Yushun Wang

Segregation of lead in Cu-Zn alloy under electric current pulses

In this letter, it is found that when the critical electric current pulse (ECP) passes through a Cu-Zn alloy with lead inclusions, those inclusions will disappear and transfer into grain boundaries or defects, forming many dispersed small particles of lead. Such kind of lead transfer can be produced by no other heat treatments than ECP. The theoretical analysis points out that this phenomenon is attributed to its specific effect on reducing considerably the diffusion activation energy of lead in the alloy. Therefore, the ECP treatment would provide a promising method to refine materials and to improve their physical properties. (c) 2006 American Institute of Physics.

Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs

Many partial differential equations (PDEs) can be written as a multi-symplectic Hamiltonian system, which has three local conservation laws, namely multi-symplectic conservation law, local energy conservation law and local momentum conservation law. In this paper, we give several systematic methods for discretizing general multi-symplectic formulations of Hamiltonian PDEs, including a local energy-preserving algorithm, a class of global energy-preserving methods and a local momentum-preserving algorithm. The methods are illustrated by the nonlinear Schrodinger equation and the Korteweg-de Vries equation. Numerical experiments are presented to demonstrate the conservative properties of the proposed numerical methods.

High-order multi-symplectic schemes for the nonlinear Klein-Gordon equation

In this paper, we construct multi-symplectic schemes with any order of accuracy for the nonlinear Klein-Gordon equation by concatenating the symplectic schemes for ODEs. Some existing schemes, such as the Preissman scheme and the Leap-frog scheme, and new multi-symplectic schemes are constructed. We also show that the composition method, which plays a crucial role in finding the high-order symplectic integrators for the ODEs, can also be applied to construct high-order multi-symplectic schemes for PDEs. Extension of the concatenating method to more than one space dimension is also discussed. Numerical experiments are presented to show the order and the efficiency of the constructed multi-symplectic schemes.

Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes

We analyze the multisymplectic Preissman scheme for the KdV equation with the periodic boundary condition and show that the unconvergence of the widely used iterative methods to solve the resulting nonlinear algebra system of the Preissman scheme is due to the introduced potential function. A artificial numerical condition is added to the periodic boundary condition. The added boundary condition makes the numerical implementation of the multisymplectic Preissman scheme practical and is proved not to change the numerical solutions of the KdV equation. Based on our analysis, we derive some new schemes which are not restricted by the artificial boundary condition and more efficient than the Preissman scheme because of less computing cost and less computer storages. By eliminating the auxiliary variables, we also derive two schemes for the KdV equation, one is a 12-point scheme and the other is an 8-point scheme. As the byproducts, we present two new explicit schemes which are not multisymplectic but still have remarkable numerical stable property. Numerical experiments on soliton collisions are also provided to confirm our conclusion and to show the benefits of the multisymplectic schemes with comparison of the spectral method and Zabusky-Kruskal scheme.

New multisymplectic self-adjoint scheme and its composition scheme for the time-domain Maxwell’s equations

In this paper, we investigate Euler-box scheme for Bridges’ multisymplectic form of Maxwell’s equations. A new multisymplectic scheme is derived for Maxwell’s equations. We prove that it is also a self-adjoint scheme in time direction. The multisymplecticity of composition schemes based on the new scheme is also discussed. Two numerical examples are proposed to indicate that the derived multisymplectic schemes are effective when used to integrate the 2+1 dimensional Maxwell’s equations.

Oriented nanotwins induced by electric current pulses in Cu-Zn alloy

After applying an electrical current pulse (ECP) to samples of Cu–Zn alloy, {111} oriented nanotwins parallel to the ECP direction in α phase grains have been observed at ambient temperature. It seems that (a) these samples have heated up to a temperature much higher than the α to β phase transformation temperature and (b) new β nuclei on the {110} planes have formed in the original α phase. As a result, with the samples being rapidly cooled, these oriented nanotwins will be formed with the β to α martensitic transformation.

On multi-symplectic partitioned Runge-Kutta methods for Hamiltonian wave equations

Many conservative PDEs, such as various wave equations, Schrodinger equations, KdV equations and so on, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. In this note, we show the discretization to Hamiltonian wave equations in space and time using two symplectic partitioned Runge-Kutta methods respectively leads to multi-symplectic integrators which preserve a symplectic conservation law. Under some conditions, we discuss the energy and momentum conservative property of partitioned Runge-Kutta methods for the wave equations with a quadratic potential.

Numerical dispersion analysis of a multi-symplectic scheme for the three dimensional Maxwell's equations

In this paper, we study a multi-symplectic scheme for three dimensional Maxwells equations in a simple medium. This is a system of PDEs with multi-symplectic structures. We prove that this multi-symplectic scheme preserves the discrete version of local and global energy conservation law and the discrete divergence. Furthermore, we extend the discussion to several dispersion properties of the multi-symplectic scheme including the numerical dispersion relation, the numerical group velocity, the effect of large time steps and the CFL condition.

Numerical Analysis of AVF Methods for Three-Dimensional Time-Domain Maxwell's Equations

We propose two schemes [AVF(2) and AVF(4)] for Maxwell’s equations, by discretizing the Hamiltonian formulation with Fourier pseudospectral method for spatial discretization and average vector field method for time integration. Both AVF(2) and AVF(4) hold the two Hamiltonian energies automatically, while being energy-, momentum- and divergence-preserving, unconditionally stable, non-dissipative and spectral accurate. Rigorous error estimates are obtained for the proposed schemes. The numerical dispersion relations are also investigated. Numerical experiments support well the theoretical analysis results. The proposed schemes are valid for the regular domain, but invalid for the domain with complex geometries.

Variational discretizations for the generalized Rosenau-type equations

The generalized Rosenau-type equations include the Rosenau-RLW equation and the Rosenau-KdV equation, which both admit the third-order Lagrangians. In the Lagrangian framework, this paper presents the variational formulations of the generalized Rosenau-type equations as well as their multisymplectic structures. Based on the discrete variational principle, we construct the variational discretizations for solving the evolutions of solitary solutions of this class of equations. We simulate the motion of the single solitary wave, and also observe the different kind of collisions for the generalized Rosenau-type equations with various coefficients.