Successive Jumps Research Articles

Bouncing trimer: a random self-propelled particle, chaos and periodical motions

A trimer is an object composed of three centimetrical stainless steel beads equidistant from each other and is predestined to show richer behaviour than a bouncing ball or a bouncing dimer. A rigid trimer was placed on the plate of an electromagnetic shaker and was vertically vibrated according to a sinusoidal signal. The horizontal translational and rotational motions of the trimer were recorded for a range of frequencies between 25 and 100 Hz, while the amplitude of the forcing vibration was tuned to obtain maximal acceleration of the plate up to 10 times gravity. Several modes have been detected such as, e.g., rotational and pure translational motions. These modes are found at determined accelerations of the plate and do not depend on the frequency. Chaotic behaviour is observed for other accelerations. By recording the time delays between two successive contacts when the frequency and the amplitude are fixed, a map of the bouncing regime was constructed and compared with that of the dimer and the bouncing ball. Period-2 and period-3 orbits were experimentally observed. In these modes, according to observations, the contact between the trimer and the plate is persistent between two successive jumps. This persistence erases the memory of the jump preceding the contact. A model based on the conditions for obtaining persistent contact is proposed and allows us to explain the values of the particular accelerations for which period-2 and period-3 modes were observed. Finally, numerical simulations allow us to reproduce the experimental results. This allows us to conclude that the friction between the beads and the plate is the major dissipative process.

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.

Diffusion of particles on a dice lattice with two nonequivalent sites

We investigated the diffusion of particles on a dice lattice with two kinds of nonequivalent sites. It is shown that the character of the particle migration depends crucially on the relative rates of the jumps from deep and shallow sites. The site inhomogeneity imposes specific pair correlation between the successive jumps. A general analytical expression for the chemical diffusion coefficient has been derived in the case of strong inhomogeneity. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for the different values of the lateral pairwise interaction between the particles. The analytical data have been compared with the numerical data obtained by the kinetic Monte Carlo simulations. Almost perfect agreement between the respective results has been found.

Heterogeneous dynamics of ionic liquids from molecular dynamics simulations

Molecular dynamics simulations have been performed to study the complex and heterogeneous dynamics of ions in ionic liquids. The dynamics of cations and anions in 1-ethyl-3-methyl imidazolium nitrate (EMIM-NO(3)) are characterized by van Hove functions and the corresponding intermediate scattering functions F(s)(k,t) and elucidated by the trajectories augmented by the use of singular spectrum analysis (SSA). Several time regions are found in the mean squared displacement of the ions. Change in the slope in a plot of the diffusion coefficient against temperature is found at around 410 K in the simulation. Heterogeneous dynamics with the presence of both localized ions and fast ions capable of successive jumps were observed at long time scales in the self-part of the van Hove functions and in the trajectories. Non-Gaussian dynamics are evidenced by the self-part of the van Hove functions and wave number dependence of F(s)(k,t) and characterized as Levy flights. Successive motion of some ions can continue even after several nanoseconds at 370 K, which is longer than the onset time of diffusive motion, t(dif). Structure of the long time dynamics of fast ions is clarified by the phase space plot of the successive motion using the denoised data by SSA. The continual dynamics are shown to have a long term memory, and therefore local structure is not enough to explain the heterogeneity. The motion connecting localized regions at about 370 K is jumplike, but there is no typical one due to local structural changes during jump motion. With the local motion, mutual diffusion between cation and anion occurs. On decreasing temperature, mutual diffusion is suppressed, which results in slowing down of the dynamics. This "mixing effect of cation and anion" is compared with the "mixed alkali effect" found in the ionics in the ionically conducting glasses, where the interception of paths by different alkali metal ions causes the large reduction in the dynamics [J. Habasaki and K. L. Ngai, Phys. Chem. Chem. Phys. 9, 4673 (2007), and references herein]. Although a similar mechanism of the slowing down is observed, strong coupling of the motion of cation and anion prevents complete interception unless deeply supercooled, and this explains the wide temperature region of the existence of the liquid and supercooled liquid states in the ionic liquid.

