Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System

We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state.The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effects on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.     

A three-body scattering problem in the molecular mass limit

A three-body problem is studied that involves the scattering of a heavy particle from a bound state of a heavy and a light particle. For fairly large mass ratios we find many partial waves involved in the scattering with both elastic and inelastic resonances present. It is also found that virtually all of the breakup inelasticity is in the odd partial waves, if the heavy particles are identical bosons. The same problem is solved in the Born-Oppenheimer approximation and it is found that the effective potential between the heavy particles develops an imaginary part in the odd partial waves and thus gives a quantitative account of the three-body results including the inelasticity. The linear combination of nuclear orbitais method is applied to the same problem and is found to be inadequate.     

Kinematics of sputtered excited atoms

The kinematics of binary inelastic collisions, when the inelasticity is strong enough in order to influence the collision dynamics, has been derived. It has been shown that neutral and excited sputtered atoms differ from each other in regions of kinetic energy and angular variables. The structure of these physical regions, due to their general character, can be used to obtain direct information on the inelastic processes which are responsible for the formation of the excited states. In particular, on the basis of a limiting angle for the recoiling particle, we show a simple equation and a cross-section which enable us to obtain direct information about inelastic processes. Applications on Si-sputtered species are shown.     

Competition of Brazil nut effect,buoyancy, and inelasticity induced segregation in a granular mixture

It has been recently reported that a granular mixture in which grains differ in their restitution coefficients presents segregation: the more inelastic particles sink to the bottom. When other segregation mechanisms as buoyancy and the Brazil nut effect are present, the inelasticity induced segregation can compete with them. First, a detailed analysis, based on numerical simulations of two dimensional systems, of the competition between buoyancy and the inelasticity induced segregation is presented, finding that there is a transition line in the parameter space that determines which mechanism is dominant. In the case of neutrally buoyant particles having different sizes the inelasticity induced segregation can compete with the Brazil nut effect (BNE). Reverse Brazil nut effect (RBNE) could be obtained at large inelasticities of the intruder. At intermediate values, BNE and RBNE coexist and large inelastic particles are found both near the bottom and at the top of the system.     

The effects of forcing and dissipation on phase transitions in thin granular layers

Recent experimental and computational studies of vibrated thin layers of identical spheres have shown transitions to ordered phases similar to those seen in equilibrium systems. Motivated by these results, we carry out simulations of hard inelastic spheres forced by homogenous white noise. We find a transition to an ordered state of the same symmetry as that seen in the experiments, but the clear phase separation observed in the vibrated system is absent. Simulations of purely elastic spheres also show no evidence for phase separation. We show that the energy injection in the vibrated system is dramatically different in the different phases, and suggest that this creates an effective surface tension not present in the equilibrium or randomly forced systems. We do find, however, that inelasticity suppresses the onset of the ordered phase with random forcing, as is observed in the vibrating system, and that the amount of the suppression is proportional to the degree of inelasticity. The suppression depends on the details of the energy injection mechanism, but is completely eliminated when inelastic collisions are replaced by uniform system-wide energy dissipation.     

Geometrical scaling at inelastic threshold

The possibility of geometrical scaling being a low energy phenomenon is investigated using phase shift data. For exotic reactions, in particular in K⁺p scattering, scaling is observed and the high energy (NAL-ISR)GS curve agrees with phase shift inelasticity η down to the inelastic threshold. For reactions with resonances the high energy curves average the phase shift inelasticities. The consequences of these results are discussed and predictions for ππ and Kπ scattering are presented.     

Effect of Miniband Dispersion on Inelastic Scattering of Superlattice Electrons by Acoustic Phonons

Within the framework of the Boltzmann equation, formulas for calculating the effective relaxation time and mobility of superlattice electrons are derived with allowance for inelastic scattering on acoustic phonons and dispersion of the miniband energy spectrum depending on the longitudinal wave vector. The dependences of longitudinal and transverse mobilities of the nondegenerate electronic gas of the GaAs/Al_0.36Ga_0.64As superlattice with the quantum well 5 nm wide on the potential barrier width and temperature are analyzed numerically. It is demonstrated that inelasticity of scattering and miniband dispersion significantly increase the electron mobility, and its temperature dependence becomes more pronounced at low temperatures.     

Energy and power fluctuations in vibrated granular gases

Using two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study the fluctuations of its total kinetic energy, of the power injected into the gas by the moving boundary and of the power dissipated by inelastic collisions. We show that an effective number N _f of degrees of freedom that depends on the inelasticity of collisions can be extracted from the probability density function (PDF) of the fluctuations of the total kinetic energy E. is then an intensive variable contrary to the usually defined granular temperature . We then show that an intensive temperature can also be calculated from the probability of certain large deviations of the injected power. Finally, we show that the fluctuations of injected and dissipated power are related such that their ratio is inversely proportional to the square-root of the ratio of their correlation times. This allows to define a quantity homogenous to a temperature that is intensive and conserved in the process of energy dynamics from its injection by the driving piston to its dissipation by inelastic collisions.Received: 3 August 2004, Published online: 14 December 2004PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

质点从可自由移动的凹曲面上滑下的速度、加速度和时间

对于一个质点从可自由移动的光滑的凹曲面上滑下的速度、加速度和时间作了一般性讨论,建立了相应的公式.并对质点的运动平面与凹曲面的交线分别为直线、抛物线和椭圆等情况进行了具体的计算.     

