Dynamics of kinks in biological membranes

kinks created in a biological membrane by the interaction with a movable bead. We arrive at the evolution equations for both the bead and the membrane, whence we conclude that the force exerted on the bead by a fixed membrane points in the direction along which the curvature of the membrane is more concentrated. This is the first step towards understanding the basic mechanism behind the dynamics of protein aggregation which takes place on biological membranes. Received November 6, 2001 / Published online February 4, 2002     

Nucleation of Topological Dipoles¶in Nematic Liquid Crystals

A topological dipole is a pair of point defects with opposite topological charges. In this paper we show by example how the nucleation of such a dipole within a smooth field can drive a metastable state into a stable one. Building on our previous work, we construct a mathematical model for the dynamics of both monopoles and dipoles in a capillary filled with a nematic liquid crystal. Though our analysis is fit for liquid crystals, a similar mechanism is also likely to apply to the field theory for other ordered media. Received: 10 July 1997 / Accepted: 25 June 1998     

Theoretical and experimental study of the nanoparticle-driven blue phase stabilisation

We have studied theoretically and experimentally the effects of various types of nanoparticles (NPs) on the temperature stability range [Formula: see text] T (BP) of liquid-crystalline (LC) blue phases. Using a mesoscopic Landau-de Gennes type approach we obtain that the defect core replacement (DCR) mechanism yields in the diluted regime [Formula: see text] T (BP)(x) [Formula: see text] 1/(1 - xb) , where x stands for the concentration of NPs and b is a constant. Our calculations suggest that the DCR mechanism is efficient if a local NP environment resembles the core structure of disclinations, which represent the characteristic property of BP structures. These predictions are in line with high-resolution ac calorimetry and optical polarising microscopy experiments using the CE8 LC and CdSe or aerosil NPs. In mixtures with CdSe NPs of 3.5nm diameter and hydrophobic coating the BPIII stability range has been extended up to 20K. On the contrary, the effect of aerosil silica nanoparticles of 7.0nm diameter and hydrophilic coating is very weak.     

A Practical Application of Ultrasonic Thermal Stress Monitoring in Continuous Welded Rails

A methodology designed to monitor thermally induced loads on continuous welded rails (CWR) is presented. The technique is based on the use of sub-surface longitudinal ultrasonic waves (l.c.r. waves) and, by means of a daily data elaboration, allows to obtain the value of the neutral temperature of the rail as a function of time. From such information an estimation of longitudinal stresses, to be used as a reference, can be derived. The methodology here presented has undergone a 2 years testing period, through the instrumentation of about 3 km of railway track. All acquired data have been remotely processed in a single control station.     

Constrained stability for biaxial nematic phases

We study the invariance properties of the molecular Hamiltonian interaction put forward by Straley to describe biaxial nematic phases. We show that the reduction to two out of four scalar order parameters, which was accidently remarked upon in the literature, is indeed a rigorous consequence of the Hamiltonian invariance for specific values of the interaction parameters. The stability analysis of the mean-field free energy in the reduction classes for the order parameters reveals a sequence of Landau triple points.     

Cavity Volume and Free Energy in Many-Body Systems

Most models for the spread of an invasive species into a new environment are based on Fisher’s reaction–diffusion equation. They assume that habitat quality is independent of the presence or absence of the invading population. Ecosystem engineers are species that modify their environment to make it (more) suitable for them. A potentially more appropriate modeling approach for such an invasive species is to adapt the well-known Stefan problem of melting ice. Ahead of the front, the habitat is unsuitable for the species (the ice); behind the front, the habitat is suitable (the open water). The engineering action of the population moves the boundary ahead (the melting). This approach leads to a free boundary problem. In this paper, we study the well-posedness of a novel free boundary model for the spread of ecosystem engineers that was recently derived from an individual random walk model. The Stefan condition for the moving boundary is replaced by a biologically derived two-sided condition that models the movement behavior of individuals at the boundary as well as the process by which the population moves the boundary to expand their territory. Our proofs consist of several new and novel ideas that can be used in broader contexts. We assign a convex functional to this problem so that the evolution system governed by this convex potential is exactly the system of evolution equations describing the above model. We then apply variational and fixed-point methods to deal with this free boundary problem.

     

Exact Statics and Approximate Dynamics of Adhering Lipid Tubules

In this paper we are concerned with the adhesion of lipid tubules to a plane wall: we treat both the statics and the dynamics of this phenomenon. Though we provide an exact solution to the equilibrium problem, our treatment of the dynamical problem is approximate, as it is based on a simplified model, which, nevertheless allows us to obtain quantitative information about the detachment dynamics of tubules. Received September 1, 1997     

Adhesion by Curvature of Lipid Tubules

The adhesion of lipid tubules to a rigid wall is governed by an equilibrium condition that holds at the detachment points, where tubules and wall lose contact. Such an adhesion condition is derived in this paper for the most general elastic energy of the tubule and an arbitrarily curved wall. It also depends on the curvature of the wall, which thus plays a central r?le in determining whether the adhesion of a tubule is possible. This r?le is clearly illustrated by a specific equilibrium problem we solve here: the one where a tubule adheres to a rigid groove, which is modelled as a hollow half-cylinder. Received March 17, 1998