Refinements in the characterization of the heterogeneous dynamics of Li ions in lithium metasilicate

We have performed the molecular dynamics simulations of ionically conducting lithium metasilicate, Li(2)SiO(3), to get a more in depth understanding of the heterogeneous ion dynamics by separating out the partial contributions from localized and diffusive ions to the mean square displacement (MSD) <r(2)(t)>, the non-Gaussian parameter alpha(2)(t), and the van Hove function G(s)(r,t). Several different cage sizes l(c) have been used for the definition of localized ions. Behaviors of fast ions are obtained by the subtraction of the localized component from the r(2)(t) of all ions, and accelerated dynamics is found in the resultant subensemble. The fractional power law of MSD is explained by the geometrical correlation between successive jumps. The waiting time distribution of jumps also plays a role in determining <r(2)(t)> but does not affect the exponent of its fractional power law time dependence. Partial non-Gaussian parameters are found to be instructive to learn how long length-scale motions contribute to various quantities. As a function of time, the partial non-Gaussian parameter for the localized ions exhibits a maximum at around t(x2), the onset time of the fractional power law regime of <r(2)(t)>. The position of the maximum is slightly dependent on the choice of l(c). The power law increases in the non-Gaussian parameter before the maximum are attributed to the Levy distribution of length scales of successive (long) jumps. The decreases with time, after the maximum has been reached, are due to large back correlation of motions of different length scales. The dynamics of fast ions with superlinear dependence in their MSD also start at time around the maximum. Also investigated are the changes of the characteristic times demarcating different regimes of <r(2)(t)> on increasing temperatures from the glassy state to the liquid state. Relation between the activation energies for short time and long time regimes of <r(2)(t)> is in accord with interpretation of ion dynamics by the coupling model.

Four-step evolution of spin Hall conductance: Tight-binding electrons with Rashba coupling in a magnetic field

We report the investigation of magnetotransport properties of tight-binding electrons with Rashba spin-orbit coupling (SOC). Four-step evolutions of the spin Hall and charge-Hall conductances (SHC and CHC) have been found when fixing the magnetic field and tuning the Rashba SOC: the SHC shows size-dependent resonant jumps and even changes its sign; the CHC exhibits three successive quantum jumps. More arrestingly, such four-step evolutions are reflected in topological characters of edge states of a cylindrical system and are robust against weak disorder.

On the scattering of charged particles in complex current configurations

The scattering of charged particles in the magnetic fields of current sheets with bell-shaped and double-humped current density profiles has been studied analytically and numerically. The particle scattering processes are shown to depend significantly on the structure of the current sheet. Thus, for example, when particles are scattered in double current sheets, a regime under which the compensation of two successive jumps in particle magnetic moments can lead to a quasi-regular type of motion, instead of a chaotic one, can be maintained in the system.

First passage times of Lévy flights coexisting with subdiffusion

We investigate both analytically and numerically the first passage time (FPT) problem in one dimension for anomalous diffusion processes in which Lévy flights and subdiffusion coexist. We analyze the FPT for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index mu, 0<mu<2, and skewness parameter beta=0, (ii) one-sided Lévy motions with mu , 0<mu<1, and skewness beta=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<mu<2, and skewness beta=-1. In all three cases the waiting times between successive jumps are heavy tailed with index alpha. We show that in all three cases the FPT distributions are power laws. Our findings extend earlier studies on FPTs of Lévy flights by considering the interplay between long rests and the Lévy long jumps.

