Showing papers on "Dissipation published in 1987"
IBM1
TL;DR: In this article, the authors analyze some of the less appreciated concomitants of this viewpoint, emphasizing both the generality and limitations of the viewpoint, and suggest that the limited precision available,in principle, in calculating the behavior of physical systems limits our ability to retrieve energy from supposedly conservative systems.
Abstract: Electrical conductance is typically calculated by approaches which view the electrical field as a causative source and the motion of carriers as a response. An alternative viewpoint, which starts from the flux of carriers maintained at the edges of a sample, and then calculates how charges build up and fields develop, has gained acceptance in the treatment of disordered systems, the solid state Aharanov-Bohm effect, and universal fluctuations. We analyze some of the less appreciated concomitants of this viewpoint, emphasizing both the generality and limitations of the viewpoint. Particular emphasis is given to the Residual Resistivity Dipole; localized scatterers in metallic conductivity are accompanied by highly localized transport fields. Closed Hamiltonian systems, e.g. a metallic ring with elastic scattering and driven by a time-dependent magnetic flux, are conservative. They cannot exhibit dissipation, under our conventionally accepted forms of physics. It is suggested that the limited precision available,in principle, in calculating the behavior of physical systems limits our ability to retrieve energy from supposedly conservative systems. This can be regarded as the ultimate source of dissipative processes.
297 citations
01 Jan 1987
255 citations
TL;DR: In this article, the authors examined the derivation of constitutive relations from the free energy and the dissipation function of an elastic body and found that if the deformation of a body is neither isothermal nor adiabatic, the strain tensor has to be supplemented by the additional independent state variable.
Abstract: Publisher Summary This chapter examines the derivation of constitutive relations from the free energy and the dissipation function. Continuum mechanics allows one to establish constitutive relations, deducing them from a single pair of scalar functions characterizing the material. The simplest materials dealt with in continuum mechanics are elastic. More general processes and those taking place in more general materials are irreversible and require more constitutive relations, connecting the dissipative forces with the velocities. The orthogonality condition and the equivalent extremum principles have been established for velocities in the form of vectors or symmetric tensors. It is found that if the deformation of an elastic body is neither isothermal nor adiabatic, the strain tensor has to be supplemented by the additional independent state variable. The connection between stress and elastic strain is given by the generalized Hooke's law and connects the stress with the plastic strain and its time rate. It is found that orthogonality in velocity space, which is essentially responsible for the results, does not necessarily imply orthogonality in force space.
226 citations
01 Nov 1987
TL;DR: In this paper, the authors make a connection between the multifractal approach (described in section 2) and the traditional language used in the turbulence literature, and use it to measure the (infinite) set of generalized dimensions of the turbulent energy dissipation field.
Abstract: It has been pointed out (Mandelbrot 1974) that the turbulent energy dissipation field has to be regarded as a non-homogenous fractal and that other more general quantities than the fractal dimension of its support have to be invoked for describing its scaling (metric) properties completely. This work is an attempt on amplifying this idea by using direct experimental data, and on making proper connections between the multifractal approach (described in section 2) and the traditional language used in the turbulence literature. In the multifractal approach (Frisch & Parisi, 1983), the local behavior of the dissipation rate is described by a fractal power-law. We verify that this is so, and use it to measure the (infinite) set of ‘generalized dimensions’, and thus obtain the multifractal spectrum f(α) for one-dimensional sections through the dissipation field. Two operational approximations are made: first, for most of the results, a single component of the energy dissipation will be used as a representative of the total dissipation; second, we use Taylor's forzen flow hypothesis. The validity of both these approximations will be briefly assessed. We relate our results to lognormality, velocity structure functions, auto-correlation function of the dissipation rate, Kolmogorov's -5/3 law for the energy spectrum, the skewness and flatness factor of velocity derivatives, as well as to possible improvements in estimating various interface dimensions. We conclude that the multifractal approach provides a useful and unifying framework for describing the scaling properties of the turbulent dissipation field.
