Showing papers on "Dissipative system published in 1975"
343 citations
TL;DR: In this article, two types of nonlinear Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time-dependent one and an alternative class of non-linear Hamiltonian.
Abstract: Two types of Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time‐dependent one and an alternative class of nonlinear Hamiltonians. In the latter group we propose a new form. By Ehrenfest’s theorem the expectation values of the operators of physical observables correspond to the classical quantities. For all Schrodinger equations we derive and discuss wavepacket, wave, stationary, and pseudostationary solutions of force free motion, free fall, and harmonic oscillator.
280 citations
01 Jan 1975
TL;DR: In this article, a unified viewpoint on the dynamics of spatio-temporal organization in various reaction-based diffusion systems is presented, and a dynamical similarity law attained near the instability points plays a decisive role in the whole theory.
Abstract: A unified viewpoint on the dynamics of spatio-temporal organization in various reaction diffusion systems is presented. A dynamical similarity law attained near the instability points plays a decisive role in our whole theory. The method of reductive perturbation is used for extracting a scale-invariant part from original macroscopic equations of motion. It is shown that in many cases the dynamics near the instability point is governed by the time dependett Ginzburg-Landau equation with coefficients which are in general complex numbers. A~ important effeCt of the imaginary parts of these coefficients on the stability of a spatially uniform limit cycle against inhomogeneous perturbation is also discussed.
193 citations
TL;DR: In this paper, a unified microscopic statistical theory of preequilibrium and equilibrium processes of the compound nucleus, valid for mass numbers A ⪆ 40, light incident projectiles (A ′4), and for excitation energies a few MeV above neutron threshold or larger, is presented.
193 citations
TL;DR: In this paper, the finite amplitude behavior of global magnetic fields and the large-scale flows induced by them in rotating systems is investigated, where viscous and ohmic dissipative mechanisms both play a role in determining the amplitude and structure of the flows and magnetic fields.
Abstract: Past study of the large-scale consequences of forced small-scale motions in electrically conducting fluids has led to the ‘α-effect’ dynamos. Various linear kinematic aspects of these dynamos have been explored, suggesting their value in the interpretation of observed planetary and stellar magnetic fields. However, large-scale magnetic fields with global boundary conditions can not be force free and in general will cause large-scale motions as they grow. I n this paper the finite amplitude behaviour of global magnetic fields and the large-scale flows induced by them in rotating systems is investigated. In general, viscous and ohmic dissipative mechanisms both play a role in determining the amplitude and structure of the flows and magnetic fields which evolve. In circumstances where ohmic loss is the principal dissipation, it is found that determination of a geo- strophic flow is an essential part of the solution of the basic stability problem. Nonlinear aspects of the theory include flow amplitudes which are independent of the rotation and a total magnetic energy which is directly proportional to the rotation. Constant a is the simplest example exhibiting the various dynamic balances of this stabilizing mechanism for planetary dynamos. A detailed analysis is made for this case to determine the initial equilibrium of fields and flows in a rotating sphere.
182 citations
TL;DR: In this paper, the guiding center kinetic equation with Fokker-Planck collision term is used to study a class of dissipative instabilities of which the classical tearing mode is an archetype.
Abstract: The guiding‐center kinetic equation with Fokker‐Planck collision term is used to study, in cylindrical geometry, a class of dissipative instabilities of which the classical tearing mode is an archetype. Variational solution of the kinetic equation obviates the use of an approximate Ohm’s law or adiabatic assumption, as used in previous studies, and it provides a dispersive relation which is uniformly valid for any ratio of wave frequency to collision frequency. One result of using the rigorous collision operator is the prediction of a new instability. This instability, driven by the electron temperature gradient, is predicted to occur under the long mean‐free path conditions of present tokamak experiments, and has significant features in common with the kink‐like oscillations observed in such experiments.
169 citations
TL;DR: In this article, a model nonlinear network involving chemical reactions and diffusion is studied and the time evolution and bounds on the steady state solutions of the dissipative structure type are found by bifurcation theory.
163 citations
TL;DR: In this paper, the existence of first integrals for non-convex systems with non-conservative forces is established. But the existence depends on the existence either of solutions of the generalized Noether-Bessel-Hagen equation or of the Killing system of partial differential equations.
Abstract: Noether's theorem and Noether's inverse theorem for mechanical systems with nonconservative forces are established. The existence of first integrals depends on the existence of solutions of the generalized Noether-Bessel-Hagen equation or, which is the same, on the existence of solutions of the Killing system of partial differential equations. The theory is based on the idea that the transformations of time and generalized coordinates together with dissipative forces determine the transformations of generalized velocities, as it is the case with variations in a variational principle of Hamilton's type for purely nonconservative mechanics [17], [18]. Using the theory a few new first integrals for nonconservative problems are obtained.
