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Artificial dissipation in modern computational fluid dynamics is something of an art. In spite of the dramatic strides made over the last decade, dissipation continues to lack a quantitative theory with predictive power. Such a theory, based on entropy production, is presented. An important side-effect is nonlinear stability for schemes which satisfy certain conditions.
Understanding the dynamics of equilibration processes in quantum systems as well as their interplay with dissipation and fluctuation is a major challenge in quantum many-body theory. The timescales of such processes are investigated in collisions of atomic nuclei using fully microscopic approaches. Findings from time-dependent Hartree-Fock and time-dependent random-phase approximation calculations are compared for 13 systems over a broad range of energies. The timescale for full mass equilibration ( ~ 2 × 10 - 20 s ) is found to be much larger than timescales for neutron-to-proton equilibration, kinetic energy, and angular momentum dissipations which are on the order of 10 - 21 s . Fluctuations of mass numbers in the fragments and correlations between their neutron and proton numbers build up within only a few 10 - 21 s . This suggests that dissipation is basically not impacted by mass equilibration, but is mostly driven by the exchange of nucleons between the fragments.
We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma-alpha (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation Epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma-alpha s are functions of both Ri and Rq (Richardson number and density ratio representing double diffusion, DD); the Gamma-alpha are different for heat, salt and momentum; in the case of heat, the traditional value Gamma-h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Gamma-h can be three times as large, a result that we reproduce. The salt Gamma-s is given in terms of Gamma-h. The momentum Gamma-m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma-m(Ri,R-rho). Having tested Gamma-h, we then test the momentum Gamma-m by showing that the turbulent Prandtl number Gamma-m/Gamma-h vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean;s bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon/N(exp 2) from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma-alpha = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma-alpha; the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma-h(Ri,Rq). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon (Ri < 1) approximately equals 10epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri much greater than 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve.
Thermal remote sensing instruments can function as environmental measuring tools, with capabilities leading toward new directions in functional landscape ecology. Theoretical deduction and phenomenological observation leads us to believe that the second law of thermodynamics requires that all dynamically systems develop in a manner which dissipates gradients as rapidly as possible within the constraints of the system at hand. The ramification of this requirement is that dynamical systems will evolve dissipative structures which grow and complexify over time. This perspective has allowed us to develop a framework for discussing ecosystem development and integrity. In the context of this framework we have developed measures of development and integrity for ecosystems. One set of these measures is based on destruction of the exergy content of incoming solar energy. More developed ecosystems will be more effective at dissipating the solar gradient (destroying its exergy content). This can be measured by the effective surface temperature of the ecosystem on a landscape scale. These surface temperatures are measured using airborne thermal scanners such as the Thermal Infrared Multispectral Scanner (TIMS) and the Airborne Thermal/Visible Land Application Sensor(ATLAS) sensors. An analysis of agriculture and forest ecosystems will be used to illustrate the concept of ecological thermodynamics and the development of ecosystems.
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In simulations of aqueous systems, it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time step δt for integrating the equations of motion. Thus, δt = 2 fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using δt from 0.5 to 3.0 fs and up to 4 fs using hydrogen mass repartitioning. In these simulations, we find that for all but δt = 0.5 fs, equipartition is not obtained between translational and rotational modes, with the rotational modes exhibiting a lower temperature than the translation modes. To probe the reasons for the lack of equipartition, we study the autocorrelation of the translational velocity of the center of mass and the angular velocity of the rigid water molecule, respectively. Here, we find that the rotational relaxation occurs on a timescale comparable to vibrational periods, calling into question the original motivations for freezing the vibrations. Furthermore, a time step with δt ≥ 1 fs is not able to capture accurately the fast rotational relaxation, which reveals its impact as an effective slowing-down of rotational relaxation. The fluctuation–dissipation relation then leads to the conclusion that the rotational temperature should be cooler for δt greater than the reference value of 0.5 fs. Consideration of fluctuation–dissipation in equilibrium molecular dynamics simulations also emphasizes the need to capture the temporal evolution of fluctuations with fidelity and the role of δt in this regard. The time step also influences the solution thermodynamic properties: both the mean system potential energies and the excess entropy of hydration of a soft repulsive cavity are sensitive to δt.
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I. Novikau, I. Y. Dodin, E. A. Startsev, I. Joseph, Quantum algorithms for simulating dissipative linear and nonlinear dynamics of plasmas. Invited talk at the 66th Annual Meeting of the APS Division of Plasma Physics, Atlanta, Georgia. Novikau I., Dodin I.Y., Startsev E.A., Encoding of linear kinetic plasma problems in quantum circuits via data compression, Journal of Plasma Physics. 2024;90(4):805900401, doi:10.1017/S0022377824000795. We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation to be solved by using the quantum signal processing algorithm. The latter requires encoding of a matrix in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.
General theory of dissipative periodic systems for dynamic systems defined by differential equations
Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.
Effective utilization of flexible loads for grid services, while satisfying end-user preferences and constraints, requires an accurate estimation of the aggregated predictive flexibility offered by the electrical loads. Recently, there have been efforts to quantify the predictive flexibility of thermostatic loads (e.g. residential air-conditioners, electric water-heaters) using the notion of virtual battery (VB), whose state evolution is governed by a first order dynamics including self-dissipation rate, and power and energy capacities. Identifying the VB model parameters for a collection of thermostatic loads, however, is challenging primarily due to uncertainties and lack of information regarding the end-user behavior, underlying device models and parameters. In this paper, we propose a \textit{variational autoencoder}-based deep learning algorithm to identify the parameters of the VB model. Using available sensors and meters data, the proposed algorithm generates not only point estimates of the VB parameters, but also confidence intervals around those values. Effectiveness of the proposed frameworks is demonstrated on a collection of electric water-heater loads, whose operation is driven by uncertain water usage profiles.