217 citations
TL;DR: In this article, the wave equation for a dissipative, compressible plasma is derived from the linearized magnetohydrodynamic equations for a plasma with transverse Alfven speed gradients.
Abstract: An improved method for calculating the resonance absorption heating rate is discussed and the results are compared with observations in the solar corona. To accomplish this, the wave equation for a dissipative, compressible plasma is derived from the linearized magnetohydrodynamic equations for a plasma with transverse Alfven speed gradients. For parameters representative of the solar corona, it is found that a two-scale description of the wave motion is appropriate. The large-scale motion, which can be approximated as nearly ideal, has a scale which is on the order of the width of the loop. The small-scale wave, however, has a transverse scale much smaller than the width of the loop, with a width of about 0.3-250 km, and is highly dissipative. These two wave motions are coupled in a narrow resonance region in the loop where the global wave frequency equals the local Alfven wave frequency. Formally, this coupling comes about from using the method of matched asymptotic expansions to match the inner and outer (small and large scale) solutions. The resultant heating rate can be calculated from either of these solutions. A formula derived using the outer (ideal) solution is presented, and shown to be consistent with observations of heatingmore » and line broadening in the solar corona. 34 references.« less
203 citations
TL;DR: In this article, the authors discuss the one-body dissipation model in its richness of phenomena and compare its predictions to measured data, focusing on the non-equilibrium relation between friction (or mobility) and diffusion.
Abstract: As the study of Brownian movement is the key to the understanding of all dissipative phenomena, the author uses it to introduce the concepts which are then made use of in a specific dissipative model. The author discusses the 'one-body dissipation model' in its richness of phenomena and compares its predictions to measured data. Special attention is paid to the non-equilibrium relation between friction (or mobility) and diffusion.
175 citations
TL;DR: In this paper, the nine major terms that make up the total dissipation have been measured in the self-preserving region of a cylinder wake for a small turbulence Reynolds number.
Abstract: The average turbulent energy dissipation is often estimated by assuming isotropy and measuring the temporal derivative of the longitudinal velocity fluctuation. In this paper, the nine major terms that make up the total dissipation have been measured in the self-preserving region of a cylinder wake for a small turbulence Reynolds number. The results indicate that local isotropy is not satisfied; the isotropic dissipation, computed by assuming isotropic relations, being smaller than the total dissipation by about 45% on the wake centreline and by about 80% near the wake edge. Indirect verification of the dissipation measurements is provided by the budget of the turbulent kinetic energy. This budget leads to a plausible distribution for the pressure diffusion term, obtained by difference.
168 citations
TL;DR: Saturated resistive pressuregradient driven turbulence is studied analytically and with numerical calculations in this article, which guarantees the existence of a stable, high-m dissipation range, which serves as an energy sink.
Abstract: Saturated resistive pressure‐gradient‐driven turbulence is studied analytically and with numerical calculations Fluid viscosity and thermal diffusivity are retained in the analysis and calculations Such dissipation guarantees the existence of a stable, high‐m dissipation range, which serves as an energy sink An accurate saturation criterion is proposed The resulting predicted pressure diffusivity scales similarly to the mixing length estimate but is significantly larger in magnitude The predictions of the analytic theory are in good quantitative agreement with the numerical results for fluctuation levels
135 citations
TL;DR: In this article, the transfer of angular momentum in a disk subjected to a linear perturbation at Lindblad resonance is studied, whenever the physics include friction, nonstationarity, or self-gravitation, pressure, and viscosity.
134 citations
TL;DR: In this article, it was shown that the driving force per unit mass is closely proportional to the wave energy dissipation per unit area and that diffraction-related terms give insignificant contributions.
91 citations
TL;DR: In this paper, the role of dissipation in curve crossing phenomena in condensed phases is discussed, and adiabaticity criteria are found in two regimes via path integral arguments.
