Showing papers on "Dissipation published in 1984"

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

Abstract: A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ e ⋅dσ from the constitutive equation relating the strain rate (e) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

On the existence of a fully developed wind-sea spectrum

Abstract: We consider the energy transfer equation for well-developed ocean waves under the influence of wind, and study the conditions for the existence of an equilibrium solution in which wind input, wave-wave interaction and dissipation balance each other. For the wind input we take the parameterization proposed by Snyder and others, which was based on their measurements in the Bight of Abaco and which agrees with Miles's theory. The wave-wave interaction is computed with an algorithm given recently by S. Hasselmann and others. The dissipation is less well-known, but we will make the general assumption that it is quasi-linear in the wave spectrum with a factor coefficient depending only on frequency and integral spectral parameters. In the first part of this paper we investigate whether the assumption that the equilibrium spectrum exits and is given by the Pierson-Moskowitz spectrum with a standard type of angular distribution leads to a reasonable dissipation function. We find that this is not the case...

Short-circuit dissipation of static CMOS circuitry and its impact on the design of buffer circuits

Abstract: A simple formula is derived for quick calculation of the maximum short-circuit dissipation of static CMOS circuits. A detailed discussion of this short-circuit dissipation is given based on the behavior of the inverter when loaded with different capacitances. It was found that if each inverter of a string is designed in such a way that the input and output rise and fall times are equal, the short-circuit dissipation will be much less than the dynamic dissipation (<20%). This result has been applied to a practical design of a CMOS driving circuit (buffer), which is commonly built up of a string of inverters. An expression has also been derived for a tapering factor between two successive inverters of such a string to minimize parasitic power dissipation. Finally, it is concluded that optimization in terms of power dissipation leads to a better overall performance (in terms of speed, power, and area) than is possible by minimization of the propagation delay.

Wave diffraction due to areas of energy dissipation

Abstract: A parabolic model for calculating the combined refraction/diffraction of monochromatic linear waves is developed, including a term which allows for the dissipation of wave energy. The coefficient of the dissipation term is related to a number of dissipative models. Wave calculations are performed for a localized area of dissipation, based on a friction model for a spatial distribution of rigid vertical cylinders. The region of localized dissipation creates a shadow region of low wave energy, which may have important implications for the response of neighboring shore lines.

Rigorous new limits on magnetic helicity dissipation in the solar corona

Abstract: The Cauchy-Schwarz inequality is employed to find geometry-independent limits on the magnetic helicity dissipation rate in a resistive plasma. These limits only depend upon the total energy of the plasma, the energy dissipation rate, and a mean diffusion coefficient. For plasmas isolated from external energy sources, limits can also be set on the minimum time necessary to dissipate a net amount of helicity ΔH. As evaluated in the context of a solar coronal loop, these limits strongly suggest that helicity decay occurs on a diffusion timescale which is far too great to be relevant to most coronal processes. Furthermore, rapid reconnection is likely to approximately conserve magnetic helicity. The dilliculties involved in determining the free energy residing in a magnetic structure (given the constraint of magnetic helicity conservation) are discussed.

Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates

Abstract: While component dissipation patterns and system operating modes vary widely, many electronic packaging configurations can be modeled by symmetrically or asymmetrically isothermal or isoflux plates. The idealized configurations are amenable to analytic optimization based on maximizing total heat transfer per unit volume or unit primary area. To achieve this anlaytic optimization, however, it is necessary to develop composite relations for the variation of the heat transfer coefficient along the plate surfaces. The mathematical development and verification of such composite relations as well as the formulation and solution of the optimizing equations for the various boundary conditions of interest constitute the core of this presentation.

On the scaling of the turbulence energy dissipation rate

Abstract: From an examination of all data to date on the dissipation of turbulent energy in grid turbulence, it is concluded that, for square‐mesh configuration, the ratio of the time scale characteristic of dissipation rate to that characteristic of energy‐containing eddies is a constant independent of Reynolds number, for microscale Reynolds numbers in excess of about 50. Insufficient data available for other grid configurations suggest a possibility that the ratio could assume different numerical values for different configurations. This persistent effect of initial conditions on the time scale ratio is further illustrated by reference to the jet‐grid data of Gad‐el‐Hak and Corrsin.

