Equipartition Of Kinetic Energy Research Articles

Population balance modeling of formation and breakage of nanoparticle agglomerates in a spouted bed

A population balance framework for fluidization of Al2O3 nano-agglomerates in a ProCell-type spouted bed considering agglomeration and breakage phenomena is developed. An equipartition of kinetic energy (EKE kernel) is used to model the agglomeration phenomena. For breakage, two different fragment distribution functions are considered, the Dirac delta function and a function with confined uniform binary breakage. The fractal dimension property is incorporated in both the agglomeration and breakage models. The model parameters are extracted from batch fluidization experiments conducted by varying the air pressure of the top nozzle. The developed model shows a good agreement with experimental observation in regard of the temporal change in the area and volume-weighted average size of nano-agglomerates and of their final size distribution. The developed population balance model is simulated to study the influence of model parameters on the evolution of average size and coefficient of variation of the nano-agglomerates.

Kinetic energy equipartition: A tool to characterize quantum thermalization

Kinetic energy equipartition: A tool to characterize quantum thermalization

Dynamics of intermediate mass black holes in globular clusters

Context. We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with N. Our method is based on the multi-particle collision (MPC) scheme, previously applied in fluid dynamics and plasma physics. We were able to simulate globular clusters with a realistic number of stellar particles (at least up to several times 106) on a standard workstation. Aims. We simulated clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH–average-star mass ratios, unrestricted by the computational constraints that affect direct N-body codes. Methods. We set up a grid of hybrid particle-in-cell-MPC N-body simulations using our implementation of the MPC method, MPCDSS. We used either single mass models or models with a Salpeter mass function (a single power law with an exponent of −2.35), with the IMBH initially sitting at the centre. The force exerted by and on the IMBH was evaluated with a direct sum scheme with or without softening. For all simulations we measured the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we also measured the evolution of the velocity anisotropy profiles. Results. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower they are, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function of the model. For the models with Salpeter MF, we observed that equipartition of kinetic energies is never achieved, even long after core collapse. Orbital anisotropy at large radii appears to be driven by energetic escapers on radial orbits, triggered by strong collisions with the IMBH in the core. We measured the wander radius, that is the distance of the IMBH from the centre of mass of the parent system over time, finding that its distribution has positive kurtosis. Conclusions. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-centre more frequently than expected, with implications on observational IMBH detection.

Addressing Dynamics at Catalytic Heterogeneous Interfaces with DFT-MD: Anomalous Temperature Distributions from Commonly Used Thermostats.

Density functional theory-based molecular dynamics (DFT-MD) has been widely used for studying the chemistry of heterogeneous interfacial systems under operational conditions. We report frequently overlooked errors in thermostated or constant-temperature DFT-MD simulations applied to study (electro)catalytic chemistry. Our results demonstrate that commonly used thermostats such as Nosé–Hoover, Berendsen, and simple velocity-rescaling methods fail to provide a reliable temperature description for systems considered. Instead, nonconstant temperatures and large temperature gradients within the different parts of the system are observed. The errors are not a “feature” of any particular code but are present in several ab initio molecular dynamics implementations. This uneven temperature distribution, due to inadequate thermostatting, is well-known in the classical MD community, where it is ascribed to the failure in kinetic energy equipartition among different degrees of freedom in heterogeneous systems (Harvey et al. J. Comput. Chem.1998, 726−740) and termed the flying ice cube effect. We provide tantamount evidence that interfacial systems are susceptible to substantial flying ice cube effects and demonstrate that the traditional Nosé–Hoover and Berendsen thermostats should be applied with care when simulating, for example, catalytic properties or structures of solvated interfaces and supported clusters. We conclude that the flying ice cube effect in these systems can be conveniently avoided using Langevin dynamics.

Collective excitations in active fluids: Microflows and breakdown in spectral equipartition of kinetic energy.

The effect of particle activity on collective excitations in active fluids of microflyers is studied. With an in silico study, we observed an oscillating breakdown of equipartition (uniform spectral distribution) of kinetic energy in reciprocal space. The phenomenon is related to short-range velocity-velocity correlations that were realized without forming of long-lived mesoscale vortices in the system. This stands in contrast to well-known mesoscale turbulence operating in active nematic systems (bacterial or artificial) and reveals the features of collective dynamics in active fluids, which should be important for structural transitions and glassy dynamics in active matter.

