We prove that n-dimensional radial symmetric Landau-Lifshitz equation possesses at least two classes of global smooth solutions with suitable initial-boundary conditions.
We prove that n-dimensional radial symmetric Landau-Lifshitz equation possesses at least two classes of global smooth solutions with suitable initial-boundary conditions.
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell avera...
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example.
Multidimensional tunneling appears in many problems at nano *** high dimensionality of the potential energy surface(*** degrees of freedom)poses a great challenge in both theoretical and numerical description of *** s...
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Multidimensional tunneling appears in many problems at nano *** high dimensionality of the potential energy surface(*** degrees of freedom)poses a great challenge in both theoretical and numerical description of *** simulation based on Schrodinger equation is often prohibitively *** propose an accurate,efficient,robust and easy-to-implement numerical method to calculate the ground state tunneling splitting based on imaginary-time path integral(‘instanton’formulation).The method is genuinely multi-dimensional and free from any additional ad hoc assumptions on potential energy *** enables us to calculate the effects of all coupling modes on the tunneling degree of freedom without *** also review in this paper some theoretical background and survey some recent work from other groups in calculating multidimensional quantum tunneling effects in chemical reactions.
Over the past decades, our understanding of thermal transport in amorphous materials has predominantly relied on the inherently harmonic Allen-Feldman theory, which has been found to be insufficient. In this study, th...
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Over the past decades, our understanding of thermal transport in amorphous materials has predominantly relied on the inherently harmonic Allen-Feldman theory, which has been found to be insufficient. In this study, the Wigner transport formalism is adopted to explicitly account for anharmonicity. In studying the thermal transport in amorphous silicon, the results highlight that amorphous materials are not generally computationally equivalent to crystals with disordered primitive cells. A method that leverages the properties of the two-mode terms in the Wigner transport formalism is proposed to predict the bulk thermal conductivity of amorphous materials using finite-size models. In doing so, the need for mode classification schemes required in the Allen-Feldman theory is eliminated, and similarities are discovered between the two-mode terms and the carriers commonly used to describe thermal transport in amorphous materials, i.e., propagons, diffusons, and locons. Two competing trends are identified that shed light on the recently discovered anomalous decrease in the high-temperature thermal conductivity in some amorphous materials.
There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-delta commutation rel...
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There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-delta commutation relation in the classical nonholonomic mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions in terms of variation calculus.
We improve previous results on the asymptotic behavior and the expected value of the joint linear complexity of random multisequences over finite *** results are of interest for word-based stream ciphers in cryptology.
We improve previous results on the asymptotic behavior and the expected value of the joint linear complexity of random multisequences over finite *** results are of interest for word-based stream ciphers in cryptology.
We show that certain mixed displacement/traction problems (including live pressure tractions) of nonlinear elastostatics that are solved by a homogeneous deformation, admit no other classical equilibrium solution unde...
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Photodissociation cross sections of SiH+ have been explored within the uncoupled theoretical framework, notably in the work of Stancil et al. [Astrophys. J. 486, 574 (1997)]. However, in the SiH+ system, there are sig...
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Photodissociation cross sections of SiH+ have been explored within the uncoupled theoretical framework, notably in the work of Stancil et al. [Astrophys. J. 486, 574 (1997)]. However, in the SiH+ system, there are significant nonadiabatic interactions between the 31Π and 41Π states, which substantially affect the photodissociation process, particularly in the region between the Lyman α line and the Lyman limit. These nonadiabatic couplings give rise to numerous Feshbach resonances, significantly altering the final photodissociation cross sections. The present study highlights the critical importance of incorporating nonadiabatic electronic couplings to achieve accurate cross-section calculations. The results substantially enrich the data set on small molecular structures and spectra in interstellar clouds, providing essential theoretical support for future experimental investigations and for the modeling and analysis of stellar spectra. Additionally, this work offers key insights into the underlying physical mechanisms by which Feshbach resonances modulate line shapes in coupled photodissociation scattering cross sections.
This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreov...
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This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreover, it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.
A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 ...
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A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 to a more general class of constrained time-delayed optimal control problems, which involves terminal state equality constraints as well as terminal state inequality constraints and continuous state constraints. Two examples have been solved to illustrate the efficiency of the method.
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