Single-particle Dynamics Research Articles

Theory of spatially non-symmetric kinetic equilibria for collisionless plasmas

The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas, this involves the construction of stationary solutions of the Vlasov-Maxwell equations. In this paper, the issue is addressed for non-relativistic plasmas both in astrophysical and laboratory contexts. The treatment is based on a Lagrangian variational description of single-particle dynamics. Starting point is a non-perturbative formulation of gyrokinetic theory, which allows one to construct “a posteriori” with prescribed order of accuracy an asymptotic representation for the magnetic moment. In terms of the relevant particle adiabatic invariants generalized bi-Maxwellian equilibria are proved to exist. These are shown to recover, under suitable assumptions, a Chapman-Enskog form which permits an analytical treatment of the corresponding fluid moments. In particular, the constrained posed by the Poisson and the Ampere equations are analyzed, both for quasi-neutral and non-neutral plasmas. The conditions of existence of the corresponding non-symmetric kinetic equilibria are investigated. As a notable feature, both astrophysical and laboratory plasmas are shown to exhibit, under suitable conditions, a kinetic dynamo, whereby the equilibrium magnetic field can be self-generated by the equilibrium plasma currents.

Secondary Organic Aerosol Coating Formation and Evaporation: Chamber Studies Using Black Carbon Seed Aerosol and the Single-Particle Soot Photometer

We report a protocol for using black carbon (BC) aerosol as the seed for secondary organic aerosol (SOA) formation in an environmental chamber. We employ a single-particle soot photometer (SP2) to probe single-particle SOA coating growth dynamics and find that SOA growth on nonspherical BC aerosol is diffusion-limited. Aerosol composition measurements with an Aerodyne high resolution time-of-flight aerosol mass spectrometer (AMS) confirm that the presence of BC seed does not alter the composition of SOA as compared to self-nucleated SOA or condensed SOA on ammonium sulfate seed. We employ a 3-wavelength photoacoustic soot spectrometer (PASS-3) to measure optical properties of the systems studied, including fullerene soot as the surrogate BC seed, nucleated naphthalene SOA from high-NO_x photooxidation, and nucleated α-pinene SOA from low-NO_x photooxidation. A core-and-shell Mie scattering model of the light absorption enhancement is in good agreement with measured enhancements for both the low- and high-NO_x α-pinene photooxidation systems, reinforcing the assumption of a core-shell morphology for coated BC particles. A discrepancy between measured and modeled absorption enhancement factors in the naphthalene photooxidation system is attributed to the wavelength-dependence of refractive index of the naphthalene SOA. The coating of high-NO_x α-pinene SOA decreases after reaching a peak thickness during irradiation, reflecting a volatility change in the aerosol, as confirmed by the relative magnitudes of f_(43) and f_(44) in the AMS spectra. The protocol described here provides a framework by which future studies of SOA optical properties and single-particle growth dynamics may be explored in environmental chambers.

The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains

A nano-scale metallic grain in which the single-particle dynamics are chaotic is described by the so-called universal Hamiltonian. This Hamiltonian includes a superconducting pairing term and a ferromagnetic exchange term that compete with each other: pairing correlations favor minimal ground-state spin, while the exchange interaction favors maximal spin polarization. Of particular interest is the fluctuation-dominated regime where the bulk pairing gap is comparable with or smaller than the single-particle mean level spacing and the Bardeen–Cooper–Schrieffer theory of superconductivity breaks down. Superconductivity and ferromagnetism can coexist in this regime. We identify signatures of the competition between superconductivity and ferromagnetism in a number of quantities: ground-state spin, conductance fluctuations when the grain is weakly coupled to external leads and the thermodynamic properties of the grain, such as heat capacity and spin susceptibility.