Small-scale Dynamo in Supernova-driven Interstellar Turbulence

Abstract Magnetic fields grow quickly even at early cosmological times, suggesting the action of a small-scale dynamo (SSD) in the interstellar medium of galaxies. Many studies have focused on idealized turbulent driving of the SSD. Here we simulate more realistic supernova-driven turbulence to determine whether it can drive an SSD. Magnetic field growth occurring in our models appears inconsistent with simple tangling of magnetic fields, but consistent with SSD action, reproducing and confirming models by Balsara et al. that did not include physical resistivity η. We vary η, as well as the numerical resolution and supernova rate, , to delineate the regime in which an SSD occurs. For a given we find convergence for SSD growth rate with resolution of a parsec. For , with the solar neighborhood rate, the critical resistivity below which an SSD occurs is , and this increases with the supernova rate. Across the modeled range of 0.5–4 pc resolution we find that for , the SSD saturates at about 5% of kinetic energy equipartition, independent of growth rate. In the range growth rate increases with . SSDs in the supernova-driven interstellar medium commonly exhibit erratic growth.

Tuning the distance to equipartition by controlling the collision rate in a driven granular gas experiment.

In a granular gas experiment of magnetized particles confined in a thin layer, the rate of dissipative collisions is tuned by adjusting the amplitude of an external magnetic field. The velocity statistics are analyzed using the dynamic and static structure factors of transverse velocity modes. Using the fluctuating hydrodynamics theory, we measure the deviation from kinetic energy equipartition in this out-of-equilibrium system as a function of the dissipative collision rate. When the collision rate is decreased, the distance to equipartition becomes smaller, meaning that the dynamical properties of this granular gas approach by analogy those of a molecular gas in thermal equilibrium.

Proper Thermal Equilibration of Simulations with Drude Polarizable Models: Temperature-Grouped Dual-Nosé-Hoover Thermostat.

An explicit treatment of electronic polarization is critically important to accurate simulations of highly charged or interfacial systems. Compared to the iterative self-consistent field (SCF) scheme, extended Lagrangian approaches are computationally more efficient for simulations that employ a polarizable force field. However, an appropriate thermostat must be chosen to minimize heat flow and ensure an equipartition of kinetic energy among all unconstrained system degrees of freedom. Here we investigate the effects of different thermostats on the simulation of condensed phase systems with the Drude polarizable force field using several examples that include water, NaCl/water, acetone, and an ionic liquid (IL) BMIM+/BF4-. We show that conventional dual-temperature thermostat schemes often suffer from violations of equipartitioning and adiabatic electronic state, leading to considerable errors in both static and dynamic properties. Heat flow from the real degrees of freedom to the Drude degrees of freedom leads to a steady temperature gradient and puts the system at an incorrect effective temperature. Systems with high-frequency internal degrees of freedom such as planar improper dihedrals or C-H bond stretches are most vulnerable; this issue has been largely overlooked in the literature because of the primary focus on simulations of rigid water molecules. We present a new temperature-grouped dual-Nosé-Hoover thermostat, where the molecular center of mass translations are assigned to a temperature group separated from the rest degrees of freedom. We demonstrate that this scheme predicts correct static and dynamic properties for all the systems tested here, regardless of the thermostat coupling strength. This new thermostat has been implemented into the GPU-accelerated OpenMM simulation package and maintains a significant speedup relative to the SCF scheme.

Refinement of thermostated molecular dynamics using backward error analysis.

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs.

Extended stellar systems in the solar neighborhood

We report the discovery of two well-defined tidal tails emerging from the Hyades star cluster. The tails were detected in Gaia DR2 data by selecting cluster members in the 3D galactocentric cylindrical velocity space. The robustness of our member selection is reinforced by the fact that the sources depict an almost noiseless, coeval stellar main sequence in the observational Hertzsprung-Russel diagram. The spatial arrangement of the selected members represents a highly flattened shape with respect to the direction of movement along the clusters’ orbit in the Galaxy. The size of the entire structure, within the limits of the observations, measures about 200 pc in its largest extent, while being only about 25 pc thick. This translates into an on-sky extent of well beyond 100 deg. Intriguingly, a top-down view on the spatial distribution reveals a distinct S-shape, reminiscent of tidal tails that have been observed for globular clusters and also of tails that were modeled for star clusters bound to the Galactic disk. Even more remarkable, the spatial arrangement as well as the velocity dispersion of our source selection is in excellent agreement with previously published theoretical predictions for the tidal tails of the Hyades. An investigation into observed signatures of equipartition of kinetic energy, that is, mass segregation, remains unsuccessful, most likely because of the sensitivity limit for radial velocity measurements with Gaia.

