Energy flows in vibrated granular media

We study vibrated granular media, investigating each of the three components of the energy flow: particle-particle dissipation, energy input at the vibrating wall, and particle-wall dissipation. Energy dissipated by interparticle collisions is well estimated by existing theories when the granular material is dilute, and these theories are extended to include rotational kinetic energy. When the granular material is dense, the observed particle-particle dissipation rate decreases to as little as 2/5 of the theoretical prediction. We observe that the rate of energy input is the weight of the granular material times an average vibration velocity times a function of the ratio of particle to vibration velocity. `Particle-wall' dissipation has been neglected in all theories up to now, but can play an important role when the granular material is dilute. The ratio between gravitational potential energy and kinetic energy can vary by as much as a factor of 3. Previous simulations and experiments have shown that E ~ V^delta, with delta=2 for dilute granular material, and delta ~ 1.5 for dense granular material. We relate this change in exponent to the departure of particle-particle dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR

Regulation of the spectral peak in gamma-ray bursts

Observations indicate that the peak of gamma-ray burst spectrum forms in the opaque region of an ultra-relativistic jet. Recent radiative transfer calculations support this picture and show that the spectral peak is inherited from initially thermal radiation, which is changed by heating into a broad photon distribution with a high-energy tail. We discuss the processes that regulate the observed position of the spectral peak E_pk. The opaque jet has three radial zones: (1) Planck zone r<R_P where a blackbody spectrum is enforced; this zone ends where Thomson optical depth decreases to tau~10^5. (2) Wien zone R_P>1 where radiation has a Bose-Einstein spectrum, and (3) Comptonization zone r>R_W where the radiation spectrum develops the high-energy tail. Besides the initial jet temperature, an important factor regulating E_pk is internal dissipation (of bulk motions and magnetic energy) at large distances from the central engine. Dissipation in the Planck zone reduces E_pk, and dissipation in the Wien zone increases E_pk. In jets with sub-dominant magnetic fields, the predicted E_pk varies around 1 MeV up to a maximum value of about 10 MeV. If the jet carries an energetically important magnetic field, E_pk can be additionally increased by dissipation of magnetic energy. This increase is hinted by observations, which show E_pk up to about 20 MeV. We also consider magnetically dominated jets; then a simple model of magnetic dissipation gives E_pk~30 Gamma_W keV where Gamma_W is the jet Lorentz factor at the Wien radius R_W.Comment: 12 pages, 1 figure, accepted to Ap

Improved variational principle for bounds on energy dissipation in turbulent shear flow

We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to the dissipation rate. Its optimization leads to improved bounds without entailing additional technical difficulties. For plane Couette flow, the high-Re-bounds obtainable with one-dimensional background flows are methodically lowered by a factor of 27/32.Comment: 15 pages, RevTeX, 3 postscript figure

Thermodynamics of an Accretion Disk Annulus with Comparable Radiation and Gas Pressure

We explore the thermodynamic and global structural properties of a local patch of an accretion disk whose parameters were chosen so that radiation pressure and gas pressure would be comparable in magnitude. Heating, radiative transport, and cooling are computed self-consistently with the structure by solving the equations of radiation MHD in the shearing-box approximation. Using a fully 3-d and energy-conserving code, we compute the structure and energy balance of this disk segment over a span of more than forty cooling times. As is also true when gas pressure dominates, the disk's upper atmosphere is magnetically-supported. However, unlike the gas-dominated case, no steady-state is reached; instead, the total (i.e., radiation plus gas) energy content fluctuates by factors of 3--4 over timescales of several tens of orbits, with no secular trend. Because the radiation pressure varies much more than the gas pressure, the ratio of radiation pressure to gas pressure varies over the approximate range 0.5--2. The volume-integrated dissipation rate generally increases with increasing total energy, but the mean trend is somewhat slower than linear, and the instantaneous dissipation rate is often a factor of two larger or smaller than the mean for that total energy level. Locally, the dissipation rate per unit volume scales approximately in proportion to the current density; the time-average dissipation rate per unit mass is proportional to m^{-1/2}, where m is the horizontally-averaged mass column density to the nearer of the top or bottom surface. As in our earlier study of a gas-dominated shearing-box, we find that energy transport is completely dominated by radiative diffusion, with Poynting flux carrying less than 1% of the energy lost from the box.Comment: ApJ, in pres

Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence

We relate the intermittent fluctuations of velocity gradients in turbulence to a whole range of local dissipation scales generalizing the picture of a single mean dissipation length. The statistical distribution of these local dissipation scales as a function of Reynolds number is determined in numerical simulations of forced homogeneous isotropic turbulence with a spectral resolution never applied before which exceeds the standard one by at least a factor of eight. The core of the scale distribution agrees well with a theoretical prediction. Increasing Reynolds number causes the generation of ever finer local dissipation scales. This is in line with a less steep decay of the large-wavenumber energy spectra in the dissipation range. The energy spectrum for the highest accessible Taylor microscale Reynolds number R_lambda=107 does not show a bottleneck.Comment: 8 pages, 5 figures (Figs. 1 and 3 in reduced quality

Mid-J CO observations of Perseus B1-East 5: evidence for turbulent dissipation via low-velocity shocks

Giant molecular clouds contain supersonic turbulence and magnetohydrodynamic simulations predict that this turbulence should decay rapidly. Such turbulent dissipation has the potential to create a warm (T ~100 K) gas component within a molecular cloud. We present observations of the CO J = 5-4 and 6-5 transitions, taken with the Herschel Space Observatory, towards the Perseus B1-East 5 region. We combine these new observations with archival measurements of lower rotational transitions and fit photodissociation region models to the data. We show that Perseus B1-E5 has an anomalously large CO J = 6-5 integrated intensity, consistent with a warm gas component existing within the region. This excess emission is consistent with predictions for shock heating due to the dissipation of turbulence in low velocity shocks with the shocks having a volume filling factor of 0.15 per cent. We find that B1-E has a turbulent energy dissipation rate of 3.5 x 10$^{32}$ erg / s and a dissipation time-scale that is only a factor of 3 larger than the flow crossing time-scale.Comment: 18 pages, 15 figures, 4 tables, accepted by MNRAS, fixed errors described in erratu

Force-gradient-induced mechanical dissipation of quartz tuning fork force sensors used in atomic force microscopy

We have studied the dynamics of quartz tuning fork resonators used in atomic force microscopy taking into account mechanical energy dissipation through the attachment of the tuning fork base. We find that the tuning fork resonator quality factor changes even for the case of a purely elastic sensor-sample interaction. This is due to the effective mechanical imbalance of the tuning fork prongs induced by the sensor-sample force gradient which in turn has an impact on the dissipation through the attachment of the resonator base. This effect may yield a measured dissipation signal that can be different to the one exclusively related to the dissipation between the sensor and the sample. We also find that there is a second order term in addition to the linear relationship between the sensor-sample force gradient and the resonance frequency shift of the tuning fork that is significant even for force gradients usually present in atomic force microscopy which are in the range of tens of N/m.Comment: 9 pages, 3 figures and supplemental informatio

High Quality Factor Silicon Cantilever Driven by PZT Actuator for Resonant Based Mass Detection

A high quality factor (Q-factor) piezoelectric lead zirconat titanate (PZT) actuated single crystal silicon cantilever was proposed in this paper for resonant based ultra-sensitive mass detection. Energy dissipation from intrinsic mechanical loss of the PZT film was successfully compressed by separating the PZT actuator from resonant structure. Excellent Q-factor, which is several times larger than conventional PZT cantilever, was achieved under both atmospheric pressure and reduced pressures. For a 30 micrometer-wide 100 micrometer-long cantilever, Q-factor was measured as high as 1113 and 7279 under the pressure of 101.2 KPa and 35 Pa, respectively. Moreover, it was found that high-mode vibration can be realized by the cantilever for the pursuit of great Q-factor, while support loss became significant because of the increased vibration amplitude at the actuation point. An optimized structure using node-point actuation was suggested then to suppress corresponding energy dissipation.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838