Showing papers on "Dissipation published in 2006"
TL;DR: In this article, an elastically mounted magnetic seismic mass moving past a coil, considered previously by several authors, is analyzed in detail. And the overall damping coefficient (part of which is mechanical) is associated with the harvesting and dissipation of energy and also the transfer of energy from the vibrating base into the system.
813 citations
TL;DR: Two new formulations of a symmetric WENO method for the direct numerical simulation of compressible turbulence are presented, designed to maximize order of accuracy and bandwidth, while minimizing dissipation.
434 citations
TL;DR: In this article, the authors investigate the spectral properties of the dissipation range that forms at spacecraft frequencies ≥03 Hz and show that while the inertial range at lower frequencies displays a tightly constrained range of spectral indexes, the Dissipation range exhibits a broad range of power-law indexes.
Abstract: We investigate the nature of turbulent magnetic dissipation in the solar wind We employ a database describing the spectra of over 800 intervals of interplanetary magnetic field and solar wind measurements recorded by the ACE spacecraft at 1 AU We focus on the spectral properties of the dissipation range that forms at spacecraft frequencies ≥03 Hz and show that while the inertial range at lower frequencies displays a tightly constrained range of spectral indexes, the dissipation range exhibits a broad range of power-law indexes We show that the explanation for this variation lies with the dependence of the dissipation range spectrum on the rate of energy cascade through the inertial range such that steeper spectral forms result from greater cascade rates
342 citations
TL;DR: In this paper, the effect of a thermal radiative component on the observable spectrum was analyzed, assuming that the observable effects are due to a dissipation process occurring below or near the thermal photosphere.
Abstract: A thermal radiative component is likely to accompany the first stages of the prompt emission of gamma-ray bursts (GRBs) and X-ray flashes (XRFs) We analyze the effect of such a component on the observable spectrum, assuming that the observable effects are due to a dissipation process occurring below or near the thermal photosphere We consider both the internal shock model and a "slow heating" model as possible dissipation mechanisms For comparable energy densities in the thermal and leptonic components, the dominant emission mechanism is Compton scattering This leads to a nearly flat energy spectrum (νFν ∝ ν0) above the thermal peak at ≈10-100 keV and below 10-100 MeV, for a wide range of optical depths 003 τγe 100, regardless of the details of the dissipation mechanism or the strength of the magnetic field At lower energies steep slopes are expected, while above 100 MeV the spectrum depends on the details of the dissipation process For higher values of the optical depth, a Wien peak is formed at 100 keV-1 MeV, and no higher energy component exists For any value of τγe, the number of pairs produced does not exceed the baryon-related electrons by a factor of larger than a few We conclude that dissipation near the thermal photosphere can naturally explain both the steep slopes observed at low energies and a flat spectrum above 10 keV, thus providing an alternative scenario to the optically thin synchrotron-SSC model
339 citations
TL;DR: The technique represents a valuable way to minimize energy dissipation in nanocontacts by exciting the mechanical resonances of the sliding system perpendicular to the contact plane to reduce friction below 10 piconewtons.
Abstract: Stiction and wear are demanding problems in nanoelectromechanical devices, because of their large surface-to-volume ratios and the inapplicability of traditional liquid lubricants. An efficient way to switch friction on and off at the atomic scale is achieved by exciting the mechanical resonances of the sliding system perpendicular to the contact plane. The resulting variations of the interaction energy reduce friction below 10 piconewtons in a finite range of excitation and load, without any noticeable wear. Without actuation, atomic stick-slip motion, which leads to dissipation, is observed in the same range. Even if the normal oscillations require energy to actuate, our technique represents a valuable way to minimize energy dissipation in nanocontacts.
296 citations
TL;DR: Identification of energy-dissipation processes at the nanoscale is demonstrated by using amplitude-modulation atomic force microscopy and the agreement obtained between theory and experiments performed on silicon and polystyrene validates the method.
