Showing papers on "Dissipative system published in 1977"

Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations

Abstract: Conservation Equations. Thermodynamics of Irreversible Processes: The Linear Region. Nonlinear Thermodynamics. Systems Involving Chemical Reactions and Diffusion-Stability. Mathematical Tools. Simple Autocatalytic Models. Some further Aspects of Dissipative Structures and Self-Organization Phenomena. General Comments. Birth and Death Descriptions of Fluctuations: Nonlinear Master Equation. Self-Organization in Chemical Reactions. Regulatory Processes at the Subcellular Level. Regulatory Processes at the Cellular Level. Cellular Differentiation and Patter Formation. Thermodynamics of Evolution. Thermodynamics of Ecosystems. Perspectives and Concluding Remarks. References. Index.

Coherent non-linear interaction of waves in plasmas

Abstract: The following chapters are included: (1) simple nonlinear examples, (2) coupled mode theory, (3) field energy in dissipative media, (4) formulation of nonlinear wave equations in terms of nonlinear current, (5) three-wave interactions, (6) energy relations, (7) negative energy waves, (8) coupled-mode equations, (9) stability criteria and asymptotic behavior for a general system of three interacting waves, (10) explosively unstable cases, (11) linear damping coefficients, (12) electromagnetic and plasma wave interactions, (13) stabilization of explosive instabilities, (14) third-order nonlinear effects, (15) coupling factors for three explosively unstable waves in a beam-plasma system, (16) second order dissipative effects, (17) interaction between waves with finite spread in wave vectors, (18) nonlinear excitation of collective waves, (19) parametric excitation of hybrid resonances, (20) nonresonant wave-wave interaction and wave-partial effects, (21) nonlinear effects, and (22) nonlinear plasma research developments. (MOW)

On the quantization of dissipative systems

Abstract: A recent paper of Dekker on the quantization of dissipative systems is examined in some detail. It is argued that one can construct a large number of classical equivalent Hamiltonians for damped systems. These can be formally quantized according to Dirac's method, and the resulting equations are mathematically consistent, but yield different eigenfunctions for the same classical system. However, this procedure should be rejected on physical grounds. That is in quantum mechanics, unlike classical dynamics, the definition of the time derivative of a dynamical variable is unique, and is given by the commutator of the proper Hamiltonian (or the energy operator) and that variable. If the proper Hamiltonian is used for the quantization of a damped system, then the quantal equations are inconsistent for the cases where the rate of energy dissipation depends on the velocity of the particle. As an alternative approach to the quantal theory of dissipative phenomena, a generalization of the Hamilton-Jacobi formalism is considered, where the equation for the principle functionS, depends not only on the space and time derivatives ofS, but onS itself. This leads to a new class of damped systems in classical mechanics. The original Schrodinger method of quantization via the Hamilton-Jacobi equation has been applied to this class of dissipative systems, with the result that the wave equation in this case is a solution of a non-linear Schrodinger-Langevin equation. This formulation has no analogue in the Hamiltonian approach, since in the latter, the resulting wave equation is always linear.

The correlation function for density perturbations in an expanding universe. I. Linear theory.

Abstract: The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

The Excitation of Surface Waves near a Cut-Off Frequency

Abstract: This paper describes a study of surface waves in a uniform channel, where the waves are generated by a plane flap executing torsional oscillations about a vertical axis at a frequency near a cut-off value for a wave mode. Experiments indicate that, near a cut-off frequency, the wave response is relatively large, and indeed linear inviscid theory suggests that the wave amplitudes are infinitely large at the cut-off frequency itself. Here we present theories for the modification of this result by making allowance (separately) for nonlinear terms in the surface boundary condition and for viscous dissipation. In order to estimate the effectiveness of the wavemaker in forcing the motions, a separate calculation was made to apportion the driving condition into a part driving a parasitic non-propagating field and a part forcing the wave modes. Also described in the paper are experiments in which the wave response has been measured in a similar situation to that modelled by the analytic work, and one of the main purposes of this study is to try to ascertain how well the theoretical model describes the experimental situation. An important feature to emerge from the comparison is that, even though the observed wave amplitudes were rather large and the temporal decay rate of standing waves corresponding to the cut-off mode was quite small, the dissipative effect played a crucial role in determining the structure of the response. Because of this the theoretical response was determined by numerical computation. Some of the results show a similarity with the response of a nonlinear spring, but there are significant differences. The results indicate that the model gave a good qualitative description of the experiments, and accordingly our main conclusions to the study are: (i) the multiple-scale calculation, by which the nonlinear effects were estimated, appears to have given useful results in this particular case; (ii) the way in which the dissipative effects were modelled appears to have been satisfactory; (iii) the method of estimating the effective driving condition at the wavemaker seems to have worked very well.

