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Showing papers on "Dissipative system published in 1986"



Journal ArticleDOI
TL;DR: In this paper, the generalized Langevin equation of motion for a particle trapped in a one-dimensional well with a barrier height V 0 and coupled to a dissipative medium is modeled by a harmonic bath.
Abstract: The generalized Langevin equation of motion for a particle trapped in a one‐dimensional well with a barrier height V0 and coupled to a dissipative medium is modeled by a harmonic bath. Using the properties of the bath and a normal mode analysis we prove that the reactive frequency defined by Grote and Hynes for averaged motion across the barrier is actually a renormalized effective barrier frequency. We then show that the Kramers–Grote–Hynes expression for the rate of escape over the barrier is just the continuum limit of the usual gas phase harmonic transition state theory expression.

350 citations


Journal ArticleDOI
TL;DR: In this paper, a paradigm for describing dynamical systems that have both Hamiltonian and dissipative parts is presented, where features of generalized Hamiltonian systems and metric systems are combined to produce what are called metriplectic systems.

244 citations


Journal ArticleDOI
TL;DR: In this article, a large number of new geometric, ergodic and statistical properties of the Kuramoto-Sivashinsky equation were presented for modeling interfacial turbulence in various physical contexts.

191 citations


Journal ArticleDOI
TL;DR: Leis as mentioned in this paper gave an account of some recent developments in the theory of partial differential equations for readers thoroughly familiar with functional analysis, dealing with various types of problem for the wave equation, Maxwell's equations, Schrodinger's equation, the plate equation etc.
Abstract: R Leis 1986 Chichester: John Wiley viii + 266 pp price £2450 ISBN 0 471 90863 0 This book is an account of some recent developments in the theory of partial differential equations for readers thoroughly familiar with functional analysis It deals with various types of problem for the wave equation, Maxwell's equations, Schrodinger's equation, the plate equation etc, but dissipative systems are hardly discussed

148 citations



Journal ArticleDOI
TL;DR: In this paper, the authors derived sufficient conditions for dissipative analytic n-dimensional ω-periodic differential equations to have only a finite number of ωperiodic solutions.
Abstract: Upper bounds are obtained for the Hausdorff dimension of compact invariant sets of ordinary differential equations which are periodic in the independent variable. From these are derived sufficient conditions for dissipative analytic n-dimensional ω-periodic differential equations to have only a finite number of ω-periodic solutions. For autonomous equations the same conditions ensure that each bounded semi-orbit converges to a critical point. These results yield some information about the Lorenz equation and the forced Duffing equation.

131 citations


Journal ArticleDOI
TL;DR: In this paper, the mathematical structure of a model for three-phase, incompressible flow in a porous medium is examined and it is shown that, in the absence of diffusive forces, the system of conservation laws describing the flow is not necessarily hyperbolic.
Abstract: In this paper we examine the mathematical structure of a model for three-phase, incompressible flow in a porous medium. We show that, in the absence of diffusive forces, the system of conservation laws describing the flow is not necessarily hyperbolic. We present an example in which there is an elliptic region in saturation space for reasonable relative permeability data. A linearized analysis shows that in nonhyperbolic regions solutions grow exponentially. However, the nonhyperbolic region, if present, will be of limited extent which inherently limits the exponential growth. To examine these nonlinear effects we resort to fine grid numerical experiments with a suitably dissipative numerical method. These experiments indicate that the solutions of Riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space. In particular, when initial states are outside the elliptic region the Riemann problem solution appears to stay outside the region. Further...

123 citations


01 Jan 1986
TL;DR: In this article, Krommes attempts to extrapolate results and intuition of homogeneous Navier-Stokes turbulence (HN-ST) to the more complicated case of dissipative drift-wave turbulence (DD-WT).
Abstract: We appreciate the interest of Krommes in our recent paper and welcome the opportunity to discuss his comments and other related issues. In our opinion, most of the objections hea has raised follow from a misunderstanding of the physics treated by clump and hole theory. In particular, throughout his critique Krommes attempts to extrapolate results and intuition of homogeneous Navier-Stokes turbulence (HN-ST) to the more complicated case of dissipative drift-wave turbulence (DD-WT). Since these two cases are so dissimilar with regard to their fundamental constituents, drive, characteristic scales and interaction mechanisms, extrapolations from one case to the other are unwarranted and misleading. Moreover, the hypotheses and results of clump and hole theories have fared well in several tests using laboratory and simulation data which is relevant to the theoretical models analyzed. 7 refs.

