Showing papers on "Dissipation published in 2002"

Acoustics of friction.

Abstract: This article presents an overview of the acoustics of friction by covering friction sounds, friction-induced vibrations and waves in solids, and descriptions of other frictional phenomena related to acoustics. Friction, resulting from the sliding contact of solids, often gives rise to diverse forms of waves and oscillations within solids which frequently lead to radiation of sound to the surrounding media. Among the many everyday examples of friction sounds, violin music and brake noise in automobiles represent the two extremes in terms of the sounds they produce and the mechanisms by which they are generated. Of the multiple examples of friction sounds in nature, insect sounds are prominent. Friction also provides a means by which energy dissipation takes place at the interface of solids. Friction damping that develops between surfaces, such as joints and connections, in some cases requires only microscopic motion to dissipate energy. Modeling of friction-induced vibrations and friction damping in mechanical systems requires an accurate description of friction for which only approximations exist. While many of the components that contribute to friction can be modeled, computational requirements become prohibitive for their contemporaneous calculation. Furthermore, quantification of friction at the atomic scale still remains elusive. At the atomic scale, friction becomes a mechanism that converts the kinetic energy associated with the relative motion of surfaces to thermal energy. However, the description of the conversion to thermal energy represented by a disordered state of oscillations of atoms in a solid is still not well understood. At the macroscopic level, friction interacts with the vibrations and waves that it causes. Such interaction sets up a feedback between the friction force and waves at the surfaces, thereby making friction and surface motion interdependent. Such interdependence forms the basis for friction-induced motion as in the case of ultrasonic motors and other examples. Last, when considered phenomenologically, friction and boundary layer turbulence exhibit analogous properties and, when compared, each may provide clues to a better understanding of the other.

Efficient acceleration and radiation in Poynting flux powered GRB outflows

Abstract: We investigate the eects of magnetic energy release by local magnetic dissipation processes in Poynting flux- powered GRBs. For typical GRB parameters (energy and baryon loading) the dissipation takes place mainly outside the pho- tosphere, producing non-thermal radiation. This process converts the total burst energy into prompt radiation at an eciency of 10-50%. At the same time the dissipation has the eect of accelerating the flow to a large Lorentz factor. For higher baryon loading, the dissipation takes place mostly inside the photosphere, the eciency of conversion of magnetic energy into radia- tion is lower, and an X-ray flash results instead of a GRB. We demonstrate these eects with numerical one-dimensional steady relativistic MHD calculations.

Large-Eddy Simulation on Curvilinear Grids Using Compact Differencing and Filtering Schemes

Abstract: This work investigates the application of a high-order finite difference method for compressible large-eddy simulations on stretched, curvilinear and dynamic meshes. The solver utilizes 4th and 6th-order compact-differencing schemes for the spatial discretization, coupled with both explicit and implicit time-marching methods. Up to 10th order, Pade-type low-pass spatial filter operators are also incorporated to eliminate the spurious high-frequency modes which inevitably arise due to the lack of inherent dissipation in the spatial scheme. The solution procedure is evaluated for the case of decaying compressible isotropic turbulence and turbulent channel flow. The compact/filtering approach is found to be superior to standard second and fourth-order centered, as well as third-order upwind-biased approximations. For the case of isotropic turbulence, better results are obtained with the compact/filtering method (without an added subgrid-scale model) than with the constant-coefficient and dynamic Smagorinsky models. This is attributed to the fact that the SGS models, unlike the optimized low-pass filter, exert dissipation over a wide range of wave numbers including on some of the resolved scales

The Role of Internal Tides in Mixing the Deep Ocean

Abstract: Internal wave theory is used to examine the generation, radiation, and energy dissipation of internal tides in the deep ocean. Estimates of vertical energy flux based on a previously developed model are adjusted to account for the influence of finite depth, varying stratification, and two-dimensional topography. Specific estimates of energy flux are made for midocean ridge topography. Weakly nonlinear theory is applied to the wave generation at idealized topography to examine finite amplitude corrections to the linear theory. Most internal tide energy is generated at low modes associated with spatial scales from roughly 20 to 100 km. The Richardson number of the radiated internal tide typically exceeds unity for these motions, and so direct shear instability of the generated waves is not the dominant energy transfer mechanism. It also seems that wave–wave interactions are ineffective at transferring energy from the large wavelengths that dominate the energy flux. Instead, it appears that most of ...

