Showing papers on "Dissipation published in 2005"

Dissipative photosphere models of gamma-ray bursts and X-ray flashes

Abstract: We consider dissipative effects occurring in the optically thick inner parts of the relativistic outflows producing gamma-ray bursts and X-ray flashes, emphasizing in particular the Comptonization of the thermal radiation flux that is advected from the base of the outflow. Such dissipative effects—e.g., from magnetic reconnection, neutron decay, or shocks would boost the energy density of the thermal radiation. The dissipation can lead to pair production, in which case the pairs create an effective photosphere farther out than the usual baryonic one. In a slow dissipation scenario, pair creation can be suppressed, and the effects are most important when dissipation occurs below the baryonic photosphere. In both cases an increased photospheric luminosity is obtained. We suggest that the spectral peak in gamma-ray bursts is essentially due to the Comptonized thermal component from the photosphere, where the comoving optical depth in the outflow falls to unity. Typical peak photon energies range between those of classical bursts and X-ray flashes. The relationship between the observed photon peak energy and the luminosity depends on the details of the dissipation, but under plausible assumptions can resemble the observed correlations.

Spectral wave dissipation over a barrier reef

Abstract: [1] A 2 week field experiment was conducted to measure surface wave dissipation on a barrier reef at Kaneohe Bay, Oahu, Hawaii. Wave heights and velocities were measured at several locations on the fore reef and the reef flat, which were used to estimate rates of dissipation by wave breaking and bottom friction. Dissipation on the reef flat was found to be dominated by friction at rates that are significantly larger than those typically observed at sandy beach sites. This is attributed to the rough surface generated by the reef organisms, which makes the reef highly efficient at dissipating energy by bottom friction. Results were compared to a spectral wave friction model, which showed that the variation in frictional dissipation among the different frequency components could be described using a single hydraulic roughness length scale. Surveys of the bottom roughness conducted on the reef flat showed that this hydraulic roughness length was comparable to the physical roughness measured at this site. On the fore reef, dissipation was due to the combined effect of frictional dissipation and wave breaking. However, in this region the magnitude of dissipation by bottom friction was comparable to wave breaking, despite the existence of a well-defined surf zone there. Under typical wave conditions the bulk of the total wave energy incident on Kaneohe Bay is dissipated by bottom friction, not wave breaking, as is often assumed for sandy beach sites and other coral reefs.

Equality connecting energy dissipation with a violation of the fluctuation-response relation.

Abstract: In systems driven away from equilibrium, the velocity correlation function and the linear-response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems under nonequilibrium conditions. This equality enables us to calculate the rate of energy dissipation by quantifying the extent of the FRR violation, which can be measured experimentally.

Existence results for energetic models for rate-independent systems

Abstract: We consider mechanical models which are driven by an external loading on a time scale much slower than any internal time scale (like viscous relaxation times) but still much faster than the time needed to find the thermo-dynamical equilibrium. Typical phenomena involve dry friction, elasto-plasticity, certain hysteresis models for shape-memory alloys and quasistatic delamination or fracture. The main feature is the rate-independency of the system response, which means that a loading with twice (or half) the speed will lead to a response with exactly twice (or half) the speed. We refer to [BrS96, KrP89, Vis94, Mon93] for approaches to these phenomena involving either differential inclusions or abstract hysteresis operators. Our method is different, as we avoid time derivatives and use energy principles instead. As is well-known from dry friction, such systems will not necessarily relax into a complete equilibrium, since friction forces do not tend to 0 for vanishing velocities. One way to explain this phenomenon on a purely energetic basis is via so-called “wiggly energies”, where the macroscopic energy functional has a super-imposed fluctuating part with many local minimizers. Only after reaching a certain activation energy it is possible to leave these local minima and generate macroscopic changes, cf. [ACJ96, Jam96, Men02]. Here we use a different approach which involves a dissipation distance which locally behaves homogeneous of degree 1, in contrast to viscous dissipation which is homogeneous of degree 2. This approach was introduced in [MiT99, MiT03, MTL02, GMH02] for models for shape-memory alloys and is now generalized to many other rate-independent systems. See [Mie03a] for a general setup for rate-independent material models in the framework of “standard generalized materials”. To be more specific we consider the following continuum mechanical model. Let Ω ⊂ R be the undeformed body and t ∈ [0, T ] the slow process time. The deformation or displacement φ(t) : Ω → R is considered to lie in the space F of admissible deformations containing suitable Dirichlet boundary conditions. The internal variable z(t) : Ω → Z ⊂ R describes the internal state which may involve plastic deformations, hardening variables, magnetization or phase indicators. The elastic (Gibbs) stored energy is given

Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with a small-scale dissipation.

Abstract: The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. We introduce the dissipation term which works only in the scale smaller than the healing length to remove short wavelength excitations which may hinder the cascade process of quantized vortices in the inertial range. The obtained energy spectrum is consistent with the Kolmogorov law.

Study of the collapse of granular columns using two-dimensional discrete-grain simulation

Abstract: Numerical simulations of the collapse and spreading of granular columns onto a horizontal plane using the Contact Dynamics method are presented. The results are in agreement with previous experimental work. The final shape of the deposit appears to depend only on the initial aspect ratio a of the column. The normalized runout distance has a power-law dependence on the aspect ratio a , a dependence incompatible with a simple friction model. The dynamics of the collapse is shown to be mostly controlled by a free fall of the column. Energy dissipation at the base of the column can be described simply by a coefficient of restitution. Hence the energy available for the sideways flow is proportional to the initial potential energy $E_0$ . The dissipation process within the sideways flow is approximated well by basal friction, unlike the behaviour of the runout distance. The proportion of mass ejected sideways is shown to play a determining role in the spreading process: as a increases, the same fraction of initial potential energy $E_0$ drives an increasing proportion of the initial mass against friction. This gives a possible explanation for the power-law dependence of the runout distance on a . We propose a new scaling for the runout distance that matches the data well, is compatible with a friction model, and provides a qualitative explanation of the column collapse.

Quantum mechanics of dissipative systems

Abstract: Quantum dissipation involves both energy relaxation and decoherence, leading toward quantum thermal equilibrium. There are several theoretical prescriptions of quantum dissipation but none of them is simple enough to be treated exactly in real applications. As a result, formulations in different prescriptions are practically used with different approximation schemes. This review examines both theoretical and application aspects on various perturbative formulations, especially those that are exact up to second-order but nonequivalent in high-order system-bath coupling contributions. Discrimination is made in favor of an unconventional formulation that in a sense combines the merits of both the conventional time-local and memory-kernel prescriptions, where the latter is least favorite in terms of the applicability range of parameters for system-bath coupling, non-Markovian, and temperature. Also highlighted is the importance of correlated driving and dissipation effects, not only on the dynamics under strong external field driving, but also in the calculation of field-free correlation and response functions.

Stabilizing the Benjamin–Feir instability

Abstract: The Benjamin–Feir instability is a modulational instability in which a uniform train of oscillatory waves of moderate amplitude loses energy to a small perturbation of other waves with nearly the same frequency and direction. The concept is well established in water waves, in plasmas and in optics. In each of these applications, the nonlinear Schrodinger equation is also well established as an approximate model based on the same assumptions as required for the derivation of the Benjamin–Feir theory: a narrow-banded spectrum of waves of moderate amplitude, propagating primarily in one direction in a dispersive medium with little or no dissipation. In this paper, we show that for waves with narrow bandwidth and moderate amplitude, any amount of dissipation (of a certain type) stabilizes the instability. We arrive at this stability result first by proving it rigorously for a damped version of the nonlinear Schrodinger equation, and then by confirming our theoretical predictions with laboratory experiments on waves of moderate amplitude in deep water. The Benjamin–Feir instability is often cited as the first step in a nonlinear process that spreads energy from an initially narrow bandwidth to a broader bandwidth. In this process, sidebands grow exponentially until nonlinear interactions eventually bound their growth. In the presence of damping, this process might still occur, but our work identifies another possibility: damping can stop the growth of perturbations before nonlinear interactions become important. In this case, if the perturbations are small enough initially, then they never grow large enough for nonlinear interactions to become important.