Calibration and Verification of a Dissipation Model for Random Breaking Waves

Abstract: A model describing the average rate of energy dissipation in random waves breaking in shallow water, published previously by the first author and Janssen (1978), has been applied to an extensive set of data for the purposes of calibration and verification. Both laboratory and field data were used, obtained on beaches with a more or less plane slope as well as on barred beaches, and for a wide range of wave conditions. Optimal values have been estimated for an adjustable breaking waveheight-coefficient in the model; these appear to vary slightly but systematically with the incident wave steepness, in a range which is physically realistic. A parameterization of this dependence allows the use of the model for prediction. Applied to the present data set, the correlation coefficient between measured and predicted rms wave heights is 0.98, with an rms normalized error of 6% and a bias which does not differ significantly from zero.

Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps

Abstract: We have studied the transition to chaos caused by interaction and overlap of resonances in some condensed-matter systems by constructing and analyzing appropriate return maps. In particular, the resistively shunted Josephson junction in microwave fields and charge-density waves in rf electric fields may be described by the differential equation of the damped driven pendulum in a periodic force. The two-dimensional return map for this equation is shown to collapse to a one-dimensional circle map in a parameter regime including the transition to chaos. Phase locking, noise, and hysteresis in these systems can thus be understood in a simple and coherent way by taking over theoretical results for the circle map, some of which were derived in the preceding paper. In order to understand the contraction to one dimensionality we have studied the two-dimensional Chirikov standard map with dissipation. A well-defined transition line along which the system exhibits circle-map critical behavior was found. At this line the system is always phase locked. We conclude that recent theoretical results on universal behavior can readily be checked experimentally by studying systems in condensed-matter physics. The relation between theory and experiment is simple and direct.

A model for breaker decay on beaches

Abstract: Based on the observation that a shallow water breaking wave propagating over a region of uniform depth will reform and stabilize after some distance, an intuitive expression for the rate of energy dissipation is developed. Using linear wave theory and the energy balance equation, analytical solutions for monochromatic waves breaking on a flat shelf, plane slope, and "equilibrium" beach profile are presented and compared to laboratory data from Horikawa and Kuo (1966) with favorable results. Set-down/up in the mean water level, bottom friction losses, and bottom profiles of arbitrary shape are then introduced and the equations solved numerically. The model is calibrated and verified to laboratory data with very good results for wave decay for a wide range of beach slopes and incident conditions, but not so favorable for set-up. A test run on a prototype scale profile containing two bar and trough systems demonstrates the model's ability to describe the shoaling, breaking, and wave reformation process commonly observed in nature. Bottom friction is found to play a negligible role in wave decay in the surf zone when compared to shoaling and breaking.

A Dissipative Galerkin Scheme for Open‐Channel Flow

Abstract: The finite element method based on the classical Galerkin formulation produces very poor results when applied to discontinuous channel flow. A variance of the Galerkin method is proposed that exhibits highly selective damping characteristics. The dissipation affects only the numerically-generated high-frequency parasitic waves, while maintaining remarkable accuracy in the approximation to the true solution of the problem. In fact, it is shown that the phase error of the finite element simulation is improved by the introduction of dissipation. The resulting model is second-order accurate with respect to the time step and produces a clean, sharp jump structure that agrees favorably with the exact solution of some test problems. The method is based on discontinuous weighting functions that produce “upwind” effects but at the same time maintain the accuracy of a central difference scheme. The dissipation level is selected by analytical investigations, so that the numerical error is minimized. No second-order pseudo viscosity terms are required, which relaxes the inter-element continuity conditions and results in a very simple and inexpensive scheme.

Coulomb Suppression of Tunneling Rate from Small Metal Particles

Abstract: ac measurements on a "tunnel capacitor," in which small metal particles make tunnel junctions with one of the capacitor plates, reveal information about the electron tunneling process at the junctions. A simple zero-temperature model for the process is presented for the regime in which the Coulomb charging energy suppresses the conductance of the junctions. The prediction of the model that the capacitance and dissipation constant of the structure should scale as (frequency)/(applied ac voltage) is confirmed by the experimental results.