Power gain and dissipation in quantum-dot cellular automata

Abstract: Quantum-dot cellular automata (QCA) may provide a novel way to bypass the transistor paradigm to form molecular-scale computing elements. In the QCA paradigm information is represented by the charge configuration of a QCA cell. We develop a theoretical approach, based on the density matrix formalism, which permits examination of energy flow in QCA devices. Using a simple two-state model to describe the cell, and an energy relaxation time to describe the coupling to the environment, we arrive at an equation of motion well suited to the quasi-adiabatically switched regime. We use this to examine the role of power gain and power dissipation in QCA cells. We show that QCA cells can exhibit true signal power gain. The energy lost to dissipative processes is restored by the clock. We calculate the power dissipated to the environment in QCA circuits and show that it is possible to achieve the ultralow levels of power dissipation required at molecular densities.

Heat Dissipation for Au Particles in Aqueous Solution: Relaxation Time versus Size

Abstract: The rate of energy dissipation from Au nanoparticles to their surroundings has been examined by pump−probe spectroscopy. These experiments were performed for particles suspended in aqueous solution, with average sizes ranging from 4 to 50 nm in diameter. The results show that energy relaxation is a very nonexponential process. Fitting the data to a stretched exponential function yields a characteristic time scale for relaxation that varies from ca. 10 ps for the smallest particles examined (∼4 nm diameter) to almost 400 ps for the 50 nm diameter particles. The relaxation times are proportional to the square of the radius, but do not depend on the initial temperature of the particles (i.e., the pump laser power). For very small particles, the time scale for energy dissipation is comparable to the time scale for electron−phonon coupling, which implies that significant energy loss occurs before the electrons and phonons reach thermal equilibrium within the particle.

The Vlasov‐Poisson‐Boltzmann system near Maxwellians

Abstract: The dynamics of dilute electrons can be modeled by the Vlasov-Poisson-Boltz-mann system, where electrons interact with themselves through collisions and with their self-consistent electric field. It is shown that any smooth, periodic initial perturbation of a given global Maxwellian that preserves the same mass, momentum, and total energy (including both kinetic and electric energy), leads to a unique global-in-time classical solution. The construction of global solutions is based on an energy method with a new estimate of dissipation from the collision: ∫0t〈Lf(s), f(s)〉ds is positive definite for solution f(t,x,v) with small amplitude to the Vlasov-Poisson-Boltzmann system (1.4). © 2002 Wiley Periodicals, Inc.

Intrinsic dissipation in high-frequency micromechanical resonators

Abstract: We report measurements of intrinsic dissipation in micron-sized suspended resonators machined from single crystals of galium arsenide and silicon. In these experiments on high-frequency micromechanical resonators, designed to understand intrinsic mechanisms of dissipation, we explore dependence of dissipation on temperature, magnetic field, frequency, and size. In contrast to most of the previous measurements of acoustic attenuation in crystalline and amorphous structures in this frequency range, ours is a resonant measurement; dissipation is measured at the natural frequencies of structural resonance, or modes of the structure associated with flexural and torsional motion. In all our samples we find a weakly temperature dependent dissipation at low temperatures. We compare and contrast our data to various probable mechanisms, including thermoelasticity, clamping, anharmonic mode-coupling, surface anisotropy and defect motion, both in bulk and on surface. The observed parametric dependencies indicate that the internal defect motion is the dominant mechanism of intrinsic dissipation in our samples.

Onset of energy dissipation in ballistic atomic wires.

