Vidar Frette

Pearling Instabilities of Membrane Tubes with Anchored Polymers

We have studied the pearling instability induced on hollow tubular lipid vesicles by hydrophilic polymers with hydrophobic side groups along the backbone. The results show that the polymer concentration is coupled to local membrane curvature. The relaxation of a pearled tube is characterized by two different well-separated time scales, indicating two physical mechanisms. We present a model, which explains the observed phenomena and predicts polymer segregation according to local membrane curvature at late stages.

TRACER DISPERSION IN A SELF-ORGANIZED CRITICAL SYSTEM

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette et al., Nature (London) 379, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a 1D cellular automaton modeling the experiment.

Coiling of Cylindrical Membrane Stacks with Anchored Polymers

(Received 22 April 1999) We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer concentration. Indeed, only maximally tight coils are observed experimentally. Our system is unique in that coils form in the absence of twist and adhesion. The coil motif is ubiquitous in a wide range of natural contexts. One-dimensional filaments of mutant bacteria [1], supercoiled DNA molecules [2], and tendrils of climbing plants [3] all exhibit a writhing instability as a result of forcing or interaction with an external agent. Such systems are dominated by elastic properties, and the appearance of coils is a result of the relief of twist. In this paper we show that coiling can also be effected in cylindrical multilamellar tubes of phospholipid bilayers, by anchoring hydrophilic polymers with hydrophobic side groups grafted along the backbone. This system is unique in that, in contrast with the above examples, fluid membranes cannot support any twist. Yet coils are

Gradient stabilized and destabilized invasion percolation

The effects of gravity stabilization and destabilization on the slow displacement of a wetting fluid by a non-wetting fluid in two-dimensional and three-dimensional porous media have been investigated experimentally. The characteristic features of the resulting displacement patterns can be reproduced quite well by invasion percolation models with a spatial gradient added to the usual random threshold distribution. In the case of destabilized displacement the patterns can be described in terms of a string of blobs of size ξ that form a directed walk. The internal structure of the blobs is like that of an invasion percolation cluster (with trapping in the two-dimensional case). In the stabilized case the structure is like that of a fractal invasion percolation cluster on short length scales (lengths ⪡ξ) and is uniform on longer lengths. The correlation length (ξ) also describes the maximum hole diameter. The invasion front is a self-similar fractal on length scales shorter than ξ and flat on longer length scales. In both the experiments and the simulations the correlation length ξ is related to the Bond number (B0, the ratio between buoyancy and capillary forces) by ξ ∼ |B0|−ʋ(ʋ+1) where ʋ is the ordinary percolation correlation length exponent) in accord with the theoretical arguments of Wilkinson (Phys. Rev. A 30 (1984) 520; 34 (1986) 1380).

Construction of a DLA cluster model

On the occasion of the 50th birthday of a distinguished colleague, a three-dimensional wood model of a computer-generated DLA cluster was built. In this paper the design of the model and the construction process are described. The experiment may be carried out in the framework of a classroom experiment to demonstrate some of the fundamental concepts used in current research on growth phenomena. It is suitable as a first introduction to fractal geometry. Zusammenfassung. Anlaslich des 50sten Geburtstag eines bedeutenden Kollegen wurde ein dreidimensionales Holzmodell eines computererzeugten DLA-Clusters gebaut. Hier beschreiben wir die Entwickelung des Modells und den Konstruktionsprozess. Das Experiment kann im Rahmen eines Klassenzimmerexperiments durchgefuhrt werden um einige der fundamentalen Konzepte innerhalb der aktuellen Forschung auf dem Gebiet der Wachstumsphanomene zu demonstrieren. Es eignet sich als eine erste Einfuhrung in die fraktale Geometrie.

Fractal Structures in Secondary Migration

Secondary migration is the process by which hydrocarbons are transported from mature source rocks through water-saturated rocks, faults or fractures and become concentrated as trapped accumulations of oil and gas. The forces governing secondary migration of hydrocarbons are buoyancy and capillarity (Schowalter, 1979). Experimental data suggest that the secondary migration of oil in porous, permeable sediments takes place along restricted pathways or conduits (Dembicki and Anderson, 1989). These conduits are formed after the oil has penetrated far enough into the reservior rock for the bouyancy forces acting on the oil to overcome the capillary pressure in the pore throats. Long-range petroleum migration of the order of 100 km in the horizontal direction and about 2 km in the vertical direction is not uncommon (England et al., 1987).

FRACTALS AND SECONDARY MIGRATION

The process of secondary migration, in which oil and gas are transported from the source rocks, through water saturated sedimentary carrier rocks, to a trap or reservoir can be described in terms of the gravity driven penetration of a low-density non-wetting fluid through a porous medium saturated with a wetting fluid. This process has been modeled in the laboratory and by computer simulations using homogeneous porous media. Under these conditions, the pattern formed by the migrating fluid can be described in terms of a string of fractal blobs. The low density internal structure of the fractal blobs and the concentration of the transport process onto the self-affine strings of blobs (migration channels) both contribute to the small effective hydrocarbon saturation in the carrier rocks. This allows the hydrocarbon fluids to penetrate the enormous volume of carrier rock without all of the hydrocarbon being trapped in immobile isolated bubbles. In practice, heterogeneities in the carrier rocks play an important role. In some cases, these heterogeneities can be represented by fractal models and these fractal heterogeneity models provide a basis for more realistic simulations of secondary migration. Fractures may play a particularly important role and migration along open fractures was simulated using a self-affine fractal model for the fluctuating fracture aperture.

Queues on narrow roads and in airplanes

We consider N particles with unidirectional motion in one dimension. The particles never pass each other, and they are distinguishable (labelled). We have studied two types of particle interactions, both of which lead to queue formation due to bottlenecks. There are variations in queue structure from particle scale up to system size. We are interested in quantities obtained after averaging over all N! permutations of particles.

Analysis of ship maneuvering data from simulators

We analyze complex manuevering histories of ships obtained from training sessions on bridge simulators. Advanced ships are used in fields like offshore oil exploration: dive support vessels, supply vessels, anchor handling vessels, tugs, cable layers, and multi‐purpose vessels. Due to high demands from the operations carried out, these ships need to have very high maneuverability. This is achieved through a propulsion system with several thrusters, water jets, and rudders in addition to standard propellers. For some operations, like subsea maintenance, it is crucial that the ship accurately keeps a fixed position. Therefore, bridge systems usually incorporate equipment for Dynamic Positioning (DP). DP is a method to keep ships and semi submersible rigs in a fixed position using the propulsion systems instead of anchors. It may also be used for sailing a vessel from one position to another along a predefined route. Like an autopilot on an airplane, DP may operate without human involvement. The method relie...

The average velocity in a queue

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean value calculation. Approximate and exact results are obtained using sampling, enumeration and calculations. The geometrical nature of the problem as well as the separate levels of averaging involved are emphasized. Further problems suitable for exploration in student projects are outlined.