Search results for "Linear system"
showing 10 items of 1558 documents
Noise stabilization effects in models of interdisciplinary physics
2009
Metastability is a generic feature of many nonlinear systems, and the problem of the lifetime of metastable states involves fundamental aspects of nonequilibrium statistical mechanics. The investigation of noise-induced phenomena in far from equilibrium systems is one of the approaches used to understand the behaviour of physical and biological complex systems. The enhancement of the lifetime of metastable states through the noise enhanced stability effect and the role played by the resonant activation phenomenon will be discussed in models of interdisciplinary physics: (i) polymer translocation dynamics; (ii) transient regime of FitzHugh-Nagumo model; (iii) market stability in a nonlinear …
Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device
2018
International audience; A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10¹⁸ Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structu…
Incoherent solitons and condensation processes
2006
International audience; We study the nonlinear interaction of partially incoherent nonlinear optical waves. We show that, in spite of the incoherence of the waves, coherent phase effects may play a relevant role during the propagation, in contrast with the usual wave turbulence description of the interaction. These nonlinear phase effects may lead the system to unexpected processes of self-organization, such as condensation, or incoherent soliton generation in instantaneous response nonlinear media. Such self-organization processes may be characterized by a reduction of the non-equilibrium entropy, which violates the Boltzmann's H-theorem of entropy growth inherent to the wave turbulence th…
General approach to spatiotemporal modulational instability processes
2011
International audience; In this article, we derive the general exact solution of the modulation instability gain. The solution described here is valid for 1-D, 2-D, and 3-D cases considering any temporal response function of the medium and with possible higher order Kerr nonlinearities. In particular, we show that the gain induced by modulation instability is initial condition dependent, while the usual calculations do not lead to such a dependence. Applications for current and high-interest nonlinear propagation problems, such as 1-D optical fiber propagation with delayed Raman response and 2-D filamentation in gases, are investigated in detail. More specifically, we demonstrate that the 2-D …
Kramers–Kronig transformation, dc behaviour and steady state response of the Warburg impedance for a disk electrode inlaid in an insulating surface
2002
Abstract As the frequency approaches zero, the impedance described by the Warburg function tends to infinity. This means that the resistance of the equivalent circuit representing the electrochemical process has an infinite resistor and then the current cannot flow through it. This asymptotic behaviour also prevents the application of the Kramers–Kronig transformations, a set of integrals which should be fulfilled by any linear system. Using a more general expression of the impedance for a disk electrode inlaid in an insulating surface developed by Fleischmann and Pons (J. Electroanal. Chem. 250 (1988) 277), the Warburg impedance can be deduced and the Kramers–Kronig transformation is possi…
Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution
1998
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…
Nonlinear scaled models in 3D calculation of transformer magnetic circuits
2006
PurposeTo make easier and faster the designing of transformers using scale models.Design/methodology/approachThe scale modeling in designing of transformers is included. Both computer and physical models of high leakage reactance (HLR) and 3‐phase (TP3C) transformers have been considered. The 3D field computations have been executed for the scaled models, and the results were recalculated to the full‐scaled ones.FindingsIt is possible to calculate the scale coefficients for nonlinear models of transformers using finite element method (FEM) software. Obtained coefficients are useful in the designing process. Measurements confirm correctness of the scaling laws.Research limitations/implicatio…
Response Correlations of Linear Systems with White Noise Linearly Parametric Inputs
1996
Relationships between moments and correlations of the response of linear systems subjected to linearly parametric normal white noise inputs are here reported. They are obtained by extensively using the properties of the stochastic integral calculus.
Robust control of a Hammerstein model of DC/DC converters
2007
This paper deals with the robust control of a Hammerstein mathematical model of DC/DC converters, consisting of the nonlinear static characteristics of the converter followed by one of a few number of linear time- invariant models which describe the converter in the useful working range. One of these models is assumed as the nominal model of the system and the remaining models are used for describing the model uncertainty. Nominal behaviour is assured using H-2 optimal control method, Robust stability and behaviour are assured by imposing H-infin specifications. The closed loop control system consisting of the converter Hammerstein model and the robust controller is analyzed by means of sim…
Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities
2010
In this article, the fault detection (FD) problem for a class of discrete-time Markov jump linear system (MJLS) with partially known transition probabilities is investigated. The proposed systems are more general, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be completely known. A residual generator is constructed and the corresponding FD is formulated as an H ∞ filtering problem by which the error between residual and fault are minimised in the H ∞ sense. The linear matrix inequality-based sufficient conditions for the existence of FD filter are derived. A numerical example on a multiplier–accelerator model economic system is give…