Showing papers on "Dissipation published in 2015"

The affine particle-in-cell method

Abstract: Hybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particle-in-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, without suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

Surface participation and dielectric loss in superconducting qubits

Abstract: We study the energy relaxation times (T1) of superconducting transmon qubits in 3D cavities as a function of dielectric participation ratios of material surfaces. This surface participation ratio, representing the fraction of electric field energy stored in a dissipative surface layer, is computed by a two-step finite-element simulation and experimentally varied by qubit geometry. With a clean electromagnetic environment and suppressed non-equilibrium quasiparticle density, we find an approximately proportional relation between the transmon relaxation rates and surface participation ratios. These results suggest dielectric dissipation arising from material interfaces is the major limiting factor for the T1 of transmons in 3D circuit quantum electrodynamics architecture. Our analysis also supports the notion of spatial discreteness of surface dielectric dissipation.

Momentum dissipation and effective theories of coherent and incoherent transport

Abstract: We study heat transport in two systems without momentum conservation: a hydrodynamic system, and a holographic system with spatially dependent, massless scalar fields. When momentum dissipates slowly, there is a well-defined, coherent collective excitation in the AC heat conductivity, and a crossover between sound-like and diffusive transport at small and large distance scales. When momentum dissipates quickly, there is no such excitation in the incoherent AC heat conductivity, and diffusion dominates at all distance scales. For a critical value of the momentum dissipation rate, we compute exact expressions for the Green’s functions of our holographic system due to an emergent gravitational self-duality, similar to electric/magnetic duality, and SL(2, $$ \mathrm{\mathbb{R}} $$ ) symmetries. We extend the coherent/incoherent classification to examples of charge transport in other holographic systems: probe brane theories and neutral theories with non-Maxwell actions.

A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency

Abstract: Understanding thermal transport from nanoscale heat sources is important for a fundamental description of energy flow in materials, as well as for many technological applications including thermal management in nanoelectronics and optoelectronics, thermoelectric devices, nanoenhanced photovoltaics, and nanoparticle-mediated thermal therapies. Thermal transport at the nanoscale is fundamentally different from that at the macroscale and is determined by the distribution of carrier mean free paths and energy dispersion in a material, the length scales of the heat sources, and the distance over which heat is transported. Past work has shown that Fourier’s law for heat conduction dramatically overpredicts the rate of heat dissipation from heat sources with dimensions smaller than the mean free path of the dominant heat-carrying phonons. In this work, we uncover a new regime of nanoscale thermal transport that dominates when the separation between nanoscale heat sources is small compared with the dominant phonon mean free paths. Surprisingly, the interaction of phonons originating from neighboring heat sources enables more efficient diffusive-like heat dissipation, even from nanoscale heat sources much smaller than the dominant phonon mean free paths. This finding suggests that thermal management in nanoscale systems including integrated circuits might not be as challenging as previously projected. Finally, we demonstrate a unique capability to extract differential conductivity as a function of phonon mean free path in materials, allowing the first (to our knowledge) experimental validation of predictions from the recently developed first-principles calculations.

Optimal control of energy extraction in wind-farm boundary layers

Abstract: In very large wind farms the vertical interaction with the atmospheric boundary layer plays an important role, i.e. the total energy extraction is governed by the vertical transport of kinetic energy from higher regions in the boundary layer towards the turbine level. In the current study, we investigate optimal control of wind-farm boundary layers, considering the individual wind turbines as flow actuators, whose energy extraction can be dynamically regulated in time so as to optimally influence the flow field and the vertical energy transport. To this end, we use Large-Eddy Simulations (LES) of a fullydeveloped pressure-driven wind-farm boundary layer in a receding-horizon optimal control framework. For the optimization of the wind-turbine controls, a conjugate-gradient optimization method is used in combination with adjoint LESs for the determination of the gradients of the cost functional. In a first control study, wind-farm energy extraction is optimized in an aligned wind farm. Results are accumulated over one hour of operation. We find that the energy extraction is increased by 16% compared to the uncontrolled reference. This is directly related to an increase of the vertical fluxes of energy towards the wind turbines, and vertical shear stresses increase considerably. A further analysis, decomposing total stresses in dispersive and Reynolds stresses, shows that the dispersive stresses increase drastically, and that the Reynolds stresses decrease on average, but increase in the wake region, leading to better wake recovery. We further observe that also turbulent dissipation levels in the boundary layer increase, and overall the outer layer of the boundary layer enters into a transient decelerating regime, while the inner layer and the turbine region attain a new statistically steady equilibrium within approximately one wind-farm through-flow time. Two additional optimal-control cases study penalization of turbulent dissipation. For the current wind-farm geometry, it is found that the ratio between wind-farm energy extraction and turbulent boundary-layer dissipation remains roughly around 70%, but can be slightly increased with a few percent by penalizing the dissipation in the optimization objective. For a pressure-driven boundary layer in equilibrium, we estimate that such a shift can lead to an increase in wind-farm energy extraction of 6%.

