Collective Particle Dynamics Research Articles

Polytropic representation of the kinetic pressure tensor of non-ideal magnetized fluids in equilibrium toroidal structures

Non-ideal fluids are generally subject to the occurrence of non-isotropic pressure tensors, whose determination is fundamental in order to characterize their dynamical and thermodynamical properties. This requires the implementation of theoretical frameworks provided by appropriate microscopic and statistical kinetic approaches in terms of which continuum fluid fields are obtained. In this paper, the case of non-relativistic magnetized fluids forming equilibrium toroidal structures in external gravitational fields is considered. Analytical solutions for the kinetic distribution function are explicitly constructed, to be represented by a Chapman–Enskog expansion around a Maxwellian equilibrium. In this way, different physical mechanisms responsible for the generation of non-isotropic pressures are identified and proved to be associated with the kinetic constraints imposed on single and collective particle dynamics by phase-space symmetries and magnetic field. As a major outcome, the validity of a polytropic representation for the kinetic pressure tensors corresponding to each source of anisotropy is established, whereby directional pressures exhibit a specific power-law functional dependence on fluid density. The astrophysical relevance of the solution for the understanding of fluid plasma properties in accretion-disk environments is discussed.

Is there a one-to-one correspondence between interparticle interactions and physical properties of liquid?

In this study, we present the original method for reconstructing the potential of interparticle interaction from statistically averaged structural data, namely, the radial distribution function of particles in many-particle system. This method belongs to a family of machine learning methods and is implemented through the differential evolution algorithm. As demonstrated for the case of the Lennard-Jones liquid taken as an example, there is no one-to-one correspondence between structure and potential of interparticle interaction of a many-particle disordered system at a certain thermodynamic state. Namely, a whole family of the Mie potentials determined by two parameters p1 and p2 related to each other according to a certain rule can reproduce properly a unique structure of the Lennard-Jones liquid at a given thermodynamic state. It is noteworthy that this family of the potentials quite correctly reproduces for the Lennard-Jones liquid the transport properties (in particular, the self-diffusion coefficient) over a temperature range as well as the dynamic structure factor, which is one of the key characteristics of the collective dynamics of particles.

Particle momentum variation under interaction with wavepackets of finite spatial width

The single and collective particle interaction with spatially localized wavepackets is analytically and numerically studied. The role of the finite spatial width of the wavepacket on the momentum and energy variation of particles passing through the wavepacket is investigated. The range of validity of analytical results, based on a perturbative approach, is investigated and clearly defined. Strongly nonlinear effects are shown to qualitatively differentiate the collective particle dynamics, for larger interaction strengths. These effects are manifested through the complex dependency of averaged momentum variations on the initial particle momentum, as shown by dissecting a particle distribution in terms of partitioning the ensemble of particles with respect to their initial momentum. The results provide understanding on the relation between single and collective particle dynamics and the emerging of complexity for weak and strong particle interactions with localized wavepackets.

Effect of viscosity on surface acoustic wave driven collective particle dynamics in sessile droplets: Cloud, cavities, and aggregates

Surface acoustic waves (SAWs) can concentrate micro-particles in droplets within seconds. Yet, the mechanism is not clear and existing explanations fail by several orders of magnitude. In this paper, we analyze the effect of fluid viscosity and particle size on SAW-driven collective particle dynamics in droplets. In most of our experiments, the particles do not aggregate but instead remain away from the droplet center, thereby forming “cavities.” We show that the cavities are due to steric hindrance wherein the poloidal streamlines that should drive particles to the center of the droplet come too close to the solid, so that the particles carried along these streamlines touch the solid wall on the edge of the cavity before reaching the center of the droplet. The size of these cavities is correlated with the size of the aggregates formed in less viscous droplets. This suggests a common formation mechanism for cavities and aggregates. In the former, the particles touching the solid would be washed away by the fluid, whereas in the latter, the particles would remain in contact with the solid and roll to the center of the droplet where an aggregate is formed. We also discuss the stability conditions of the aggregate at the bottom of the droplet. The concept of hydrodynamic shielding is then used to concentrate 1 μm particles using 10 μm beads as shields.

Local density dynamics in a supercritical Lennard-Jones fluid

The collective particle dynamics of supercritical Lennard-Jones fluid is investigated on the basis of molecular dynamic modeling data. The intermediate scattering functions and dynamic structure factor spectra for the wavenumber range k ∈ [0.18; 3.26] σ−1 were calculated. The characteristics of dynamic structure factor spectra such as the thermal diffusivity and the sound velocity were estimated.