106 citations


Journal ArticleDOI
TL;DR: Externally injected class-B lasers are shown to be approximately described by a reversible three-dimensional flow and symmetry breaking is shown to explain the onset of the very stable periodic solutions exhibited by the physical system.
Abstract: Externally injected class-B lasers are shown to be approximately described by a reversible three-dimensional flow. For critical values of the external field such a model displays symmetry-breaking bifurcations, where the structure of space changes from conservative to dissipative either in a continuous or discontinuous manner. As a consequence, the coexistence of the two behaviors is observed in suitable parameter ranges. Symmetry breaking is shown to explain the onset of the very stable periodic solutions exhibited by the physical system. Such bifurcations are then studied in the simpler context of two-dimensional flows and recognized as degenerate codimension-2 phenomena. Generic normal forms are finally introduced which describe the local bifurcation unfolding.

95 citations


Book
01 Jan 1986
TL;DR: A selection of the invited talks given at the Malvern seminar on Dynamical Systems held at RSRE, Malvern in April 1985, presenting very recent developments in the fields of fluids, chemical reactions, nonlinear and quantum optics, and theories of Hamiltonian and dissipative systems can be found in this article.
Abstract: A selection of the invited talks given at the Malvern seminar on Dynamical Systems held at RSRE, Malvern in April 1985, presenting very recent developments in the fields of fluids, chemical reactions, non-linear and quantum optics, and theories of Hamiltonian and dissipative systems.

Journal ArticleDOI
TL;DR: The quantum theory of activated events in condensed phases, developed by Wolynes using path integral techniques, was derived via harmonic quantum state theory as discussed by the authors, which is derived via path integral technique.

Journal ArticleDOI
TL;DR: Dissipative quantum systems such as an unstable field, thermal field, and cosmological particle production are investigated and Equations of motion for each appropriate mean field are revealed to be Langevin type.
Abstract: Dissipative quantum systems such as an unstable field, thermal field, and cosmological particle production are investigated. Equations of motion for each appropriate mean field are revealed to be Langevin type. The derived correlation of the random field turns out not to be Gaussian nor white in general. A relation between a popular quantum average and the statistical correlation is also clarified.

Journal ArticleDOI
TL;DR: In this article, the complex energy shifts of the energy levels of a macroscopic system subject to dissipation are calculated as a function of the phenomenological damping parameters describing the classical motion of the system.
Abstract: The complex energy shifts of the energy levels of a macroscopic system subject to dissipation are calculated as a function of the phenomenological damping parameters describing the classical motion of the system. These results are applied to the energy levels of the zero-voltage state of a current-biased Josephson junction in parallel with an arbitrary dissipative circuit. Following the approach of Leggett, the influence of the same dissipative circuit on the tunneling rate out of the zero-voltage state is also calculated. The dependences of both phenomena, quantization of energy levels, and quantum tunneling, on the admittance of the circuit are compared.

Journal ArticleDOI
TL;DR: The dynamic stability of supported cylindrical pipes converying fluid, when the flow velocity is harmonically perturbed about a constant mean value, is considered in this paper, and explicit stability conditions for perturbations of small intensity are obtained by using the method of averaging.

Journal ArticleDOI
TL;DR: In this paper, the dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations, analyzed in terms of space-time correlation functions and modal probability distributions.
Abstract: The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Journal ArticleDOI
TL;DR: The recently developed theory for tunneling in dissipative systems is rederived using quantal transition-state theory and finds an exponential damping of the tunneling rate at 0 K and the exponential rate enhancement at low temperatures as well as the crossover temperature are obtained with this approach.
Abstract: The recently developed theory for tunneling in dissipative systems is rederived using quantal transition-state theory. As predicted by Caldeira and Leggett, we find an exponential damping of the tunneling rate at 0 K. The exponential rate enhancement at low temperatures as well as the crossover temperature are also obtained with this approach. Moreover, the rate enhancement is given explicitly in terms of energy transfer from the bath to the dissociative mode. The present derivation includes memory effects.

Journal ArticleDOI
TL;DR: In this paper, higher-order turbulence closure models include as particular solutions damped oscillations in the statically stable case, and possibly amplifying and propagating oscillations for the statically unstable case.
Abstract: It is shown that higher-order turbulence-closure models include as particular solutions damped oscillations in the statically stable case, and possibly amplifying and propagating oscillations in the statically unstable case. These two kinds of oscillatory motions are shown to be strongly affected by molecular and pressure damping, both from analytical linear analysis and one-dimensional numerical simulation. The results are applied to the case of a stratocumulus capped boundary-layer and compared to the ones of Moeng and Randall. Indications are given on how to achieve stable nunneries simulations by improving the formulation of the mixing (dissipative) length.


Journal ArticleDOI
TL;DR: In this article, it was shown that for those full discretizations obtained by applying to a space-discretization of the equations an energy conservative discrete time-marching method, the energy reflected at the boundary is independent of the value of Δt, and is strictly equal to the reflected energy in the semidiscrete case.


Journal ArticleDOI
TL;DR: In this paper, the Benjamin-Ono-Burgers equation is used to describe nonlinear, long wavelength motions in a ducted weakly dissipative mhd system and the slow decay of the solitary wave solutions is investigated.