Noise activated granular dynamics

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized "phase" one encounters two different scenarios: For moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.     

Single-Δ production contribution to proton-proton inelasticity parameters

We present here a meson exchange calculation of the nucleon-nucleon peripheral partial wave inelasticity parameters below 1 GeV lab kinetic energy. These theoretical estimates if used as constraints in future NN phase-shift analyses should reduce the ambiguities in the inelastic region.     

Charged particle multiplicities and inelastic cross sections in high energy nuclear collisions

Inelastic cross sections at 60 and 200 GeV/nucleon are determined in a streamer chamber for ¹⁶O on several nuclear targets. Charged particle multiplicity distributions for inelastic and central collisions are studied and compared with theoretical predictions. The inelastic cross section exhibit a geometrical dependence on nuclear radii. The multiplicity data are governed by the collision geometry. They are consistent with a picture of superposition of independent nucleon-nucleus interactions.     

Inelastic collisional effect on a dilute granular shock layer with a heated wall

The inelastic collisional effect on a shock layer of a dilute granular gas with a heated wall is numerically studied. To investigate the inelastic collisional effect via the gain term in the inelastic Boltzmann equation on the shock layer, an inelastic Bhatnagar-Gross-Krook (BGK) type equation, whose loss term is equivalent to that in the inelastic Boltzmann equation, is formulated on the basis of the kinetic theory of the granular gas. The inelastic BGK-type equation formulated for a hard-sphere particle is generalized to that for an inverse power law (IPL) molecule. Numerical results in a weakly inelastic regime confirm the nonequilirium contribution to the cooling rate, when the collision frequency depends on the particle velocity. The profile of the negative high-velocity tail of the distribution function in the generation regime of the shock wave obtained by the Direct Simulation Monte Carlo method is higher than that obtained by the proposed BGK-type equation when the collision frequency depends on the particle velocity because of the inelastic collisional effect via the gain term in the inelastic Boltzmann equation, which is not included in the proposed BGK-type equation.     

A unified treatment of the ρ and ρ′

A two-channelN/D method is used to analyze the ππ scatteringp-wave phase shift and inelasticity data up to 2 GeV c.m. energy. We show that if the inelastic scattering of the pions is represented by the second quasi-two-body channel, a two-channel parametrization with two subtractions provides an excellent representation of the data. In addition, the correctp-wave scattering length is obtained in agreement with dispersive sum rules.     

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards.     

Phase segregation in driven diffusive systems

Driven diffusive models describe an array of atoms in an external periodic potential, when the motion is damped due to energy exchange with the substrate. The systems of this class have wide application in modeling of charge and mass transport in solids. Recently, the driven diffusive models have been used in tribology, where the driving force emerges due to motion of one of two substrates, which are separated by a thin atomic layer. When a dc force is applied to the atoms, the system exhibits the locked-to-sliding transition. During the transition the system may split in domains of two kinds, the running domains where the atoms move with almost maximum velocity, and the immobile domains (“traffic jams”). We discuss a new model for a 1D chain, where the particles have a complex structure treated in a mean-field fashion: particle collisions are inelastic and also each particle is considered as having its own thermostat. This model exhibits a hysteresis and the “traffic jams” state even at high temperatures due to the clustering of atoms with the same velocity.     

Does the Chapman-Enskog expansion for sheared granular gases converge?

The fundamental question addressed in this Letter is whether or not the partial Chapman-Enskog expansion P(xy)= [see text for formula] of the shear stress converges for a gas of inelastic hard spheres. By using a simple kinetic model it is shown that, in contrast to the elastic case, the above series does converge, the radius of convergence increasing with inelasticity. It is argued that this paradoxical conclusion is not an artifact of the kinetic model and can be understood in terms of the time evolution of the scaled shear rate in the uniform shear flow.     

Determination of partial-wave inelasticities for elastic pion-nucleon scattering with the aid of experimental data on π N → ππ N processes in the beam-momentum range 300 < P beam < 500 MeV/ c

The partial-wave inelasticity parameters of the amplitude for elastic pion-nucleon scattering are determined with the aid of the phenomenological amplitude for inelastic πN → ππN processes in the energy range extending to the threshold for the production of two pions. The resulting inelasticity parameters are compared with their counterparts derived from modern partial-wave analyses. The largest inelastic-scattering cross section in the P11 wave is in excellent agreement with the analogous value from the analysis performed at the George Washington University in 2006. For other waves, however, the present results differ in the majority of cases from respective values given by partial-wave analyses (the distinctions are especially large for the isospin-3/2 amplitudes). Original Russian Text ? V.A. Kozhevnikov, S.G. Sherman, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 11, pp. 1891–1909.     

The nucleon-antinucleon interaction and resonances

We present predictions for nucleon-nucleon elastic scattering phase parameters based on a unitary, relativistic, one-pion-exchange model, which takes single-pion-production inelasticity into account. The agreement of the high-L phase shifts with data is considerably improved at intermediate energies by inclusion of the NΔ inelastic channel. Our predicted inelasticities are in generally good agreement with the data, but are smaller than the predictions of Green and Sainio. The Argand plots of the ¹D₂, ³F₃, ³P₁, and ¹G₄ all show counterclockwise motion resulting from the onset of inelastic channels.     

Convection in horizontally shaken granular material

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucially on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with varying inelasticity. Received 3 March 1999