1,333 research outputs found
Granular gases
No full textThe dynamic evolution of granular gases is fundamentally different from molecular gases due to the energy loss during collisions. Nevertheless techniques of kinetic theory are useful in a regime, when the granular particles are moving rapidly and the gas is sufficiently dilute. In these lecture notes we analyse in detail the collision of two rough particles which is inelastic due to incomplete normal and tangential restitution as well as Coulomb friction. Based on the Walton model a time evolution operator for the many particle system is introduced, a formalism which is well suited for simple approximations. We discuss free cooling of granular particles with particular emphasis on the exchange of energy between rotational and translational degrees of freedom. (c) 2006 Elsevier B.V. All rights reserved
Liquid Fluidized Beds of Granular Particles
No full textAbstract We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate N = O(106) particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after fast and slow changes in flow rate and determine the timescales to reach a stationary state
Dynamics of a one-dimensional granular gas with a stochastic coefficient of restitution
No full textRecently, we have modelled inelastic collisions of one-dimensional rods [1,2] by the absorption of translational energy E-tr through internal degrees of freedom, in particular elastic vibrations. We arrived at a stochastic description of collision processes, characterised by a stochastic coefficient of restitution a. In this paper, we construct an analytic approximation for the transition probability E-tr --> E-tr' =(1 - epsilon(2))E-tr. This allows us to perform much longer simulations of large, strongly inelastic granular systems and study relaxation to the true equilibrium state. If the internal vibrations are undamped, equilibrium is characterised by propagating sound waves. In the case of damping, the system develops towards a final state which consists of one big cluster, containing all particles at rest. (C) 2000 Elsevier Science B.V. All rights reserved
Driven Granular Fluids
No full textDense granular media can be prepared in a stationary state by suitable driving. Such driving can be given by a random, momentum-conserving external force acting upon, say, a fluid comprised of inelastic hard spheres. While this out-of-equilibrium stationary state violates time reversal symmetry, it can still be investigated by means similar to ordinary fluids. For high enough density, the driven granular fluid undergoes a glass transition, and for this transition an extension to the mode-coupling theory can be derived. In addition to the quiescent stationary state, a kinetic theory as well as experiments in 2D for the active microrheology can be devised, where a selected intruder is pulled through the system as a probe for either constant velocity or force
Amoeboid propulsion of active solid bodies, vesicles and droplets: a comparison
No full textRace between micro swimmers: droplets (blue), vesicles (orange) and deformable solids (green), driven by the same swim stroke, exhibit very different velocities and efficiencies.We present a unified discussion of three types of near-spherical amoeboid microswimmers, driven by periodic, axially symmetric, achiral deformations (swim strokes): a solid deformable body, a vesicle with incompressible fluid membrane, and a droplet. Minimal models are used, which characterize the swimmer type only by boundary conditions. We calculate the swimming velocities, the dissipated power and the Lighthill efficiencies within a second order perturbation expansion in the small deformation amplitudes. For solid bodies, we reproduce older results by Lighthill and Blake, for vesicles and for droplets we add new results. The unified approach allows for a detailed comparison between the three types of microswimmers. We present such comparisons for swim strokes made up of spherical harmonics of adjacent orders l and l + 1, as well as for a manifold of swim strokes, made up of spherical harmonics up to order l = 4, which respect volume- and surface-incompressibility. This manifold is two-dimensional, which allows to present swimming velocities and efficiencies in compact graphical form. In a race in which each swimmer can choose the stroke that maximizes its speed, the droplet always comes in first, the vesicle comes in second, while the particle finishes third. However, if the three swimmers perform the same stroke, other order of rankings become possible. The maximum of the total efficiency of a droplet is greater than that of a vesicle if the internal dissipation is small. The efficiency of the solid body turns out to be typically two orders of magnitude smaller than that of vesicles and droplets. Optimizing the Lighthill efficiency and optimizing the swimming velocity result in different optimal swim strokes.Race between micro swimmers: droplets (blue), vesicles (orange) and deformable solids (green), driven by the same swim stroke, exhibit very different velocities and efficiencies.We present a unified discussion of three types of near-spherical amoeboid microswimmers, driven by periodic, axially symmetric, achiral deformations (swim strokes): a solid deformable body, a vesicle with incompressible fluid membrane, and a droplet. Minimal models are used, which characterize the swimmer type only by boundary conditions. We calculate the swimming velocities, the dissipated power and the Lighthill efficiencies within a second order perturbation expansion in the small deformation amplitudes. For solid bodies, we reproduce older results by Lighthill and Blake, for vesicles and for droplets we add new results. The unified approach allows for a detailed comparison between the three types of microswimmers. We present such comparisons for swim strokes made up of spherical harmonics of adjacent orders l and l + 1, as well as for a manifold of swim strokes, made up of spherical harmonics up to order l = 4, which respect volume- and surface-incompressibility. This manifold is two-dimensional, which allows to present swimming velocities and efficiencies in compact graphical form. In a race in which each swimmer can choose the stroke that maximizes its speed, the droplet always comes in first, the vesicle comes in second, while the particle finishes third. However, if the three swimmers perform the same stroke, other order of rankings become possible. The maximum of the total efficiency of a droplet is greater than that of a vesicle if the internal dissipation is small. The efficiency of the solid body turns out to be typically two orders of magnitude smaller than that of vesicles and droplets. Optimizing the Lighthill efficiency and optimizing the swimming velocity result in different optimal swim strokes
Heterogeneities in the glassy state
No full textWe study heterogeneities in a binary Lennard-Jones system below the glass transition using molecular dynamics simulations. We identify mobile and immobile particles and measure their distribution of vibrational amplitudes. For temperatures near the glass transition the distribution of vibrational amplitudes obeys scaling and compares reasonably well with a mean-field theory for the amorphous solid state. To investigate correlations among the immobile and mobile particles we identify clusters and analyze their size and shape. For a fixed number of immobile particles we observe that the immobile particles cluster more strongly together as the temperature is increased which allows the particles to block each other more effectively and to therefore stay immobile. For the mobile particles, on the other hand, the clustering is most pronounced at low temperatures, indicating that mobility at low temperatures can only be sustained in cooperative motion
Mobilities of a drop and an encapsulated squirmer
No full textAbstract We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position 1487911\varvec{r}_s1487911 r s . The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of 1487911\varvec{r}_s1487911 r s , relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer. Graphical AbstractGeorg-August-Universität Göttinge
Biophysical model of a single synaptic connection: Transmission properties are determined by the cooperation of pre- and postsynaptic mechanisms
No full textA stochastic model of synaptic transmission has been designed on the basis of electrophysiological experiments. The model includes presynaptic mechanisms of recruitment and calcium related release of vesicles, transmitter dynamics in the cleft and postsynaptic receptor kinetics. Monte Carlo simulations of a single synaptic connection are performed and demonstrate that synapses depress during repetitive presynaptic stimulation due to depletion of presynaptic vesicles as well as receptor desensitization. Only for stimulation frequencies below 40 Hz depression is caused solely presynaptically by depletion of vesicles. It is shown that specific physiological conditions determine the frequency dependence of steady state depression currents and set limits on the range of possibly rate-coded transmission. (C) 2001 Elsevier Science B.V. All rights reserved
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