Showing papers on "Dissipative system published in 1978"

Time, structure, and fluctuations.

Abstract: Fundamental conceptual problems that arise from the macroscopic and microscopic aspects of the second law of thermodynamics are considered. It is shown that nonequilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures." The thermodynamic theory of such structures is outlined. A microscopic definition of irreversible processes is given, and a transformation theory is developed that allows one to introduce nonunitary equations of motion that explicitly display irreversibility and approach to thermodynamic equilibrium. The work of the group at the University of Brussels in these fields is briefly reviewed. In this new development of theoretical chemistry and physics, it is likely that thermodynamic concepts will play an ever-increasing role.

Asymptotic Behavior of Solutions of Evolution Equations

Abstract: Publisher Summary This chapter presents the methods of investigation of the asymptotic behavior of solutions of evolution equations, endowed with a dissipative mechanism, based on the study of the structure of the ω-limit set of trajectories of the evolution operator generated by the equation. The dissipative mechanism usually manifests itself by the presence of a Liapunov functional, which is constant on ω -limit sets; the central idea of the approach presented in the chapter is to use this information in conjunction with properties of ω -limit sets such as invariance and minimality. The chapter discusses two examples of wave equations with weak damping for which the scheme set up by Hale applies. In particular, this requires that the Liapunov functional be continuous on phase space. The chapter explores the case of a hyperbolic conservation law that generates a semigroup on space. It also presents a survey of various applications and extensions of these ideas that may serve as a guide to those interested in learning more about the method.

Stochastic self-oscillations and turbulence

Abstract: Until quite recently, it was thought that turbulence, i.e., stochastic self-oscillations of a continuous medium, was related exclusively to the excitation of an exceedingly large number of degrees of freedom. This review is devoted to the discussion of new ideas on the nature of the unpredictable turbulent motions in dissipative media connected with the discovery of strange attractors, i.e., attractive regions in phase space within which all paths are unstable and behave in a very complex fashion (motions on an attractor of this kind are characterized by a continuous spectrum). Turbulence represented by a strange attractor is described by a finite number of degrees of freedom, i.e., modes whose physical nature may be different. The example of a simple electronic noise generator is used to illustrate how the instability (divergence) of such paths leads to stochastic behavior. The analysis is based on the introduction of a nonreciprocally single-valued Poincare mapping onto itself, which is then used to describe the strange attractors encountered in different physical problems. An example of this mapping is used to demonstrate the discrete, symbolic, description of dynamic systems. The properties of such systems which indicate their stochastic nature, for example, positive topologic entropy and hyperbolicity are discussed. Specific physical mechanisms leading to the appearance of stochastic behavior and characterized by a continuous time spectrum are discussed. Strange attractors that appear in the case of parametric instability of waves in plasmas, laser locking by an external field, and so on, are demonstrated. "Attractor models" of hydrodynamic turbulence are reviewed, and in particular, finite-dimensional hydrodynamic models of convection in a layer and of Couette flow between rotating cylinders are constructed and found to exhibit stochastic behavior.

A theory of spontaneous fluctuations in viscous fluids far from equilibrium

Abstract: It has recently been observed that the dissipative nonlinearities for a variety of transport processes can be written in a formally identical fashion. This ’’canonical form’’ expresses the spontaneous changes of extensive variables in terms of exponentials of intensive variables and depends on the molecular processes causing the dissipation. It is shown here that the dissipative terms in Newtonian fluid mechanics can be written in canonical form. Using a postulated relationship between these dissipative terms and fluctuations, the canonical form is used to describe the molecular fluctuations in the flow of Newtonian fluids. The theory describes the effect of nonlinearities, including the streaming terms, and is consistent whenever the phenomenological equations are valid. Close to equilibrium the theory reduces to the Fox–Uhlenbeck theory of hydrodynamic fluctuations, and away from equilibrium it gives an unambiguous generalization of the Landau–Lifshitz theory.

Stability in the dissipative steady state

Abstract: Stability questions arise in a number of different ways. At the simplest level we can ask about the stability of a particle in a force field. It is stable if any deviations of the particle from its initial location cause it to be exposed to forces returning it back to the initial point. With time, however, “stability” has taken on a broader meaning. We find references to the stability of an orbit, of a laser's mode of oscillation, or of a set of biological populations. Harry L. Swinney and Jerry P. Gollub recently discussed the stability of liquid flow patterns in PHYSICS TODAY (August, page 41). In all of these cases there are questions about the persistence of an initial behavior pattern.

