1,354,601 research outputs found
Self-propulsion of droplets driven by an active permeating gel
No full textWe discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. The latter is modelled as a porous medium which gives rise to permeation forces. In the simplest model, the Brinkman equation, the porous medium is characterised by a single lengthscale --the square root of the permeability. We compute the flow fields inside and outside of the droplet as well as the energy dissipation as a function of . We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit , corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, , corresponding to a space filling gel, is singular and not equivalent to Darcy’s equation, which cannot account for self-propulsion
Deformations of an active liquid droplet
Full text linkA fluid droplet in general deforms, if subject to active driving, such as a
finite slip velocity or active tractions on its interface. We show that these
deformations and their dynamics can be computed analytically in a perturbation
theory in the inverse surface tension using an approach based on vector
spherical harmonics. In lowest order, the deformation is of first order, yet it
affects the flow fields inside and outside of the droplet in zeroth order.
Hence a correct description of the flow has to allow for shape fluctuations,
even in the limit of large surface tension
Anisotropic Random Networks of Semiflexible Polymers
No full textMotivated by the organization of cross-linked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent cross-links which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the cross-link density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization is accompanied by a continuous isotropic-to-nematic (IN) transition occurring at the same cross-link density. As the polymer stiffness decreases, the IN transition becomes first order, shifts to a higher cross-link density, and is preceded by an amorphous solid where the average polymer orientations freeze in random directions
The Integrated Density of States of the Random Graph Laplacian
Full text linkWe analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating cluster (DSPC) alone, thereby eliminating trivially localised states due to finite subgraphs. We derive a nonlinear integral equation for the integrated DSPC and solve it with a population dynamics algorithm. We discuss the possible existence of a mobility edge and give strong evidence for the existence of discrete eigenvalues in the whole range of the spectrum
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
Stability of Freely Falling Granular Streams
Full text linkA freely falling stream of weakly cohesive granular particles is modeled and analyzed with the help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a function of cohesive energy. Extensional flow is an exact solution of the one-dimensional Navier-Stokes equation, corresponding to a strain rate, decaying like t-1 from its initial value, γ˙0. Expanding around this basic state, we show that the flow is stable for short times, γ˙0t≪1, whereas for long times, γ˙0t≫1, perturbations of all wavelengths grow. The growth rate of a given wavelength depends on the instant of time when the fluctuation occurs, so that the observable patterns can vary considerabl
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
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