Abstract: The role of dissipation in curve crossing phenomena in condensed phases is discussed. Adiabaticity criteria are found in two regimes via path integral arguments. In the high temperature regime a stochastic quantum Langevin approach is developed. In the low temperature region an instanton method is used. In both cases the curve crossing time scale competes with the time scale of molecular motion. Dissipation causes the process to be more likely to be adiabatic.
TL;DR: In this article, the linear stability of the ABC flows u = (A sinz + C cosy, B sinx + A cosz, C siny + B cosx) is investigated numerically, in the presence of dissipation, for the case where the perturbation has the same 2π-periodicity as the basic flow.
Abstract: The linear stability of the ‘ABC’ flows u = (A sinz + C cosy, B sinx + A cosz, C siny + B cosx) is investigated numerically, in the presence of dissipation, for the case where the perturbation has the same 2π-periodicity as the basic flow. Above a critical Reynolds number, the flows are in general found to be unstable, with a growth time that becomes comparable to the dynamical timescale of the flow as the Reynolds number becomes large. The fastest-growing disturbance field is spatially intermittent, and reaches its peak intensity in features which are localized within or at the edge of regions where the undisturbed flow is chaotic, as occurs in the corresponding MHD problem.
TL;DR: In this paper, a simple, analytically tractable model of recirculating inertial gyres is presented, which is contained in a rectangular box in an attempt to simplify the geometry as much as possible and to isolate the processes occurring in the Recirculating region.
Abstract: Some essential features of a recirculating inertial gyre (the “recirculation”) can be analyzed with a very simple, analytically tractable model. In wind-driven eddy-resolving general circulation models the recirculation appears as a strong sub-basin-scale inertial flow with homogeneous potential vorticity. The constant value of potential vorticity decreases with increasing forcing/dissipation ratio while the size and the strength of the recirculating gyre increases. In the subtropical gyre the recirculating gyre might be driven by anomalous values of low potential vorticity carried northward by the western boundary current. We have modeled this process using a barotropic model and prescribing the values of potential vorticity at the edge of the gyre. Our model gyre is contained in a rectangular box in an attempt to simplify the geometry as much as possible and to isolate the processes occurring in the recirculating region. With weak diffusion the prescribed boundary forcing induces a flow with co...
TL;DR: The dynamics of an electron in a finite one-dimensional system, subject to a uniform electric field, is considered, and the Ohmic resistance of the system depends crucially on the inelastic rate even in the weak-localization limit.
Abstract: We consider the dynamics of an electron in a finite one-dimensional system, subject to a uniform electric field (or an electron in a ring; subject to an emf induced by a time-dependent magnetic flux). In the presence of elastic scattering due to localized potentials the driving source does not supply energy to the system in the steady state. The dissipation in the presence of inelastic scattering is evaluated. The Ohmic resistance of the system depends crucially on the inelastic rate even in the weak-localization limit.
TL;DR: In this article, a transport equation for the kinetic energy dissipation rate e is investigated using the results from a two-scale direct interaction approximation, and a model equation for e is constructed from the equation for kinetic energy k with the aid of a differential transformation.
Abstract: A transport equation for the kinetic energy dissipation rate e is investigated using the results from a two‐scale direct‐interaction approximation. A model equation for e is constructed from the equation for kinetic energy k with the aid of a differential transformation. A comparison between the present equation and the counterpart in the k‐e model is performed.
IBM1
TL;DR: The effects of dissipation and quantum fluctuations on the onset of superconductivity are discussed and a model for a granular superconductor is considered which consists of a d-dimensional array of resistively shunted Josephson junctions with charging energy incorporating the long-ranged Coulomb interaction.