The minimal work cost of information processing

Abstract: Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer's principle, is increasingly relevant today, as the energy dissipation of computing devices impedes the development of their performance. Here we determine the minimal work required to carry out any logical process, for instance a computation. It is given by the entropy of the discarded information conditional to the output of the computation. Our formula takes precisely into account the statistically fluctuating work requirement of the logical process. It enables the explicit calculation of practical scenarios, such as computational circuits or quantum measurements. On the conceptual level, our result gives a precise and operational connection between thermodynamic and information entropy, and explains the emergence of the entropy state function in macroscopic thermodynamics.

Underwater optical communication performance for laser beam propagation through weak oceanic turbulence.

Abstract: In clean ocean water, the performance of a underwater optical communication system is limited mainly by oceanic turbulence, which is defined as the fluctuations in the index of refraction resulting from temperature and salinity fluctuations. In this paper, using the refractive index spectrum of oceanic turbulence under weak turbulence conditions, we carry out, for a horizontally propagating plane wave and spherical wave, analysis of the aperture-averaged scintillation index, the associated probability of fade, mean signal-to-noise ratio, and mean bit error rate. Our theoretical results show that for various values of the rate of dissipation of mean squared temperature and the temperature-salinity balance parameter, the large-aperture receiver leads to a remarkable decrease of scintillation and consequently a significant improvement on the system performance. Such an effect is more noticeable in the plane wave case than in the spherical wave case.

Surface participation and dielectric loss in superconducting qubits

Abstract: We study the energy relaxation times ($T_1$) of superconducting transmon qubits in 3D cavities as a function of dielectric participation ratios of material surfaces. This surface participation ratio, representing the fraction of electric field energy stored in a dissipative surface layer, is computed by a two-step finite-element simulation and experimentally varied by qubit geometry. With a clean electromagnetic environment and suppressed non-equilibrium quasiparticle density, we find an approximately proportional relation between the transmon relaxation rates and surface participation ratios. These results suggest dielectric dissipation arising from material interfaces is the major limiting factor for the $T_1$ of transmons in 3D cQED architecture. Our analysis also supports the notion of spatial discreteness of surface dielectric dissipation.

The free-energy cost of accurate biochemical oscillations

Abstract: Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study three different types of biochemical oscillations representing three basic oscillation motifs shared by all known oscillatory systems. In all the systems studied, we find that the phase diffusion constant depends on the free energy dissipation per period following the same inverse relation parameterized by system specific constants. This relationship and its range of validity are shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyze the fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this general relationship and testable predictions are also presented.

Intermittent Dissipation and Heating in 3D Kinetic Plasma Turbulence.

Abstract: High resolution, fully kinetic, three dimensional (3D) simulation of collisionless plasma turbulence shows the development of turbulence characterized by sheetlike current density structures spanning a range of scales. The nonlinear evolution is initialized with a long wavelength isotropic spectrum of fluctuations having polarizations transverse to an imposed mean magnetic field. We present evidence that these current sheet structures are sites for heating and dissipation, and that stronger currents signify higher dissipation rates. The analyses focus on quantities such as $\mathbf{J}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{E}$, electron, and proton temperatures, and conditional averages of these quantities based on local electric current density. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform. Comparison with previous results from 2D kinetic simulations, as well as high frequency solar wind observational data, are discussed.

Relaxation times of dissipative many-body quantum systems.

Abstract: We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap cannot be larger than ∼1/L. In integrable systems with boundary dissipation one typically observes scaling of ∼1/L(3), while in chaotic ones one can have faster relaxation with the gap scaling as ∼1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