Abstract: The trend toward miniaturization in electronics will soon lead to devices of nanometer scale in which quantum effects become relevant. The ultimate quantum conductor is a perfect one-dimensional wire, such as an atomic chain [1,2] or semiconducting heterostructure [3]. In these wires the electrons are ballistic since there are no defects to inhibit resistance-free currents [3]. The limiting factor in the current-carrying capacity of a wire is dissipation, which results in heating. Two mechanisms contribute to the resistance of a metallic wire: elastic scattering with defects and impurities and inelastic scattering with the lattice vibrations [4]. In the absence of scattering, electrons can propagate freely and transport is said to be ballistic. This situation is possible in the nanoscale where the mean-free path of electrons can be much longer than the length of the device. The two-terminal zero-bias resistance of a single-mode ballistic wire is the resistance quantum h2e 2 . This resistance is entirely associated with the connections of the wire to the electrodes [5], being the intrinsic resistance of the wire zero, as recently demonstrated in quantum wires fabricated from GaAsAlGaAs heterostructures [3], and in agreement with Landauer framework [6,7]. Within this framework, the applied voltage serves to unbalance the chemical potentials for propagating electrons in each direction and drops entirely at the contacts and not within the wire. The Joule dissipation associated with this resistance is assumed to take place far away from the contact (at an inelastic relaxation length), where electrons and holes relax to the Fermi level of the electrodes. This picture is correct for bias voltages close to zero, which implies vanishingly small currents (note that the resistance-free currents in the experiment of Ref. [3] were smaller than 1 nA).

Acceleration of GRB outflows by Poynting flux dissipation

Abstract: We study magnetically powered relativistic outflows in which a part of the magnetic energy is dissipated internally by reconnection. For GRB parameters, and assuming that the reconnection speed scales with the Alfv en speed, signicant dissipation can take place both inside and outside the photosphere of the flow. The process leads to a steady increase of the flow Lorentz factor with radius. With an analytic model we show how the eciency of this process depends on GRB parameters. Estimates are given for the thermal and non-thermal radiation expected to be emitted from the photosphere and the optically thin part of the flow respectively. A critical parameter of the model is the ratio of Poynting flux to kinetic energy flux at some initial radius of the flow. For a large value (>100) the non-thermal radiation dominates over the thermal component. If the ratio is small (<40) only prompt

Bubble collapse near a solid boundary: a numerical study of the influence of viscosity

Abstract: The effect of viscosity on jet formation for bubbles collapsing near solid boundaries is studied numerically. A numerical technique is presented which allows the Navier-Stokes equations with free-surface boundary conditions to be solved accurately and efficiently. Good agreement is obtained between experimental data and numerical simulations for the collapse of large bubbles. However, it is shown that compressible and thermal effects must be taken into account in order to describe the energy dissipation occurring during jet impact correctly. A parametric study of the effect of viscosity on jet impact velocity is undertaken. The jet impact velocity is found to decrease as viscosity increases and above a certain threshold jet impact is impossible. We study how this critical Reynolds number depends on the initial radius and the initial distance from the wall. A simple scaling law is found to link this critical Reynolds number to the other non-dimensional parameters of the problem.

Kinetic theory for identical, frictional, nearly elastic spheres

Abstract: We derive a simple kinetic theory for collisional flows of identical, slightly frictional, nearly elastic spheres that is based on a physically realistic model for a frictional collision between two spheres. When the coefficient of friction is small, the equations of balance for rotational momentum and energy can be solved in approximation. This permits the rotational temperature to be related to the translation temperature and the introduction of an effective coefficient of restitution in the rate of dissipation of translation fluctuation energy. With this incorporation of the additional loss of translational energy to friction and the rotational degrees of freedom, the structure of the resulting theory is the same as for frictionless spheres.

On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation

Abstract: Long time behavior of a semilinear wave equation with nonlinear boundary dissipation and critical exponent is considered. It is shown that weak solutions generated by the wave dynamics converge asymptotically to a global and compact attractor. In addition, regularity and structure of the attractor are discussed in the paper. While this type of results are known for wave dynamics with interior dissipation this is, to our best knowledge, first result pertaining to boundary and nonlinear dissipation in the context of global attractors and their properties.

Energy dissipation in body-forced turbulence

Abstract: Bounds on the bulk rate of energy dissipation in body-force-driven steady-state turbulence are derived directly from the incompressible Navier–Stokes equations We consider flows in three spatial dimensions in the absence of boundaries and derive rigorous a priori estimates for the time-averaged energy dissipation rate per unit mass, e, without making any further assumptions on the flows or turbulent fluctuations We provee [les ] c1v U2/l2 + c2 U3/l,where v is the kinematic viscosity, U is the root-mean-square (space and time averaged) velocity, and l is the longest length scale in the applied forcing function The prefactors c1 and c2 depend only on the functional shape of the body force and not on its magnitude or any other length scales in the force, the domain or the flow We also derive a new lower bound on e in terms of the magnitude of the driving force F For large Grashof number Gr = Fl3/v2, we findc3 vFl/λ2 [les ] ewhere λ = √vU2/e is the Taylor microscale in the flow and the coefficient c3 depends only on the shape of the body force This estimate is seen to be sharp for particular forcing functions producing steady flows with λ/l ∼ O(1) as Gr → 1 We interpret both the upper and lower bounds on e in terms of the conventional scaling theory of turbulence – where they are seen to be saturated – and discuss them in the context of experiments and direct numerical simulations

Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part I: Maximum Work and Frictional Dissipation

Abstract: The entropy budget of an atmosphere in radiative–convective equilibrium is analyzed here. The differential heating of the atmosphere, resulting from surface heat fluxes and tropospheric radiative cooling, corresponds to a net entropy sink. In statistical equilibrium, this entropy sink is balanced by the entropy production due to various irreversible processes such as frictional dissipation, diffusion of heat, diffusion of water vapor, and irreversible phase changes. Determining the relative contribution of each individual irreversible process to the entropy budget can provide important information on the behavior of convection. The entropy budget of numerical simulations with a cloud ensemble model is discussed. In these simulations, it is found that the dominant irreversible entropy source is associated with irreversible phase changes and diffusion of water vapor. In addition, a large fraction of the frictional dissipation results from falling precipitation, and turbulent dissipation accounts fo...

A new approach to modelling near-wall turbulence energy and stress dissipation

Abstract: A new model for the transport equation for the turbulence energy dissipation rate e and for the anisotropy of the dissipation rate tensor eij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanovic, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part eh of the energy dissipation rate. The algebraic expression for the components of eij was then reformulated in terms of eh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of eij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than eij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (uiui) All Overbar, using eh instead of e, agree well with the direct numerical simulations.

A bus energy model for deep submicron technology

Abstract: We present a comprehensive mathematical analysis of the energy dissipation in deep submicron technology buses. The energy estimation is based on an elaborate bus model that includes distributed and lumped parasitic elements that appear as technology scales. The energy drawn from the power supply during the transition of the bus is evaluated in a closed form. The notion of the transition activity of an individual line is generalized to that of the transition activity matrix of the bus. The transition activity matrix is used for statistical estimation of the power dissipation in deep submicron technology buses.

Fabrication and use of a transient contractional flow device to quantify the sensitivity of mammalian and insect cells to hydrodynamic forces

Abstract: A microfluidic device was fabricated via photolithographic techniques which can create transient elongational and shear forces ranging over three orders of magnitude while still maintaining laminar flow conditions. The contractional fluid flow inside the microfluidic device was simulated with FLUENT (a computational fluid dynamics computer program) and the local deformation forces were characterized with the scalar quantity, local energy dissipation rate. The sensitivities of four cell lines (CHO, HB-24, Sf-9, and MCF7) were tested in the device. The results indicate that all four cell lines are able to withstand relatively intense energy dissipation rates (up to 104–105 kW/m3), which is orders of magnitude higher than the maximum local energy dissipation rates generated by impellers in bioreactors, but comparable to that associated with small bursting bubbles. While the concept that suspended animal cells are relatively robust with respect to purely hydrodynamic forces in bioprocess equipment is well known, these results quantitatively demonstrate these observations. © 2002 Wiley Periodicals, Inc. Biotechnol Bioeng 80: 428–437, 2002.

Splitting for Dissipative Particle Dynamics

Abstract: We study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature control, is compared to the modified velocity Verlet method used in many previous papers.

Measurements of the turbulent energy dissipation rate

Abstract: The one-dimensional surrogate for the dimensionless energy dissipation rate Ce is measured in shear flows over a range of the Taylor microscale Reynolds number Rλ, 70≲Rλ≲1217. We recommend that Ce should be defined with respect to an energy length scale derived from the turbulent energy spectrum. For Rλ≳300, a value of Ce≈0.5 appears to be a good universal approximation for flow regions free of strong mean shear. The present results for Ce support a key assumption of turbulence—the mean turbulent energy dissipation rate is finite in the limit of zero viscosity.

Heat conduction and entropy production in a one-dimensional hard-particle gas.