Abstract: Identification of energy-dissipation processes at the nanoscale is demonstrated by using amplitude-modulation atomic force microscopy. The variation of the energy dissipated on a surface by a vibrating tip as a function of its oscillation amplitude has a shape that singles out the dissipative process occurring at the surface. The method is illustrated by calculating the energy-dissipation curves for surface energy hysteresis, long-range interfacial interactions and viscoelasticity. The method remains valid with independency of the amount of dissipated energy per cycle, from 0.1 to 50 eV. The agreement obtained between theory and experiments performed on silicon and polystyrene validates the method.
283 citations
TL;DR: In this paper, a methodology for the dynamical analysis of mechanical systems considering realistic joint characteristics, namely, joints with clearance and lubrication, is presented, in which the energy dissipation in form of hysteresis damping is considered.
266 citations
TL;DR: In this paper, the vertical structure of a local patch of an accretion disk in which heating by dissipation of MRI-driven MHD turbulence is balanced by radiative cooling is computed self-consistently with the structure by solving the equations of radiation MHD in the shearing box approximation.
Abstract: We calculate the vertical structure of a local patch of an accretion disk in which heating by dissipation of MRI-driven MHD turbulence is balanced by radiative cooling. 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 three-dimensional and energy-conserving code, we compute the structure of this disk segment over a span of more than five cooling times. After a brief relaxation period, a statistically steady state develops. Measuring height above the midplane in units of the scale height predicted by a Shakura-Sunyaev model, we find that magnetic pressure causes the disk atmosphere to stretch upward, with the photosphere rising to 7H, in contrast to the 3H predicted by conventional analytic models. This more extended structure, as well as fluctuations in the height of the photosphere, may lead to departures from Planckian form in the emergent spectra. Dissipation is distributed across the region within 3H of the midplane but is very weak at greater altitudes. As a result, the temperature deep in the disk interior is less than that expected when all heat is generated in the midplane. With only occasional exceptions, the gas temperature stays very close to the radiation temperature, even above the photosphere. Because fluctuations in the dissipation are particularly strong away from the midplane, the emergent radiation flux can track dissipation fluctuations with a lag that is only 0.1-0.2 times the mean cooling time of the disk. Long-timescale asymmetries in the dissipation distribution can also cause significant asymmetry in the flux emerging from the top and bottom surfaces of the disk. Radiative diffusion dominates Poynting flux in the vertical energy flow throughout the disk.
241 citations
TL;DR: In this article, structural representations of solutions to the Cauchy problem for wave equations with time-dependent dissipation above scaling were presented, which are used to give estimates of the solution and its derivatives based on L q (R n ), q ⩾ 2.
210 citations
TL;DR: In this article, the basis of the energetic approach is discussed and the application of the model to experimental studies on bulk materials reveals a promising and powerful tool to analyse experimental results and to use in the mechanical design.
208 citations
TL;DR: The influence of the local heating on the rubber friction is studied, and it is shown that in a typical case the temperature increase results in a decrease in rubber friction with increasing sliding velocity for v>0.01 m s(-1).
Abstract: When a rubber block is sliding on a hard rough substrate, the substrate asperities will exert time-dependent deformations of the rubber surface resulting in viscoelastic energy dissipation in the rubber, which gives a contribution to the sliding friction. Most surfaces of solids have roughness on many different length scales, and when calculating the friction force it is necessary to include the viscoelastic deformations on all length scales. The energy dissipation will result in local heating of the rubber. Since the viscoelastic properties of rubber-like materials are extremely strongly temperature dependent, it is necessary to include the local temperature increase in the analysis. At very low sliding velocity the temperature increase is negligible because of heat diffusion, but already for velocities of order 10(-2) m s(-1) the local heating may be very important. Here I study the influence of the local heating on the rubber friction, and I show that in a typical case the temperature increase results in a decrease in rubber friction with increasing sliding velocity for v>0.01 m s(-1). This may result in stick-slip instabilities, and is of crucial importance in many practical applications, e.g. for tyre-road friction and in particular for ABS braking systems.
TL;DR: A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented in this paper, where a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler-Lagrange equations.
