may be arbitrary smooth *** is shown that the error estima...
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In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional *** interface may be arbitrary smooth *** is shown that the error estimates in L;-norm for the solution and the flux are O(h;|log h|)and O(h|log h|;),*** numerical experiments,the successive substitution iterative methods are used to solve the LDG *** results verify the efficiency and accuracy of the method.
The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecu...
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In this paper,a statistical second-order twoscale(SSOTS) method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous *** this kind of composite material,the random d...
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In this paper,a statistical second-order twoscale(SSOTS) method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous *** this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all ***,the *** for the microscopic configuration of the statistically inhomogeneous materials is ***,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and *** then the algorithm procedure corresponding to the SSOTS method is brought *** numerical results obtained by using the SSOTS algorithm are compared with those by classical *** addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled *** demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very *** results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.
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