Search results for " Nonlinear"
showing 10 items of 1224 documents
On the propagation of a perturbation in an anharmonic system
2007
We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.
Quantum dynamics of the intensity-dependent Tavis-Cummings model
1999
An exactly solvable generalization of the intensity-dependent Jaynes-Cummings model to the case of N0 atoms is introduced together with its solution. The quantum dynamics of the model including the squeezing properties of the su(1,1) Perelomov and Glauber coherent states is investigated. The cases of one and two atoms present in the cavity are analysed in detail. These two cases are compared in the situation when the atomic subsystem is initially prepared in the ground state, the Dicke state and the state of thermal equilibrium.
Thermalization and condensation in an incoherently pumped passive optical cavity
2011
International audience; We study theoretically and numerically the condensation and the thermalization of classical optical waves in an incoherently pumped passive Kerr cavity. We show that the dynamics of the cavity exhibits a turbulent behavior that can be described by the wave turbulence theory. A mean-field kinetic equation is derived, which reveals that, in its high finesse regime, the cavity behaves essentially as a conservative Hamiltonian system. In particular, the intracavity turbulent field is shown to relax adiabatically toward a thermodynamic equilibrium state of energy equipartition. As a consequence of this effect of wave thermalization, the incoherent optical field undergoes …
Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases
2022
We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.
A method for the time-varying nonlinear prediction of complex nonstationary biomedical signals
2009
A method to perform time-varying (TV) nonlinear prediction of biomedical signals in the presence of nonstationarity is presented in this paper. The method is based on identification of TV autoregressive models through expansion of the TV coefficients onto a set of basis functions and on k -nearest neighbor local linear approximation to perform nonlinear prediction. The approach provides reasonable nonlinear prediction even for TV deterministic chaotic signals, which has been a daunting task to date. Moreover, the method is used in conjunction with a TV surrogate method to provide statistical validation that the presence of nonlinearity is not due to nonstationarity itself. The approach is t…
Applications of Topological *-Algebras of Unbounded Operators
1998
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the time evolution of two interacting models of matter and bosons. We show that for all these systems it is possible to build up a common framework where the thermodynamical limit of the algebraic dynamics can be conveniently studied and obtained.
Fractional viscoelastic behaviour under stochastic temperature process
2018
Abstract This paper deals with the mechanical behaviour of a linear viscoelastic material modelled by a fractional Maxwell model and subject to a Gaussian stochastic temperature process. Two methods are introduced to evaluate the response in terms of strain of a material under a deterministic stress and subjected to a varying temperature. In the first approach the response is determined making the material parameters change at each time step, due to the temperature variation. The second method, takes advantage of the Time–Temperature Superposition Principle to lighten the calculations. In this regard, a stochastic characterisation for the Time–Temperature Superposition Principle method is p…
Analytically solvable Hamiltonians for quantum two-level systems and their dynamics
2014
A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented. In this method, a time-dependent Hamiltonian and the resulting unitary evolution operator are connected through an arbitrary function of time, furnishing us with new analytically solvable cases. The method is surprisingly simple, direct, and transparent and is applicable to a wide class of two-level Hamiltonians with no involved constraint on the input function. A few examples illustrate how the method leads to simple solvable Hamiltonians and dynamics.
Smooth surjections and surjective restrictions
2017
Given a surjective mapping $f : E \to F$ between Banach spaces, we investigate the existence of a subspace $G$ of $E$, with the same density character as $F$, such that the restriction of $f$ to $G$ remains surjective. We obtain a positive answer whenever $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values of $f$ has zero-measure.
TWO-LANE TRAFFIC WITH PLACES OF OBSTRUCTION TO TRAFFIC
2004
As the Nagel–Schreckenberg model (NaSch model) became known as a realistic approach to describe traffic flow on single-lane streets, this model was extended to two-lane traffic by several groups. On the base of our two-lane model, we will now investigate the impact of a place of obstruction, e.g., because of road works, on partial fractions, densities and mean velocities.