On the nature of the heterogeneous dynamics of ions in ionic conducting glasses

Molecular dynamics simulations were performed to study the complex and heterogeneous dynamics of ions in ionically conducting glasses. The dynamics of Li ions in lithium silicate glasses have been characterized by van-Hove functions, fractal dimension of random walks, multifractal analysis of density profile, and principal component analyses of time series. Hierarchy dynamics with local and successive jumps, which are followed by cooperative jumps involving more ions, are observed in the self-part of the van-Hove functions and in trajectories where they form a multifractal density profile. Fractal dimensions of the random walks can be used to characterize the motions of ions in both the short and long length-scale regions. Difference between them becomes clearer in the glassy state, and the corresponding power law dependences of the mean squared displacements can be well explained by these exponents. Phase-space plot using the de-noised data obtained by principal component analysis reveals that the trajectory extending from the short time to the long time dynamics in the plot is continuous and has long term memory. The motion examined by the principal component analysis of the time series shows the deterministic character of the single particle ion dynamics. Each ion moves among domains of collective motion. Recurrence plot and mutual information function shows long correlation of the dynamics. Therefore, the cause of the dynamic heterogeneity is rather deterministic in nature.

Gas Adsorption in Mesoporous Micelle-Templated Silicas: MCM-41, MCM-48, and SBA-15

This paper reports a molecular simulation and experimental study on the adsorption and condensation of simple fluids in mesoporous micelle-templated silicas MCM-41, MCM-48, and SBA-15. MCM-41 is described as a regular cylindrical silica nanopore, while SBA-15 is assumed to be made up of cylindrical nanopores that are connected through lateral channels. The 3D-connected topology of MCM-48 is described using a gyroid periodic minimal surface. Argon adsorption at 77 K is calculated for the three materials using Grand Canonical Monte Carlo simulations. Qualitative comparison with experiments for nitrogen adsorption in mesoporous micelle-templated silicas is made. The adsorption isotherm for SBA-15 resembles that for MCM-41. In particular, capillary condensation and evaporation are not affected by the presence of the connecting lateral channels. In contrast, the argon adsorption isotherm for MCM-48 departs from that for MCM-41 having the same pore size. While condensation in MCM-41 is a one-step process, filling of MCM-48 involves two successive jumps in the adsorbed amounts which correspond to condensation in different domains of the porosity. The condensation pressure for MCM-48 is larger than that for MCM-41. We attribute this result to the morphology of the MCM-48 surface (made up of both concave and convex regions) that differs from that for MCM-41 (concave only). Our results suggest that the pore connectivity affects pore filling when the size of the connections is comparable to that of the nanopores.

Precursors to avalanches in a granular monolayer

We investigate the stability of a granular monolayer composed of spherical grains on an inclined plate. When the tilt angle alpha increases, some reorganizations are observed throughout the pile. The packing fraction rho of the packing evolves by successive jumps. Those discontinuous events precede the collapse of the pile at a critical angle alphac. The occurrence of precursors before avalanches is modeled by stop-and-go motions of blocks due to the competition between sliding friction and the Janssen effect [J. Durand, (Springer-Verlag, New York, 2000)].

Ion and polymer dynamics in polymer electrolytes PPO-LiClO4. I. Insights from NMR line-shape analysis

We investigate ion and polymer dynamics in polymer electrolytes PPO-LiClO4 performing 2H and 7Li NMR line-shape analysis. Comparison of temperature dependent 7Li and 2H NMR spectra gives evidence for a coupling of ion and polymer dynamics. 2H NMR spectra for various salt concentrations reveal a strong slowdown of the polymer segmental motion when the salt content is increased. The 2H NMR line shape further indicates that the segmental motion is governed by dynamical heterogeneities. While the width of the distribution of correlation times G(log tau) is moderate for low and high salt content, an extremely broad distribution exists for an intermediate salt concentration of 15:1 PPO-LiClO4. For the latter composition, a weighted superposition of two spectral components, reflecting the fast and the slow polymer segments of the distribution, describes the 2H NMR line shape over a broad temperature range. Analysis of the temperature dependent relative intensity of both spectral components indicates the existence of a continuous rather than a discontinuous distribution G(log tau). Such continuous distribution is consistent with gradual fluctuations of the local salt concentration and, hence, of the local environments of the polymer segments, whereas it is at variance with the existence of large salt-depleted and salt-rich domains featuring fast and slow polymer dynamics, respectively. Finally, for all studied PPO-LiClO4 mixtures, the 2H NMR line shape strongly depends on the echo delay in the applied echo-pulse sequence, indicating that the structural relaxation of the polymer segments involves successive rotational jumps about small angles gamma < 20 degrees .