Dielectric response of nanoscopic spherical colloids in alternating electric fields: a dissipative particle dynamics simulation

We study the response of single nanosized spherical colloids in electrolyte solution to an alternating electric field (AC field) by computer simulations. We use a coarse-grained mesoscopic simulation approach that accounts in full for hydrodynamic and electrostatic interactions as well as for thermal fluctuations. The solvent is modeled as a fluid of single dissipative particle dynamics (DPD) beads, and the colloidal particle is modeled as a rigid body made of DPD beads. We compute the mobility and the polarizability of a single colloid and investigate systematically the effect of amplitude and frequency of the AC fields. Even though the thickness of the Debye layer is not ‘thin’ compared to the radius of the colloid, and the thermal fluctuations are significant, the results are in good agreement with the theoretical prediction of the Maxwell–Wagner–O’Konski theory, especially for uncharged colloids.

Driven wave generated electric field in the solar corona

We investigate the evolution of waves driven by the linearly polarized Alfvén wave in the magnetic field‐aligned cross‐field shear flow. The generated electric field is derived in ideal MHD using analytical solutions for the driven waves. A single particle dynamics in the generated electromagnetic field is considered and governing equations for the particle's total kinetic energy and particle parallel velocity are obtained. Our goal is to show how the driven wave inclusion modifies the evolution of these quantities. It is shown that the total kinetic energy of the particle as well as the particle's parallel velocity is not conserved in the driven wave fields and there is a force exerted on particles. A specific example is considered using solar coronal hole plasma parameters. The process presented in this work might also be important in the laboratory, terrestrial and astrophysical plasma processes where the inhomogeneous flows are present.

Computational studies of ionic liquids: Size does matter and time too

Taking the molecular ionic liquid 1-ethyl-3-methylimidazolium triflate as a reference system, the size and time dependence of molecular dynamics simulation studies is analyzed in a systematic way. Based on an all atom force field, trajectories of 70 ns length, covering samples of 8-2000 ion pairs, were generated and analyzed in terms of structure as well as single particle and collective dynamics. Although 50 ion pairs seemed sufficient for structure, at least 500 ion pairs were needed for the correct handling of dynamics. For larger systems a linear regime is found, i.e., the respective dynamical properties are a linear function of the inverse box length. In case of translational diffusion coefficients, this linear relation can be rationalised in hydrodynamic terms. The respective formula is essentially determined by viscosity and the inverse box length. Concerning the time dependence, consistent dynamical properties required a time period of 20-30 ns. Nevertheless, size dependence dominates time dependence and has to be primarily addressed.

Pressure dependence on the single-particle dynamics and hydrogen-bond structural relaxation of water–DMSO mixtures under ambient and cold conditions

The effects of pressure on the single-particle translational and rotational dynamics and the hydrogen-bond structural relaxation of water–dimethyl sulfoxide (DMSO) mixtures were investigated under ambient and cold conditions using classical molecular dynamics simulations. We considered five different concentrations of DMSO with mole fractions X DMSO = 0.012, 0.09, 0.20, 0.35, and 0.50 and seven different pressures ranging from 0.1 to 500 MPa. It was found that the addition of DMSO to water leads to slow dynamics for both water and DMSO molecules under pressure. At very low concentrations of DMSO, water exhibits anomalous behavior with the application of pressure at 258 K, whereas DMSO molecules exhibit average pressure dependencies. The formation of strong hydrogen bonds between water and DMSO molecules occurs when DMSO is added to water, but the extended network is altered due to the absence of any hydrogen-bond donating ability of DMSO. Our calculated water–water and DMSO–water hydrogen-bond structural relaxation times show an initial decrease with the application of pressure at 258 K for solutions with low DMSO concentrations. However, at higher concentrations of DMSO, the relaxation times increase, on average, and no anomalous behavior of the dynamical properties is found on the application of pressure.

Compressed exponential relaxation in liquid silicon: Universal feature of the crossover from ballistic to diffusive behavior in single-particle dynamics

We report a first-principles molecular-dynamics study of the relaxation dynamics in liquid silicon (l-Si) over a wide temperature range (1000-2200 K). We find that the intermediate scattering function for l-Si exhibits a compressed exponential decay above 1200 K including the supercooled regime, which is in stark contrast to that for normal "dense" liquids which typically show stretched exponential decay in the supercooled regime. The coexistence of particles having ballistic-like motion and those having diffusive-like motion is demonstrated, which accounts for the compressed exponential decay in l-Si. An attempt to elucidate the crossover from the ballistic to the diffusive regime in the "time-dependent" diffusion coefficient is made and the temperature-independent universal feature of the crossover is disclosed.