Abstract: A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.
TL;DR: In this article, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry, and a dynamic procedure of determining the model coefficient is proposed based on the "global equilibrium" between the subgridscale dissipation and the viscous dissipation.
Abstract: In the present study, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry. A subgrid-scale eddy viscosity model recently proposed by Vreman [Phys. Fluids 16, 3670 (2004)] which guarantees theoretically zero subgrid-scale dissipation for various laminar shear flows, is considered as a base model. A priori tests with the original Vreman model show that it predicts the correct profile of subgrid-scale dissipation in turbulent channel flow but the optimal model coefficient is far from universal. A dynamic procedure of determining the model coefficient is proposed based on the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation. An important feature of the proposed procedure is that the model coefficient determined is globally constant in space but varies only in time. A posteriori tests of the proposed dynamic model are conducted through large eddy simulations of forced isotropic turbulence at Reλ=103, tur...
TL;DR: In this paper, a toroidal gyrokinetic-Vlasov simulation code with high velocity-space resolution was developed to reproduce the neoclassical polarization of trapped ions as well as ballistic mode structures produced by collisionless particle motions.
Abstract: Velocity–space structures of ion distribution function associated with the ion temperature gradient (ITG) turbulence and the collisionless damping of the zonal flow are investigated by means of a newly developed toroidal gyrokinetic-Vlasov simulation code with high velocity–space resolution. The present simulation on the zonal flow and the geodesic acoustic mode (GAM) successfully reproduces the neoclassical polarization of trapped ions as well as ballistic mode structures produced by collisionless particle motions. During the collisionless damping of GAM, the finer-scale structures of the ion distribution function in the velocity–space continue to develop while preserving an invariant defined by a sum of an entropy variable and the potential energy. The simulation results of the toroidal ITG turbulent transport clearly show generation of the fine velocity–space structures of the distribution function and their collisional dissipation. Detailed calculation of the entropy balance confirms the statistically steady state of turbulence, where the anomalous transport balances with the dissipation are given by the weak collisionality. The above results obtained by simulations with high velocity–space resolution are also understood in terms of generation, transfer and dissipation processes of the entropy variable in the phase–space.
TL;DR: In this article, the role of sheath dissipation was investigated in the radial convection of isolated filamentary structures in magnetized plasmas and it was shown that sheaths significantly reduced the radial velocity of isolated filaments.
Abstract: Radial convection of isolated filamentary structures due to interchange motions in magnetized plasmas is investigated. Following a basic discussion of vorticity generation, ballooning, and the role of sheaths, a two-field interchange model is studied by means of numerical simulations on a biperiodic domain perpendicular to the magnetic field. It is demonstrated that a blob-like plasma structure develops dipolar vorticity and electrostatic potential fields, resulting in rapid radial acceleration and formation of a steep front and a trailing wake. While the dynamical evolution strongly depends on the amount of collisional diffusion and viscosity, the structure travels a radial distance many times its initial size in all parameter regimes in the absence of sheath dissipation. In the ideal limit, there is an inertial scaling for the maximum radial velocity of isolated filaments. This velocity scales as the acoustic speed times the square root of the structure size relative to the length scale of the magnetic field. The plasma filament eventually decelerates due to mixing and collisional dissipation. Finally, the role of sheath dissipation is investigated. When included in the simulations, it significantly reduces the radial velocity of isolated filaments. The results are discussed in the context of convective transport in scrape-off layer plasmas, comprising both blob-like structures in low confinement modes and edge localized mode filaments in unstable high confinement regimes.
TL;DR: In this paper, the photosphere of an ultrarelativistic flow with internal dissipation of energy was explored using the magnetic reconnection model (AC model) that makes robust predictions on the energy dissipation rates at different radii in the flow.