Minimum-dissipation models for large-eddy simulation

Abstract: Minimum-dissipation eddy-viscosity models are a class of sub-filter models for large-eddy simulation that give the minimum eddy dissipation required to dissipate the energy of sub-filter scales. A previously derived minimum-dissipation model is the QR model. This model is based on the invariants of the resolved rate-of-strain tensor and has many desirable properties. It appropriately switches off for laminar and transitional flows, has low computational complexity, and is consistent with the exact sub-filter tensor on isotropic grids. However, the QR model proposed in the literature gives insufficient eddy dissipation. It is demonstrated that this can be corrected by increasing the model constant. The corrected QR model gives good results in simulations of decaying grid turbulence on an isotropic grid. On anisotropic grids the QR model is not consistent with the exact sub-filter tensor and requires an approximation of the filter width. It is demonstrated that the results of the QR model on anisotropic grids are primarily determined by the used filter width approximation, and that no approximation gives satisfactory results in simulations of both a temporal mixing layer and turbulent channel flow. A new minimum-dissipation model for anisotropic grids is proposed. This anisotropic minimum-dissipation (AMD) model generalizes the desirable practical and theoretical properties of the QR model to anisotropic grids and does not require an approximation of the filter width. The AMD model is successfully applied in simulations of decaying grid turbulence on an isotropic grid and in simulations of a temporal mixing layer and turbulent channel flow on anisotropic grids.

Multiscale Nature of the Dissipation Range in Gyrokinetic Simulations of Alfvénic Turbulence.

Abstract: Nonlinear energy transfer and dissipation in Alfven wave turbulence are analyzed in the first gyrokinetic simulation spanning all scales from the tail of the MHD range to the electron gyroradius scale. For typical solar wind parameters at 1 AU, about 30% of the nonlinear energy transfer close to the electron gyroradius scale is mediated by modes in the tail of the MHD cascade. Collisional dissipation occurs across the entire kinetic range k(⊥)ρ(I)≳1. Both mechanisms thus act on multiple coupled scales, which have to be retained for a comprehensive picture of the dissipation range in Alfvenic turbulence.

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

Abstract: We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations.

Abstract: We consider a quantum mechanical system represented in phase space (referred to hereafter as “Wigner space”), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.

Stabilization of quantum metastable states by dissipation

Abstract: Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. Here we show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system-bath coupling and the temperature, producing a stabilizing effect.

Anisotropy in solar wind plasma turbulence.

Abstract: A review of spectral anisotropy and variance anisotropy for solar wind fluctuations is given, with the discussion covering inertial range and dissipation range scales. For the inertial range, theory, simulations and observations are more or less in accord, in that fluctuation energy is found to be primarily in modes with quasi-perpendicular wavevectors (relative to a suitably defined mean magnetic field), and also that most of the fluctuation energy is in the vector components transverse to the mean field. Energy transfer in the parallel direction and the energy levels in the parallel components are both relatively weak. In the dissipation range, observations indicate that variance anisotropy tends to decrease towards isotropic levels as the electron gyroradius is approached; spectral anisotropy results are mixed. Evidence for and against wave interpretations and turbulence interpretations of these features will be discussed. We also present new simulation results concerning evolution of variance anisotropy for different classes of initial conditions, each with typical background solar wind parameters.

Field Measurements of Surface and Near-Surface Turbulence in the Presence of Breaking Waves

Abstract: Wave breaking removes energy from the surface wave field and injects it into the upper ocean, where it is dissipated by viscosity. This paper presents an investigation of turbulent kinetic energy (TKE) dissipation beneath breaking waves. Wind, wave, and turbulence data were collected in the North Pacific Ocean aboard R/P FLIP, during the ONR-sponsored High Resolution Air-Sea Interaction (HiRes) and Radiance in a Dynamic Ocean (RaDyO) experiments. A new method for measuring TKE dissipation at the sea surface was combined with subsurface measurements to allow estimation of TKE dissipation over the entire wave-affected surface layer. Near the surface, dissipation decayed with depth as z−1, and below approximately one significant wave height, it decayed more quickly, approaching z−2. High levels of TKE dissipation very near the sea surface were consistent with the large fraction of wave energy dissipation attributed to non-air-entraining microbreakers. Comparison of measured profiles with large-eddy s...

Resonant Absorption of Transverse Oscillations and Associated Heating in a Solar Prominence. I. Observational Aspects

Abstract: Transverse magnetohydrodynamic waves have been shown to be ubiquitous in the solar atmosphere and can, in principle, carry sufficient energy to generate and maintain the Sun’s million-degree outer atmosphere or corona. However, direct evidence of the dissipation process of these waves and subsequent heating has not yet been directly observed. Here we report on high spatial, temporal, and spectral resolution observations of a solar prominence that show a compelling signature of so-called resonant absorption, a long hypothesized mechanism to efficiently convert and dissipate transverse wave energy into heat. Aside from coherence in the transverse direction, our observations show telltale phase differences around 180° between transverse motions in the plane-of-sky and line-of-sight velocities of the oscillating fine structures or threads, and also suggest significant heating from chromospheric to higher temperatures. Comparison with advanced numerical simulations support a scenario in which transverse oscillations trigger a Kelvin–Helmholtz instability (KHI) at the boundaries of oscillating threads via resonant absorption. This instability leads to numerous thin current sheets in which wave energy is dissipated and plasma is heated. Our results provide direct evidence for wave-related heating in action, one of the candidate coronal heating mechanisms.