Nuclear kinetic energies from final-state effects in the harmonic limit

This work shows a simple, yet quite powerful, data pre-treatment protocol for mass-resolved neutron spectroscopy, aimed at a better estimation of the main quantum observable linked to a nuclear-momentum distribution, its second moment. From a methodological point of view, the immediate benefit of having such a protocol is twofold. Firstly, a good estimate of a second moment of a nuclear-momentum distribution, and hence nuclear kinetic energy, provided as input for subsequent data fitting, accelerates the convergence of a data fit and minimises the likelihood of it being stuck in a non-physical solution. Secondly, it provides a simple screening tool in the search for quantum systems exhibiting statistically significant departures for a classical behaviour of equipartition of kinetic energy at any given temperature. This second benefit renders the presented protocol an important data screening tool in the search of materials exhibiting exotic properties, possibly attributed to nuclear quantum effects.

Rapid mass segregation in small stellar clusters

In this paper we focus our attention on small-to-intermediate N-body systems that are, initially, distributed uniformly in space and dynamically cool (virial ratios $Q=2T/|\Omega|$ below ~0.3). In this work, we study the mass segregation that emerges after the initial violent dynamical evolution. At this scope, we ran a set of high precision N-body simulations of isolated clusters by means of HiGPUs, our direct summation N-body code. After the collapse, the system shows a clear mass segregation. This (quick) mass segregation occurs in two phases: the first shows up in clumps originated by sub-fragmentation before the deep overall collapse; this segregation is partly erased during the deep collapse to re-emerge, abruptly, during the second phase, that follows the first bounce of the system. In this second stage, the proper clock to measure the rate of segregation is the dynamical time after virialization, which (for cold and cool systems) may be significantly different from the crossing time evaluated from initial conditions. This result is obtained for isolated clusters composed of stars of two different masses (in the ratio $m_h/m_l=2$), at varying their number ratio, and is confirmed also in presence of a massive central object (simulating a black hole of stellar size). Actually, in stellar systems starting their dynamical evolution from cool conditions, the fast mass segregation adds to the following, slow, secular segregation which is collisionally induced. The violent mass segregation is an effect persistent over the whole range of N ($128 \leq N \leq 1024$) investigated, and is an interesting feature on the astronomical-observational side, too. The semi-steady state reached after virialization corresponds to a mass segregated distribution function rather than that of equipartition of kinetic energy per unit mass as it should result from violent relaxation.

Molecular dynamics with rigid bodies: Alternative formulation and assessment of its limitations when employed to simulate liquid water.

Sets of atoms collectively behaving as rigid bodies are often used in molecular dynamics to model entire molecules or parts thereof. This is a coarse-graining strategy that eliminates degrees of freedom and supposedly admits larger time steps without abandoning the atomistic character of a model. In this paper, we rely on a particular factorization of the rotation matrix to simplify the mechanical formulation of systems containing rigid bodies. We then propose a new derivation for the exact solution of torque-free rotations, which are employed as part of a symplectic numerical integration scheme for rigid-body dynamics. We also review methods for calculating pressure in systems of rigid bodies with pairwise-additive potentials and periodic boundary conditions. Finally, simulations of liquid phases, with special focus on water, are employed to analyze the numerical aspects of the proposed methodology. Our results show that energy drift is avoided for time step sizes up to 5 fs, but only if a proper smoothing is applied to the interatomic potentials. Despite this, the effects of discretization errors are relevant, even for smaller time steps. These errors induce, for instance, a systematic failure of the expected equipartition of kinetic energy between translational and rotational degrees of freedom.

Brownian colloids in underdamped and overdamped regimes with nonhomogeneous temperature.

The motion of Brownian particles when temperature is spatially dependent is studied by stochastic simulations and theoretical analysis. Nonequilibrium steady probability distributions P(st)(z,v) for both underdamped and overdamped regimes are analyzed. The existence of local kinetic energy equipartition theorem is also discussed. The transition between both regimes is characterized by a dimensionless friction parameter. This study is applied to three physical systems of colloidal particles.

Anomalous transport of impurities in inelastic Maxwell gases.