Hydrated Ionic Liquids with and without Solute: The Influence of Water Content and Protein Solutes.

In this computational study, the network of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate/water mixtures is analyzed in the presence (and absence) of the protein ubiquitin and a zinc finger motif. Thereby, common radial distribution functions are decomposed into contributions from different Voronoi shells, and the mutual orientation of cations, anions, and water in the bulk phase as a function of the water mole fraction is discussed. Single particle translation and the reorientation of the dipolar axis seem to follow hydrodynamic relations. Using the body-fixed frame as an alternative reference system, translation and rotation can be decomposed into contributions along and about the axes of a well-defined orthogonal trihedron, thus elucidating the principal motions of the cations and anions as a function of the water mole fraction. The structural dipolar orientation may be correlated with single particle dynamics and can be characterized by the static collective Kirkwood order parameter.

Relaxation mechanisms in glassy dynamics: The Arrhenius and fragile regimes

Generic glass formers exhibit at least two characteristic changes in their relaxation behavior, first to an Arrhenius-type relaxation at some characteristic temperature and then at a lower characteristic temperature to a super-Arrhenius (fragile) behavior. We address these transitions by studying the statistics of free energy barriers for different systems at different temperatures and space dimensions. We present a clear evidence for changes in the dynamical behavior at the transition to Arrhenius and then to a super-Arrhenius behavior. A simple model is presented, based on the idea of competition between single-particle and cooperative dynamics. We argue that Arrhenius behavior can take place as long as there is enough free volume for the completion of a simple T1 relaxation process. Once free volume is absent one needs a cooperative mechanism to "collect" enough free volume. We show that this model captures all the qualitative behavior observed in simulations throughout the considered temperature range.

Variational cluster approach to the single-impurity Anderson model

We study the single impurity Anderson model by means of cluster perturbation theory and the variational cluster approach (VCA). An expression for the VCA grand potential for a system in a non interacting bath is presented. Results for the single-particle dynamics in different parameter regimes are shown to be in good agreement with established renormalization group results. We aim at a broad and comprehensive overview of the capabilities and shortcomings of the methods. We address the question to what extent the elusive low energy properties of the model are reproducible within the framework of VCA. These are furthermore benchmarked against continuous time quantum Monte Carlo calculations. We also discuss results obtained by an alternative, i.e. self consistent formulation of VCA, which was introduced recently in the context of non equilibrium systems.

Origin of de-swelling and dynamics of dense ionic microgel suspensions

A direct consequence of the finite compressibility of a swollen microgel is that it can shrink and deform in response to an external perturbation. As a result, concentrated suspensions of these particles exhibit relaxation dynamics and rheological properties which can be very different with respect to those of a hard sphere suspension or an emulsion. We study the reduction in size of ionic microgels in response to increasing number of particles to show that particle shrinkage originates primarily from steric compression, and that the effect of ion-induced de-swelling of the polymer network is negligible. With increasing particle concentration, the single particle dynamics switch from those typical of a liquid to those of a super-cooled liquid and finally to those of a glass. However, the transitions occur at volume fractions much higher than those characterizing a hard sphere system. In the super-cooled state, the distribution of displacements is non-gaussian and the dependence of the structural relaxation time on volume fraction is describable by a Volger-Fulcher-Tammann function.