Stochastic mechanics and dissipative forces

Abstract: We analyze a simple velocity dependent potential in the framework of stochastic mechanics. A nonlinear Schrodinger–Langevin equation is obtained. This equation turns out to have solutions with the remarkable property of giving an approach to stationary quantum states. Information theoretical aspects on the irreversible behavior of the model is also briefly discussed.

Variational Finite-Element Solution for Dissipative Waveguides and Transportation Application

Abstract: A procedure is developed for determining the complex propagation constants and associated complex electromagnetic fields as a function of frequency for electromagnetic waves propagating along an inhomogeneous waveguide composed of dissipative materials and having a complicated shape. The wave equation, which is complex because of the presence of dissipative materials, is transformed for computer solution into a matrix eigenvalue equation by the application of the Rayleigh-Ritz variational method in conjunction with the finite-element method. The results are reviewed for several simple dissipative waveguides for which analytical results are computed for comparison. A novel proposal is then investigated in which a railroad track acts as a surface waveguide for a rapid-transit collision-avoidance system. The results illustrate the usefulness of the numerical method developed and suggest that the modified steering rail warrants further investigation for rapid-transit systems.

Nonlinear saturation of the dissipative trapped-electron instability

Abstract: It is shown that trapping-electron--induced scattering can be dominant over nonlinear ion Landau damping in the saturation of short-wavelength, dispersive, trapped-electron instabilities in tokamaks. Trapped-electron-induced scattering transfers the wave energy to shorter wavelengths, where it can be dissipated by ion viscosity.

Canonical approach to the quantum problem of the motion of a particle in a viscous medium

Abstract: (ricevnto il 4 Marzo 1977) The problem of the quantum treatment of dissipative phenomena is still an open one and many different approaches have been proposed, that never could lead to com- pletely satisfying results. A simple way which can be followed consists in starting from a classical problem and then quantizing it via the usual correspondence principle and the canonical for- malism. Limiting us to the case of a particle of mass ~ in a viscous medium whose friction coefficient is ? (a constant), the classical problem of motion is governed by Langevin's equation (1) mF + m~ =f(t)--VV(r), where r is the particle position,

Theoretical Study of a Chemical Turbulence

Abstract: Recently Kuramoto and one of the present authors have carried out a computer simula­ tion for a chemically oscillating system and found a turbulence-like behavior similar to the hydrodynamic turbulence. The steady turbulent state of this system is theoretically studied. It is shown that there exist two characteristic regions of wavenumber k. One is a cascade region with ks~1, and the other is a dissipative region with kS> 1, where s is a characteristic length which is much larger than the reaction mean free path lr. Over these two regions = = =

Theory of an insulated linear antenna in a dissipative medium

Abstract: The theoretical model of an insulated antenna in a general ambient medium is reviewed briefly. Attention is then directed to the solution of the integral equation for the current distribution in the antenna. The properties of the kernel are discussed in detail, and approximate solutions for the complex wave number are obtained. The evaluation of the kernel and other related numerical problems are discussed and a numerical method of computation is presented. A discussion of approximate solutions is included. A comparison of the theoretical results with measured data and numerical computations is made to check the applicable range of the theory.