Abstract: I explore the observational appearance of the photosphere of an ultrarelativistic flow with internal dissipation of energy ("dissipative" GRB model). As a case study, I use the magnetic reconnection model (AC model) that makes robust predictions on the energy dissipation rates at different radii in the flow. With analytical and numerical tools for the radiative transfer problem, I show that the flow develops a hot photosphere where inverse Compton scattering leads to highly non-thermal spectrum. For a wide range of luminosities and baryon loadings of the flow, this spectrum is very close to the observed prompt GRB emission. Its luminosity ranges from ∼3 to 20% of that of the total energy input.
TL;DR: In this paper, the photosphere of an ultrarelativistic flow with internal dissipation of energy was explored by calculating the spectra for a large range of the characteristics of the flow, and an accurate fitting formula was given that provided the photospheric spectral energy distribution in the ~10 keV to ~10 MeV energy range (in the central engine frame) as a function of the basic physical parameters of flow.
Abstract: We explore the observational appearance of the photosphere of an ultrarelativistic flow with internal dissipation of energy as predicted by the magnetic reconnection model. Previous study of the radiative transfer in the photospheric region has shown that gradual dissipation of energy results in a hot photosphere. There, inverse Compton scattering of the thermal radiation advected with the flow leads to powerful photospheric emission with spectral properties close to those of the observed prompt GRB emission. Here, we build on that study by calculating the spectra for a large range of the characteristics of the flow. An accurate fitting formula is given that provides the photospheric spectral energy distribution in the ~10 keV to ~10 MeV energy range (in the central engine frame) as a function of the basic physical parameters of the flow. It facilitates the direct comparison of the model predictions with observations, including the variability properties of the lightcurves. We verify that the model naturally accounts for the observed clustering in peak energies of the E*f(E) spectrum. In this model, the Amati relation indicates a tendency for the most luminous bursts to have more energy per baryon. If this tendency also holds for individual GRB pulses, the model predicts the observed narrowing of the width of pulses with increasing photon energy.
TL;DR: In this article, a series resonance between the capacitive sheath and the inductive and ohmic bulk of the plasma was investigated, and a simple analytical investigation was introduced to solve the nonlinear equations analytically, a series of approximation is necessary.
Abstract: Self-excited plasma series resonances (PSR) are observed in capacitve discharges as high-frequency oscillations superimposed on the normal rf current. This high-frequency contribution to the current is generated by a series resonance between the capacitive sheath and the inductive and ohmic bulk of the plasma. The nonlinearity of the sheath leads to a complex dynamic. The effect is applied, e.g., as a diagnostic technique in commercial etch reactors where analysis is performed by a numerical model. Here a simple analytical investigation is introduced. In order to solve the nonlinear equations analytically, a series of approximation is necessary. Nevertheless, the basic physics is conserved and excellent agreement with numerical solutions is found. The model provides explicit and simple formula for the current waveform and the spectral range of the oscillations. In particular, the dependence on the discharge parameters is shown. Further, the model gives insight into an additional dissipation channel opened by the high-frequency oscillations. With decreasing pressure, the ohmic resistance of the bulk decreases as well, while the amplitude of the PSR oscillations grows. This results in substantially higher power dissipation that exceeds the contribution of classical stochastic heating.
TL;DR: It is shown that phase shift measurements can be converted into energy dissipation values and energy Dissipation maps provide a robust method to image material properties because they do not depend directly on the tip-surface interaction regime.
Abstract: By recording the phase angle difference between the excitation force and the tip response in amplitude modulation AFM it is possible to image compositional variations in heterogeneous samples. In this contribution we address some of the experimental issues relevant to perform phase contrast imaging measurements. Specifically, we study the dependence of the phase shift on the tip?surface separation, interaction regime, cantilever parameters, free amplitude and tip?surface dissipative processes. We show that phase shift measurements can be converted into energy dissipation values. Energy dissipation curves show a maximum (~10?eV/cycle) with the amplitude ratio. Furthermore, energy dissipation maps provide a robust method to image material properties because they do not depend directly on the tip?surface interaction regime. Compositional contrast images are illustrated by imaging conjugated molecular islands deposited on silicon surfaces.
15 Apr 2006
TL;DR: This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation.
