Velocity correlations in granular materials

A system of inelastic hard disks in a thin pipe capped by hot walls is studied with the aim of investigating velocity correlations between particles. Two effects lead to such correlations: inelastic collisions help to build localized correlations, while momentum conservation and diffusion produce long ranged correlations. In the quasi-elastic limit, the velocity correlation is weak, but it is still important since it is of the same order as the deviation from uniformity. For system with stronger inelasticity, the pipe contains a clump of particles in highly correlated motion. A theory with empirical parameters is developed. This theory is composed of equations similar to the usual hydrodynamic laws of conservation of particles, energy, and momentum. Numerical results show that the theory describes the dynamics satisfactorily in the quasi-elastic limit, however only qualitatively for stronger inelasticity.Comment: 12 pages (REVTeX), 15 figures (Postscript). submitted to Phys. Rev.

Energy flows in vibrated granular media

We study vibrated granular media, investigating each of the three components of the energy flow: particle-particle dissipation, energy input at the vibrating wall, and particle-wall dissipation. Energy dissipated by interparticle collisions is well estimated by existing theories when the granular material is dilute, and these theories are extended to include rotational kinetic energy. When the granular material is dense, the observed particle-particle dissipation rate decreases to as little as 2/5 of the theoretical prediction. We observe that the rate of energy input is the weight of the granular material times an average vibration velocity times a function of the ratio of particle to vibration velocity. `Particle-wall' dissipation has been neglected in all theories up to now, but can play an important role when the granular material is dilute. The ratio between gravitational potential energy and kinetic energy can vary by as much as a factor of 3. Previous simulations and experiments have shown that E ~ V^delta, with delta=2 for dilute granular material, and delta ~ 1.5 for dense granular material. We relate this change in exponent to the departure of particle-particle dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR

Nontrivial Velocity Distributions in Inelastic Gases

We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In the freely evolving case, we find that the velocity distribution decays algebraically, P(v,t) ~ v^{-sigma} for sufficiently large velocities. We derive the exponent sigma(d,epsilon), which exhibits nontrivial dependence on both d and epsilon, exactly. In the forced case, the velocity distribution approaches a steady-state with a Gaussian large velocity tail.Comment: 4 pages, 1 figur

Granular cooling of hard needles

We have developed a kinetic theory of hard needles undergoing binary collisions with loss of energy due to normal and tangential restitution. In addition, we have simulated many particle systems of granular hard needles. The theory, based on the assumption of a homogeneous cooling state, predicts that granular cooling of the needles proceeds in two stages: An exponential decay of the initial configuration to a state where translational and rotational energies take on a time independent ratio (not necessarily unity), followed by an algebraic decay of the total kinetic energy $\sim t^{-2}$. The simulations support the theory very well for low and moderate densities. For higher densities, we have observed the onset of the formation of clusters and shear bands.Comment: 7 pages, 8 figures; major changes, extended versio

The dynamics of thin vibrated granular layers

We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a `collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure

Shocks in supersonic sand

We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge and calculate a speed of granular pressure disturbances (sound speed) equal to 10% of the flow speed. The flow is supersonic, forming shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton's laws and Monte Carlo simulations of the Boltzmann equation yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.Comment: 4 pages, 5 figure

Structure and Instability of High-Density Equations for Traffic Flow

Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The calculations are carried out up to Navier-Stokes order. A linear instability analysis indicates an additional kind of instability compared to previous macroscopic traffic models. The relevance for describing granular flows is outlined.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

Study of economically valuable traits and technological properties in maize from the Zea mays L. collection of VIR

Background. Innovative technologies for deep processing of grain are widely used in maize grain processing with the release of the grain germ for subsequent extraction of oil and starch from it or production of sugar substitutes in the form of fructose syrup and alcohol, bakery or feed protein. A search for economically valuable sources of maize starch, useful byproducts of its processing, and natural modification of starch for deep processing is vital.Materials and methods. Ten high-starch maize accessions from the VIR collection, isolated by IR spectrometry, were studied. Starch content was measured according to GOST 10845-98, GOST 13586.5-93, GOST 10847-74 and GOST ISO 6647-1-2015 standards. Processing of grain into starch and assessment of the content of amylose and byproducts were carried out at the All-Russian Scientific Research Institute for Starch Products in 2018 according to L. P. Nosovskaya et al. The actual content of starch and its byproducts during deep grain processing was determined. The values of the actual percentage of dry matter (DM, %) in grain, mass fraction of starch, ash content, as well as the yield of extract, pulp, embryo, gluten, process water and starch were determined.Results. Accessions with a high yield of starch (k-4520, k-9301 and k-24730), germ (k-4520. k-8785 and k-24731), pulp (k-4520, k-8785, k-9991 and k-24732) and protein (k8785) were identified as well as those with a percentage of amylopectin in starch above 82% (k-24730 and k-24733) and 100% (k-5461 and k-9991), and amylose above 30% (k4520 and k-9301).Conclusion. Of practical interest in terms of the actual yield of starch (% DM in grain) are accessions k-4520, k-9301, k-24730, k-9991, k-5461 and k-4520. According to the results of breeding tests, accessions k-24730, k-24732 and k-24733 had the following values of starch harvest calculated for grain yield: 4.66, 4.41 and 4.18 t/ha, respectively

A Langevin Approach to One-Dimensional Granular Media Fluidized by Vibrations

We present a Langevin approach to describe the steady-state dynamics of one-dimensional granular media fluidized by a vibrating bottom plate. We adopt a linear Langevin equation to describe the motion of the center of mass. Within this framework, we derive analytical expressions for several macroscopic quantities. We also predict the power spectrum for the height of the center of mass. We find good agreement between our theoretical predictions and extensive event-driven molecular dynamics simulations.Comment: 11 pages, 3 figures, to be published in J. Phys. Soc. Jp