Showing papers on "Dissipative system published in 1982"

Quantum Dynamics of Tunneling between Superconductors

Abstract: A functional integral formulation is used to treat the quantum dynamics of a microscopic model of a Josephson junction, including the dissipative effects of quasiparticle tunneling. The calculation is carried to a point where it makes contact with, and therefore substantiates, recent work by Caldeira and Leggett in which the system is treated by analogy with the quantum Brownian motion of a massive particle coupled to a phenomenological heat bath.

On a quasiclassical Langevin equation

Abstract: It is shown that the motion of a quantum mechanical particle coupled to a dissipative environment can be described by a Langevin equation where the stochastic force is generalized such that its power spectrum is in accordance with the fluctuation-dissipation theorem. This generalized Langevin equation has an interesting range of applicability. It includes the quasiclassical regime provided that the damping, that is, the coupling of the particle to its environment, is sufficiently strong.

Large volume limit of the distribution of characteristic exponents in turbulence

Abstract: For spatially extended conservative or dissipative physical systems, it appears natural that a density of characteristic exponents per unit volume should exist when the volume tends to infinity. In the case of a turbulent viscous fluid, however, this simple idea is complicated by the phenomenon of intermittency. In the present paper we obtain rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation. These bounds have a reasonable large volume behavior. For two-dimensional fluids a particularly striking result is obtained: the total information creation is bounded above by a fixed multiple of the total energy dissipation (at fixed viscosity). The distribution of characteristic exponents is estimated in an intermittent model of turbulence (see [7]), and it is found that a change of behavior occurs at the valueD=2.6 of the self-similarity dimension.

Kink dynamics in one-dimensional nonlinear systems

Abstract: A certain class of nonlinear evolution equations of one space dimension which permits kink type solutions and includes one-dimensional time-dependent Ginzburg-Landau (TDGL) equations and certain nonlinear wave equations is studied in some strong coupling approximation where the problem can be reduced to the study of kink dynamics. A detailed study is presented for the case of TDGL equation with possible applications to the late stage kinetics of order-disorer phase transitions and spinodal decompositions. A special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics. A new conservation law for dissipative systems is found which corresponds to the momentum conservation law for wave equations.

Finite amplitude Alfvén waves in a multi-ion plasma: Propagation, acceleration, and heating

Abstract: An expression is derived for the wave action flux of finite-amplitude Alfven waves in a multi-ion plasma. The expression is valid in the presence of dissipative forces and permits an arbitrary angle between the average magnetic field and the wave vector. Applying the conservation of wave action and the first law of thermodynamics yields, for a multi-ion plasma, an expression for the spatial evolution of Alfven wave amplitude in the absence of dissipation. It also gives the relationship between the wave amplitude and the dissipative heating, as well as an expression for the acceleration of an ion species by finite-amplitude Alfven waves. It is pointed out that the acceleration comprises a nondissipative wave pressure that is identical to that derived previously under more restrictive conditions and a new term giving the acceleration that must accompany dissipative heating. The results are discussed in the context of the observations of heavy ions in the solar wind.

Diffusive dynamics in systems with translational symmetry: A one-dimensional-map model

Abstract: A one-dimensional, one-parameter-map model for dissipative systems with translational symmetry is studied. The map possesses confined periodic and chaotic solutions which form an infinite array on the real line, periodic or chaotic running solutions which propagate coherently to the left or right, and a variety of diffusive motions where iterates wander over the entire interval like a random walk. The onset of diffusion in various regions of parameter space is studied in detail and simple dynamical models for the behavior of the diffusion coefficient near bifurcation points are constructed.

On some quasilinear wave equations with dissipative terms

Abstract: In this paper we consider the initial value problems for the following quasilinear wave equations with dissipative terms with initial conditions where

Repeated yield drop phenomenon: a temporal dissipative structure

Abstract: Based on well known mechanisms, the authors set up a system of coupled nonlinear rate equations for the densities of three types of dislocations, namely, the mobile, the immobile and those with clouds of solute atoms, and for the load sensed by the load cell. For a range of values of the parameters, these equations admit periodic solutions called limit cycles, leading to repeated yield drops. The model exhibits many experimentally observed features. The new temporal order is an example of a dissipative structure.

Analysis of flow hysteresis by a one-dimensional map

Abstract: The structure of a region of stable period three for a nonlinear dissipative system described by the R\"ossler equations and a two-parameter cubic map is studied. The intricate configuration of this region, which is bordered by intermittent-type chaos on one side, subharmonic cascades on the other, and possesses several sharp features, is shown to be associated with bistability and hysteresis of the orbits of the flow or map. Locally, the two-parameter cubic map successfully models many features of the differential flow. The mechanism which gives rise to the hysteresis is quite general and corresponds to a cusp catastrophe. This process is described in detail for the map and related to the same phenomenon in the flow.

A search for Chandler and nearly diurnal free wobbles using Liouville equations

Abstract: Summary. The basic equations describing the dynamical effects of the Earth's fluid core (Liouville, Navier-Stokes and elasticity equations) are derived for an ellipsoidal earth model without axial symmetry but with an homogeneous and deformable fluid core and elastic mantle. We develop the balance of moment of momentum up to the second order and use Love numbers to describe the inertia tensor's variations. The inertial torque takes into account the ellipticity and the volume change of the liquid core. On the core—mantle boundary we locate dissipative, magnetic and viscous torques. In this way we obtain quite a complete formulation for the Liouville equations. These equations are restricted in order to obtain the usual Chandler and nearly diurnal eigenfrequencies. Then we propose a method for calculating the perturbations of these eigenfrequencies when considering additional terms in the Liouville equations.

