Search results for " Nonlinear"
showing 10 items of 1224 documents
EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES
2008
International audience; An approximate analytical solution characterizing initial condi- tions leading to action potential ¯ring in smooth nerve ¯bres is determined, using the bistable equation. In the ¯rst place, we present a non-trivial sta- tionary solution wave. Then, we extract the main features of this solution to obtain a frontier condition between the initiation of the travelling waves and a decay to the resting state. This frontier corresponds to a separatrix in the projected dynamics diagram depending on the width and the amplitude of the stationary wave.
Stability measures in metastable states with Gaussian colored noise
2009
We present a study of the escape time from a metastable state of an overdamped Brownian particle, in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise enhanced stability effect for all the initial unstable states used, and for all values of the correlation time $\tau_c$ investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noise respectively, depending on the value of $\tau_c$ with respect to …
On the geometry of the characteristic class of a star product on a symplectic manifold
2001
The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we replace the symplectic structure by one of its formal deformations in the parameter $\hbar$. We then s…
Finite-size scaling analysis of the ?4 field theory on the square lattice
1986
Monte-Carlo calculations are performed for the model Hamiltonian ℋ = ∑i[(r/2)Φ 2(i)+(u/4)/gF4(i)]+∑ (C/2)[Φ (i)−Φ(j)]2 for various values of the parametersr, u, C in the crossover region from the Ising limit (r→-∞,u+∞) to the displacive limit (r=0). The variableφ(i) is a scalar continuous spin variable which can lie in the range-∞<φ(i)<+∞, for each lattice site (i).φ(i) is a priori selected proportional to the single-site probability in our Monte Carlo algorithm. The critical line is obtained in very good agreement with other previous approaches. A decrease of apparent critical exponents, deduced from a finite-size scaling analysis, is attributed to a crossover toward mean-field values at t…
Atypical transistor-based chaotic oscillators: Design, realization, and diversity
2017
In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predom…
Statistics of nonlinear stochastic dynamical systems under Lévy noises by a convolution quadrature approach
2010
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficie…
Wronskian and Casorati determinant representations for Darboux–Pöschl–Teller potentials and their difference extensions
2009
We consider some special reductions of generic Darboux?Crum dressing formulae and of their difference versions. As a matter of fact, we obtain some new formulae for Darboux?P?schl?Teller (DPT) potentials by means of Wronskian determinants. For their difference deformations (called DDPT-I and DDPT-II potentials) and the related eigenfunctions, we obtain new formulae described by the ratios of Casorati determinants given by the functional difference generalization of the Darboux?Crum dressing formula.
Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime
2016
We investigate the quantum dynamics of a multilevel bistable system coupled to a bosonic heat bath beyond the perturbative regime. We consider different spectral densities of the bath, in the transition from sub-Ohmic to super-Ohmic dissipation, and different cutoff frequencies. The study is carried out by using the real-time path integral approach of the Feynman-Vernon influence functional. We find that, in the crossover dynamical regime characterized by damped \emph{intrawell} oscillations and incoherent tunneling, the short time behavior and the time scales of the relaxation starting from a nonequilibrium initial condition depend nontrivially on the spectral properties of the heat bath.
Response functions in multicomponent Luttinger liquids
2012
We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for the case of three components.
Other 2N− 2 parameters solutions of the NLS equation and 2N+ 1 highest amplitude of the modulus of theNth order AP breather
2015
In this paper, we construct new deformations of the Akhmediev-Peregrine (AP) breather of order N (or APN breather) with real parameters. Other families of quasirational solutions of the nonlinear Schrodinger (NLS) equation are obtained. We evaluate the highest amplitude of the modulus of the AP breather of order N; we give the proof that the highest amplitude of the APN breather is equal to . We get new formulas for the solutions of the NLS equation, which are different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We simultaneously get triangular configurations and isolated rings. Moreover,…