Mixing and dissipation in particle-driven gravity currents

Abstract: Results are presented from a high-resolution computational study of particle-driven gravity currents in a plane channel. The investigation was conducted in order to obtain better insight into the energy budget and the mixing behaviour of such flows. Two- and three-dimensional simulations are discussed, and the effects of different factors influencing the flow are examined in detail. Among these are the aspect ratio of the initial suspension reservoir, the settling speed of the particles, and the initial level of turbulence in the suspension. While most of the study is concerned with the lock-exchange configuration, where the initial height of the suspension layer is equal to the height of the channel, part of the analysis is also done for a deeply submerged case. Here, the suspension layer is only one-tenth of the full channel height. Concerning the energy budget, a careful analysis is undertaken of dissipative losses in the flow. Dissipative losses arising from the macroscopic fluid motion are distinguished from those due to the microscopic flow around each sedimenting particle. It is found that over a large range of settling velocities and suspension reservoir aspect ratios, sedimentation accounts for roughly half of all dissipative losses. The analysis of the mixing behaviour of the flow concentrates on the mixing between interstitial and ambient fluid, which are taken to be of identical density. The former is assumed to carry a passive contaminant, whose dispersion with time is analysed qualitatively and quantitatively by means of Lagrangian markers. The simulations show the mixing between interstitial and ambient fluid to be more intense for larger values of the particle settling velocity. Finally, the question is addressed of whether or not initial turbulence in the suspension may exert a significant effect on the flow evolution. To this end, results from three simulations with widely different levels of initial kinetic energy are compared. While the initial turbulence level strongly affects the mixing within the current, it has only a small influence on the front velocity and the overall sedimentation rate.

Effective dissipation and turbulence in spectrally truncated euler flows.

Abstract: A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3D Euler equation with a high-wave-number spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wave number and the maximum wave number, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus obeys (at least approximately) Kolmogorov scaling.

Characterizing energy dissipation in single-walled carbon nanotube polycarbonate composites

Abstract: In this study, single-walled carbon nanotube and bisphenol-A-polycarbonate composite beams were fabricated by a solution mixing process and dynamic (cyclic) load tests were performed to characterize energy dissipation. We report up to an order of magnitude (>1000%) increase in loss modulus of the polycarbonate system with the addition of 2% weight fraction of oxidized single-walled nanotube fillers. We show that the increase in damping is derived from frictional sliding at the nanotube-polymer interfaces. The nanoscale dimensions of the tubes not only result in large interfacial contact area, thereby generating high damping efficiency, but also enable seamless integration of the filler materials into the composite structure.

Thermodynamics of rate-independent plasticity

Abstract: We show that the singular dissipative potential of the phenomenological rate-independent plasticity can be obtained by homogenization of a micro-model with quadratic dissipation. The essential ingredient making this reduction possible is a rugged energy landscape at the micro-scale, generating under external loading a regular cascade of subcritical bifurcations. Such landscape may appear as a result of a sufficiently strong pinning or jamming of defects, leading to elastic micro-metastability. The rate-independent plastic deformation emerges in this description as a continuous succession of infinitesimal viscous events; the limiting procedure presumes the elimination of small time and length scales. We present an explicit example of a simple viscoelastic mass-spring system whose macroscopic dissipative behavior is plastic, rate independent.