Abstract: We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses and correct several claims in recent literature based on much smaller simulations. We find heat conductivities kappa to diverge with the number N of particles. These depended strongly on the mass ratio, and extrapolations to N--> infinity, and t--> infinity, are difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa approximately N(alpha) with alpha approximately 0.33 suggesting a relation to the Kardar-Parisi-Zhang model. We finally discuss why the system leads nevertheless to energy dissipation and entropy production, in spite of not being chaotic in the usual sense.

Non-breaking and breaking solitary wave run-up

Abstract: The run-up of non-breaking and breaking solitary waves on a uniform plane beach connected to a constant-depth wave tank was investigated experimentally and numerically. If only the general characteristics of the run-up process and the maximum run-up are of interest, for the case of a breaking wave the post-breaking condition can be simplified and represented as a propagating bore. A numerical model using this bore structure to treat the process of wave breaking and subsequent shoreward propagation was developed. The nonlinear shallow water equations (NLSW) were solved using the weighted essentially non-oscillatory (WENO) shock capturing scheme employed in gas dynamics. Wave breaking and post-breaking propagation are handled automatically by this scheme and ad hoc terms are not required. A computational domain mapping technique was used to model the shoreline movement. This numerical scheme was found to provide a relatively simple and reasonably good prediction of various aspects of the run-up process. The energy dissipation associated with wave breaking of solitary wave run-up (excluding the effects of bottom friction) was also estimated using the results from the numerical model.

Experimental Study of Air-Water Flow Properties on Low-Gradient Stepped Cascades

Abstract: Stepped cascades are recognised for both aeration potential and energy dissipation, and have been employed in hydraulic structures for over 3,500 years. Yet little detailed information exists on their performance, especially pertaining to low-gradient cascades. This study presents a detailed investigation of both the macro and micro-scale flow properties on a low-gradient cascade (3.4 degree slope). Research is conducted on two large-size physical models: a 24m long multi-step cascade (10-2.4m long steps), and a single-step model with identical step height and length. The large size of the model allows near full-scale data acquisition under controlled flow conditions, minimising potential scale effects. The study comprises three distinct components: 1. A global investigation of the general flow properties of nappe flow on a low-gradient, multi-step cascade. Unforeseen three-dimensional characteristics of the flow, including supercritical shockwaves and sidewall standing-waves downstream of nappe impact, are identified and examined by the study. Although comparable to similar phenomena at channel bends and expansions, these have not been previously described on stepped cascades. Energy dissipation on the cascade is investigated, and is found to be over twice that observed for a smooth chute of similar gradient. 2. A complete characterisation of the air-water structure of flow in a nappe regime. Significant outcomes of the analysis include: - Air-concentration Distribution: The air-concentration distribution at the lower nappe of the free-falling jet shows good agreement with an analytical solution of the diffusion equation. The experimental results from the study, and a reanalysis of existing data, indicate a distinct relationship between the turbulent diffusivity in the shear layer and distance from the step brink. This contradicts earlier investigations that assumed constant diffusivity. Strong aeration of the flow, with a large volume of spray, occurs downstream of the nappe impact. Depth-averaged air concentrations of 40% to 50% are observed within the spray region, decreasing towards the downstream end of the step. -Velocity Distribution: A theoretical analysis of the momentum transfer process imparts an improved understanding of the momentum transfer and velocity redistribution within the free-falling jet. An analytical solution based on twodimensional wake flow is developed, superseding existing solutions based upon a monophase free-mixing layer. - Bubble-frequency Distribution: A quasi-parabolic relationship between bubble frequency and time-average air concentration across a cross-section is observed. A theoretical explanation for the parabolic relationship is developed, and two correction factors are introduced to provide a better representation of the experimental data. - Air-bubble and Water-droplet Size Distributions: Chord-length distributions are compared with standard probability distributions, showing good agreement with standard Weibull, gamma and log-normal probability distributions within various regions of the flow on the step. A computer model is developed to model interaction between a bubbly transition from water to air and fluctuations of the free surface. 3. A parallel investigation of the oxygen aeration efficiency of a stepped cascade. Measured air-water property data is used to calculate the air-water interface area in bubbly flow, and to estimate the theoretical aeration efficiency of the stepped cascade based upon the integration of the mass transfer equation. The aeration performance of the stepped cascade model is also measured experimentally in terms of dissolved oxygen content. This analysis allows a unique, successful comparison of experimental dissolved oxygen measurements with the numerical integration of the mass transfer equation.