Variation of tidal dissipation in the convective envelope of low-mass stars along their evolution ?

Abstract: Context. Since 1995, more than 1500 exoplanets have been discovered around a wide variety of host stars (from M- to A-type stars). Tidal dissipation in stellar convective envelopes is an important factor that shapes the orbital architecture of short-period systems.Aims. Our objective is to understand and evaluate how tidal dissipation in the convective envelope of low-mass stars (from M to F types) depends on their mass, evolutionary stage, and rotation.Methods. Using a simplified two-layer assumption, we analytically compute the frequency-averaged tidal dissipation in the convective envelope. This dissipation is due to the conversion into heat of the kinetic energy of tidal non-wavelike/equilibrium flow and inertial waves because of the viscous friction applied by turbulent convection. Using grids of stellar models allows us to study the variation of the dissipation as a function of stellar mass and age on the pre-main sequence and on the main sequence for stars with masses ranging from 0.4 to 1.4 M⊙.Results. During their pre-main sequence, all low-mass stars have an increase in the frequency-averaged tidal dissipation for a fixed angular velocity in their convective envelope until they reach a critical aspect and mass ratios (respectively α = Rc/Rs and β = Mc/Ms, where Rs,Ms,Rc, and Mc are the star’s radius and mass and its radiative core’s radius and mass). Next, the dissipation evolves on the main sequence to an asymptotic value that is highest for 0.6 M⊙ K-type stars and that then decreases by several orders of magnitude with increasing stellar mass. Finally, the rotational evolution of low-mass stars strengthens the importance of tidal dissipation during the pre-main sequence for star-planet and multiple star systems.Conclusions. As shown by observations, tidal dissipation in stars’ convection zones varies over several orders of magnitude as a function of stellar mass, age, and rotation. We demonstrate that i) it reaches a maximum value on the pre-main sequence for all stellar masses and ii) on the main sequence and at fixed angular velocity, it is at a maximum for 0.6 M⊙ K-type stars and decreases with increasing mass.

The variation of tidal dissipation in the convective envelope of low-mass stars along their evolution

Abstract: Since 1995, more than 1500 exoplanets have been discovered around a large diversity of host stars (from M- to A-type stars). Tidal dissipation in stellar convective envelopes is a key actor that shapes the orbital architecture of short-period systems. Our objective is to understand and evaluate how tidal dissipation in the convective envelope of low-mass stars (from M to F types) depends on their mass, evolutionary stage and rotation. Using a simplified two-layer assumption, we compute analytically the frequency-averaged tidal dissipation in their convective envelope. This dissipation is due to the conversion into heat of the kinetic energy of tidal non wave-like/equilibrium flow and inertial waves because of the viscous friction applied by turbulent convection. Using grids of stellar models allows us to study the variation of the dissipation as a function of stellar mass and age on the Pre-Main-Sequence and on the Main-Sequence for stars with masses spanning from $0.4$ to $1.4M_{\odot}$. As shown by observations, tidal dissipation in stars varies over several orders of magnitude as a function of stellar mass, age and rotation. During their Pre-Main-Sequence, all low-mass stars have an increase of the frequency-averaged tidal dissipation for a fixed angular velocity in their convective envelope until they reach a critical aspect and mass ratios. Next, the dissipation evolves on the Main Sequence to an asymptotic value that becomes maximum for $0.6M_{\odot}$ K-type stars and that decreases by several orders of magnitude with increasing stellar mass. Finally, the rotational evolution of low-mass stars strengthens the importance of tidal dissipation during the Pre-Main-Sequence for star-planet and multiple star systems.

Onsager Coefficients in Periodically Driven Systems.

Abstract: Periodically driven thermodynamic systems near equilibrium cannot have finite fluxes with zero dissipation.

Eightfold Classification of Hydrodynamic Dissipation.

Abstract: We provide a complete characterization of hydrodynamic transport consistent with the second law of thermodynamics at arbitrary orders in the gradient expansion. A key ingredient in facilitating this analysis is the notion of adiabatic hydrodynamics, which enables isolation of the genuinely dissipative parts of transport. We demonstrate that most transport is adiabatic. Furthermore, in the dissipative part, only terms at the leading order in gradient expansion are constrained to be sign definite by the second law (as has been derived before).