Abstract: The effects of dissipation and quantum fluctuations on the onset of superconductivity are discussed. A model for a granular superconductor is considered which consists of a d-dimensional array of resistively shunted Josephson junctions with charging energy incorporating the long-ranged Coulomb interaction. In one dimension the model exhibits a T = 0 dynamical transition into a state with vanishing resistivity at a critical value of the shunt resistance, R/sub S/. Most surprisingly the system is always statically disordered even in the superconducting state. For dgreater than or equal to2 both the dynamical response and static ordering depend sensitively on R/sub S/. Specifically, for R/sub S/ less than a critical value of order the quantum of resistance, h/4e/sup 2/, the dissipation suppresses quantum fluctuations enabling the array to order at T = 0 for arbitrarily weak Josephson coupling. Above this critical resistance and for weak coupling, the order parameter suffers phase slips due to quantum tunneling driving the system normal.
TL;DR: In this article, a particle dynamics approach relying on particle dynamics is exploited to provide an independent estimate of the total cross-shock potential of slow mode shocks which form the plasma sheet boundary in the deep geomagnetic tail as observed by ISEE 3.
Abstract: In the de Hoffmann-Teller reference frame, the cross-shock electric field is simply the thermoelectric field responsible for preserving charge neutrality. As such, it gives information regarding the heating and dissipation occurring within the shock. The total cross-shock potential can be determined by integrating a weighted electron pressure gradient through the shock, but this requires knowledge of the density and temperature profiles. Here, a recently proposed alternative approach relying on particle dynamics is exploited to provide an independent estimate of this potential. Both determinations are applied to slow mode shocks which form the plasma sheet boundary in the deep geomagnetic tail as observed by ISEE 3. The two methods correlate well. There is no indication of the expected transition from resistive to viscous shocks, although the highest Mach number shocks show the highest potentials. The implications of these results for the electron dissipation mechanisms and turbulence at the shock are discussed.
TL;DR: In this paper, the authors studied the entropy production associated with gas radiation and showed that the most common dissipation process is of diffusive nature, and the expression for entropy production is in terms of this stress, and includes also the dissipation result.
TL;DR: In this paper, the response of a wind-sea spectrum to a step function change in wind direction is investigated theoretically for a sequence of direction changes ranging from 30° to 180°, in increments of 30°.
Abstract: The response of a wind-sea spectrum to a step function change in wind direction is investigated theoretically for a sequence of direction changes ranging from 30° to 180°, in increments of 30°. Two spectral energy balance models are used: the model EXACT-NL, in which the nonlinear transfer is represented exactly, and the model 3G-WAM, in which the nonlinear transfer is approximated by the discrete interaction parameterization. In both modes the input and dissipation source functions are taken from the energy balance proposed by Komen et al. The operational model 3G-WAM reproduces fairly closely the EXACT-NL results. For wind direction changes less than 60°, the wind-sea direction adjusts smoothly. The high-frequency components relax more rapidly to the new wind direction than the low-frequency components. The computed relaxation rates are generally consistent with the analysis of measured directional spectra by D.E. Hasselman et al. and Allender et al. However, the relaxation rate is found to be ...
TL;DR: The influence of dissipative quasiparticle tunneling currents on quantum effects and phase transitions in d-dimensional arrays of Josephson junctions is investigated and a reentrant transition between a resistive and a superconducting state is found for weak dissipation.
Abstract: We investigate the influence of dissipative quasiparticle tunneling currents on quantum effects and phase transitions in d-dimensional arrays of Josephson junctions. We show how the dissipative phase transition, which is known from single junctions at zero temperature, is modified due to the multidimensional coupling. The transition depends on the strength of the dissipation but also on the ratio of Josephson coupling energy to the capacitive charging energy ${e}^{2}$/2C. It separates an ordered (superconducting) regime from a disordered (resistive) regime where fluctuations prevent phase coherence. In arrays with small capacitance junctions and weak dissipation, the disordered phase persists down to zero temperature. Finite temperatures modify the phase diagram significantly. A reentrant transition between a resistive and a superconducting state is found for weak dissipation. We also make contact with the familiar phase transitions of d-dimensional XY models and show how the charging energy and dissipation in Josephson-junction arrays influence these transitions. The results are of relevance for granular superconductors.