148 citations
TL;DR: In this article, it was shown that the ratio of dissipative heating to the convected heat flux is approximately equal to c(d/HT), where the constant c is independent of the Rayleigh number.
Abstract: Dissipative heating is produced by irreversible processes, such as viscous or ohmic heating, in a convecting fluid; its importance depends on the ratio d/HT of the depth of the convecting region to the temperature scale height. Integrating the entropy equation for steady flow yields an upper bound to the total rate of dissipative heating in a convecting layer. For liquids there is a regime in which the ratio of dissipative heating to the convected heat flux is approximately equal to c(d/HT), where the constant c is independent of the Rayleigh number. This result is confirmed by numerical experiments using the Boussinesq approximation, which is valid only if d/HT is small. For deep layers the dissipative heating rate may be much greater than the convected heat flux. If the earth's magnetic field is maintained by a convectively driven dynamo, ohmic losses are limited to 5% of the convected flux emerging from the core. In the earth's mantle viscous heating may be important locally beneath ridges and behind island arcs.
137 citations
TL;DR: In this paper, general expressions for the frictional term of the Schrodinger equation were derived for both the dissipative and the non-deterministic terms, and a proof was given showing that the Frictional term causes the quantum system to lose energy.
Abstract: Frictional and dissipative terms of the Schrodinger equation are studied. A proof is given showing that the frictional term of the Schrodinger-Langevin equation causes the quantum system to lose energy. General expressions are derived for the frictional term of the Schrodinger equation.
106 citations
TL;DR: In this paper, the steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network, and a detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions.
TL;DR: In this paper, the steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network, and a detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions.
TL;DR: In this article, the authors examined the mechanics of dumbbell suspensions and found that the friction coefficient increases with molecular extension, both in weak flows and in strong flows, and the most interesting result occurs in steady elongational flows where a "hysteresis" loop is found, so that in a certain range of elongation rates two elongational viscosities are possible, the one occurring depending on the previous history of the elongation rate.
Abstract: The examination of the mechanics of dumbbell suspensions is extended to include the increase of the friction coefficient with molecular extension, both in weak flows and in strong flows. The most interesting result occurs in steady elongational flows where a “hysteresis” loop is found, so that in a certain range of elongation rates two elongational viscosities are possible, the one occurring depending on the previous history of the elongation rate. This result is of interest because it increases the plausibility of those explanations of turbulent drag reduction which depend on maintaining the molecules in an extended, highly dissipative configuration. The hysteresis loop is also of interest in that it represents an effectively infinite memory of a selective type which is not compatible with the usual hypotheses about fading memory usually associated with the simple fluid concepts of continuum mechanics, although our dilute solution model is clearly a simple fluid. No hysteresis loop was found in steady shearing flows, but an increase in viscosity above the zero‐shear viscosity is predicted at intermediate shear rates.
TL;DR: In this paper, deep inelastic heavy ion collisions are investigated in a classical model including dissipative forces, and degrees of freedom are taken into account explicitly in the dynamical calculation.
TL;DR: In this paper, a general formalism of scattering theory with dissipative interactions is presented from a time-dependent viewpoint, and a definition of time delay is proposed in this framework, generalizing that given for simple scattering systems.
Abstract: The general formalism of scattering theory with dissipative interactions is presented from the time-dependent viewpoint. A definition of time delay is proposed in this framework, generalizing that given for simple scattering systems. The time delay is expressed by a formula which reduces to that of Eisenbud and Wigner when there is no absorption.
TL;DR: In this paper, the collisional contribution to fluctuating number and current density was calculated from the linearized electron kinetic equation with a Lorentz collision operator, and the dominant dissipative contribution was shown to arise from the low energy electrons that contribute a damping proportional to (ωνe/k2v2e)3/5.
Abstract: The collisional contribution to the fluctuating number and current density are calculated from the linearized electron kinetic equation with a Lorentz collision operator. In the weakly collisional regimes of practical importance for low frequency drift, sound, and Alfven waves, the dominant dissipative contribution is shown to arise from the low energy electrons that contribute a damping proportional to (ωνe/k2v2e)3/5.
TL;DR: In this article, the pathintegral method is employed systematically throughout for the derivation of the propagator associated with the most general form of a quadratic Lagrangian.
Abstract: The path-integral method is employed systematically throughout for the derivation of the propagator associated with the most general form of a quadratic Lagrangian. The result is applied for the evaluation of the propagator of a constrained particle having a dissipative Lagrangian.
TL;DR: In this paper, the concepts of kinetic energy, potential energy and energy flux are clarified and quantified for atmospheric tides, and an understanding of the tidal energy relations provides physical insight into the problem of dissipative effects an tidal structure.
