Showing papers on "Dissipation published in 1982"

The thermodynamics of computation—a review

Abstract: Computers may be thought of as engines for transforming free energy into waste heat and mathematical work. Existing electronic computers dissipate energy vastly in excess of the mean thermal energykT, for purposes such as maintaining volatile storage devices in a bistable condition, synchronizing and standardizing signals, and maximizing switching speed. On the other hand, recent models due to Fredkin and Toffoli show that in principle a computer could compute at finite speed with zero energy dissipation and zero error. In these models, a simple assemblage of simple but idealized mechanical parts (e.g., hard spheres and flat plates) determines a ballistic trajectory isomorphic with the desired computation, a trajectory therefore not foreseen in detail by the builder of the computer. In a classical or semiclassical setting, ballistic models are unrealistic because they require the parts to be assembled with perfect precision and isolated from thermal noise, which would eventually randomize the trajectory and lead to errors. Possibly quantum effects could be exploited to prevent this undesired equipartition of the kinetic energy. Another family of models may be called Brownian computers, because they allow thermal noise to influence the trajectory so strongly that it becomes a random walk through the entire accessible (low-potential-energy) portion of the computer's configuration space. In these computers, a simple assemblage of simple parts determines a low-energy labyrinth isomorphic to the desired computation, through which the system executes its random walk, with a slight drift velocity due to a weak driving force in the direction of forward computation. In return for their greater realism, Brownian models are more dissipative than ballistic ones: the drift velocity is proportional to the driving force, and hence the energy dissipated approaches zero only in the limit of zero speed. In this regard Brownian models resemble the traditional apparatus of thermodynamic thought experiments, where reversibility is also typically only attainable in the limit of zero speed. The enzymatic apparatus of DNA replication, transcription, and translation appear to be nature's closest approach to a Brownian computer, dissipating 20–100kT per step. Both the ballistic and Brownian computers require a change in programming style: computations must be renderedlogically reversible, so that no machine state has more than one logical predecessor. In a ballistic computer, the merging of two trajectories clearly cannot be brought about by purely conservative forces; in a Brownian computer, any extensive amount of merging of computation paths would cause the Brownian computer to spend most of its time bogged down in extraneous predecessors of states on the intended path, unless an extra driving force ofkTln2 were applied (and dissipated) at each merge point. The mathematical means of rendering a computation logically reversible (e.g., creation and annihilation of a history file) will be discussed. The old Maxwell's demon problem is discussed in the light of the relation between logical and thermodynamic reversibility: the essential irreversible step, which prevents the demon from breaking the second law, is not the making of a measurement (which in principle can be done reversibly) but rather the logically irreversible act of erasing the record of one measurement to make room for the next. Converse to the rule that logically irreversible operations on data require an entropy increase elsewhere in the computer is the fact that a tape full of zeros, or one containing some computable pseudorandom sequence such as pi, has fuel value and can be made to do useful thermodynamic work as it randomizes itself. A tape containing an algorithmically random sequence lacks this ability.

Sensible and Latent Heat Flux Measurements over the Ocean

Abstract: This papar presents an extensive act of sensible heat (Reynolds flux and dissipation methods) and latent heat (dissipation method) flux measurements from a stable deep water tower and from ships on the deep sea. Operational difficulties associated with ship spray and flow distortion and with sensor calibration, response and contamination are discussed. The influence of atmospheric stability on the dissipation measurements and the bulk transfer coefficients is considered and a parameterization of Z/ L in terms of wind speed and the sea-air potential temperature difference is found to be adequate. Temperature variances, Stanton numbers and w–t cospectra from the Roynolds flux measurements are compared to previous results. The dissipation method is shown to be a viable means of measuring the heal fluxes over the deep sea by comparison with simultaneous Reynolds flux measurements, using our data for the sensible heat and the data of others for the latent heat. The neutral drag coefficient at 10 m hei...