Two-dimensional spatial structure of the dissipative trapped-electron mode

Abstract: The complete two‐dimensional structure of the dissipative trapped‐electron mode over its full width, which may extend over several mode‐rational surfaces, is discussed. The complete integrodifferential equation is studied in the limit krρi<1, where ρi is the ion gyroradius, and kr, the radial wavenumber, is regarded as a differential operator. This is converted into a matrix equation which is then solved by standard numerical methods. Solutions obtained are in reasonably good agreement with one‐dimensional analytic solutions, in the limits where such results are expected to be valid. More significantly, the present approach can readily treat many physically important cases for which purely analytic solutions are difficult to obtain. The results indicate that the differential equation formulation of the eigenmode equation is valid only for long wavelength modes (kϑρi≲0.3, with kϑ being the poloidal wavenumber). For such cases it is found that shear stabilization estimates obtained from the one‐dimensional ...

Relativistic elasticity of dissipative media and its wave propagation modes

Abstract: A phenomenological, general relativistic theory of dissipative elastic solids whose equations form a hyperbolic system is proposed. The non-stationary transport equations for dissipative fluxes containing new cross-effect terms, as required by compatibility with irreversible thermodynamics, have been adopted. As opposed to some conventional theories which are parabolic and predict instantaneous propagation of wavefronts, the theory formulated, consisting of 14 partial differential equations (in the case of special relativity), of total order 17, is hyperbolic and predicts, for all existing propagation modes, finite front speeds. The complete system of special relativistic propagation modes of an elastic solid is determined from the linearised equations. There are four mutually distinct non-trivial propagation modes, two for longitudinal waves and two for transverse waves. If the rigidity modulus decreases to zero one obtains as a special case the normal modes for fluid according to the theory of Muller (1972) and Israel (1976). Weber's equation is also briefly discussed.

A chaotic cosmology

Abstract: An anisotropic, inhomogeneous cosmological model is proposed in which the inhomogeneity is generated by shear fluctuations. This is a sufficient condition for dissipative heating by collisional neutrinos to explain the present large heat content of the universe, Sb o ∼ 108, together with its isotropy and comparative homogeneity on large scales when the photons were last scattered. The model does not require the chaotic motions to be arbitrarily truncated on large scales and isotropises early enough with high entropy to ensure the synthesis of light elements with the observed abundancies. A population of black holes which arises in a natural way can also provide the necessary ingredients for a theory of galaxy formation and morphology. The 1015-g black holes, predicted by some authors, are not necessarily expected to be a feature of chaotic cosmologies.

Hyperbolic elasticity of dissipative media and its wave propagation modes

Abstract: A phenomenological theory of dissipative elastic solids whose equations form a hyperbolic system is proposed. The Muller-Israel non-stationary transport equations for dissipative fluxes containing new cross-effect terms, as required by compatibility with irreversible thermodynamics, have been adopted. As opposed to usual conventional theories, which are parabolic and predict instantaneous propagation of wavefronts, the theory formulated, formed of 14 partial differential equations, all of 17th order, is hyperbolic and predicts, for all existing propagation modes, finite front speeds. The complete system of propagation modes is determined from the linearized equations. There are four mutually distinct non-trivial propagation modes, two for longitudinal waves and two for transverse waves.

Theory of turbulence in superfluid /sup 4/He

Abstract: A consideration of the dynamics of a vortex tangle leads to a new equation describing turbulence in superfluid helium. The equation is seen to be remarkably successful in predicting the steady-state properties of dissipative counterflow.

Stationary Random Vibration of Hysteretic Systems

Abstract: A more rigorous derivation of the modified power balance method is given for general yielding systems. It is demonstrated that the physical meaning of the equivalent linearization criteria derived by the mean-square minimization (Krylov-Bogoliubov) method are the equivalency of the dissipative and potential energies of the linear and nonlinear systems. Thus, linearization by power balance can be the same as by mean-square minimization. Simple gradient-stiffness approximations for the amplitude-dependent average frequency of hysteresis cycles and the overall average frequency of random response are presented for systems of Masing's type. In addition to the previously studied bilinear hysteretic system, the method is applied to compute rms response levels of trilinear hysteretic and Ramberg-Osgood type systems.