Abstract: This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation (lattice Poisson method) with a density evolution method on discrete lattices to solve the Boltzmann-BGK equation (lattice Boltzmann method). In an electrically driven osmotic flow field, the flow velocity increases with both the external electrical field strength and the surface zeta potential for flows in a homogeneous channel. However, for a given electrical field strength and zeta potential, electrically driven flows have an optimal ionic concentration and an optimum width that maximize the flow velocity. For pressure-driven flows, the electro-viscosity effect increases with the surface zeta potential, but has an ionic concentration that yields the largest electro-viscosity effect. The zeta potential arrangement has little effect on the electro-viscosity for heterogeneous channels. For flows driven by both an electrical force and a pressure gradient, various zeta potential arrangements were considered for maximize the mixing enhancement with a less energy dissipation.
Book•
01 Jan 2006
TL;DR: Oscillations in Systems with Dry Friction, Systems with Almost Elastic Collisions, and Systems with Strong Dissipation Due to High Damping or Inelastic Collisions as discussed by the authors.
Abstract: Oscillations in Systems with Dry Friction.- Systems with Almost Elastic Collisions.- Systems with Strong Dissipation Due to High Damping or Inelastic Collisions.- Short Notes on the Significantly Nonlinear Resonance.- High Frequency Excitation: Basic Ideas and Elementary Effects.- Systems with High-Frequency Excitation: Advanced Analysis and Generalizations.
01 Jan 2006
TL;DR: In this article, a semi-discrete central-upwind scheme for hyperbolic conservation laws is proposed, in which the numerical dissipation is reduced further by a more accurate projection of the evolved quantities onto the original grid.
Abstract: We study central-upwind schemes for systems of hyperbolic conservation laws, recently introduced in [13]. Similarly to staggered non-oscillatory central schemes, these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution, simplicity, universality and robustness. At the same time, the central-upwind framework allows one to decrease a relatively large amount of numerical dissipation present at the staggered central schemes. In this paper, we present a modification of the one-dimensional fullyand semi-discrete central-upwind schemes, in which the numerical dissipation is reduced even further. The goal is achieved by a more accurate projection of the evolved quantities onto the original grid. In the semi-discrete case, the reduction of dissipation procedure leads to a new, less dissipative numerical flux. We also extend the new semi-discrete scheme to the two-dimensional case via the rigorous, genuinely multidimensional derivation. The new semi-discrete schemes are tested on a number of numerical examples, where one can observe an improved resolution, especially of the contact waves.
TL;DR: In this article, the authors analyzed the impact of resonator design (i.e., slots machined into flexural beams) on TED-limited quality factor for complex geometries of micromechanical resonators.
Abstract: Thermoelastic dissipation (TED) is analyzed for complex geometries of micromechanical resonators, demonstrating the impact of resonator design (i.e., slots machined into flexural beams) on TED-limited quality factor. Zener first described TED for simple beams in 1937. This work extends beyond simple beams into arbitrary geometries, verifying simulations that completely capture the coupled physics that occur. Novel geometries of slots engineered at specific locations within the flexural resonator beams are utilized. These slots drastically affect the thermal-mechanical coupling and have an impact on the quality factor, providing resonators with quality factors higher than those predicted by simple Zener theory. The ideal location for maximum impact of slots is determined to be in regions of high strain. We have demonstrated the ability to predict and control the quality factor of micromechanical resonators limited by thermoelastic dissipation. This enables tuning of the quality factor by structure design without the need to scale its size, thus allowing for enhanced design optimization
TL;DR: In this paper, an experimental attempt to estimate the spectral distribution of the dissipation due to breaking of dominant waves was made, and it was shown that the dominant breaking causes energy dissipation throughout the entire spectrum at scales smaller than the spectral peak waves.