A new sodium cobaltophosphate with a tunnel structure, ionic conductor

The exploration of the Na–Co–P–O system has allowed a new cobaltophosphate Na2Co8(PO4)6 with an original tunnel structure to be synthesized. The framework [Co8P6O24]∞ consists of a complex arrangement of corner and edge sharing CoO5 pyramids and PO4 tetrahedra forming large tunnels running along and . In this structure two partially occupied Na+ sites distributed along the axis of the “hexagonal” tunnels ( axis) are evidenced. Complex impedance measurements show that this phosphate is an ionic conductor above 600 K. The mobility of the Na+ ions in the structure is explained by their particular location, which allows successive jumps between the two different sodium sites in the “hexagonal” tunnels.

Tracer Diffusion by Six-Jump-Cycles in Nonstoichiometric B2 Intermetallic Compounds

Tracer diffusion in non-stoichiometric B2 intermetallic compounds having antistructural disorder is investigated using the six-jump-cycle (6JC) as a fundamental diffusion unit. For non-stoichiometric compositions, the antistructural atoms are assumed to be isolated and located at one of the six [110]-type and [100]-type sites (as only these sites are involved in the 6JC or 2JC). The jump frequencies for the 6JC involving a perfectly ordered configuration are calculated in terms of a four-frequency-model, using the meanfirst- passage concept of Arita et al. The jump frequency of an antistructural atom at [110] or [100]-type sites is taken to be the harmonic mean of frequencies of two successive nearestneighbour jumps of the same kind of atoms. The expressions for the tracer diffusion coefficients are derived for both atomic components at deviations from stoichiometry, assuming that the 6JC mechanism is valid. The results are compared with Monte Carlo simulations based on single vacancy jumps and found to be in fair agreement for compositions close to stoichiometry.

From DNA Sequence Analysis to Modeling Replication in the Human Genome

We explore the large-scale behavior of nucleotide compositional strand asymmetries along human chromosomes. As we observe for 7 of 9 origins of replication experimentally identified so far, the (TA+GC) skew displays rather sharp upward jumps, with a linear decreasing profile in between two successive jumps. We present a model of replication with well positioned replication origins and random terminations that accounts for the observed characteristic serrated skew profiles. We succeed in identifying 287 pairs of putative adjacent replication origins with an origin spacing approximately 1-2 Mbp that are likely to correspond to replication foci observed in interphase nuclei and recognized as stable structures that persist throughout subsequent cell generations.

Two magnetic phases in cold-drawn Fe-rich amorphous wire

Magnetic properties have been studied in ferromagnetic amorphous wires of nominal composition Fe 77.5B 15Si 7.5 and diameter 0.05 mm prepared by cold-drawing technique. Conventional and surface hysteresis loops were measured by fluxmetric method and by magneto-optical Kerr effect method, respectively. Saturation magnetization dependence with the current density has been obtained. Two Curie points were clearly distinguishable on this dependence that could be associated with the existence of two ferromagnetic phases. On the other hand, two successive jumps of magnetization have been observed in fluxmetric as well as in magneto-optical curves. The joint analysis of the bulk and surface hysteresis loops permits us to conclude that the cold-drawing post process induces strong helical anisotropy in the Fe-rich wires studied. The helical magnetic structure exists in the surface and, also, in the volume of the wire. We consider that the helical magnetic structure forms the separate magnetic phase that finds the reflection in the two Curie points behavior.

