Abstract:
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of discrete exterior calculus method for numerical simulation of wave equation. The advantage of this method is that it can be used to compute equation on the space manifold and the time. The analysis of its stable condition and error is also accomplished.

Abstract:
The research on the propagation of seismic waves in anisotropic media is an important topic in the research of seismic exploration. In this paper, the optimal nearly-analytic discrete method of high precision and low dispersion was adopted in vertical transverse isotropic (VTI) medium of two-dimensional elastic wave equation numerical simulation. Based on the elastic wave equations in two dimensional VTI of the medium, the paper began with a discussion of the significance of the physical parameters of Thomsen, and then a different equation of elastic wave equation was established with the optimal nearly-analytic discrete method (ONAD). Finally, through the method of numerical simulation of a uniform and layered VTI model, the author focused on the research of snapshots and ground seismic records of different Thomsen parameters. In this paper, not only was the impact of the value of Thomsen parameters on the elastic wave propagation analyzed, but also the propagation laws of elastic wave in VTI medium were discussed, which have provided some reference and basis for practical seismic exploration.

Abstract:
The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this huge linear system, one uses a iterative Krylov method with a preconditioning by a separable matrix. The corresponding linear system is solved with a block cyclic reduction method. Some enlightments on the parallel implementation are also given. Lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture.

Abstract:
In this article the performance analysis of the new model, used to integration between QoS and Security, is introduced. OPNET modeler simulation testing of the new model with comparation with the standard model is presented. This new model enables the process of cooperation between QoS and Security in MANET. The introduction how the model is implemented to the simulation OPNET modeler is also showed. Model provides possibilities to integration and cooperation of QoS and security by the cross layer design (CLD) with modified security service vector (SSV). An overview of the simulation tested of the new model, comparative study in mobile ad-hoc networks, describe requirements and directions for adapted solutions are presented. Main idea of the testing is to show how QoS and Security related services could be provided simultaneously with using minimal interfering with each service.

Abstract:
Forward simulation in crosswell seismic is the process of solving the numerical solution of the wave equation under the defined formation parameters and limited condtions.In this paper,I present a detailed deduction for fourth-order difference equation of crosswell two-dimensional acoustic equation: By using a theoretical model including a wedge and a mound,the corresponding wave field is detailedly analyzed.By a delicate velocity model according to two real wells logging data in the Ken71 block of Shengli oil field,we analyzed the computed synthetic seismogram and gived a comparison between inversion result of reflection wave of model and corresponding 3D seismic profile across the two wells.It verified the rationality of our designed observation system.

Abstract:
Compressed sensing is a method that allows a significant reduction in the number of samples required for accurate measurements in many applications in experimental sciences and engineering. In this work, we show that compressed sensing can also be used to speed up numerical simulations. We apply compressed sensing to extract information from the real-time simulation of atomic and molecular systems, including electronic and nuclear dynamics. We find that for the calculation of vibrational and optical spectra the total propagation time, and hence the computational cost, can be reduced by approximately a factor of five.

Abstract:
An passive infrared or millimeter wave imaging system based on the theory of compressed sensing is designed. Compressed sensing is a technology using sparse or compressed priority information to acquire and reconstruct signals. It can sample signals at a rate much lower than the Nyquist sampling rate and implement high precision reconstruction of the signals. The above designed system has overcome the shortcomings of the traditional systems and can conduct its imaging according to the theory of compressed sensing. The simulation result shows that the system has good imaging performance, its peak signal to noise ratio and resolution are improved and the data required to be stored are reduced greatly.

Abstract:
The dispersion relation of ultracold atoms in variably shaped optical lattices can be tuned to resemble that of a relativistic particle, i.e. be linear instead of the usual nonrelativistic quadratic dispersion relation of a free atom. Cold atoms in such a lattice can be used to carry out quantum simulations of relativistic wave equation predictions. We begin this article by describing a Raman technique that allows to selectively load atoms into a desired Bloch band of the lattice near a band crossing. Subsequently, we review two recent experiments with quasirelativistic rubidium atoms in a bichromatic lattice, demonstrating the analogs of Klein tunneling and Veselago lensing with ultracold atoms respectively.

Abstract:
A new alternative perfectly matched layer (PML) absorbing boundary condition is developed to attenuate the artificial boundary reflections generated in numerical simulation of the second-order elastic wave equation. The second-order equation can be described by displacement, which is more appropriate than the first-order one. Its PML condition conventionally needs to split the displacement into four parts, which occupies a large amount of memory and requires solving a third-order differential equation in time. As for the other choice, non-splitting PML method may be applied to the second-order equation, but it requires solving the dual integral in time. The new method can solve or simplity the above problems. Finally, a staggered-grid finite difference method with this PML condition is used to simulate an anisotropic media model and the results show that the method is efficient.

Abstract:
The Fourier law and the diffusion equation are derived from the Schrodinger equation of a diffusive medium (consisting of a random potential). The theoretical model is backed by numerical simulation. This derivation can easily be generalized to demonstrate the transition from any random wave equation to the diffusive equation.