Abstract: The concepts of kinetic energy, potential energy and energy flux are clarified and quantified for atmospheric tides. An understanding of the tidal energy relations provides physical insight into the problem of dissipative effects an tidal structure. It is shown that mode coupling effects due to dissipative forces are related to the coupling of kinetic energy between different tidal modes, and the mode-coupling coefficients are computed for several tidal modes. A relation is derived linking energy density and variations of the eigenvalues of Laplace's tidal equation with frequency. A formalism of “analogous atmospheric oscillations” in a plane-parallel, uniformly rotating atmosphere is proposed to provide an approximate method of computing tidal structure in the presence of dissipative forces.
01 Jan 1975
TL;DR: The theory of nonlinear wave propagation in both bounded and semi-infinite dissipative media is followed from its origins in the theories of linear geometrical acoustics, simple waves, and acceleration fronts as discussed by the authors.
Abstract: : The development of the theory of nonlinear wave propagation in both bounded and semi-infinite dissipative media is followed from its origins in the theories of linear geometrical acoustics, simple waves, and acceleration fronts. In Part I, Sections 2 to 5, we consider examples in which only one component wave is excited and describe the effects of three types of dissipative mechanisms on unidirectional waves. In Part II, Sections 6 to 9 we consider nonlinear waves in media of finite extent. In general, more than one component wave is excited. The coupling between the interaction and distortion of the different components is described. The effect of radiation from the boundaries is included for both transient and forced, time-periodic motions.
TL;DR: In this paper, the same screw sense of the sine-Gordon equation is used to model the interaction of two solitons with the same sink sense of sine−Gordon equation, which can couple when the bias is greater than a critical value.
Abstract: By computer simulation, interaction of two solitons with the same screw sense of the sine‐Gordon equation, which retain their shapes and velocities upon collision with other solitons even in the presence of bias and loss terms, are examined. It is confirmed that they can couple when the bias is greater than a critical value. The conditions and mechanism of coupling are examined in detail. They are explained in terms of the energy of interaction between the ripple structures trailed by energy dissipative moving solitons. The distance D between coupled solitons can be expressed as D= (n−1/2−δ) λ (n is an integer), where λ is a wavelength of the ripple structure and δ≪1.
TL;DR: It is shown that all solutions to a generic system of reaction-diffusion equations evolve dynamically to a unique steady state, lim t → ∞ c i (x, t ) = ĉ i ( x ) , if the diffusivity constants are all sufficiently large in magnitude.
TL;DR: The problem of multiplicity of stable ordered solutions which turns out to increase sharply from one to two dimensions, is discussed, and the comparison of the numerical results with bifurcation theory is outlined.
01 Nov 1975
TL;DR: In this article, a study of the poloidal mode structure of the dissipative trapped electron drift mode by Fourier analysis is presented, showing that when ion inertia effects are small compared with trapped electron effects, the mode balloons out in the region of trapped particles.
Abstract: A study of the poloidal mode structure of the dissipative trapped electron drift mode by Fourier analysis shows that when ion inertia effects are small compared with trapped electron effects, the mode balloons out in the region of trapped particles. When ion inertia effects are large, there is no ballooning and the growth rates are correspondingly smaller.
TL;DR: In this article, the authors considered the problem of constructing a model equation for the wave processes in a thermoelastic medium in the presence of cylindrical and spherical symmetry, and gave a solution to the boundary value problem.
TL;DR: In this paper, a multipoint filter for use as a dissipative mechanism in a numerical model is formulated, and some of its properties discussed, and results of three numerical experiments are compared, of which one employs a nonlinear diffusion term, another has the filter applied in the zonal direction only, and the third employs the filter in both zonal and meridional directions.
Abstract: A multipoint filter for use as a dissipative mechanism in a numerical model is formulated, and some of its properties discussed. The results of three numerical experiments are compared, of which one employs a non-linear diffusion term, another has the filter applied in the zonal direction only, and the third employs the filter in both zonal and meridional directions. The simulated climatology of the filtered experiments is seen to be significantly better in some respects than that of the experiment using a diffusion term.
TL;DR: In this article, a study of the dissipative trapped electron instability is greatly simplified, both experimentally and theoretically, when posed in a cylindrical geometry and a derivation of the linear dispersion relation is presented.
Abstract: A study of the dissipative trapped electron instability is greatly simplified, both experimentally and theoretically, when posed in a cylindrical geometry. A derivation of the linear dispersion relation for a finite cylindrical system with two localized magnetic mirrors shows that a linear machine can support the instability with strong localization between the mirrors. The growth rate can be larger than 10% of the wave frequency which is approximately the drift frequency. A simple physical explanation is provided for the dynamics of the instability. An experiment was performed in a Q-machine converted to an ODE-type device in which the dissipative trapped electron instability was definitively identified through the dependence of the wave amplitude on mirror ratio, axial position, temperature gradient, electron collision frequency, and radial position. The wave, with the azimuthal mode number 1, is nearly monochromatic at approximately 50 kHz which is in the neighbourhood of the drift frequency. The density fluctuation in the wave can be as high as 30%.