The dynamics and energetics of intergranular crack growth along a flat grain boundary in aluminum is studied by a molecular-dynamics simulation model for crack propagation under steady-state conditions. Using the ability of the molecular-dynamics simulation to identify atoms involved in different atomistic mechanisms, it was possible to identify the energy contribution of different processes taking place during crack growth. The energy contributions were divided as: elastic energy, defined as the potential energy of the atoms in fcc crystallographic state; and plastically stored energy, the energy of stacking faults and twin boundaries; grain-boundary and surface energy. In addition, monitoring the amount of heat exchange with the molecular-dynamics thermostat gives the energy dissipated as heat in the system. The energetic analysis indicates that the majority of energy in a fast growing crack is dissipated as heat. This dissipation increases linearly at low speed, and faster than linear at speeds approaching 1/3 the Rayleigh wave speed when the crack tip becomes dynamically unstable producing periodic dislocation bursts until the crack is blunted.
An analytical technique for the prediction of the effects of rigid baffles on the stability of liquid propellant combustors is presented. This analysis employs both two and three dimensional combustor models characterized by concentrated combustion sources at the chamber injector and a constant Mach number nozzle. An eigenfunction-matching method is used to solve the linearized partial differential equations describing the unsteady flow field for both models. Boundary layer corrections to this unsteady flow are in a mechanical energy dissipation model to evaluate viscous and turbulence effects within the flow. An integral instability relationship is then employed to predict the decay rate of the oscillations. Results of this analysis agree qualitatively with experimental observations and show that sufficient dissipation exists to indicate that the proper mechanism of baffle damping is a fluid dynamic loss. The response of the dissipation model to varying baffle blade length, mean flow Mach number, oscillation amplitude, baffle configuration, and oscillation mode is examined.
An analytical technique for the prediction of the effects of rigid baffles on the stability of liquid propellant combustors is presented. This analysis employs a three dimensional combustor model characterized by a concentrated combustion source at the chamber injector and a constant Mach number nozzle. An eigenfunction-matching method is used to solve the linearized partial differential equations describing the unsteady flow field. Boundary layer corrections to this unsteady flow are used in a mechanical energy dissipation model to evaluate viscous and turbulence effects within the flow. An integral stability relationship is then employed to predict the decay rate of the oscillations. Results of this analysis agree qualitatively with experimental observations and show that sufficient dissipation exists to indicate that the proper mechanism of baffle damping is a fluid dynamic loss. The response of the dissipation model to varying baffle blade length, mean flow Mach number and oscillation amplitude is examined.
Transport of charge and valley (axial) degrees of freedom coupled to order-parameter dynamics in magnetic Weyl semimetals is studied in the framework of nonequilibrium thermodynamics. In addition to the established valley-related transport anomalies that are rooted in band-structure topology, we construct dissipative couplings between the three dynamic constituents of the system driven out of equilibrium by electromagnetic perturbations. We show how the valley degree of freedom mediates an effective coupling between the charge and magnetic sectors of the system, through a combination of the chiral anomaly, on the electric side, and the Onsager-paired valley torque and pumping, on the magnetic side. This work complements previous studies of magnetic Weyl semimetals by a more systematic analysis of collective dissipation. We discuss several concrete examples of the valley-mediated current-driven magnetic instabilities and charge pumping, and extend the theory to the antiferromagnetic case.
At solid-liquid interfaces, the viscosity increases markedly from the bulk due to the collective interactions of ions and water molecules, influencing phenomena relevant to nanofluidics, colloidal dynamics, and electrochemistry. Here, in this study, we investigated dissipative forces at the boehmite-water interface using 3D atomic force microscopy. We observed an increase in interfacial solution viscosity, η, by 10-100-fold as the nanoprobe approached the surface in normal direction, with up to four oscillatory features showing average peaks of η/η bulk = 44-71. Moreover, the viscosity showed sub-nanometer variations within 0.5 nm from the interface, templated by the underlying crystal lattice and correlated with the interfacial solution structure. Beyond a near-wall region of approximately 1.2 nm, the dissipative response was comparable to that in bulk solution. Molecular dynamics simulations, along with statistical mechanical analyses, provided details on hydrodynamic structures near the interface. Specifically, the lattice-dependent dissipative responses are correlated with extensive hydrogen bonding by interfacial water molecules, which increased friction, particularly along the [001] direction. These results demonstrate how solution viscosity at mineral-water interfaces is anisotropic and correlated with the local solution structure, providing insights into the dynamics of nanocrystal attachment.
The propagation path of topologically protected states is bound to the interface between regions with different topology, and as such, the functionality of linear photonic devices leveraging these states is fixed during fabrication. Here, we propose a mechanism for dynamic control over a driven dissipative system’s local topology, yielding reconfigurable topological interfaces and thus tunable paths for protected routing. We illustrate our approach in non-resonantly pumped polariton lattices, where the nonlinear interaction between the polaritons and the exciton reservoir due to non-resonant pumping can yield picosecond-scale changes in the propagation paths of the chiral edge states. To analytically confirm the numerically observed topological dynamics, we generalize the spectral localizer framework to non-linear non-Hermitian Chern materials and apply this framework to a continuous model of the polariton system based on a driven-dissipative Gross-Pitaevskii equation. In doing so, we show that the local changes in the polariton lattice’s topology are captured by a local Chern marker. Looking forward, we anticipate such reconfigurable topological routing will enable the realization of novel classes of topological photonic devices.