A turbulent bore on a beach

Abstract: A theoretical model is developed giving a moderately detailed description of the flow in a turbulent bore, the velocity profiles, the shear stresses, the energy dissipation, etc. An analysis of the flow conditions at the toe of the turbulent front indicates significant differences from the usual description based on the finite-amplitude shallow-water equations, and it is shown that the present model gives a closer description of the actual physical conditions. Finally, numerical results are presented that illustrate how the model works, and test its validity on an example with known properties.

Friction, Restitution, and Energy Loss in Planar Collisions

Abstract: Both particle and rigid body planar collisions are covered in this paper. For particles, the classical equations for oblique impacts are derived using Newton’s laws along with definitions of the coefficient of restitution and equivalent coefficient of friction. A general expression is obtained for the kinetic energy loss explicity containing the two coefficients. This expression for energy loss as a function of the friction coefficient possesses a maximum. The value of the friction coefficient at the maximum is a limiting value which can be used to determine whether or not sliding exists at separation. The maximum energy loss is independent of the physical mechanism of generation of tangential forces (friction) and serves as an upper bound for two-particle collisions. It is shown that to properly formulate and solve the rigid body problem, a moment must be considered at the common “point” of impact. A moment coefficient of restitution must be defined. This leads to six linear algebraic equations from which the six final velocity components can be calculated. An analytical solution is obtained for the general rigid body problem. In a reduced form, it is used to solve the problem of a single rigid body impacting a rigid barrier. This solution is then applied to a classical textbook problem. As shown for particle impacts, the concepts of limiting friction coefficient and maximum energy loss apply to rigid body impacts.

Dissipation in Computation

Abstract: The question of the energy dissipation in the computational process is considered. Contrary to previous studies, dissipation is found to be an integral part of computation. A complementarity is suggested between systems that are describable in thermodynamic terms and systems that can be used for computation.

On the Fluid Dynamical Theory of Turbulent Gas Transfer Across an Air-Sea Interface in the Presence of Breaking Wind-Waves

Abstract: It is shown that in order to describe the transfer of gases in the liquid near the air-sea interface, the vertical structure of three-dimensional small-scale turbulence in turbulent patches generated by breaking waves must be considered. The dependence of eddy diffusivity on distance from a gas-liquid interface inside such turbulent patches is determined, and the pseudothickness of the molecular diffusion sublayer for gases with main resistance to transfer in the liquid phase is calculated. The proposed theory indicates that the appropriate transfer velocity (ratio of gas flux to its concentration difference) is proportional to Pr−½[νϵν(0)]¼, where ϵν(0) is the dissipation of turbulent energy uniformly distributed in the upper part of the turbulent patch, ν is the viscosity and Pr the Prandtl number. Also, the pseudothickness of the molecular diffusion layer has been found to be proportional to Pr−½η, where η = lsqb;ν3/ϵν(0)]¼, Kolmogoroff's internal scale. It is noted that the dependence of gas ...

The dissipation of frictional energy from the interface of an annular disc brake

Abstract: The performance of resin bonded composite friction materials in a particular brake design is strongly dependent upon the dissipation of frictional heat from the interface. This energy transformation has been studied using finite element techniques for a simulation of the braking friction process in an annular disc brake, which combines both brake performance and brake temperature analysis and avoids many of the assumptions necessary in conventional analyses.Negligible amounts of energy interchange, compared with the total kinetic energy dissipated, arise from chemical reactions within the friction material, but the formation of surface layers and interfacial wear products do have a significant effect upon heat transfer from the interface. Calculated temperature distributions over individual brake applications indicate that interface contact resistance leads to different temperatures at the surfaces of disc and lining so that heat partition between the two mating bodies cannot realistically be assumed cons...

On the production and dissipation of mechanical energy in the ocean

Abstract: The equation for the conservation of total mechanical energy (kinetic, gravitational, and elastic energy) is derived from the conservation of momentum and mass and averaged over the volume of the oceans to equate the production and dissipation of mechanical energy in a statistically steady ocean. The work done by the atmosphere dominates production and is estimated as 0.1 W/m2 from synoptic data which is consistent with most (but not all) of the reported observations of turbulent dissipation. Potential energy production contributes only .0.2% to the total production implying an eddy diffusivity of buoyancy of 10−5 m2/s and a thermal Cox number of 200. The “low” values of diffusivity derived from microstructure observations appear to reflect a relatively small potential energy production.