TL;DR: In this paper, the velocity field of a fully developed isotropic turbulent flow is decomposed into a smoothed field and a strongly fluctuating part depending on a length which is varied through all scales.
Abstract: The velocity field of a fully developed isotropic turbulent flow is decomposed into a smoothed fieldu
and a strongly fluctuating partũ
depending on a lengthr which is varied through all scales. The eddies described byu
loose their energy either by direct dissipation or by energy transfer to theũ
-eddies. Both contributions can be traced back to the second order static structure functionD(r) and the Lagrangian time correlation function. The latter can also be evaluated in terms ofD(r). The energy balance then gives an integro-differential equation forD(r) which determinesD(r) uniquely. The solution is not only in agreement with the scaling behaviour in the viscous and inertial subranges as predicted by dimensional arguments, but it also gives the correct transition between the two regimes. A comparison with experimental data is offered.
TL;DR: In this paper, the cooling behavior of a layer composed of many small droplets was studied by numerical solution of the radiative integral equations, and it was found that the cooling process goes through a starting transient; a constant emittance condition is then achieved where the emittance is lower than that for a layer at uniform temperature.
Abstract: A proposed lightweight radiator system for waste heat dissipation in space would eject streams of coolant in the form of small, hot liquid droplets. The droplets would lose radiative energy by direct exposure to the very low-temperature environment of space, and would then be collected for reuse. The cooling behavior of a layer composed of many small droplets was studied by numerical solution of the radiative integral equations. Since there is mutual interference for radiative energy dissipation, an array droplet will cool more slowly than if each drop is exposed individually. Since liquid metal droplets may be used, the study includes results for conditions with high scattering. For optically thin regions, especially with high scattering, the temperature distribution is sufficiently uniform that the cooling can be computed using the approximation of a constant layer emittance. For optically thick layers starting at uniform temperature, the temperature distributions become nonuniform with time. It was found that the cooling process goes through a starting transient; a constant emittance condition is then achieved where the emittance is lower than that for a layer at uniform temperature.
TL;DR: In this article, the phase diagram of Josephson junctions with quasiparticle tunneling is investigated, which is formally equivalent to a one-dimensional X-Y model with easy axis and long-range interaction.
Abstract: We investigate the dynamics and the phase diagram of Josephson junctions where the dissipation is due to quasiparticle tunneling. This system is formally equivalent to a one-dimensional X-Y model with easy axis and long-range interaction. It has a phase transition at a critical strength of the dissipation, which differs in several respects from the one encountered if the dissipation is Ohmic. Quantum effects are reduced, though not destroyed, above this transition. We discuss the response of a junction to an imposed current. In the linear regime Coulomb blockade is important; in the nonlinear regime under suitable conditions Bloch oscillations can occur.
TL;DR: In this article, it was shown that sub-scale coherent vortices (SCVs, "meddies" or "bullets") can also cause significant vertical fluxes across neutral surfaces, which are not measurable with microstructure measurements of the dissipation of kinetic energy.
Abstract: Submesoscale coherent vortices (SCVs, “meddies” or “bullets”) are shown not to move along either potential density surfaces or neutral surfaces, due to the compressibility of sea water being a function of potential temperature and salinity. While it has been recognized that SCVs may make an important contribution to lateral property fluxes in the ocean, it is shown in this paper that they can also cause significant vertical fluxes across neutral surfaces. Since they represent the slow vertical translation of macroscopic water masses, these fluxes are not measurable with microstructure measurements of the dissipation of kinetic energy, but are nonetheless real. These vertical fluxes of heat and salt can be either down-gradient or up-gradient, corresponding to either a positive or a negative vertical diffusivity. The magnitude of the effective diffusivity for salt is different from that for heat. Formulae are derived for estimating the mean vertical velocity of SCVs through neutral surfaces.
TL;DR: In this paper, a one-body Frenkel-Kontorova model for isothermal electronic conduction is presented, which exhibits several interesting features: deterministic and reversible equations of motion; Lyapunov instability, with phase-space offsets increasing exponentially with time; limit cycles; and dissipative conversion of work (potential energy) into heat (kinetic energy).