Photoluminescence and stimulated emission from microcrystallineCsPbCl3films prepared by amorphous-to-crystalline transformation

Highly excited photoluminescence of $\mathrm{Cs}\mathrm{Pb}{\mathrm{Cl}}_{3}$, which is known to be one of the most photoluminescent semiconductors, has been measured for thin films prepared by crystallization from the amorphous phase into microcrystalline/polycrystalline states. With the increase of excitation intensity, the microcrystalline state shows successive jumps of the dominant emission band, from a free-exciton band to its phonon replica and finally to a lowest-energy band originating from exciton-exciton inelastic collision. For the exciton-exciton porcess stimulated emission occurs at very low threshold excitation intensities of the order of $10\phantom{\rule{0.3em}{0ex}}\mathrm{kW}∕{\mathrm{cm}}^{2}$ at $77\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. At higher excitation intensities above $50\phantom{\rule{0.3em}{0ex}}\mathrm{kW}∕{\mathrm{cm}}^{2}$, single-path-light-amplification stimulated emission across the film thickness is observed suggesting a very large optical gain. The large-gain mechanism is attributable to giant oscillator strength effect characteristic of excitonic superradiance recently reported for films prepared in the same way.

Single particle jumps in a binary Lennard-Jones system below the glass transition.

We study a binary Lennard-Jones system below the glass transition with molecular dynamics simulations. To investigate the dynamics we focus on events (jumps) where a particle escapes the cage formed by its neighbors. Using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position. We find two kinds of jumps: "reversible jumps," where a particle jumps back and forth between two or more average positions, and "irreversible jumps," where a particle does not return to any of its former average positions, i.e., successfully escapes its cage. For all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur. With increasing temperature, relaxation is enhanced by an increasing number of jumps and growing jump lengths in position and potential energy. However, the waiting time between two successive jumps is independent of temperature. This temperature independence might be due to aging, which is present in our system. We therefore also present a comparison of simulation data with three different histories. The ratio of irreversible to reversible jumps is also increasing with increasing temperature, which we interpret as a consequence of the increased likelihood of changes in the cages, i.e., a blocking of the "entrance" back into the previous cage. In accordance with this interpretation, the fluctuations both in position and energy are increasing with increasing temperature. A comparison of the fluctuations of jumping particles and nonjumping particles indicates that jumping particles are more mobile even when not jumping. The jumps in energy normalized by their fluctuations are decreasing with increasing temperature, which is consistent with relaxation being increasingly driven by thermal fluctuations. In accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position.

Radial migration of developing microglial cells in quail retina: a confocal microscopy study.

Microglial cells spread within the nervous system by tangential and radial migration. The cellular mechanism of tangential migration of microglia has been described in the quail retina but the mechanism of their radial migration has not been studied. In this work, we clarify some aspects of this mechanism by analyzing morphological features of microglial cells at different steps of their radial migration in the quail retina. Microglial cells migrate in the vitreal half of the retina by successive jumps from the vitreal border to progressively more scleral levels located at the vitreal border, intermediate regions, and scleral border of the inner plexiform layer (IPL). The cellular mechanism used for each jump consists of the emission of a leading thin radial process that ramifies at a more scleral level before retraction of the rear of the cell. Hence, radial migration and ramification of microglial cells are simultaneous events. Once at the scleral border of the IPL, microglial cells migrate through the inner nuclear layer to the outer plexiform layer by another mechanism: they retract cell processes, become round, and squeeze through neuronal bodies. Microglial cells use radial processes of s-laminin-expressing Müller cells as substratum for radial migration. Levels where microglial cells stop and ramify at each jump are always interfaces between retinal strata with strong tenascin immunostaining and strata showing weak or no tenascin immunoreactivity. When microglial cell radial migration ends, tenascin immunostaining is no longer present in the retina. These findings suggest that tenascin plays a role in the stopping and ramification of radially migrating microglial cells.

Plastic instabilities with propagating deformation bands in Cu–Al alloys

A multizone laser scanning extensometric technique is used to measure, in parallel with sensitive and rapid stress recording, the sudden strain avalanches and accompanying stress drops during the Portevin–Le Châtelier (PLC) plastic instabilities of type B, which are characterized by jerky propagation in successive short jumps of a deformation band along the specimen axis during deformation with constant strain rate. For the example of Cu–15 at% Al polycrystals the breakaway process for the plastic avalanches is analysed from their strain rate and temperature dependence. It is concluded that local stress concentrations are essential in addition to the dynamic-strain-ageing effect in producing the PLC effect.