Self-consistent relaxation theory of collective ion dynamics in Yukawa one-component plasmas under intermediate screening regimes.

The self-consistent relaxation theory is employed to describe the collective ion dynamics in strongly coupled Yukawa classical one-component plasmas. The theory is applied to equilibrium states corresponding to intermediate screening regimes with appropriate values of the structure and coupling parameters. The information about the structure (the radial distribution function and the static structure factor) and the thermodynamics of the system are sufficient to describe collective dynamics over a wide range of spatial scales, namely, from the extended hydrodynamic to the microscopic dynamics scale. The main experimentally measurable characteristics of the equilibrium collective dynamics of ions-the spectrum of the dynamic structure factor, the dispersion parameters, the speed of sound, and the sound attenuation-are determined within the framework of the theory without using any adjustable parameters. The results demonstrate agreement with molecular dynamics simulations. Thus a direct realization is presented of the key idea of statistical mechanics: for the theoretical description of the collective particle dynamics in equilibrium fluids it is sufficient to know the interparticle interaction potential and the structural characteristics. Comparison with alternative or complementary theoretical approaches is provided.

Collective particle dynamics of molten NaCl by inelastic x-ray scattering

An inelastic x-ray scattering experiment has been performed on molten NaCl over wide wave vector and energy transfer ranges. Data of high statistical quality are analyzed using a memory function approach within a generalized Langevin equation. The approach with two relaxation times for the memory function provides a very good data description over the whole wave vector range beyond the hydrodynamic regime. A slow thermal and a fast structural relaxation process in the memory function completely define the density fluctuations in molten NaCl and evidences the thermal-viscoelastic model as the minimal description for collective particle dynamics in molten alkali halides. The obtained excitation frequencies demonstrate a large positive dispersion effect, which can be related to the viscoelastic reaction of the molten salt. A transition from the viscoelastic to a hydrodynamic response of the molten salt at small wave vectors is observed. In the hydrodynamic regime the resulting thermal diffusivity agrees well with values obtained through light scattering. The modeling indicates some deficiencies at small wave vectors and large energy transfers and the spectra of the current correlation function evidences additional intensity at high frequency. The frequency of these additional modes approach a non-zero value at zero wave vector and indicates a non-acoustic character of these excitations. The frequency center of this additional inelastic intensity coincides with optic-type modes in molten NaCl predicted by simulations.

Relativistic plasma physics in supercritical fields

Since the invention of chirped pulse amplification, which was recognized by a Nobel Prize in physics in 2018, there has been a continuing increase in available laser intensity. Combined with advances in our understanding of the kinetics of relativistic plasma, studies of laser–plasma interactions are entering a new regime where the physics of relativistic plasmas is strongly affected by strong-field quantum electrodynamics (QED) processes, including hard photon emission and electron–positron (e−–e+) pair production. This coupling of quantum emission processes and relativistic collective particle dynamics can result in dramatically new plasma physics phenomena, such as the generation of dense e−–e+ pair plasma from near vacuum, complete laser energy absorption by QED processes, or the stopping of an ultra-relativistic electron beam, which could penetrate a cm of lead, by a hair's breadth of laser light. In addition to being of fundamental interest, it is crucial to study this new regime to understand the next generation of ultra-high intensity laser-matter experiments and their resulting applications, such as high energy ion, electron, positron, and photon sources for fundamental physics studies, medical radiotherapy, and next generation radiography for homeland security and industry.

Universal aspects of collective behavior in chemotactic systems.

We investigate the collective dynamics of particles (e.g., microorganisms) interacting via chemotactic gradients. Specifically, we focus on continuum models for chemotaxis that include a damping of the chemical production with increasing local particle density and/or systems where the chemotactic sensitivity is reduced with increasing local concentration of the chemical. Using a recently introduced perturbative method [Phys. Rev. E 98, 020603 (2018)10.1103/PhysRevE.98.020603], we show that the onset of particle clustering in these systems is described by the universal Cahn-Hilliard (CH) model. On the one hand, this establishes particle-conserving models for chemotaxis as a further example for the universal class of nonequilibrium demixing phenomena we call active phase separation. On the other hand, the reduction to the CH model allows an analytical determination of suitable parameter ranges wherein, e.g., the transition to spatial density modulations is continuous and/or undesired blow-up solutions can be avoided. A comparison between the numerical solutions of the chemotaxis model and the derived CH model also provides the parameter range where the basic chemotaxis model behaves like other systems showing active phase separation, including the coarsening behavior in two spatial dimensions. Our approach highlights how basic principles of pattern formation theory allow the identification of common basic properties in different chemotaxis models.

Hydrodynamic synchronization and collective dynamics of colloidal particles driven along a circular path.

We study theoretically the collective dynamics of particles driven by an optical vortex along a circular path. Phase equations of N particles are derived by taking into account both hydrodynamic and repulsive interactions between them. For N=2, the particles attract with each other and synchronize, forming a doublet that moves faster than a singlet. For N=3 and 5, we find periodic rearrangement of doublets and a singlet. For N=4 and 6, the system exhibits either a periodic oscillating state or a stable synchronized state depending on the initial conditions. These results reproduce main features of previous experimental findings. We quantitatively discuss the mechanisms governing the nontrivial collective dynamics.

Coincidence of the freezing and the onset of caging in hard sphere and Lennard-Jones fluids.

In this article, we examine the collective particle dynamics, as expressed by the time correlation function of the longitudinal particle current density, of several different fluids in the vicinity of their freezing points/lines. We consider and compare results obtained by dynamic light scattering for a suspension of hard spheres and by molecular dynamics for fluids with hard sphere and Lennard-Jones interactions. The latter are performed along both an isotherm and an isochore. In all cases, we find a qualitative change in the collective dynamics, within the resolution of the data, when their respective freezing lines are crossed. We associate this change with the onset of caging. The new results for the Lennard-Jones fluid reported here confirm that the occurrence of caging, found previously for systems of hard spheres, is a more general feature that distinguishes a metastable fluid from one in thermodynamic equilibrium.

Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids.

A fluid particle changes its dynamics from diffusive to oscillatory as the system density increases up to the melting density. Hence the notion of the Frenkel line was introduced to demarcate the fluid region into rigid and nonrigid liquid subregions based on the collective particle dynamics. In this work, we apply a topological framework to locate the Frenkel lines of the soft-sphere and the hard-sphere models relying on the system configurations. The topological characteristics of the ideal gas and the maximally random jammed state are first analyzed, then the classification scheme designed in our earlier work is applied to soft-sphere and hard-sphere fluids. The dependence of the classification result on the bulk density is understood based on the theory of fluid polyamorphism. The percolation behavior of solid-like clusters is described based on the fraction of solid-like molecules in an integrated manner. The crossover densities are obtained by examining the percolation of solid-like clusters. The resultant crossover densities of soft-sphere fluids converge to that of hard-sphere fluid. Hence the topological method successfully highlights the generality of the Frenkel line.

"Two-Phase" Thermodynamics of the Frenkel Line.

The Frenkel line, a crossover line between rigid and nonrigid dynamics of fluid particles, has recently been the subject of intense debate regarding its relevance as a partitioning line of the supercritical phase, where the main criticism comes from the theoretical treatment of collective particle dynamics. From an independent point of view, this Letter suggests that the two-phase thermodynamics model may alleviate this contentious situation. The model offers new criteria for defining the Frenkel line in the supercritical region and builds a robust connection among the preexisting, seemingly inconsistent definitions. In addition, one of the dynamic criteria locates the rigid-nonrigid transition of the soft-sphere and the hard-sphere models. Hence, we suggest the Frenkel line be considered as a dynamic rigid-nonrigid fluid boundary, without any relation to gas-liquid transition. These findings provide an integrative viewpoint combining fragmentized definitions of the Frenkel line, allowing future studies to be carried out in a more reliable manner.

A physical approach to model occlusions in the retinal microvasculature.