Abstract: Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nose-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox ...
TL;DR: In this article, experimental and theoretical studies of sloshing waves in a rectangular channel in the vicinity of the second cutoff frequency are presented. Butler et al. showed that the importance of dissipation on the physical processes of wave evolution is discussed, and a simple dissipative model is suggested and incorporated in the governing equations.
Abstract: Experimental and theoretical studies of sloshing waves in a rectangular channel in the vicinity of the second cutoff frequency are presented. The experiments were performed in a wave tank which is 1.2 m wide, 18 m long and 0.9 m deep. Sloshing waves were generated by a computer-controlled segmented wavemaker consisting of four independent modules. A sharp transition between two wave patterns, which exhibited hysteresis-type behaviour, was observed. At lower forcing frequencies a steady wave regime was obtained, while at higher frequencies modulation on a long timescale appeared. At stronger forcing, solitons were generated periodically at the wavemaker and then propagated away with a seemingly constant velocity. Experimental results are compared with numerical solutions of the appropriate nonlinear Schrodinger equation, a derivation of which is also presented. The importance of dissipation on the physical processes of wave evolution is discussed, and a simple dissipative model is suggested and incorporated in the governing equations.
TL;DR: In this article, the applicability of the Mel'nikov technique to include a general class of highly dissipative systems was discussed, where the dissipation may be in the form of large positive or negative damping.
Abstract: We present explicit calculations that extend the applicability of the Mel’nikov technique to include a general class of highly dissipative systems. In particular, the dissipation may be in the form of large positive or negative damping. The only required assumption is that each system of this class possesses a homoclinic or a heteroclinic orbit. We also show that sufficiently small time-sinusoidal perturbation of these systems results in (nonempty) transversal intersection of stable and unstable manifolds for all but at most discretely many frequencies. The results are then demonstrated via computer simulation of the highly damped pendulum with constant plus small time-sinusoidal forcing.
TL;DR: In this article, a detailed analysis of the temporal evolution and spatial structure of the terms in the kinetic energy balance equation shows significant differences in the behavior of two different classes of modes of the system: class A waves, which are destabilized by increased dissipation in the membrane, and class B waves which are stabilized by membrane dissipation.
Abstract: Direct numerical simulations have been performed to study boundary layer flow over a compliant membrane. While coupling directly to the fluid dynamics code through the wall boundary condition, this membrane model displays many of the important features of other compliant coatings. While membrane parameters are identified that increase the critical Reynolds number by a factor of 2 compared with the rigid wall, this is mitigated by a significant increase in the growth rates in the unstable region. A detailed analysis of the temporal evolution and spatial structure of the terms in the kinetic energy balance equation shows significant differences in the behavior of two different classes of modes of the system: class A waves, which are destabilized by increased dissipation in the membrane, and class B waves, which are stabilized by membrane dissipation. For class A waves, the dominant dissipative mechanism is viscous damping in the fluid augmented by negative energy production, the principal stabilization mechanism seen in the ‘‘smart wall’’ algorithm simulations. For class B waves, direct transfer of energy to, and dissipation by, the membrane dominates stabilization of the flow. For class A waves, the membrane stabilizes the flow not by dissipating energy, but by modifying the flow to decrease energy production and enhance viscous dissipation in the fluid.
TL;DR: For the stationary case, the canonical formalism of thermally dissipative fields with both positive and negative frequency parts is constructed in this article, which enables one to follow the self-consistent renormalization scheme which creates the dissipation spontaneously.
Abstract: For the stationary case the canonical formalism of thermally dissipative fields with both positive‐ and negative‐frequency parts is constructed. This formulation enables one to follow the self‐consistent renormalization scheme which creates the dissipation spontaneously. The self‐interacting φ3 model is examined as an example of the spontaneous creation of dissipation. The parameter α appearing in the thermal state conditions as well as observables independent of the choice of α are discussed.