Coherent dynamics of meta-toluidine investigated by quasielastic neutron scattering

The coherent dynamics of a typical fragile glass former, meta-toluidine, was investigated at the molecular level using quasielastic neutron scattering, with time-of-flight and neutron spin echo spectrometers. It is well known that the static structure factor of meta-toluidine shows a prepeak originating from clustering of the molecules through hydrogen bonding between the amine groups. The dynamics of meta-toluidine was measured for several values of the wavevector transfer Q, which is equivalent to an inverse length scale, in a range encompassing the prepeak and the structure factor peak. Data were collected in the temperature range corresponding to the liquid and supercooled states, down to the glass transition. At least two dynamical processes were identified. This paper focuses on the slowest relaxation process in the system, the α-relaxation, which was found to scale with the macroscopic shear viscosity at all the investigated Q values. No evidence of "de Gennes" narrowing associated with the prepeak was observed, in contrast with what happens at the Q value corresponding to the interparticle distance. Moreover, using partially deuterated samples, the dynamics of the clusters was found to be correlated to the single-particle dynamics of the meta-toluidine molecules.

Water dynamics in a lithium chloride aqueous solution probed by Brillouin neutron andx-ray scattering

We studied the collective excitations in an aqueous solution of lithium chlorideover the temperature range of 270–205 K using neutron and x-ray Brillouinscattering. Both neutron and x-ray experiments revealed the presence of low- andhigh-frequency excitations, similar to the low- and high-frequency excitations in purewater. These two excitations were detectable through the entire temperature rangeof the experiment, at all probed values of the scattering momentum transfer (0.2 Å − 1 < Q < 1.8 Å − 1). A wider temperature range was investigated using elastic intensity neutron and x-rayscans. Clear evidence of the crossover in the dynamics of the water molecules inthe solution was observed in the single-particle relaxational dynamics on theµeV (nanosecond) time scale, but not in the collective dynamics on the meV (picosecond) timescale.

Water dynamics as affected by interaction with biomolecules and change of thermodynamicstate: a neutron scattering study

The dynamics of water as subtly perturbed by both the interaction with biomolecules andthe variation of temperature and pressure has been investigated via neutron scatteringspectroscopy. A measurement of inelastic neutron scattering devoted to the study of the coherentTHz dynamics of water in a water-rich mixture with DNA (hydration level of 1 g DNA/15 gD2O) at room temperature is reported. The DNA hydration water coherent dynamics ischaracterised by the presence of collective modes, whose dispersion relations are similar tothose observed in bulk water. These dispersion relations are well described by theinteraction model developed in the case of bulk water, and the existence of a fast sound isexperimentally demonstrated.The behaviour of the collective water dynamics was complemented bystudying the single-particle dynamics of bulk water along the isothermT = 298 K in the pressure range 0.1–350 MPa by means of incoherent scattering. Thisexperiment is an attempt to simulate the change of the water molecular arrangementdue to the interaction with DNA, by increasing the pressure as the presence ofthe biomolecule produces an increase in the density. An anomaly is found in thebehaviour of the relaxation time derived from the quasi-elastic scattering signal,which can be related to the hypothetical second critical point in water. Thisanomaly and the transition from slow to fast sound take place in the sameQ range, thus suggesting that the two phenomena could be related at some microscopiclevel.

The non-Gaussian dynamics of glycerol

We have combined incoherent quasielastic neutron scattering experiments and atomistic molecular simulations to investigate the microscopic dynamics of glycerol moving away from the hydrodynamic limit. We relate changes in the momentum transfer (Q) dependence of the relaxation time to distinct changes of the single-particle dynamics. Going from small to large values of Q, a first crossover at about 0.5 Å−1 is related to the coupling of the translational diffusion dynamics to the non-Debye structural relaxation, while the second crossover at a Q-value near the main diffraction peak is associated with the Gaussian to non-Gaussian crossover of the short-time molecular dynamics, related to the decaging processes. We offer an unprecedented extension of previous studies on polymeric systems towards the case of the typical low-molecular-weight glass-forming system glycerol.

High-speed measurement of axial grain transport in a rotating drum

Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum on short timescales. The smaller component moves towards the axis of rotation and forms a buried core, which then forms undulations that grow into axial bands. Experimental and simulational studies have provided differing accounts of the type of transport taking place in radially segregated and self-diffusing grains. We investigate the bulk axial transport of small quantities of tracer particles travelling amongst glass spheres using non-invasive high-speed synchrotron x-ray particle tracking, which allows us to access timescales not explored previously. The mixtures used have varying propensity to axially segregate based on the glass sphere sizes when the tracers are present in larger proportions; we found that the single-particle dynamics of these mixtures when the tracer concentration is low do not appreciably depend on the relative particle sizes, implying that the potential for a mixture to axially segregate cannot be inferred from the microscopic dynamics of individual small particles. From the single-particle dynamics, we also found that while the standard measure of diffusive behaviour, the slope of the mean-squared displacement, is close to that expected from diffusive transport, more detailed analyses indicate anomalous transport.