A mixture of dissipative hard grains generically exhibits a breakdown of kinetic energy equipartition. The undriven and thus freely cooling binary problem, in the tracer limit where the density of one species becomes minute, may exhibit an extreme form of this breakdown, with the minority species carrying a finite fraction of the total kinetic energy of the system. We investigate the fingerprint of this non-equilibrium phase transition, akin to an ordering process, on transport properties. The analysis, performed by solving the Boltzmann kinetic equation from a combination of analytical and Monte Carlo techniques, hints at the possible failure of hydrodynamics in the ordered region. As a relevant byproduct of the study, the behaviour of the second- and fourth-degree velocity moments is also worked out.

Car license plate recognition based on EKE-poisson transform

In this paper, a car license plate recognition (CLPR) system is presented. A CLPR system has three main subsystems such as; localization of the license plate in a given image; character segmentation of the license plate; recognition of the detected characters. Firstly, fuzzy c-means clustering is employed to determine the location of the license plate. Secondly, smearing algorithms (namely horizontal and vertical projections of the pixels of the license plate image) is used to carry out character segmentation. Finally, a novel Equipartition of Kinetic Energy (EKE)-Poisson transform is developed to recognize the characters. According to results, the proposed CLPR system is capable of supplying more than 92% of overall success rate.

High shear granulation of dolomite – II: Effect of amount of binder liquid on process kinetics

This paper, the second of a series, analyzes the effect of binder amount on the kinetics of wet granulation process. Granulation experiments were conducted in batch, lab-scale high shear mixer with formulation system that was initially studied in first part of a series. First, we identify the effect of binder content on the net granulation behaviour during early stage of the process. Single entity property (its size) was accounted only within this research. The results indicate that binder content strongly promotes growth of dolomite entities. Secondly, 1-D discretized population balance equation (PBE) and Equi-Partition of Kinetic Energy (EKE) theory were used to simulate the net granulation process. Tested “coalescence-only” models provide good prediction of real dolomite granule size distributions (GSDs) during early stage of the process for each binder content value. By using modelling procedure granule growth rates were quantified. Ultimate goal of relating the coalescence rates of dolomite entities with binder amount variable is provided. This will result in a better perspective of the meso-scale of the dolomite granulation process.

Granular gases of rod-shaped grains in microgravity.

Granular gases are convenient model systems to investigate the statistical physics of nonequilibrium systems. In the literature, one finds numerous theoretical predictions, but only few experiments. We study a weakly excited dilute gas of rods, confined in a cuboid container in microgravity during a suborbital rocket flight. With respect to a gas of spherical grains at comparable filling fraction, the mean free path is considerably reduced. This guarantees a dominance of grain-grain collisions over grain-wall collisions. No clustering was observed, unlike in similar experiments with spherical grains. Rod positions and orientations were determined and tracked. Translational and rotational velocity distributions are non-Gaussian. Equipartition of kinetic energy between translations and rotations is violated.

High shear granulation of dolomite – I: Effect of shear regime on process kinetics

Wet granulation of previously unreported formulation system is presented. Dolomite powder is granulated under different shear regimes by using three-component binder formulation, water-molasses-polyvinylpyrrolidone. 1-D discretized population balance equation (PBE) and Equi-Partition of Kinetic Energy (EKE) coalescence kernel are applied to modelling granulation in a high shear mixer. Process modelling is focused to simulation of changes of the property of a group of entities, granule size distribution (GSD). The GSD predictions indicate the presence of coalescence growth as a dominant mechanism in the dolomite granulation process. Minor deviations between simulated and real GSDs signify the probability of other granulation mechanism(s) existence. A posteriori approach by integral method was used for coalescence rate constant estimation. This research highlights discrepancy in the coalescence rate of dolomite granulation process, between its early and later stages. Moreover, kinetic analysis of the high shear granulation process provides quantification of the macroscopic variable (impeller speed) influence on regarded property of a group of granules in terms of values of growth rate parameter.

Kolmogorov cascade and equipartition of kinetic energy in numerical simulation of Superfluid turbulence

The turbulence of a superfluid is investigated by direct numerical simulations at finite temperature and high Reynolds numbers using the continuous model. The superfluid component is described by the Euler equation while the normal fluid component is described by the Navier-Stokes equation, both being coupled by mutual friction. In the high temperature limit, the Kolmogorov cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the Kolmogorov cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes.