Species segregation in one-dimensional granular-system simulations

We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10πL/Nɛ , where N is the total number of particles, L the spatial extent of the system and ɛ the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless Nɛ ≲ 10π . Species segregation, driven by the frictional force occurs as a result of the strong temperature gradients within clusters which pushes the light particles towards the clusters' edges and the heavy particles towards the center. Segregation within clusters is complete at the time of inelastic collapse.     

Antisymmetry in Strangeness −1 and −2 Three-Baryon Systems

 Using the generalized Pauli principle by adding particle labels to the usual space and spin labels a symmetric Hamiltonian and a corresponding antisymmetric wave function are constructed for systems of three baryons in the strangeness sectors S = −1 and −2. Applications are the ΞNN-ΛΛN and NNΛ-NNΣ systems. Minimal sets of generalized coupled Faddeev equations for breakup and rearrangement operators as well as (possible) bound states are derived that have the ordinary Pauli principle for identical particles built in. The equations found confirm our previous sets of coupled Faddeev equations whose derivation was made for distinguishable particles and not using the generalized Pauli principle. Received August 21, 2000; accepted for publication September 29, 2000     

Formation of PdFe alloys on silica supported catalysts

Silica supported PdFe systems were studied with Pd∶Fe ratios from 5∶1 to 1∶10. Formation of α-iron and bimetallic particles was found during the 670 K hydrogen activation. The 5∶1 PdFe system of extreme catalytic activity consisted of disordered fcc PdFe bimetallic and Fe+2 components. No evidence for occurence of other bimetallic structures was found on catalysts even after 1120 K reduction.     

Reply to “quantum tunneling times: A crucial test for the causal program?”

Because Bohm’s Interpretation models particles with continuous trajectories, a natural property to attribute to a Bohmian particle is atunneling time, the time it takes for a particle to pass through a barrier. We also attribute a property-a different property-named ‘tunneling time’ to Copenhagen systems, systems that do not have particles with continuous trajectories. Cushing presents a discussion of the possibility of measuring Bohmian particle tunneling time; however, as becomes clear when considering the differences between properties named ‘tunneling time,’ he incorrectly argues that if such a measurement were possible, the measurement might constitute an empirical test between the Copenhagen interpretation and Bohm’s interpretation.     

Implications of an extended fractal hydrodynamic model

Considering that the motions of the particles take place on continuous but non-differentiable curves, i.e. on fractals with constant fractal dimension, an extended scale relativity model in its hydrodynamic version is built. In this approach, static (particle in a box and harmonic oscillator) and time-dependent (free particle etc.) systems are analyzed. The static systems can be associated with a coherent fractal fluid (of superconductor or of super-fluid types behavior), whose particles are moving on stationary trajectories. The complex speed field of the fractal fluid proves to be essential: the zero value of the real (differentiable) part specifies the coherence of the fractal fluid, while the non-zero value of the imaginary (non-differentiable or fractal) part selects, through some “quantization” relations, the “stationary” trajectories (that may correspond to the observables from quantum mechanics) of the fractal fluid particles. Moreover, the momentum transfer in the fractal fluid is achieved only through the fractal component of the complex speed field. The free time-dependent systems can be associated with an incoherent fractal fluid, and both the differentiable and fractal components of complex speed field are inhomogeneous in fractal coordinates due to the action of a fractal potential. It exist momentum transfer on both speed components and the “observable” in the form of an uniform motion is generated through a specific mechanism of “vacuum” polarization induced by the same fractal potential. The analysis on the fractal fluid specifies conductive properties in the case of movements synchronization both on differentiable and fractal scales, and convective properties in the absence of synchronization.     

Brownian motion in granular gases of viscoelastic particles

A theory is developed of Brownian motion in granular gases (systems of many macroscopic particles undergoing inelastic collisions), where the energy loss in inelastic collisions is determined by a restitution coefficient ɛ. Whereas previous studies used a simplified model with ɛ = const, the present analysis takes into account the dependence of the restitution coefficient on relative impact velocity. The granular temperature and the Brownian diffusion coefficient are calculated for a granular gas in the homogeneous cooling state and a gas driven by a thermostat force, and their variation with grain mass and size and the restitution coefficient is analyzed. Both equipartition principle and fluctuation-dissipation relations are found to break down. One manifestation of this behavior is a new phenomenon of “relative heating” of Brownian particles at the expense of cooling of the ambient granular gas.     

Effects of the diffusive acceleration of particles by shock waves in the primordial matter of the solar system

The effects of the shock wave diffusive acceleration of particles are considered in the case of formation of isotopic relations of the anomalous Xe-HL component of xenon in relic grains of nanodiamonds in chondrites. It is shown that this component could be formed and captured simultaneously with the nanodiamond synthesis in the conditions of the explosive shock wave propagation from supernova outbursts. The specificity of isotopic composition of Xe-HL is due to the high hardness of the spectrum of nuclear-active particles at the shock wave front and its enrichment with heavy isotopes. The spallogenic nature of both the anomalous and normal components of xenon is ascertained, and the role of the subsequent evolutionary processes in the change of their isotopic systems is shown. Experimental evidence of the formation of the power law spectrum of particles with the spectral index γ ∼ 1 by the supersonic turbulence during the carbon-detonation supernova SnIa explosion is obtained; this perhaps opens new perspectives in studying the problem of the origin of cosmic rays. It is shown that at the stage of free expansion of the explosive shock wave, the degree of compression of the matter at the wave front was σ = 31 (the corresponding Mach number M ∼ 97); this led to a 31-fold increase of the magnetic field as well as of the maximum energy of accelerated particles, so that even the energy of protons reached ∼ 3 × 10¹⁵ eV, i.e., the “knee” region.     

Attraction of dust particles in current-carrying recombination plasma: influence of the space charge and recombination processes

We consider the problem about interaction of two conducting particles located in a weakly ionized collisional plasma with an external electric field. It is shown that the regions of the space charge, which are formed as a result of electrodynamical and recombination processes can lead to the attraction of “large particle–space charge” systems for similarly charged large particles. Thedependencies of the energy of interaction of the system on their mutual position are found and the conditions under which the interaction energy corresponds to the attraction of the systems are determined.     

Using the U-120 cyclotron to study the effect of 30 MeV alpha particles on a liposome membrane

We studied the effect of α particles with energies 30.5 MeV, emitted from the 120-cm cyclotron at Skobeltsyn Research Institute of Nuclear Physics, MSU, on artificial membrane systems (liposomes) to simulate the effects of ionizing galactic cosmic rays on biological subjects. The start of low-level lipid peroxidation, accompanied by a change in the ordering of fatty acid residues in a part of the membrane remote from β-carotene molecules, was observed after irradiation by α-particles. The presented method proved to be quite effective and reliable.     

Influence of particle size and concentration on the second-harmonic signal generated at colloidal surfaces

Second harmonic generation (SHG) spectroscopy is a recently developed technique for the investigation of surface properties of particles. To apply the method to technical colloidal systems, the dependences of several experimental parameters on the signal have to be studied. In this work the influence of particle concentration on the SHG signal from the surfaces of colloids (polystyrene beads in a size range of 0.1 μm to 2.9 μm) is investigated. A simple model, based on Lambert–Beer’s law, to describe the measured dependences is derived. The model agrees with the experimental observations for particles smaller 1.1 μm and with a small modification also for larger particles. Based on the new model an analytical equation for determining the optimum concentration, where highest signals in colloidal SHG spectroscopy measurements are obtained, is derived. PACS 42.25.Fx; 42.65.-k; 82.70.Dd     

Exact solution of two-species ballistic annihilation with general pair-reaction probability

The reaction processA + B → ∅ is modeled for ballistic reactants on an infinite line with particle velocitiesυ _A =c andυ _B = -c and initially segregated conditions, i.e., allA particles to the left and allB particles to the right of the origin. Previous models of ballistic annihilation have particles that always react on contact, i.e., pair-reaction probabilityp = 1. The evolutions of such systems are wholly determined by the initial distributions of particles and therefore do not have a stochastic dynamics. However, in this paper the generalization is made to p< 1, allowing particles to pass through each other without necessarily reacting. In this way, theA andB particle domains overlap to form a fluctuating, finitesized reaction zone where the product ∅ is created. Fluctuations are also included in the currents ofA andB particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by theintrinsic reaction rate, seen in a single system, and theextrinsic reaction rate, seen in an average over many systems. The intrinsic and extrinsic behaviors are examined and compared to the case of isotropically diffusing reactants     

Capture cross sections for very heavy systems

In intermediate-mass systems, collective excitations of the target and projectile can greatly enhance the subbarrier capture cross section σ _cap by giving rise to a distribution of Coulomb barriers. For such systems, capture essentially leads directly to fusion [formation of a compound nucleus (CN)], which then decays through the emission of light particles (neutrons, protons, and alpha particles). Thus, the evaporation-residue (ER) cross section is essentially equal to σ _cap. For heavier systems, the experimental situation is significantly more complicated owing to the presence of quasifission (QF) (rapid separation into two fragments before the CN is formed) and by fusion-fission (FF) of the CN itself. Thus, three cross sections need to be measured in order to evaluate σ _cap. Although the ER essentially recoil along the beam direction, QF and FF fragments are scattered to all angles and require the measurement of angular distributions in order to obtain the excitation function and barrier distribution for capture. Two other approaches to this problem exist. If QF is not important, one can still measure just the ER cross section and try to reconstruct the corresponding σ _cap through use of an evaporation-model code that takes account of the FF degree of freedom. Some earlier results on σ _cap obtained in this way will be reanalyzed with detailed coupled-channels calculations, and the “extra-push” phenomenon discussed. One may also try to obtain σ _cap by exploiting unitarity, that is, by measuring instead the flux of particles corresponding to quasielastic (QE) scattering from the Coulomb barrier. Some new QE results obtained for the ⁸⁶Kr + ²⁰⁸Pb system at iThemba LABS in South Africa will be presented. The text was submitted by the authors in English.     

C++QED: an object-oriented framework for wave-function simulations of cavity QED systems

We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting qua ntum dynamics in general. The user is provided with a number of “elements”, e.g. pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulations on such systems. A number of tools are provided to facilitate the implementation of new elements.     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.     

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U₂, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator U_n with n≥ 3 contains a “tree-reducible part”, which groups naturally with U₂ through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics. Received 18 October 2001     

Structure of the Space of Ground States in Systems with Non-Amenable Symmetries

We investigate classical spin systems in d ≥  1 dimensions whose transfer operator commutes with the action of a nonamenable unitary representation of a symmetry group, here SO(1,N); these systems may alternatively be interpreted as systems of interacting quantum mechanical particles moving on hyperbolic spaces. In sharp contrast to the analogous situation with a compact symmetry group the following results are found and proven: (i) Spontaneous symmetry breaking already takes place for finite spatial volume/finitely many particles and even in dimensions d = 1,2. The tuning of a coupling/temperature parameter cannot prevent the symmetry breaking. (ii) The systems have infinitely many non-invariant and non-normalizable generalized ground states. (iii) The linear space spanned by these ground states carries a distinguished unitary representation of SO(1, N), the limit of the spherical principal series. (iv) The properties (i)–(iii) hold universally, irrespective of the details of the interaction. Membre du CNRS     

Radar-radiometric determination of water content of rain clouds with allowance for multiple scattering

We performed combined radiometric and radar measurements of the integral water content of a small-drop fraction of rain cloud systems with allowance for the multiple scattering phenomena. The contribution of rain to emission of the “cloud-rain” system was calculated on the basis of the vector equation of radiation transfer, which enabled us to allow for all orders of multiple scattering by spherical rain drops within the framework of the model of statistically independent particles. It was found that the maximum of the integral water content of overcooled water in clouds does not correspond to the maximum of precipitation intensity. The characteristic values of the integral and specific water contents of a small-drop water fraction in cloud systems with precipitation are measured. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 6, pp. 528–534, June 1999.     

Particles of different density in thermocapillary liquid bridges under the action of travelling and standing hydrothermal waves

We observed particles of different density ratio α = ρ _p /ρ _f in thermocapillary liquid bridges with steady and with time-dependent flow under normal- and under microgravity. Particle accumulation structures (PAS) visualize some features of the hydrothermal wave in the liquid bridge. Relatively fast formation of PAS from particles which are considerably less dense than the fluid (α = 0.42) in oscillatory thermocapillary flow of top-heated liquid bridges was observed and explained by an additional buoyancy-assisted mechanism which brings the particles into the surface flow. This PAS from particles with α = 0.42 will persist under normal gravity for infinite time. In contrast to these less dense particles the heavier particles with α > 1 settle down under normal gravity on the lower end face of the liquid bridge after some time and are no longer in suspension and PAS will fade out. On the other hand, particles with α = 0.42 will be less suited for experiments under microgravity than particles with α > 1 because most of them will be trapped in the vortex centre of the thermocapillary flow. The sedimented particles with α > 1 are a means to visualize some features of standing hydrothermal waves which are visualzed and discussed for the first time.     

A nonlinear controller for three-dimensional tracking of a fluorescent particle in a confocal microscope

We describe an algorithm for using a confocal microscope for tracking single fluorescent particles diffusing in three dimensions. The algorithm uses a standard confocal setup and directly translates each fluorescence measurement into an actuator command. Through physical simulations, we illustrate 3-D tracking in both stage scanning and beam scanning confocal systems. The simulated stage scanning system achieved tracking of particles diffusing in 3-D with coefficients up to 0.2 μm²/s when the average fluorescence intensities was less than 1.84 counts per measurement cycle (corresponding to less than 18,400 counts per second) in the presence of background fluorescence with a rate of 5,000 counts per second. Increasing the fluorescence intensity to approximately 193 counts per measurement cycle (1,930,000 counts per second) allowed the system to track up to particles diffusing with coefficients as large as 0.7 μm²/s. The beam steering system allowed for faster motion of the focal volume of the microscope and successfully tracked particles diffusing with coefficients up to 0.7 μm²/s with fluorescence measurement intensities of approximately 0.189 counts per measurement cycle (37,570 counts per second) and with coefficients up to 90 μm²/s when the fluorescence intensity was increased to 19 counts per measurement cycle (3,807,500 counts/sec).