Naive model for stick-slip processes.

This paper is a tutorial description of stick-slip in soft materials (rubber beads, gels) where inertial effects are negligible. A typical example is a rubber sphere, pressed against a glass surface (JKR contact). The sphere is driven from the top at a prescribed velocity U ( approximately 100 microm/s). At moderate U (and with suitable surface treatment) a periodic stick-slip regime is often observed. We present a simple picture of the stick-slip cycle, describing the growth of a slip zone from the rear end of the sample, and the resulting plot of force vs. time. All our estimates are restricted to scaling laws.

Melt fracture of entangled polymers.

We construct a model for a slippage plane in a sheared melt, based on a balance between reptation bridging and shear debonding. The resulting state could show up at rather low shear rates and be locally stable. But it is not easy to nucleate: the conventional entangled state is also locally stable. We propose that slippage occurs on solid walls: either at the container surface, or on dust particles floating in the melt. Slippage at solid/melt interfaces was studied (experimentally and theoretically) long ago. There is a critical stress sigma* for slippage: our estimate (for strong adsorption of melt chains on the solid) gives sigma* approximately 1/3 (plateau modulus) for typical cases. Thus, melt fracture is expected at moderate stresses, in agreement with observations by S.Q. Wang and coworkers.

Collective neuronal growth and self organization of axons.

I describe an assembly of neurons that synthesizes a chemorepellant molecule and transfers this molecule to the growth cones by axonal transport. From the growth cone, the repellant diffuses in nearby regions, achieving a certain concentration profile, delta, with a gradient. The growth cone migrates preferentially toward the regions of low delta. I show that this process self-consistently generates a profile of finite width, with a relatively sharp front of neuronal growth.

Motions induced by asymmetric vibrations. The solid/solid case.

We discuss theoretically the motions of a coin on a horizontally vibrating plate, with dry friction between the coin and the plate. As first noticed by Daniel and Chaudhury in a different situation (droplets on a plate), when the periodic acceleration gamma(t) imposed by the plate is unsymmetrical, the coin can move macroscopically with a certain drift velocity V. We analyse here: (a) the vibration threshold below which V=0, and the generic behavior expected just above threshold; (b) the limiting behavior at very high amplitudes, where V should become independent of the amplitude; (c) the complications due to small, macroscopic inhomogeneities on the supporting plate.

Semiflexible polymers confined in soft tubes.

We discuss various conformations for a polymer (of persistent length l(p)) confined into a deformable tube (the wall being a lipid bilayer with a certain surface tension sigma and curvature energy K). Our study assumes that there is no adsorption of the chain on the wall. Three states are compared: (a) an unperturbed tube, plus a confined chain, (b) a tube swollen in all the region surrounding the chain (similar to a snake eating a sausage), (c) a globule, a roughly spherical coil surrounded by a strongly deformed tube. We construct a (qualitative) phase diagram for these systems with two variables: the surface tension sigma and the degree of polymerization N. Our main conclusion is that "globules" usually win over "snakes".

Vibration-actuated drop motion on surfaces for batch microfluidic processes.

When a liquid drop is subjected to an asymmetric lateral vibration on a nonwettable surface, a net inertial force acting on the drop causes it to move. The direction and velocity of the drop motion are related to the shape, frequency, and amplitude of vibration, as well as the natural harmonics of the drop oscillation. Aqueous drops can be propelled through fluidic networks connecting various unit operations in order to carry out batch processing at the miniature scale. We illustrate the integration of several unit operations on a chip: drop transport, mixing, and thermal cycling, which are precursor steps to carrying out advanced biological processes at microscale, including cell sorting, polymerase chain reaction, and DNA hybridization.

Wetting fibers with liposomes.

Giant unilamellar vesicles (GUVs) are deposited on glass microfibers. The vesicles adopt the classical "onduloidal" shape of liquid droplets on fibers. They spread by two simultaneous mechanisms: envelopment and emission of a precursor film. This film spreads faster than on a uniform plane surface and eventually stops, signaling the presence of defects on the rod. This fast spreading tenses the vesicles; transient pores open on the GUVs and the internal liquid leaks out. This process leads to a new technique for fiber coating.

Organization of a primitive memory: olfaction.

I present a tentative, and schematic, picture of the olfaction storage system in early mammalians: (i) how the excitation trains from the olfactory bulb excite selectively N types of cells in the piriform cortex and (ii) how these cells transfer their information to a storage area. Simple size and connectivity requirements impose that each odor is stored in a very small cluster of approximately 3 neurons. This surprising result holds even if the model parameters are strongly altered (e.g., if N = 10(3) rather than 10(2)).

Chemotaxis: the role of internal delays.

When exposed to certain chemoattractants, bacteria like Escherichia coli move up the concentration gradient[Delta inverted]c with a velocity kappa[delta inverted]c. Microscopically, E. coli moves at constant speed when it's flagellum is rotating counter-clockwise (ccw) and tumbles when the rotation is clockwise (cw). The lifetime of a ccw interval, tau+, is a function of the concentration c( t') experienced at earlier times. The corresponding response function was measured long ago by Berg and co-workers. We present here a detailed description of the motion taking place during one ccw interval. This gives an explicit formula relating the chemotactic coefficient kappa to the response function; the formula has some surprising features.

Frustrated rotations in nematic monolayers.

Tabe and Yokoyama found recently that the optical axis in a chiral monolayer of a ferronematic rotates when water evaporates from the bath: the chiral molecules act as propellers. When the axis is blocked at the lateral walls of the trough, the accumulated rotation inside creates huge splays and bends. We discuss the relaxation of these tensions, assuming that a single dust particle nucleates disclination pairs. For the simplest geometry, we then predict a long delay time followed by a non-periodic sequence of "bursts". These ideas are checked by numerical simulations.

Dewetting of thin polymer films near the glass transition.

Dewetting of ultrathin polymer films near the glass transition exhibits unexpected front morphologies [G. Reiter, Phys. Rev. Lett. 87, 186101 (2001)]. Here, we present the first theoretical attempt to understand these features, focusing on the shear-thinning behavior of these films. We analyze the profile of the dewetting film, and characterize the time evolution of the dry region radius, R(d)(t), and of the rim height, h(m)(t). After a transient time, depending on the initial thickness, h(m)(t) grows like square root[t] while R(d)(t) increases like exp(square root[t]). Different regimes of growth are expected, depending on the initial film thickness and experimental time range.

Dewetting of thin-film polymers.

In this paper we present a theoretical model for the dewetting of ultrathin polymer films. Assuming that the shear-thinning properties of these films can be described by a Cross-type constitutive equation, we analyze the front morphology of the dewetting film, and characterize the time evolution of the dry region radius, and of the rim height. Different regimes of growth are expected, depending on the initial film thickness, and on the power-law index involved in the constitutive equation. In the thin-films regime, the dry radius and the rim height obey power-law time dependences. We then compare our predictions with the experimental results obtained by Debrégeas et al. [Phys. Rev. Lett. 75, 3886 (1995)] and by Reiter [Phys. Rev. Lett. 87, 186101 (2001)].

Passive entry of a DNA molecule into a small pore.

I consider a vesicle with an open pore of small radius rp, exposed to a DNA solution. The crucial moment is the entry, when a chain end faces the pore and enters it. I discuss qualitatively the following three characteristic times: (i) the duration of the entry of one chain end (defining the minimum lifetime of the pore) taue approximately 10(-4) sec, (ii) the transfection time taut (the time required to be sure that one chain has gone in) taut approximately hours, and (iii) the sliding time tauS (the time between entry of one end and entry of the other end) approximately 1 sec. A fortunate feature is that sliding may proceed even if the pore tends to close itself after entry.

Thick surface flows of granular materials: effect of the velocity profile on the avalanche amplitude.

A few years ago, Bouchaud et al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. I 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion or accretion mechanism. Boutreux et al. [Phys. Rev. E 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. In this article, we therefore modify the above models by introducing a velocity profile in the flow, and study the physical consequences of this modification in the simple situation of an avalanche in an open cell. We present a complete analytical description of the avalanche in the case of a linear velocity profile, and generalize the results for a power-law dependency. We show, in particular, that the amplitude of the avalanche is strongly affected by the velocity profile.