Effect of Magnetic Shear on Dissipative Drift-Wave Instabilities

Abstract: We report the results of a linear radial-eigenmode analysis of dissipative drift waves in a plasma with magnetic shear and spatially varying density gradient. The results of the analysis are shown to be consistent with a recent experiment concerned with dissipative drift-wave instabilities in a toroidal stellarator.

Preparation and decay of unstable molecular states undergoing memory effects: Excitation by coherent electromagnetic pulses of arbitrary strength

Abstract: It is shown that the preparation and decay of non-markovian dissipative systems can be handled without any restriction on both excitation intensity and memory strength. Any perturbative approximation in the treatment of non-markovian interaction is avoided. The theory is explicity related to physical models relevant to the problem of molecular radiationless decay. In this respect, it is shown that a quantitative evaluation of the “radiative state” time evolution along the lines of the recent paper by Rhodes can easily be performed whatever the strength of external interaction. It is emphasized that no quantum beat phenomenon may be interpreted in an unambiguous way in the absence of any information on the dissipation coupling. As a new effect of coherent excitation on the nature of the excited state, it is shown that increasing light intensity may allow the molecule to be prepared in the “radiative state” without using § excitations. It is stressed, furthermore, that the excitation of a discrete set of states by long duration pulses has the effect of invalidating the replacement of a complex molecular system by a more simple one, which in turn is to be regarded as the basic idea of the theory. The above physical circumstance seems to be the unique one under which the present approach is no longer applicable. Evidence for this statement is provided by a quantitative simulation of hypothetical experiments of the same kind as the recent ones by Zewail et al.

Transport theory of dissipative heavy-ion collisions

Abstract: The non-perturbative quantum-statistical theory of dissipative heavy-ion collisions introduced earlier, is generalized by including explicitly the relative motion of the colliding nuclei. We start from the Liouville equation in the Wigner representation which allows for useful and illustrative interpretations of the resulting quantities and equations. Using the randomness of the coupling matrix elements and the semi-classical approximation for the relative motion we derive a general time-dependent transport equation for the macroscopic Wigner functions (phase-space distribution functions). The limits of weak and strong coupling are discussed.

Canonical equations of hydrodynamics of quantum liquids

Abstract: A method of constructing canonical equations for quantum liquids is proposed For superfluid /sup 4/He the forms of the Hamiltonian equations of hydrodynamics and conservation laws are obtained The kinetic terms in the equations of hydrodynamics are written out The set of equations obtained is valid up to the lambda point For anisotropic quantum liquid /sup 3/He-A canonical equations both for spin and orbital hydrodynamics are found with the spin and orbital moments taken into account The forms of the laws of the conservation of momentum, angular momentum, mass, and energy are obtained The kinetic terms in the equation of hydrodynamics are considered, and both the dissipative and reactive coefficents are classified A transfer equation for the order parameter near the A transition point is proposed with the dissipative taken into account

The efficiency of engines operating around a steady state at finite frequencies

Abstract: Linear response theory is applied to a study of the performance of engines which operate harmonically around a stable reference state which is either an equilibrium or a nonequilibrium steady state. Two kinds of quantities are relevant for efficiency and power output: those which are integrals over a semicycle (e.g., the heat input in a heat engine or the heat uptake in a refrigeration machine), and net quantities of the whole cycle, like the work exchanged with the mechanical surroundings, the net dissipative losses, and certain refractive quantities which, via Kramers–Kronig relations, correspond to the absorptive ones. We discuss their dependence on the frequency of operation and on the amplitudes of the driving forces. The general analysis is applied to three examples: The first is completely dissipative and corresponds to chemical reactions near equilibrium; the second has an inertial term in the mechanical operation; and the third is designed to have similar properties as the second example but with...

Global thermodynamical stability and correlation inequalities

Abstract: Using spatially homogeneous dissipative perturbations, we derive a correlation inequality for states satisfying the variational principle for infinitely extended quantum lattice systems.

An experimental study of the trapped electron instability using a feedback diagnostic

Abstract: The dissipative trapped electron instability has been studied experimentally and theoretically in a linear device. Special emphasis is given to the effects of changing the length of the magnetic trapping cell (30 cm<2L<75 cm) and to the development of feedback as a diagnostic technique. It is shown that the dominant axial wavenumber k2, is determined by the length of the trapping cell, and this in turn has an effect on the real frequency omega R approximately=50 kHz. The minimum mirror ratio for instability onset is found to be Rc approximately=1.2. The dissipative nature of the instability is also demonstrated using feedback. The mode is definitely identified as the dissipative trapped electron instability through the dependence of the growth rate on electron collision frequency mirror ratio and through the radial and axial localization of the mode. The saturation amplitude of the density fluctuations is compared with the measured growth rate to show that the growth rate is proportional to the square of the saturation level.