Determination of the Rate of Dissipation of Turbulent Energy from Simultaneous Temperature and Velocity Shear Microstructure Measurements

Abstract: Spectra of turbulence have been examined for both temperature gradient and velocity shear. The data for this comparison are 10–15 m segments of vertical microstructure profiles (at depths of 5–100 m) obtained during the 1978 Joint Air Sea Interaction experiment (JASIN). From the simultaneous measurement of them two microstructure quantities, the universal spectral constant q (the least principal rate of strain of the velocity spectrum) has been determined to be 3.7 ± 1.5. As well, the dissipation rate has been calculated from the high-wavenumber cut-off of the temperature microstructure spectra (ϵB) and from velocity shear (ϵSH). For a range of values from 8 × 10−9 to 5 × 10−7 m2 s−3 these two measures, ϵB and ϵSH, agree to within a factor of 2 on average. And finally, estimates of ξθ (temperature dissipation rate), ϵ and mean temperature gradient have been used to estimate a mixing efficiency, Γ = 0.24.

A Scale Analysis of Deep Moist Convection and Some Related Numerical Calculations

Abstract: A scale analysis valid for deep moist convection is carried out. The approximate equations of motion are anelastic with the time scale set by the Brunt- Vaisala frequency. A new assumption is that the base state potential temperature is a slowly varying function of the vertical coordinate. It is this assumption that eliminates the energetic inconsistency discussed by Wilhelmson and Ogura (1972) for a non-isentropic base state. Another key result is that the dynamic pressure is an order of magnitude smaller than the first-order temperature and potential temperature. In agreement with observations, the kinetic energy is found to be an order of magnitude smaller than the first-order thermodynamic energy. A set of six numerical simulations representing moderately deep moist convection is carried out. The base state is an idealized maritime tropical sounding with no vertical wind shear. The first calculation (Run A) shows the growth and dissipation of a typical shower cloud. The remaining calculations...

A thermomechanical description of materials with internal variables in the process of phase transitions

Abstract: A continuum mechanical description is presented for thermoplastic materials in the process of solid-solid phase transition. The material is assumed to be characterized by three different internal state variables: two internal variables which specify the crystallographic structural change during the plastic deformation, and a set of scalar internal variables which describes the extent of phase transition. Applying Edelen's decomposition theorem, the plastic quantities are determined from the dissipation potential, while the elastic quantities are specified by the internal energy. The explicit form of the flow rule and the evolutional equations for the internal variables are derived. The constitutive equations for the stress and the entropy are obtained in rate-type. It is shown that the continuous cooling transformation (C-C-T) diagram and the isothermal time-temperature-transformation (T-T-T) diagram could be derived from the theory developed here. The infinitesimal case is discussed in detail.

Observations of internal wave reflection off sloping bottoms

Abstract: Current and temperature spectra exhibit intensification and polarization near sloping bottoms over a band of frequencies centered at the local internal wave critical frequency. Examples are drawn from a variety of island, seamount, and continental slope observations. Waves propagating down from mid-depth change energy density, wave number, and azimuth when they reflect off the bottom, providing a natural perturbation to the deep ocean interior internal wave spectrum. Deviations from linear theory are interpreted as evidence for dissipation through subsequent shear instability and/or nonlinear interaction. Topographic features appear likely to be energy sinks for internal wave energy.

Dissipation Within the Surface Mixed Layer

Abstract: Observations of turbulent energy dissipation, ϵ, measured during a week-long mixed-layer study on the continental shelf off Nova Scotia are presented. This time series of dissipation measurements at a fixed site and with a wide range of wind speeds indicates that a constant fraction of the energy flux in the atmospheric boundary layer appears as dissipation in the mixed layer. Our measured velocity-shear spectra are consistent in shape with an isotropic-turbulence spectral form and simultaneous determinations of spectral level from two mutually perpendicular sensors are consistent with isotropy. Significant changes in turbulence levels between two profiles a few minutes apart are observed. These changes (often a factor of 10) emphasize the necessity of adequate space-time averaging to obtain good mean values of ϵ. Including data from measurements of the large-scale density and velocity fields, the generation of the observed turbulence is thought to be Richardson-number instabilities in the mixed ...

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.

