15,005 research outputs found
An advanced meshless method for time fractional diffusion equation
Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations
Effective generation of Ising interaction and cluster states in coupled microcavities
We propose a scheme for realizing the Ising spin-spin interaction and atomic
cluster states utilizing trapped atoms in coupled microcavities. It is shown
that the atoms can interact with each other via the exchange of virtual photons
of the cavities. Through suitably tuning the parameters, an effective Ising
spin-spin interaction can be generated in this optical system, which is used to
produce the cluster states. This scheme does not need the preparation of
initial states of atoms and cavity modes, and is insensitive to cavity decay.Comment: 11pages, 2 figures, Revtex
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