Search results for "Linear"
showing 10 items of 7165 documents
Diffusive energy growth in classical and quantum driven oscillators
1991
We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the ana…
Control of hysteretic instability in rotating machinery by elastic suspension systems subject to dry and viscous friction
2010
Abstract Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-…
Floquet spectrum for two-level systems in quasiperiodic time-dependent fields
1992
We study the time evolution ofN-level quantum systems under quasiperiodic time-dependent perturbations. The problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged Hilbert space, or equivalently of a generalized Floquet operator. We discuss criteria for the appearance of pure point as well as continuous spectrum, corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior. We discuss two types of mechanisms that lead to instability. The first one is due to near resonances, while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation. We tre…
Floquet theory: exponential perturbative treatment
2001
We develop a Magnus expansion well suited for Floquet theory of linear ordinary differential equations with periodic coefficients. We build up a recursive scheme to obtain the terms in the new expansion and give an explicit sufficient condition for its convergence. The method and formulae are applied to an illustrative example from quantum mechanics.
Objective function design for robust optimality of linear control under state-constraints and uncertainty
2009
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations. © 2009 EDP Sciences, SMAI.
Fluorometric determination of diphenhydramine by flow-injection analysis
1992
A sensitive, rapid and simple flow injection procedure for the determination of diphenhydramine has been designed based on a fluorometric approach. An aqueous solution of diphenhydramine is injected into a carrierreagent stream containing Ce(IV) in dilute sulphuric acid and the fluorescence intensity of the Ce(III) produced is monitored. Chemical, FIA and instrumental variables were optimized. Analytical features of the method are: linear range 0.2–2 ppm, precision 0.7%, sample throughput 80/h. The influence of some foreign substances which can be found in typical pharmaceutical samples containing diphenhydramine was also investigated. The diphenhydramine content of a pharmaceutical prepara…
Determination of insolubles in diesel lubricating oil by FIA-visible spectrometry
2003
Insolubles determination is one of the parameters usually recommended to evaluate the residual life of oil because their presence at elevated levels in diesel lubricating oil changes the viscosity, prematurely clogs filters and is one of the major factors in causing abrasive engine wear. The proposed method employs visible spectrophotometric detection in association with flow injection analysis. The results obtained by this method were compared with the ones obtained by Fourier transform infrared spectrometry (FT-IR) since this is the most employed method for insolubles determination. The proposed method presented a linear response from 0 to 3% (w/w) of insolubles in pentane (ASTM D-893). T…
Numerical investigation of optical heartbeats with external driving forces
2010
The role of harmonic and random external forces in a phenomenological nonlinear model of optical heartbeats is investigated. External forces trigger damped oscillations at the natural frequency of the system and higher harmonics. The numerical results are compared with experimental ones.
Asymptotic regime in N random interacting species
2005
The asymptotic regime of a complex ecosystem with \emph{N}random interacting species and in the presence of an external multiplicative noise is analyzed. We find the role of the external noise on the long time probability distribution of the i-th density species, the extinction of species and the local field acting on the i-th population. We analyze in detail the transient dynamics of this field and the cavity field, which is the field acting on the $i^{th}$ species when this is absent. We find that the presence or the absence of some population give different asymptotic distributions of these fields.
Stochastic resonance in a trapping overdamped monostable system.
2009
The response of a trapping overdamped monostable system to a harmonic perturbation is analyzed, in the context of stochastic resonance phenomenon. We consider the dynamics of a Brownian particle moving in a piecewise linear potential with a white Gaussian noise source. Based on linear-response theory and Laplace transform technique, analytical expressions of signal-to-noise ratio (SNR) and signal power amplification (SPA) are obtained. We find that the SNR is a nonmonotonic function of the noise intensity, while the SPA is monotonic. Theoretical results are compared with numerical simulations.