Seismic Q-Stratigraphy or dissipation

Abstract: The basic problems encountered in extracting estimates of seismic dissipation from data recorded on vertical seismic profiles are analyzed. Because anomalous dissipation in the subsurface is likely to be associated with conditions or lithologies of limited vertical extent, a knowledge of the factors which influence the spatial resolution of an attenuation measurement is of considerable importance. By introducing a statistical perspective, it is possible to simulate multiple measurements in an inhomogeneous interval and to draw conclusions which apply to an entire class of impedance structures. Theoretical seismograms are analyzed to demonstrate that for small receiver separations neither a single measurement nor the mean value determined from multiple measurements is likely to give a good estimate of the attenuation for an inhomogeneous depth interval. For small receiver separations, the attenuation computed from the amplitude ratios method is much more strongly influenced by the local stratigraphy in the...

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.

Uncertainty Principle and Minimal Energy Dissipation in the Computer

Abstract: Reversible computation is briefly reviewed, utilizing a refined version of the Bennett-Fredkin-Turing machine, invoked in an earlier paper. A dissipationless classical version of this machine, which has no internal frietion, and where the computational velocity is determined by the initial kinetic energy, is also described. Such a machine requires perfect parts and also requires the unrealisstic assumption that the many extraneous degrees of freedom, which contribute to the physical structure, do not couple to the information-bearing degrees of freedom, and thus cause no friction Quantum mechanical computation is discussed at two levels. First of all we deplore the assertion. repcatedly found in the literature, that the uncertainty principle. ΔEΔt≈h, with Δt equated to a switching time, yields any information about energydissipation. Similarly we point out that computation is not an iterated transmission and receiving process, and that considerations, which avoid the uncertainty principle, and instead use quantum mechanical channel capacity considerations, are equally unfounded. At a more constructive level we ask whether there is a quantum mechanical version of the dissipationless computer. Benioff has proposed one possible answer Quantum mechanical versions of dissipationless computers may suffer from the problems found in electron transport in disordered one-dimensional periodic potentials. The buildup of internal reflections may give a transmission coefficient. through the whole computation, which decreases exponentially with the length of the computation.

Magnetic field line reconnection experiments 4. Resistivity, heating, and energy flow

Abstract: Detailed spatial and temporal measurements of the total vector electric field E and current density J in a plasma with dynamic magnetic field line reconnection have been made. The resistivity calculated via the generalized Ohm's law is found to be spatially inhomogeneous with values exceeding the classical resistivity by 1 to 2 orders of magnitude. Resistivity and current density do not maximize in the same locations. The dissipation E · J is determined and analyzed in terms of particle heating and fluid acceleration. Electron heating is found to be the dominant dissipation process in the diffusion region. Independent measurements of the divergence of the Poynting vector ▽ · (E × H), the change in stored magnetic field energy ∂/∂t(B²/2µo), and the dissipation give a consistent, detailed picture of the energy flow. Efficient conversion of electromagnetic energy into particle heating is observed.

Temperature minimum heating in solar flares by resistive dissipation of Alfven waves

Abstract: The possibility that the strong heating produced at temperature-minimum levels during solar flares is due to resistive dissipation of Alfven waves generated by the primary energy release process in the corona is studied. It is shown how, for suitable parameters, these waves can carry their energy essentially undamped into the temperature-minimum layers and can then produce a degree of heating consistent with observations.