Scalar dissipation rate and dissipative anomaly in isotropic turbulence

Abstract: We examine available data from experiment and recent numerical simulations to explore the supposition that the scalar dissipation rate in turbulence becomes independent of the fluid viscosity when the viscosity is small and of scalar diffusivity when the diffusivity is small. The data are interpreted in the context of semi-empirical spectral theory of Obukhov and Corrsin when the Schmidt number, Sc, is below unity, and of Batchelor's theory when Sc is above unity. Practical limits in terms of the Taylor-microscale Reynolds number, R λ , as well as Sc, are deduced for scalar dissipation to become sensibly independent of molecular properties

Kinetics of martensitic phase transitions: lattice model*

Abstract: Martensitic phase transitions are often modeled by mixed-type hyperbolic-elliptic systems. Such systems lead to ill-posed initial-value problems unless they are supplemented by an additional kinetic relation. In this paper we explicitly compute an appropriate closing relation by replacing the continuum model with its natural discrete prototype. The procedure can be viewed as either regularization by discretization or a physically motivated account of underlying discrete microstructure. We model phase boundaries by traveling wave solutions of a fully inertial discrete model for a bi-stable lattice with harmonic long-range interactions. Although the microscopic model is Hamiltonian, it generates macroscopic dissipation which can be specified in the form of a relation between the velocity of the discontinuity and the conjugate configurational force. This kinetic relation respects entropy inequality but is not a consequence of the usual Rankine--Hugoniot jump conditions. According to the constructed solution, the dissipation at the macrolevel is due to the induced radiation of lattice waves carrying energy away from the propagating front. We show that sufficiently strong nonlocality of the lattice model may be responsible for the multivaluedness of the kinetic relation and can quantitatively affect kinetics in the near-sonic region. Direct numerical simulations of the transient dynamics suggest stability of at least some of the computed traveling waves.

The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations

Abstract: The present investigation explores the unsteady dynamics of large density contrast non-Boussinesq lock-exchange flows by means of high-resolution two-dimensional simulations of the incompressible variable-density Navier-Stokes equations, employing a combination of spectral and compact finite-difference methods. For small density contrasts, the simulations closely reproduce earlier Boussinesq results for corresponding flows. Across the entire range of density contrasts, good agreement is obtained between the computed front propagation velocities and corresponding experimental observations reported in Part 1 of this investigation and by other authors. The simulations yield the required quantitative information with respect to the light and dense front heights, their propagation velocities, and the spatial structure of the dissipation fields in order to determine conclusively which of the scenarios developed in Part 1 is observed in reality. Simulations are conducted for fluids with the same kinematic viscosity, as well as for fluids with the same dynamic viscosity. For both slip and no-slip boundary conditions, and for all Re values, we find that for larger density contrasts, the dense front dissipates an increasing amount of energy. In contrast, the energy dissipated by the light front remains near its Boussinesq level for all values of the density ratio. In addition, for all density ratios, the height of the light front is very close to half the channel height, and it propagates with a non-dimensional velocity close to a half. This provides strong evidence that the dynamics of the light front is indeed approximated by the energy-conserving solution described in an earlier theoretical analysis. In contrast, the height of the dense front is substantially less than half the channel height. In addition, its velocity is close to the value derived in Part 1 for a dissipative gravity current. Together with the above results for the dissipation field, this confirms that the dense front behaves as a dissipative gravity current.

Study of the collapse of granular columns using DEM numerical simulation

Abstract: Numerical simulations of the collapse and spreading of granular columns onto an horizontal plane using the Contact Dynamics method are presented. The final shape of the deposit seems to depend only on the aspect ratio $a$ of the columns; these results are in good agreement with previous experimental work. In particular, the renormalised runout distance shows a power law dependence on the aspect ratio $a$, which is incompatible with a simple friction model. The dynamics of the collapse is shown to be mostly controlled by the free fall of the column. The energy dissipation at the base of the column can be described simply by a coefficient of restitution. Hence the energy available for the sideways flow is proportional to the initial potential energy $E_0$. The dissipation process within the flow is well approximated by basal friction, contrary to the behaviour of the runout distance. The mass ejected sideways is showned to play a determining role in the spreading process. As $a$ increases, the same fraction of initial potential energy $E_0$ drives more mass against friction. This additional dissipation give a possible explanation for power-law dependence of the runout distance on $a$. Beyond the frictional properties of the material, we show that the flow characteristics strongly depend on the early dynamics of the collapse. We propose a new scaling for the runout distance that matches the data well, is compatible with a friction model, and provide a qualitative explanation to the column collapse phenomenology.