Journal ArticleDOI
TL;DR: In this paper, the torsion of the local flow around closed orbits and its relation to the superstructure in the bifurcation set of strictly dissipative nonlinear oscillators is investigated.
Abstract: The torsion of the local flow around closed orbits and its relation to the superstructure in the bifurcation set of strictly dissipative nonlinear oscillators is investigated. The torsion number describing the twisting behaviour of the flow turns out to be a suitable invariant for the classification of local bifurcations and resonances in those systems. Furthermore, the notions of winding number and resonance are generalized to arbitrary one-dimensional dissipative oscillators.


Journal ArticleDOI
TL;DR: The hydrodynamics of rotating superfluids at finite temperature were studied in this paper, accounting for the elastic properties of the vortex lattice, and the transverse and longitudinal normal modes of the system were investigated.
Abstract: The hydrodynamics of rotating superfluids at finite temperature is formulated, accounting for the elastic properties of the vortex lattice. This theory, which is a generalization of previous work at zero temperature, includes normal fluid motions and dissipation and is used here to investigate the transverse and longitudinal normal modes of the system. Mutual friction, arising microscopically from collisions between the vortex lines and the excitations comprising the normal fluid, leads to a profound change in the nature of the two transverse modes allowed at finite temperatures. One such mode, similar to the Tkachenko mode in zero-temperature theory, is associated with the motion of the total mass current and is damped by first viscosity but unaffected by mutual friction. The other mode, associated with the relative motion of the normal and superfluid-vortex components, is highly damped by mutual friction and cannot propagate at angles greater than a critical angle ϑ c measured from the rotation axis.

Journal ArticleDOI
TL;DR: In this paper, the dissipative layers, called Marangoni boundary layers, that can be formed along the interface of two immiscible fluids, in surface driven flows are studied under the hypothesis that the flow fields of the two interfacing fluids are uncoupled.
Abstract: The paper deals with the dissipative layers, called Marangoni boundary layers, that can be formed, along the interface of two immiscible fluids, in surface driven flows. Under the hypothesis that the flow fields of the two interfacing fluids are uncoupled, similar solutions are studied for the case in which an external pressure gradient is present. The similarity class is derived and the pertinent equations are solved numerically by mean of an algorithm based on a Quasi-Linearization Technique.

Journal ArticleDOI
TL;DR: In this article, the problem of finding a T -periodic solution of a forced dissipative system of ordinary differential equations is most conveniently reformulated as a fixed point problem of a Poincare map mapping the phase space at t = 0 into the phase spaces at T = T, and the stability of the periodic response is equivalent to the stability for the fixed point.

Journal ArticleDOI
TL;DR: In this paper, a unified protocol to treat the quantum time-dependent harmonic oscillator with friction is presented, described by two different models: an explicitly timedependent, linear Schrodinger equation (Caldirola-Kanai model) and a logarithmic nonlinear Schroeder equation (Kostin model), and it is shown that neither an exact nor an approximate invariant of Ermakov-Lewis type exists.
Abstract: Via the hydrodynamical formulation of quantum mechanics, a unified protocol to treat the quantum time‐dependent harmonic oscillator with friction is presented, described by two different models: an explicitly time‐dependent, linear Schrodinger equation (Caldirola–Kanai model) and a logarithmic nonlinear Schrodinger equation (Kostin model) For the former model, an Ermakov system that makes it possible to obtain an invariant of Ermakov–Lewis‐type is derived For the latter model, a non‐Ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of Ermakov–Lewis‐type exists

Journal ArticleDOI
TL;DR: In this paper, the authors show that a recently proposed continuum theory for purely-dissipative simple materials provides a convenient rheological framework for the description of yielding and flow of granular materials.
Abstract: We show that a recently proposed continuum theory for purely-dissipative simple materials provides a convenient rheological framework for the description of yielding and flow of granular materials. The isotropic version encompasses a number of the special models which emerge from experimental observation and from the kinetic theory of Savage and co-workers. In the present work, grain-fluctuation energy is incorporated into the model, and we provide estimates for it, and for other important physical quantities, based on elementary microstructural considerations. With the picture of a system dominated by macroscopic deformation and microdissipation, we conclude that grain-energy estimates are insensitive to microstructural detail.

Journal ArticleDOI
TL;DR: In this paper, a Lagrangian and Hamiltonian formulation for a damped harmonic oscillator with damping linear in the velocity is given, where the canonical momentum is not equal to the kinetic momentum, and the Hamiltonian is not equivalent to the energy.
Abstract: A Lagrangian and Hamiltonian formulation can be given for a damped harmonic oscillator with damping linear in the velocity. The canonical momentum is not equal to the kinetic momentum, and the Hamiltonian is not equal to the energy. On the other hand, a pendulum accreting mass has the same Lagrangian and equation of motion. However, in this case the canonical momentum is equal to the kinetic momentum, and the Hamiltonian is equal to the energy. No ambiguity arises if the physical situation is kept in mind.