In situ acceleration in extragalactic radio jets

Abstract: We have examined the energy dissipated by large-scale turbulence in an extragalactic jet. The turbulence is driven by a shear instability which does not disrupt the jet. Fluid theory should be used to treat the evolution of the turbulence, and this allows us to estimate the rate of dissipation without detailed knowledge of the dissipation process. Dissipation occurs due to Fermi acceleration at a scale length approx.10/sup -3/ R and that resonant acceleration plays no role. The Alfvenic component in the turbulent spectrum is dissipated by first being converted into magneto-acoustic waves. An alternative dissipation process due to formation of weak shocks is shown to be equivalent in some respects to Fermi acceleration. Dissipation in the thermal gas should not exceed that due to Fermi acceleration. The effect of Fermi acceleration, adiabatic losses, and radiative losses on an initial power-law distribution with an upper cutoff is studied. Radio emission extending to at least 100 GHz is shown to be possible, and no spectral index gradients are introduced by the acceleration. The upper cutoff can increase due to the acceleration alone or when the acceleration is balanced by radiative losses. The northern jet in NGC 315 is studied in detail. Usingmore » our model for the acceleration, we estimate a jet velocity > or approx. =5000 km s/sup -1/ with Mach number not much greater than 1, and a density < or approx. =1 x 10/sup -4/ f/sup -1/ cm/sup -3/ at the turn-on of the jet at 6 cm, where 0.05< or approx. =f< or approx. =1 is the ratio of synchrotron to mechanical luminosity. The acceleration time is estimated to be approx.5 x 10/sup 5/ yr, and it is predicted that the radius of the jet at the turn-on point should vary with frequency either as ..nu../sup 2/3/ or as ..nu../sup 3/2/, or there may be no frequency dependence, contingent upon the details of the acceleration.« less

Probabilities for Quantum Tunneling through a Barrier with Linear Passive Dissipation

Abstract: The transmission coefficient for passage through a barrier with a parabolic maximum is computed rigorously when linear passive dissipation is present. The exact result for energies above and below the barrier height can be expressed in terms of the Coleman renormalized one-bounce time. The quasiclassical (WKB) approximation is recovered for energies significantly below the barrier height where "friction" enhances the tunneling probability.

Estimation of formation temperature and thermal property from dissipation of heat generated by drilling

Abstract: Dissipation of heat generated in the process of drilling depends upon the physical properties and condition of the rock and drilling mud, drilling rate and duration, mud circulation rate, casing, and depth of penetration. By treating the initial condition as an instantaneous temperature drop near the bottom of a drill hole, an analytical solution is obtained to show drilling‐induced heat dissipation. Two graphical methods are presented and illustrated with examples to determine, from transient temperature measurements, the equilibrium formation temperature as well as insitu thermal conductivity ratio and diffusivity of rock and drilling mud. One method requires the measurement of initial mud temperature Tm, while the other method requires knowing the thermal diffusivity of drilling mud κ1. Either Tm or κ1 can also be estimated with the trial‐and‐error procedure. A finite‐element analysis is further developed to handle thermal disturbance for the case where the temperature drop is not necessarily instantan...

Equatorial waves in steady zonal shear flow

Abstract: The properties of equatorial Kelvin and mixed Rossby-gravity waves are investigated in an equatorial beta-plane model of the lower stratosphere. The basic state and wave amplitudes are assumed to be independent of time; the waves are dissipated by thermal and/or mechanical damping. Particular emphasis is placed on the forcing of the mean flow by the waves. In agreement with earlier studies the latitudinal structure of the mean flow forcing is found to be sensitive to the dissipation mechanism; when the mean state is one of no zonal motion the easterly mixed Rossby-gravity wave-induced acceleration of the zonal flow is zero on the equator when only thermal dissipation acts, but maximizes on the equator when dissipation is included. This latter property is also found in the presence of equatorial jets. Results from this model, with its explicit resolution of the wave structure, are compared with those from the multiple-scales approach of Boyd; good agreement is found.

Nonlinear waves near a cut-off frequency in an acoustic duct – a numerical study

Abstract: Cut-off frequencies are well known in acoustic ducts to be the thresholds of propagation and evanescence. If at one end of a duct the piston oscillates at very near the cut-off frequency, cross-duct resonance occurs and the linearized theory breaks down. This paper studies the nonlinear response, near a cut-off frequency of a guided wave, as an initial-boundary-value problem. The asymptotic state is shown to be governed by a modified cubic Schrodinger equation. Numerical solutions are then obtained for inputs of finite and long duration. In addition to the characteristics of the input envelope, two quantities control the transient phenomenon: frequency detuning and nonlinearity. Under certain circumstances, energy can be trapped near the piston long after a short-lived input has expired, while for a sustained input there is no sign of a steady state. Dissipation is not considered.