Forced magnetic reconnection

Abstract: [1] Using a multi-code approach, we investigate current sheet thinning and the onset and progress of fast magnetic reconnection, initiated by temporally limited, spatially varying, inflow of magnetic flux. The present study extends an earlier collaborative effort into the transition regime from thick to thin current sheets. Again we find that full particle, hybrid, and Hall-MHD simulations lead to the same fast reconnection rates, apparently independent of the dissipation mechanism. The reconnection rate in MHD simulations is considerably larger than in the earlier study, although still somewhat smaller than in the particle simulations. All simulations lead to surprisingly similar final states, despite differences in energy transfer and dissipation. These states are contrasted with equilibrium models derived for the same boundary perturbations. The similarity of the final states indicates that entropy conservation is satisfied similarly in fluid and kinetic approaches and that Joule dissipation plays only a minor role in the energy transfer.

Stable but nondissipative water

Abstract: This article presents a physically-based technique for simulating water. This work is motivated by the "stable fluids" method, developed by Stam [1999], to handle gaseous fluids. We extend this technique to water, which calls for the development of methods for modeling multiphase fluids and suppressing dissipation. We construct a multiphase fluid formulation by combining the Navier--Stokes equations with the level set method. By adopting constrained interpolation profile (CIP)-based advection, we reduce the numerical dissipation and diffusion significantly. We further reduce the dissipation by converting potentially dissipative cells into droplets or bubbles that undergo Lagrangian motion. Due to the multiphase formulation, the proposed method properly simulates the interaction of water with surrounding air, instead of simulating water in a void space. Moreover, the introduction of the nondissipative technique means that, in contrast to previous methods, the simulated water does not unnecessarily lose mass, and its motion is not damped to an unphysical extent. Experiments showed that the proposed method is stable and runs fast. It is demonstrated that two-dimensional simulation runs in real-time.

On the normalized turbulent energy dissipation rate

Abstract: This paper revisits values of the normalized energy dissipation rate (Cϵ) in different flows (two-dimensional wakes, grid turbulence, and homogeneous shear flow). Previously published as well as new data are considered over a relatively wide range of the Taylor-microscale Reynolds number Rλ. Cϵ exhibits wide scatter (in the range 0.5–2.5 for Rλ>50) although, for a given flow and initial conditions, it is independent of Rλ when the latter is sufficiently large. An alternative definition [B. R. Pearson, P.-A. Krogstad, and W. van de Water, “Measurements of the turbulent energy dissipation rate,” Phys. Fluids 14, 1288 (2002)] of Cϵ has been checked in the same flows but has failed to yield a universal value for the coefficient.

Energy release and conversion by reconnection in the magnetotail

Abstract: . Magnetic reconnection is the crucial process in the release of magnetic energy previously stored in the magnetotail in association with substorms. However, energy transfer and dissipation in the vicinity of the reconnection site is only a minor part of the energy conversion. We discuss the energy release, transport, and conversion based on large-scale resistive MHD simulations of magnetotail dynamics and more localized full particle simulations of reconnection. We address in particular, where the energy is released, how it propagates and where and how it is converted from one form into another. We find that Joule (or ohmic) dissipation plays only a minor role in the overall energy transfer. Bulk kinetic energy, although locally significant in the outflow from the reconnection site, plays a more important role as mediator or catalyst in the transfer between magnetic and thermal energy. Generator regions with potential auroral consequences are located primarily off the equatorial plane in the boundary regions of the plasma sheet.

Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence

Abstract: Decaying homogeneous isotropic turbulence in inertial and rotating reference frames is investigated to evaluate the capability of the lattice Boltzmann method in turbulence. In the inertial frame case, the decay exponents of kinetic energy and dissipation and the low wave-number scaling of the spectrum are studied. The results are in agreement with classical ones. In the frame-rotation case, simulations show that the energy decay rate decreases with decreasing Rossby number as the energy cascade is inhibited by rotation, again in agreement with turbulence physics. These results clearly indicate that the lattice Boltzmann method captures important features of decaying turbulence.