Abstract: This paper considers an experimental attempt to estimate the spectral distribution of the dissipation due to breaking of dominant waves. A field wave record with an approximately 50% dominant-breaking rate was analyzed. Segments of the record, comprising sequences of breaking waves, were used to obtain the “breaking spectrum,” and segments of nonbreaking waves were used to obtain the “nonbreaking spectrum.” The clear visible difference between the two spectra was attributed to the dissipation due to breaking. This assumption was supported by independent measurements of total dissipation of kinetic energy in the water column at the measurement location. It is shown that the dominant breaking causes energy dissipation throughout the entire spectrum at scales smaller than the spectral peak waves. The dissipation rate at each frequency is linear in terms of the wave spectral density at that frequency, with a correction for the directional spectral width. A formulation for the spectral dissipation fun...
TL;DR: Artificial dissipation terms for finite difference approximations of linear hyperbolic problems with variable coefficients are determined such that an energy estimate and strict stability is obtained.
Abstract: Artificial dissipation terms for finite difference approximations of linear hyperbolic problems with variable coefficients are determined such that an energy estimate and strict stability is obtained. Both conservative and non-conservative approximations are considered. The dissipation terms are computed such that there is no loss of accuracy
TL;DR: In this article, the authors introduce a phenomenological modification to the hydrodynamic equations for dense flows of identical, frictionless, inelastic disks and show that the resulting theory describes the area fraction dependence of quantities that are measured in numerical simulations of steady, homogeneous shearing flows and steady, fully developed flows down inclines.
Abstract: We introduce a simple phenomenological modification to the hydrodynamic equations for dense flows of identical, frictionless, inelastic disks and show that the resulting theory describes the area fraction dependence of quantities that are measured in numerical simulations of steady, homogeneous shearing flows and steady, fully developed flows down inclines. The modification involves the incorporation of a length scale other than the particle diameter in the expression for the rate of collisional dissipation. The idea is that enduring contacts between grains forced by the shearing reduce the collisional rate of dissipation while continuing to transmit momentum and force. The length and orientation of the chains of particles in contact are determined by a simple algebraic equation. When the resulting expression for the rate of dissipation is incorporated into the theory, numerical solutions of the boundary-value problem for steady, fully developed flow of circular disks down a bumpy incline exhibit a core w...
TL;DR: In this paper, a six-speed manual gearbox is divided into lumped elements with a uniform temperature connected by thermal resistances which account for conduction, convection, and radiation.
Abstract: A model is presented which makes it possible to predict power losses in a six-speed manual gearbox. The following sources of dissipation, i.e., power inputs in the model, are considered: (i) tooth friction; (ii) rolling element bearings; (iii) oil shearing in the synchronizers and at the shaft-free pinion interfaces; and (iv) oil churning. Based upon the first principle of Thermodynamics for transient conditions, the entire gearbox is divided into lumped elements with a uniform temperature connected by thermal resistances which account for conduction, convection, and radiation. The numerical predictions compare favorably with the efficiency measurements from the actual gearbox at different speeds and torques. The results also reveal that, at lower temperatures (about 40°C), power loss estimations cannot be disassociated from the accurate prediction of temperature distributions.
TL;DR: In this paper, the authors presented tethered balloon-borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer and showed that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale.
Abstract: Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with lon...
TL;DR: This work introduces a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations and identifies clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice.
Abstract: We introduce a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations. Stationary and traveling localized states are generated by removing atoms at the optical lattice ends. Clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice are identified. The phenomenon is universal and can also be observed in arrays of optical waveguides with mirrors at the system boundaries.
12 Jun 2006
TL;DR: The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.
Abstract: Weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer-Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, production and mixing fractions, energy spectra, statistics, probability distribution functions, numerical turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and numerical viscosity on the order and resolution is investigated to long evolution times. The results are interpreted using the implicit numerical dissipation in the characteristic projection-based, finite-difference WENO method. It is shown that higher order higher resolution simulations have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition by the second shock-interface interaction induces the formation of small-scale structures. Lower-order lower-resolution simulations preserve large-scale structures and flow symmetry to late times, while higher-order higher-resolution simulations exhibit fragmentation of the structures, symmetry breaking and increased mixing. Similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling showsmore » that increasing the order is more advantageous than increasing the resolution for the flow considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.« less