2-D Fluid Calculations of Anomalous Trapped Ion Transport in Tokamaks

Abstract: The collisional, nonlinear trapped-fluid equations of Kadomtsev and Pogutse (K.P.) are used as a description of the dissipative trapped-ion modes. The equations are solved numerically in two spatial dimensions as an initial-value problem. Numerical results are given for the resulting anomalous diffusion coefficient D at late times, when the dissipative trapped-ion instability saturates. Examples of the time development D(t) are given. The numerical values of D (at late times) are generally larger than according to the K.P. formula, and the scaling of D with the equilibrium parameters resembles Bohm scaling. The dependence of the results on the numerical grid and on the initial conditions was also studied. Several analytical results are presented, some of which have been successfully used for testing the numerical code.

Bifurcation analysis of nonlinear reaction–diffusion systems: Dissipative structures in a sphere

Abstract: The steady state spatial patterns arising in open nonlinear reaction–diffusion systems beyond an instability point of the thermodynamic branch are studied for a simple kinetic scheme derived from glycolysis. Bifurcation theory is used to derive analytic expressions for patterns within a sphere. The results indicate that a gradient of substance may arise spontaneously from a homogeneous distribution within a cell or a blastula, thus establishing a prepattern. Finally, the derived solution scheme is shown to simplify considerably if rotation matrices are introduced into the formalism.

Electric energy density in a dissipative medium by circuit analog

Abstract: In a dispersive and dissipative medium, the electric energy density is no longer given by (1/2)E⋅D. When the dielectric function is given, the electric energy density of a monochromatic wave can be calculated by considering the energy stored in an equivalent linear circuit.

Energy principle for dissipative two-fluid plasmas

Abstract: Abstract An energy principle for the dissipative two-fluid theory in Lagrangian form is given. It represents a necessary and sufficient condition for stability allowing the use of test functions. It is exact for two-dimensional disturbances but is still correct in terms of perturbation theory for long wavelengths along the magnetic field. This may well find application in tokamak plasmas. A discussion of the general case and its relation to the stability of flows in hydrodynamics is given. This energy principle may be applied for estimating the magnitude of residual tearing modes in tokamaks.

Numerical Experiments on Trajectory Instabilities in Dissipative Systems

Abstract: It is confirmed by computer experiments that a probabilistic approach is necessary for description of the dynamics of dissipative systems with unstable trajectories, although given equations of motion are deterministic. How initially close points in phase space do spread with time is examined. From this it is shown that the conditional probabilities can be defined naturally by introducing the concept of coarse graining in phase space and time, and more­ over they satisfy a definition of a Markov process. The effect of external random forces is investigated by adding the Langevin forces to the equations of motion. It is suggested that the statistical properties of unstable dissipative systems are determined mainly by the inherent stochasticity due to the nonlinearity of the systems, unlike equilibrium systems whose statistical properties are governed by external random forces coming from contact with a heat reservoir.

Application of Gyarmati Principle to Boundary Layer Flow

Abstract: The paper deals with the development of a new variational method based on Gyarmati's principle for the solution of boundary layer flow along a flat plate. It is found that the variational solution differs by about 4% from exact result when a trial function of third degree is chosen for velocity profile. The results obtained with the help of the force representation of the principle are the same as obtained by the local potential method of Glansdorff and Prigogine. A polynomial of sixth degree with the help of universal form of the principle gives a result which differs by about 0.65% from the exact solution. The governing principle of dissipative processes, it seems, will prove itself quite satisfactory analytical method for the boundary layer flows.

High-frequency gravitational waves in a dissipative fluid.

Abstract: The interaction of a gravitational wave with a dissipative fluid is studied in the high-frequency approximation. The gauge invariance and the degrees of freedom of the gravitational wave in the matter have been carefully examined.

Response of a nonlinear dumbbell with varying frictional coefficient in a pseudo-turbulent flow field

Abstract: The response of a nonlinear dumbbell with varying frictional coefficient in a pseudo‐turbulent flow field is examined. It is shown that in such flows, the dumbbells will be able to maintain their highly dissipative extended configurations even though the mean flow is weak.