Blood occlusions in the retinal microvasculature contribute to the pathology of many disease states within the eye. These events can cause haemorrhaging and retinal detachment, leading to a loss of vision in the affected patient. Here, we present a physical approach to characterising the collective cell dynamics leading to plug formation, through the use of a bespoke microfluidic device, and through the derivation of a probabilistic model. Our microfluidic device is based on a filtration design that can tune the particle volume fraction of a flowing suspension within a conduit, with sizes similar to arterioles. This allows us to control and reproduce an occlusive event. The formation of the occlusion can be examined through the extracted motion of particles within the channel, which enables the assessment of individual and collective particle dynamics in the time leading to the clogging event. In particular, we observe that at the onset of the occlusion, particles form an arch bridging the channel walls. The data presented here inform the development of our mathematical model, which captures the essential factors promoting occlusions, and notably highlights the central role of adhesion in these processes. Both the physical and probabilistic models rely on significant approximations, and future investigation will seek to assess these approximations, including the deformability and complex flow profiles of the blood constituents. However, we anticipate that the general mechanisms of occlusion may be elucidated from these simple models. As microvascular flows in the eye can now be measured in vivo and non-invasively with single cell resolution, our model will also be compared to the pathophysiological characteristics of the human microcirculation.

Forced mode coupling in 2D complex plasmas

It is demonstrated experimentally that the plasma-wake–mediated resonant coupling of the longitudinal in-plane and out-of-plane collective motion in two-dimensional plasma crystals can be induced by applying an external forcing. The experimental observations are supported by numerical analysis of the forced collective dynamics of particles with the wake-mediated interactions.

Freestyle 3D laser traps: tools for studying light-driven particle dynamics and beyond

We show that a freestyle laser trap, including high-intensity and phase gradient forces along arbitrary curves, is able to confine multiple particles and drive their motion with the ability to speed them up or slow them down. This Letter reports, for first time, to the best of our knowledge, how such a trap can be experimentally created deep within the sample to construct rotating colloidal motors and study collective particle dynamics in distinct configurations. This new laser tool opens up promising perspectives in the study of hydrodynamics and optofluidics at the microscale.

Studies of Particulate System Dynamics in Rotating Drums using Markov Chains

This work aims to develop an approach to study and capture the collective dynamics of particulate systems, which are important for operation of those processes. The collective dynamics of particles in a horizontal rotating drum are modeled based on a stochastic approach, using the Markov chains operators developed from DEM simulations. Quantitative analysis of the features of collective dynamics, namely dynamic modes of oscillatory behavior and spatial particle distribution of particle movement, are performed based on eigenvalues and singular values analysis of Markov chains operator, respectively. Furthermore, the quantitative measures are shown that it can be linked to the qualitative flow regimes of particulate systems in a horizontal rotating drum.

Single and collective particle dynamics in liquid Rb80(RbBr)20

The temperature (T) dependence of the single and the collective particle dynamics of a melt containing 80 at% Rb and 20 at% RbBr was investigated using neutron inelastic scattering. Compared to pure liquid Rb, the dispersions obtained from the maxima of the longitudinal current correlation function clearly reflect the change of the atomic interaction from a metallic to a dominantly ionic regime. The T dependence of the atomic dynamics in Rb80(RbBr)20 is characterized by a broadening of the spectra resulting in a shift to higher energies in the dispersion and in the spectrum of the velocity auto-correlation function, which was determined here for a mixture of a liquid metal with a molten salt for the first time.

Proton and deuteron distributions as signatures for collective particle dynamics and event shape geometries at ultrarelativistic energies

We present predictions for the formation of (anti)nuclear bound states in nucleus-nucleus reactions at ultrarelativistic energies. The phase-space coalescence method is used in combination with RQMD v2.4 transport calculations to demonstrate the relevance of particle production, as well as the longitudinal and transverse flow components. The formation of deuterons follows an approximate scaling law proportional to the relative freeze-out densities of nucleons and produced secondaries. For antideuterons, an additional suppression appears that is proportional to the number of nucleons, pointing toward multiple rescattering and absorption prior to freeze out.

Calculation of transport properties from molecular dynamics simulation

Using the self-diffusion as an example, we present a novel molecular dynamics method which fixes a transport property of the system to a prescribed value. We discuss the technical realization of the algorithm for this history dependent property. Owing to the monotonic temperature vs self-diffusion relationship for a given model substance at fixed density the system automatically chooses that temperature which corresponds to the input value of the self-diffusion coefficient. In principle, this approach can be applied to other transport coefficients too. In practice, however, the numerical calculation of transport properties expressed by the collective dynamics of particles is very time consuming from equilibrium molecular dynamics simulation. Our method being an equivalent of the Green–Kubo integral also performs poorly compared to nonequilibrium molecular dynamics techniques. We present details and results of model calculations for these two transport processes.