380 research outputs found
A practical density functional for polydisperse polymers
The Flory Huggins equation of state for monodisperse polymers can be turned
into a density functional by adding a square gradient term, with a coefficient
fixed by appeal to RPA (random phase approximation). We present instead a model
nonlocal functional in which each polymer is replaced by a deterministic,
penetrable particle of known shape. This reproduces the RPA and square gradient
theories in the small deviation and/or weak gradient limits, and can readily be
extended to polydisperse chains. The utility of the new functional is shown for
the case of a polydisperse polymer solution at coexistence in a poor solvent.Comment: 9 pages, 3 figure
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
Generic phase diagram of active polar films
We study theoretically the phase diagram of compressible active polar gels
such as the actin network of eukaryotic cells. Using generalized hydrodynamics
equations, we perform a linear stability analysis of the uniform states in the
case of an infinite bidimensional active gel to obtain the dynamic phase
diagram of active polar films. We predict in particular modulated flowing
phases, and a macroscopic phase separation at high activity. This qualitatively
accounts for experimental observations of various active systems, such as
acto-myosin gels, microtubules and kinesins in vitro solutions, or swimming
bacterial colonies.Comment: 4 pages, 1 figur
Molecular Weight Dependence of Spreading Rates of Ultrathin Polymeric Films
We study experimentally the molecular weight dependence of spreading
rates of molecularly thin precursor films, growing at the bottom of droplets of
polymer liquids. In accord with previous observations, we find that the radial
extension R(t) of the film grows with time as R(t) = (D_{exp} t)^{1/2}. Our
data substantiate the M-dependence of D_{exp}; we show that it follows D_{exp}
\sim M^{-\gamma}, where the exponent \gamma is dependent on the chemical
composition of the solid surface, determining its frictional properties with
respect to the molecular transport. In the specific case of hydrophilic
substrates, the frictional properties can be modified by the change of the
relative humidity (RH). We find that \gamma \approx 1 at low RH and tends to
zero when RH gets progressively increased. We propose simple theoretical
arguments which explain the observed behavior in the limits of low and high RH.Comment: 4 pages, 2 figures, to appear in PR
Critical holes in undercooled wetting layers
The profile of a critical hole in an undercooled wetting layer is determined
by the saddle-point equation of a standard interface Hamiltonian supported by
convenient boundary conditions. It is shown that this saddle-point equation can
be mapped onto an autonomous dynamical system in a three-dimensional phase
space. The corresponding flux has a polynomial form and in general displays
four fixed points, each with different stability properties. On the basis of
this picture we derive the thermodynamic behaviour of critical holes in three
different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.
Unusual Response to a Localized Perturbation in a Generalized Elastic Model
The generalized elastic model encompasses several physical systems such as
polymers, membranes, single file systems, fluctuating surfaces and rough
interfaces. We consider the case of an applied localized potential, namely an
external force acting only on a single (tagged) probe, leaving the rest of the
system unaffected. We derive the fractional Langevin equation for the tagged
probe, as well as for a generic (untagged) probe, where the force is not
directly applied. Within the framework of the fluctuation-dissipation
relations, we discuss the unexpected physical scenarios arising when the force
is constant and time periodic, whether or not the hydrodynamic interactions are
included in the model. For short times, in case of the constant force, we show
that the average drift is linear in time for long range hydrodynamic
interactions and behaves ballistically or exponentially for local hydrodynamic
interactions. Moreover, it can be opposite to the direction of external
disturbance for some values of the model's parameters. When the force is time
periodic, the effects are macroscopic: the system splits into two distinct
spatial regions whose size is proportional to the value of the applied
frequency. These two regions are characterized by different amplitudes and
phase shifts in the response dynamics
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
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