Magnetic field effects in few-level quantum dots: Theory and application to experiment

We examine several effects of an applied magnetic field on Anderson-type models for both single- and two-level quantum dots, and make direct comparison between numerical renormalization group (NRG) calculations and recent conductance measurements. On the theoretical side the focus is on magnetization, single-particle dynamics and zero-bias conductance, with emphasis on the universality arising in strongly correlated regimes; including a method to obtain the scaling behavior of field-induced Kondo resonance shifts over a very wide field range. NRG is also used to interpret recent experiments on spin-1/2 and spin-1 quantum dots in a magnetic field, which we argue do not wholly probe universal regimes of behavior; and the calculations are shown to yield good qualitative agreement with essentially all features seen in experiment. The results capture in particular the observed field-dependence of the Kondo conductance peak in a spin-1/2 dot, with quantitative deviations from experiment occurring at fields in excess of $\sim$ 5 T, indicating the eventual inadequacy of using the equilibrium single-particle spectrum to calculate the conductance at finite bias.

Molecular dynamics simulation of liquid trimethylphosphine

Structural and dynamical properties of liquid trimethylphosphine (TMP), (CH(3))(3)P, as a function of temperature is investigated by molecular dynamics (MD) simulations. The force field used in the MD simulations, which has been proposed from molecular mechanics and quantum chemistry calculations, is able to reproduce the experimental density of liquid TMP at room temperature. Equilibrium structure is investigated by the usual radial distribution function, g(r), and also in the reciprocal space by the static structure factor, S(k). On the basis of center of mass distances, liquid TMP behaves like a simple liquid of almost spherical particles, but orientational correlation due to dipole-dipole interactions is revealed at short-range distances. Single particle and collective dynamics are investigated by several time correlation functions. At high temperatures, diffusion and reorientation occur at the same time range as relaxation of the liquid structure. Decoupling of these dynamic properties starts below ca. 220 K, when rattling dynamics of a given TMP molecules due to the cage effect of neighbouring molecules becomes important.

Hamiltonian formulation for the classical EM radiation-reaction problem: Application to the kinetic theory for relativistic collisionless plasmas

A notorious difficulty in the covariant dynamics of classical charged particles subject to non-local electromagnetic (EM) interactions arising in the EM radiation-reaction (RR) phenomena is due to the definition of the related non-local Lagrangian and Hamiltonian systems. The lack of a standard Lagrangian/Hamiltonian formulation in the customary asymptotic approximation for the RR equation may inhibit the construction of consistent kinetic and fluid theories. In this paper the issue is investigated in the framework of Special Relativity. It is shown that, for finite-size spherically-symmetric classical charged particles, non-perturbative Lagrangian and Hamiltonian formulations in standard form can be obtained, which describe particle dynamics in the presence of the exact EM RR self-force. As a remarkable consequence, based on axiomatic formulation of classical statistical mechanics, the covariant kinetic theory for systems of charged particles subject to the EM RR self-force is formulated in Hamiltonian form. A fundamental feature is that the non-local effects enter the kinetic equation only through the retarded particle 4-position, which permits the construction of the related non-local fluid equations. In particular, the moment equations obtained in this way do not contain higher-order moments, allowing as a consequence the adoption of standard closure conditions. A remarkable aspect of the theory concerns the short delay-time asymptotic expansions. Here it is shown that two possible expansions are permitted. Both can be implemented for the single-particle dynamics as well as for the corresponding kinetic and fluid treatments. In the last case, they are performed a posteriori on the relevant moment equations obtained after integration of the kinetic equation over the velocity space. Comparisons with literature are pointed out.