Dislocations in uniaxial lamellar phases of liquid crystals, polymers and amphiphilic systems

Dislocations in soft condensed matter systems such as lamellar systems of polymers, liquid crystals and ternary mixtures of oil, water and surfactant (amphiphilic systems) are described in the framework of continuum elastic theory. These systems are the subject of studies of physics, chemistry and biology. They also find applications in the industry. Here we will discuss in detail the influence of dislocations on the bulk and surface properties of these lamellar phases. Especially the latter properties have only been recently studied in detail. We will present the experimental evidence of the existence of screw and edge dislocations in the systems and study their static properties such as: energy, line tension and core structure. Next we will show how does the surface influence the equilibrium position of dislocations in the system. We will give the theoretical predictions and present the experimental results on thin copolymer films, free standing films of liquid crystals and smectic droplets shapes. The surface is deformed by dislocations. These deformations are known as edge profiles. Surface deformations induce elastic interactions between edge dislocations. A new phenonenon discussed in our paper is the fluctuations induced interactions between edge dislocations.At suitable conditions edge dislocations can undergo an unbinding transition. Also a single dislocation loop in a smectic freely suspended film can undergo an unbinding transition. We shall also compute the equilibrium size of the loop contained between two hard walls. Finally we will discuss the dynamical bulk properties of dislocations such as: mobility (climb and glide),permeation, and helical instability of screw dislocations. Lubrication theory will also be discussed.Comment: plain TeX, 65 pages, review for International Journal of Modern Physics

Influence of the electric field on edge dislocations in smectics

The electric field applied perpendicularly to smectic layers breaks the rotational symmetry of the system. Consequently, the elastic energy associated with distortions induced by an edge dislocation diverges logarithmically with the size of the system. In freely suspended smectic films the dislocations in the absence of the electric field are located exactly in the middle of the film. The electric field above a certain critical value can shift them towards the surface. This critical field squared is a linear function of the surface tension and is inversly proportional to the thickness of the film. The equilibrium location of a dislocation in the smectic film subjected to the field is also calculated.Comment: Tex, 13 pages, submitted to J. de Physique II. (permanent e-mail address: [email protected]

Scaling of internode distances in weighted complex networks

We extend the previously observed scaling equation connecting the internode distances and nodes' degrees onto the case of weighted networks. We show that the scaling takes a similar form in the empirical data obtained from networks characterized by different relations between node's strength and its degree. In the case of explicit equation for s(k) (e.g. linear or scale-free), the new coefficients of scaling equation can be easily obtained. We support our analysis with numerical simulations for Erdos-Renyi random graphs with different weight distributions.Comment: 9 pages, 4 figures, submitted to International Journal of Modern Physics

Growing trees in Internet news groups and forums

We present an empirical study of the networks created by users within internet news groups and forums and show that they organ- ise themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. For news groups we find that the distribu- tion of the time intervals between when a message is posted and when it receives a response exhibits a composite power-law behaviour. From our statistics we can see if the news group or forum is free or is overseen by a moderator. The correlation function of activity, the number of messages posted in a given time, shows long range correlations connected with the users’ daily routines. The distribution of distances between each message and its root is exponential for most news groups and power-law for the fo- rums. For both formats we find that the relation between the supremacy ( the total number of nodes that are under the node i, including node i) and the degree is linear s(k) k, in contrast to the analytical relation for Barab´asi-Albert network

Anomalous oscillations of average transient lifetimes near crises

It is common that the average length of chaotic transients appearing as a consequence of crises in dynamical systems obeys a power low of scaling with the distance from the crisis point. It is, however, only a rough trend; in some cases considerable oscillations can be superimposed on it. In this letter we report anomalous oscillations due to the intertwined structure of basins of attraction. We also present a simple geometrical model that gives an estimate of the period and amplitude of these oscillations. The results obtained within the model coincide with those yielded by computer simulations of a kicked spin model and the Henon map.Comment: 5 pages, 4 figure

From the Plateau problem to periodic minimal surfaces in lipids, surfactants and diblock copolymers

We present the novel method for generation of periodic surfaces based on the simple Landau-Ginzburg model of microemulsion. We test the method on four minimal surfaces (P,D,G, and I-WP), find two new surfaces of cubic symmetry, show how to obtain periodic surfaces of high genus and n-tuply-continuous phases. We point that the Landau model used here should be generic for all systems characterized by internal interfaces, including the diblock copolymer systems.Comment: 15 pages, Plain TeX , figures available on request or at http://saka.ichf.edu.pl/WTGRH/surfaces.htm