Microscopic derivation of a class of non-linear dissipative schrödinger-like equations

Abstract: The general formalism of master equations is used together with a projection which preserves the pure states to derive a class of non-linear Schrodinger-like equations. The result is applied to a spin- 1 2 coupled to a bath of two-level systems and the Bloch equations are recovered. Finally we make a connection with Sz-Nagy's theorem on the dilations of contracting semi-groups.

On a covariant formulation of dissipative phenomena

Abstract: In this article, a covariant non-stationary theory of continuum irreversible thermodynamics is proposed. The specific entropy and the entropy flux as well as the thermodynamical forces are expanded up to second order in the dissipative fluxes. As a consequence, the speed of propagation of perturbations is finite and the phenomenological laws are non-linear in the dissipative fluxes. In the non-relativistic limit, these equations reduce to those of extended irreversible thermodynamics. RESUME. Dans cet article on propose une theorie covariante et non stationnaire de la thermodynamique irreversible des milieux continus. L’entropie specifique et le flux d’entropie, d’une part, ainsi que les forces thermodynamiques d’autre part, sont développés jusqu’au deuxième ordre dans les flux dissipatifs. Comme une consequence, on obtient des perturbations se propageant a vitesse finie et des lois non-linéaires dans les flux. Dans la limite non-relativiste ces equations se reduisent a celles de la thermodynamique irreversible generalisee.

Time-dependent shell-model theory of dissipative heavy-ion collisions

Abstract: A transport theory is formulated within a time-dependent shell-model approach. Time averaging of the equations for macroscopic quantities lead to irreversibility and justifies weak-coupling limit and Markov approximation for the (energy-conserving) one- and two-body collision terms. Two coupled equations for the occupation probabilities of dynamical single-particle states and for the collective variable are derived and explicit formulas for transition rates, dynamical forces, mass parameters and friction coefficients are given. The applicability of the formulation in terms of characteristic quantities of nuclear systems is considered in detail and some peculiarities due to memory effects in the initial equilibration process of heavy-ion collisions are discussed.

Generation of a high-energy electron tail by strong Langmuir turbulence in a plasma

Abstract: Strong Langmuir turbulence has recently been described by a statistical treatment of collapsing cavities. This work is extended and corrected by derivation of a transfer rate valid for both the inertial and dissipative ranges, and the power-law distribution of fast electrons is obtained. Self-consistent modifications of similarity laws are calculated in the dissipative range, which change dramatically the conventional features of collapse. Limitations to collapse are also discussed.

Some comments on wave motions described by non-homogeneous quasilinear first order hyperbolic systems

Abstract: In this paper a quasilinear first order hyperbolic system of partial differential equations involving a source term is considered. Thus in the usual context of the n-dimensional nonlinear wave propagation theory it is shown that the source term may produce attenuation effects against the typical nonlinear steepening of the waves. Therefore, by generalizing Whitham's ideas[9], [10], it is possible to introduce a «reduced system» of field equations which gives an approximate description of the wave process. Then, in an asymptotic way, it is possible to point out that in a wave motion governed by the reduced system there is a coupling between nonlinearity and dissipative (or dispersive) effects. A typical physical example where the present theory may be applied is shown at the end of the paper.

Current layers and filaments in a semiconductor model with an impact ionization induced instability

Abstract: Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.

Minimum Energy and Energy Dissipation Rate

Abstract: The theory of minimum energy and the minimum rate of energy dissipation have been applied to flow around bluff bodies, stability of falling bodies, statics and dynamics of gas bubbles, generation of ripples and dunes, and drag reduction by suspended load. These examples are used to illustrate how the minimization principles (variational principles) can be used to solve the problems of dissipative mechanical systems in static or dynamic equilibrium conditions. The minimization principle can be used independently or in tandem with the equations of motion to solve problems of a large degree of freedom. The equilibrium solution thus obtained has been shown to contain certain implicit information on the stability characteristics of the equilibrium state. For this reason, the method is not only a viable alternative to the vector mechanics method, but it also provides a relatively simple way of determining certain stability criteria.

Variational Principles for Perfect and Dissipative Fluid Flows

Abstract: Many versions of an extension of Hamilton's principle to perfect fluid flows exist in the literature. In this paper the most general form, due to Serrin, is identified and the limitations of some of the others discussed. An extension of the variational principle to viscous, thermally conducting fluid flows is suggested. This is compared with some other variational principles for viscous flows, and the relative merits of the various approaches are discussed.

Non-Linear Hydrodynamic Fluctuations Around Equilibrium

Abstract: We formulate a scheme describing the fluctuations in a system obeying the non-linear hydrodynamic equations. The random fluxes are assumed to be Gaussian processes with white noise. It is shown that the usual expressions for the systematic parts of the dissipative fluxes are consistent with this assumption, provided that the Onsager coefficients are constants. The linear response of the system to a small external force field is studied and the relevant fluctuation- dissipation theorems are derived.

Dissipative contributions of internal multiplicative noise: II. Spin systems☆

Abstract: We analyze the relaxation of a spin interacting with a heat bath of other spins, in an external magnetic field, starting from a fully dynamical (Hamiltonian) description. We derive a generalized Langevin equation for the spin system in which the initial conditions of the bath spins act as fluctuations. The generalized Langevin equation has multiplicative fluctuations and nonlinear dissipation (relaxation) contributions which obey a fluctuation-dissipation theorem. As a natural consequence, our spin system relaxes to a canonical distribution. We also examine the moment equations for the spin in the Langevin limit. Because of the nonlinear dissipative contributions, the moment equations form a nonlinear linked hierarchy which under certain conditions reduces to the linear Bloch equations. Our theory yields expressions for the longitudinal and transverse relaxation times in terms of the microscopic parameters of the system, the external magnetic field and the temperature.