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.

The velocity field in the molten slag region of esr systems: a comparison of measurements in a model system with theoretical predictions

Abstract: A comparison is presented between the experimentally measured velocity field in a room temperature model of an ESR system and theoretical predictions, obtained from the numerical solution of Maxwell’s equations and the turbulent Navier-Stokes equations. The experimental measurements were obtained in a horizontal trough, containing mercury, through which a current was being passedvia two electrodes. The velocity fields, which were measured, using a photographic technique were thought to model the electromagnetically driven component of the velocity field in the central plane of the slag phase in ESR systems. The agreement between the experimental measurements and the theoretical predictions is excellent, both regarding the absolute values of the velocities and the dependence of the velocity on the imposed current and on the electrode diameter. The calculations have shown that by the proper choice of the linear scale, and the current,. mercury may be used to model the electromagnetically driven flow in the slag phase of ESR systems. Furthermore, some general relationships have been developed showing the effect of the current on the velocity, the turbulence energy, and on the rate of turbulence energy dissipation. This work is thought to provide definite confirmation that the electromagnetically driven component of the velocity fields in ESR systems may be properly represented through the simultaneous solution of Maxwell’s equations and the turbulent NavierStokes equations.

A Numerical Study of Nonfrictional Decay of Mesoscale Eddies

Abstract: The decay of mesoscale eddies can be attributed to either frictional dissipation of kinetic energy through viscous effects or through dispersive spreading of the different constituent Rossby wave components at their own characteristic wave speeds. Several previous investigations of eddy decay have examined the role of variable friction in the spindown process. In addition to frictional results, these studies have shown that nonlinear advective processes can stabilize the vortex against dispersive effects. The quantification of this relation between nonlinear stabilization and beta dispersion is the primary focus of this paper. Results are obtained using a finite difference “equivalent barotropic” numerical model with a fixed biharmonic friction formulation. Variable parameters in the study are vortex size and strength. Initial conditions are in the form of a Gaussian height field in gradient balance. Nonfrictional vortex decay is parameterized in terms of lateral spreading. This spreading is dete...

Experiments on leapfrogging internal solitary waves

Abstract: Experiments on the resonant energy transfer between internal gravity-wave solitons travelling along neighbouring pycnoclines have been performed. Measurements of both amplitude and phase oscillations are found to be in qualitative agreement with theoretical predictions given in the companion paper by Liu, Pereira & KO (1982). Using averaged quantities to account approximately for wave-energy dissipation, the theoretical expression correlating the oscillation frequency with the density environ- ment parameters is reasonably well verified. A new three-soliton resonance requiring both upstream and downstream energy transfer has also been observed.

Dissipation of ionospheric irregularities by wave-particle and collisional interactions

Abstract: The nonlinear dissipation of plasma irregularities aligned parallel to an ambient magnetic field is studied numerically using a model which employs both wave-particle and collisional diffusion. A wave-particle diffusion coefficient derived from a local theory of the universal drift instability is used. This coefficient is effective in regions of nonzero plasma gradients and produces triangular-shaped irregularities with spectra which vary as f to the -4th, where f is the spatial frequency. Collisional diffusion acts rapidly on the vertices of the irregularities to reduce their amplitude. The simultaneous action of the two dissipative processes is more efficient than collisions acting alone. In this model, wave-particle diffusion mimics the forward cascade process of wave-wave coupling.

Vortex dynamics in inhomogeneous superconducting films

Abstract: A vortex moving without dissipation in a superconducting film containing random inhomogeneities is shown to have a strictly periodic trajectory. By exploiting a new percolation analogy, the voltage noise power and the electrical resistivity due to a vortex are described at low frequencies in the zero-drag limit by the universal form P(..omega..)approx...omega../sup p//sub 2/, with p/sub 2/approx. =0.4. The introduction of dissipation into the vortex equations of motion modifies this form and causes resistivity to appear at zero frequency. Analogous effects should be observable in inhomogeneous superfluid /sup 4/He films.