288,324 research outputs found
Witnessing a Poincar\'e recurrence with Mathematica
The often elusive Poincar\'e recurrence can be witnessed in a completely
separable system. For such systems, the problem of recurrence reduces to the
classic mathematical problem of simultaneous Diophantine approximation of
multiple numbers. The latter problem then can be somewhat satisfactorily solved
by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is
implemented in the Mathematica built-in function \verb"LatticeReduce". The
procedure is illustrated with a harmonic chain. The incredibly large recurrence
times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure
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Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
Copyright [2006] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria
Hadron-quark phase transition in asymmetric matter with dynamical quark masses
The two-Equation of State (EoS) model is used to describe the hadron-quark
phase transition in asymmetric matter formed at high density in heavy-ion
collisions. For the quark phase, the three-flavor Nambu--Jona-Lasinio (NJL)
effective theory is used to investigate the influence of dynamical quark mass
effects on the phase transition. At variance to the MIT-Bag results, with fixed
current quark masses, the main important effect of the chiral dynamics is the
appearance of an End-Point for the coexistence zone. We show that a first order
hadron-quark phase transition may take place in the region T=(50-80)MeV and
\rho_B=(2-4)\rho_0, which is possible to be probed in the new planned
facilities, such as FAIR at GSI-Darmstadt and NICA at JINR-Dubna. From isospin
properties of the mixed phase somepossible signals are suggested. The
importance of chiral symmetry and dynamical quark mass on the hadron-quark
phase transition is stressed. The difficulty of an exact location of
Critical-End-Point comes from its appearance in a region of competition between
chiral symmetry breaking and confinement, where our knowledge of effective QCD
theories is still rather uncertain.Comment: 13 pages, 16 figures (revtex
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