Nonlinear interaction of toroidicity‐induced drift modes

Abstract: Drift modes in toroidal geometry are destabilized by trapped electron inverse dissipation and evolve to a nonlinearly saturated state. Using renormalized one‐point turbulence theory for the nonlinear gyrokinetic equation in the ballooning representation, it is shown that ion Compton scattering is an effective saturation mechanism. Ion Compton scattering transfers wave energy from short to long perpendicular wavelength, where it is absorbed by ion resonance with extended, linearly stable, long‐wavelength modes. The fluctuation spectrum and fluctuation levels are calculated using the condition of nonlinear saturation. Transport coefficients and energy confinement time scalings are determined for several regimes. Specifically, the predicted confinement time density scaling for an Ohmically heated discharge increases from n3/8 in the collisionless regime to n9/8 in the dissipative trapped electron regime.

Friction and Particle-Hole Pairs

Abstract: The effect induced by dissipation on quantum phenomena has recently been considered, taking into account as a starting point a phenomenological Hamiltonian in which the environment is simulated by an appropriately chosen set of harmonic oscillators. It is found that this approach should be adequate to describe the low-energy behavior of a wide class of environments. The present investigation is concerned with an analysis of the case in which the environment is a gas (or liquid) of fermions, and the relevant low-energy excitations are particle-hole pairs. A study is conducted regarding the extent to which the quantum results obtained for harmonic oscillators are also valid in the considered situation. Linear-response theory is used to derive an effective action which describes the motion of an external particle coupled to a normal Fermi fluid.

Quantum decay in a dissipative system

Abstract: In view of recent interest in the problem of macroscopic quantum tunneling in systems involving the Josephson effect, we present an accurate numerical calculation of the tunneling rate of a system from a metastable well, at zero temperature, in the presence of dissipative coupling to the environment. Although we concentrate on a specific form of dissipation, as discussed by Caldeira and Leggett, we believe that such a numerical method can be extended to other forms of dissipation as well. Our method is based on the framework recently described by Caldeira and Leggett, and requires (a) a novel treatment of a nonlinear integro-differential equation and (b) an extension of the usual Fredholm scattering theory so as to be applicable to the present dissipative problem. We present explicit results for wide ranges of dissipation and estimate our error in the calculation of the exponent to be no larger than 0.1% and of the prefactor to be no larger than 2%.

Alfvénic resonant cavities in the solar atmosphere: Simple aspects

Abstract: We investigate the propagation of Alfven waves in a simple medium consisting of three uniform layers; each layer is characterized by a different value for the Alfven speed, υA. We show how the central layer can act as a resonant cavity under quite general conditions. If the cavity is driven externally, by an incident wave in one of the outer layers, there result resonant transmission peaks, which allow large energy fluxes to enter the cavity from outside. The transmission peaks result from the destructive interference between a wave which leaks out of the cavity, and a directly reflected wave. We show that there are two types of resonances. The first type occurs when the cavity has the largest (or smallest) of the three Alfven speeds; this situation occurs on coronal loops. The second type occurs when the cavity Alfven speed is intermediate between the other two values of υA; this situation may occur on solar spicules. Significant heating of the cavity can occur if the waves are damped. We show that if the energy lost to heat greatly exceeds the energy lost by leakage out of the cavity, then the cavity heating can be independent of the damping rate. This conclusion is shown to apply to coronal resonances and to the spicule resonances. This conclusion agrees with a point made by Ionson (1982) in connection with the coronal resonances. Except for a numerical factor of order unity, we recover Ionson's expression for the coronal heating rate. However, Ionson's qualities are much too large. For solar parameters, the maximum quality is of the order of 100, but the heating is independent of the damping rate only when dissipation reduces the quality to less than about 10.

Analysis of upright structure for wave dissipation using integral equation

Abstract: A theoretical analysis using an integral equation derived for the unknown horizontal velocity component in a pervious wall is proposed for estimating the reflection and transmission coefficients of upright structures for wave dissipation, and various factors related to wave and structural conditions having influences on the wave dissipating characteristics are investigated for a breakwater with pervious vertical walls at both seaward and landward sides, In two-dimensional experiments, the theoretical results are in. good agreement with experimental data with respect to reflection and transmission coefficients, and therefore, the wave dissipating characteristics of upright structures for wave dissipation can be explained by the integral equation method theory.