The Bird and Nanbu systems are particle systems used to approximate the solution of the mollified Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94], we use coupling techniques and results on branching processes to write an expansion of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems than ...

Space-only noise is a natural random perturbation in equations without time evolution. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. The Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven by space-only noise. The pape...

We consider a stochastic pressure equation with lognormal coefficient with infinite dimensional noise. Using a White Noise framework, we study spatial and stochastic regularity of solutions of the stochastic pressure equation. We first establish that a particular class of weighted Chaos spaces can be characterized by Gaussian Sobolev type norms in the random argument under the Gaussian measure....

A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finiteor infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regula...

We investigate bifurcation and chaos observed in coupled BVP neurons with external impulsive forces. Although the single neuron without the external force has only one equilibrium point, combining these n (n ≥ 3) neurons unidirectionally in a ring, n-phase periodic solutions are generated. Applying the impulsive forces, successive perioddoubling bifurcations of the n-phase solution occur and ch...

We study stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven by space-o...

We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing ...

This paper presents an improved chaotic ant colony system algorithm (ICACS) for solving combinatorial optimization problems. The existing algorithms still have some imperfections, we use a combination of two different operators to improve the performance of algorithm in this work. First, 3-opt local search is used as a framework for the implementation of the ACS to improve the solution quality;...

In recent years, the availability of wireless technologies has become prominent solution for next generation wireless networks (NGWN). Hence the demand for secure communication is an important research issue. Cryptography is recognized as the best method of data protection against active and passive attacks. Therefore a novel chaotic cryptographic scheme is proposed for real time communication....