334 research outputs found
Optimality of contraction-driven crawling
We study a model of cell motility where the condition of optimal trade-off
between performance and metabolic cost can be made precise. In this model a
steadily crawling fragment is represented by a layer of active gel placed on a
frictional surface and driven by contraction only. We find analytically the
distribution of contractile elements (pullers) ensuring that the efficiency of
self-propulsion is maximal. We then show that natural assumptions about
advection and diffusion of pullers produce a distribution that is remarkably
close to the optimal one and is qualitatively similar to the one observed in
experiments on fish keratocytes
Dissipation in Dynamics of a Moving Contact Line
The dynamics of the deformations of a moving contact line is studied assuming
two different dissipation mechanisms. It is shown that the characteristic
relaxation time for a deformation of wavelength of a contact line
moving with velocity is given as . The velocity
dependence of is shown to drastically depend on the dissipation
mechanism: we find for the case when the dynamics is governed
by microscopic jumps of single molecules at the tip (Blake mechanism), and
when viscous hydrodynamic losses inside the moving
liquid wedge dominate (de Gennes mechanism). We thus suggest that the debated
dominant dissipation mechanism can be experimentally determined using
relaxation measurements similar to the Ondarcuhu-Veyssie experiment [T.
Ondarcuhu and M. Veyssie, Nature {\bf 352}, 418 (1991)].Comment: REVTEX 8 pages, 9 PS figure
Post-Tanner spreading of nematic droplets
The quasistationary spreading of a circular liquid drop on a solid substrate
typically obeys the so-called Tanner law, with the instantaneous base radius
R(t) growing with time as R ~ t^{1/10} -- an effect of the dominant role of
capillary forces for a small-sized droplet. However, for droplets of nematic
liquid crystals, a faster spreading law sets in at long times, so that R ~
t^alpha with alpha significantly larger than the Tanner exponent 1/10. In the
framework of the thin film model (or lubrication approximation), we describe
this "acceleration" as a transition to a qualitatively different spreading
regime driven by a strong substrate-liquid interaction specific to nematics
(antagonistic anchoring at the interfaces). The numerical solution of the thin
film equation agrees well with the available experimental data for nematics,
even though the non-Newtonian rheology has yet to be taken into account. Thus
we complement the theory of spreading with a post-Tanner stage, noting that the
spreading process can be expected to cross over from the usual
capillarity-dominated stage to a regime where the whole reservoir becomes a
diffusive film in the sense of Derjaguin.Comment: 15 pages, 4 figures, accepted in JPCM special issu
Polarity patterns of stress fibers
Stress fibers are contractile actomyosin bundles commonly observed in the
cytoskeleton of metazoan cells. The spatial profile of the polarity of actin
filaments inside contractile actomyosin bundles is either monotonic (graded) or
periodic (alternating). In the framework of linear irreversible thermodynamics,
we write the constitutive equations for a polar, active, elastic
one-dimensional medium. An analysis of the resulting equations for the dynamics
of polarity shows that the transition from graded to alternating polarity
patterns is a nonequilibrium Lifshitz point. Active contractility is a
necessary condition for the emergence of sarcomeric, alternating polarity
patterns.Comment: 5 pages, 3 figure
Mechanical Instabilities of Biological Tubes
We study theoretically the shapes of biological tubes affected by various
pathologies. When epithelial cells grow at an uncontrolled rate, the negative
tension produced by their division provokes a buckling instability. Several
shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all
of which are found in pathologies of tracheal, renal tubes or arteries. The
final shape depends crucially on the mechanical parameters of the tissues :
Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since
tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey
information as to what causes the pathology. We calculate a phase diagram of
tubular instabilities which could be a helpful guide for investigating the
underlying genetic regulation
Active-to-absorbing state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling
We investigate the scaling properties of phase transitions between survival
and extinction (active-to-absorbing state phase transition, AAPT) in a model,
that by itself belongs to the directed percolation (DP) universality class,
interacting with a spatio-temporally fluctuating environment having its own
non-trivial dynamics. We model the environment by (i) a randomly stirred fluid,
governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface,
described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW)
equations. We show, by using a one-loop perturbative field theoretic set up,
that depending upon the spatial scaling of the variance of the external forces
that drive the environment (i.e., the NS, KPZ or EW equations), the system may
show {\em weak} or {\em strong dynamic scaling} at the critical point of active
to absorbing state phase transitions. In the former case AAPT displays scaling
belonging to the DP universality class, whereas in the latter case the
universal behavior is different.Comment: 17 pages, 2 figures, accepted in PR
Dynamics of Spreading of Small Droplets of Chainlike Molecules on Surfaces
Dynamics of spreading of small droplets on surfaces has been studied by the
molecular dynamics method. Simulations have been performed for mixtures of
solvent and dimer, and solvent and tetramer droplets. For solvent particles and
dimers, layering occurs leading to stepped droplet shapes. For tetramers such
shapes occur for relatively deep and strong surface potentials only. For wider
and more shallow potentials, more rapid spreading and rounded droplet shapes
occur. These results are in accordance with experimental data on small non -
volatile polymer droplets. PACS numbers: 68.10Gw, 05.70.Ln, 61.20.Ja, 68.45GdComment: to appear in Europhys. Letters (1994), Latex, 12 page
Deviations from the mean field predictions for the phase behaviour of random copolymers melts
We investigate the phase behaviour of random copolymers melts via large scale
Monte Carlo simulations. We observe macrophase separation into A and B--rich
phases as predicted by mean field theory only for systems with a very large
correlation lambda of blocks along the polymer chains, far away from the
Lifshitz point. For smaller values of lambda, we find that a locally
segregated, disordered microemulsion--like structure gradually forms as the
temperature decreases. As we increase the number of blocks in the polymers, the
region of macrophase separation further shrinks. The results of our Monte Carlo
simulation are in agreement with a Ginzburg criterium, which suggests that mean
field theory becomes worse as the number of blocks in polymers increases.Comment: 6 pages, 4 figures, Late
Fluctuations of a driven membrane in an electrolyte
We develop a model for a driven cell- or artificial membrane in an
electrolyte. The system is kept far from equilibrium by the application of a DC
electric field or by concentration gradients, which causes ions to flow through
specific ion-conducting units (representing pumps, channels or natural pores).
We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain
the membrane equation of motion within Stokes hydrodynamics. At steady state,
the applied field causes an accumulation of charges close to the membrane,
which, similarly to the equilibrium case, can be described with renormalized
membrane tension and bending modulus. However, as opposed to the equilibrium
situation, we find new terms in the membrane equation of motion, which arise
specifically in the out-of-equilibrium case. We show that these terms lead in
certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let
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