Dislike of general opinion makes for tight elections.

In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large collections of diverse individuals. Many sociophysics models reproduce the emergence of collective human behavior with interacting agents, which respond to their environment according to simple rules, modulated by random fluctuations. A paragon of this class is the Ising model which, when interactions are strong, predicts that order can emerge from a chaotic initial state. In contrast with many elections, however, this model favors a strong majority. Here we introduce a new element to this classical theory, which accounts for the influence of opinion polls on the electorate. This brings about a new phase in which two groups divide the opinion equally. These political camps are spatially segregated, and the sharp boundary that separates them makes the system size dependent, even in the limit of a large electorate. Election data show that, since the early 1990s, countries with more than about a million voters often found themselves in this state, whereas elections in smaller countries yielded more consensual results. We suggest that this transition hinges on the electorate's awareness of the general opinion.

Laplacian networks: Growth, local symmetry, and shape optimization.

Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how this formalism reduces the network's expansion to three rules, which respectively govern the velocity, the direction, and the nucleation of its growing branches. This framework allows us to establish the mathematical equivalence between three formulations of the direction rule, namely geodesic growth, growth that maintains local symmetry, and growth that maximizes flux into tips for a given amount of growth. Surprisingly, we find that this growth rule may result in a network different from the static configuration that optimizes flux into tips.

Stabilizing effect of knots on proteins.

Molecular dynamics studies within a coarse-grained, structure-based model were used on two similar proteins belonging to the transcarbamylase family to probe the effects of the knot in the native structure of a protein. The first protein, N-acetylornithine transcarbamylase, contains no knot, whereas human ormithine transcarbamylase contains a trefoil knot located deep within the sequence. In addition, we also analyzed a modified transferase with the knot removed by the appropriate change of a knot-making crossing of the protein chain. The studies of thermally and mechanically induced unfolding processes suggest a larger intrinsic stability of the protein with the knot.

Fingered growth in channel geometry: a Loewner-equation approach.

A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. Following Carleson and Makarov [L. Carleson and N. Makarov, J. Anal. Math. 87, 103 (2002)], the evolution of the fingers is studied with use of the deterministic Loewner equation. The method is then extended to study the growth in a linear channel with reflecting sidewalls. One- and two-finger solutions are found and analyzed. It turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.

Tightening of knots in proteins.

We perform theoretical studies of stretching of 20 proteins with knots within a coarse-grained model. The knot's ends are found to jump to well defined sequential locations that are associated with sharp turns, whereas in homopolymers they diffuse around and eventually slide off. The waiting times of the jumps are increasingly stochastic as the temperature is raised. Knots typically do not return to their native locations when a protein is released after stretching.

Proteins in a shear flow.

The conformational dynamics of a single protein molecule in a shear flow is investigated using Brownian dynamics simulations. A structure-based coarse grained model of a protein is used. We consider two proteins, ubiquitin and integrin, and find that at moderate shear rates they unfold through a sequence of metastable states-a pattern which is distinct from a smooth unraveling found in homopolymers. Full unfolding occurs only at very large shear rates. Furthermore, the hydrodynamic interactions between the amino acids are shown to hinder the shear flow unfolding. The characteristics of the unfolding process depend on whether a protein is anchored or not, and if it is, on the choice of an anchoring point.

Stretching of proteins in a uniform flow.

Stretching of a protein by a fluid flow is compared to that in a force-clamp apparatus. The comparison is made within a simple topology-based dynamical model of a protein in which the effects of the flow are implemented using Langevin dynamics. We demonstrate that unfolding induced by a uniform flow shows a richer behavior than that in the force clamp. The dynamics of unfolding is found to depend strongly on the selection of the amino acid, usually one of the termini, which is anchored. These features offer potentially wider diagnostic tools to investigate structure of proteins compared to experiments based on the atomic force microscopy.

Protein folding in a force clamp.

Kinetics of folding of a protein held in a force clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations in the end-to-end distance reflect microscopic events during folding. However, the folding scenarios in and out of the force clamp are distinct.

Memory effects in collective dynamics of Brownian suspensions.

We obtain macroscopic equations for average suspension velocity and particle current in a Brownian suspension valid on long time scales for which the memory effects are important. The coefficients in these equations depend solely on local properties of the medium. This formalism allows one to obtain well-defined theoretical expressions for transport coefficients, free of the integrals diverging with the size of the system. As an example, the expression for long-time collective diffusion coefficient is derived and the memory contribution to this coefficient is estimated.

Stochastic boundary conditions to the convection-diffusion equation including chemical reactions at solid surfaces.

Simulations of heat and mass transport may require complex nonlinear boundary conditions to describe the flow of mass and energy across an interface. Although stochastic methods do not suffer from the numerical diffusion of grid-based methods, they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce ideas and algorithms to account for mass (or energy) transfer at reactive interfaces, with accuracies comparable to the bulk phase. We show how to introduce particles into the system with the correct distribution near the interface, as well as the correct flux through the interface. The algorithms have been tested in a channel flow, for which accurate numerical solutions can be independently calculated.

Boundary conditions for stochastic solutions of the convection-diffusion equation.

Stochastic methods offer an attractively simple solution to complex transport-controlled problems, and have a wide range of physical, chemical, and biological applications. Stochastic methods do not suffer from the numerical diffusion that plagues grid-based methods, but they typically lose accuracy in the vicinity of interfacial boundaries. In this work we introduce some ideas and algorithms that can be used to implement boundary conditions in stochastic simulations of the convection-diffusion equation with accuracies comparable to the bulk phase. The algorithms have been tested in two-dimensional channel flows over a range of Peclet numbers, and compared with independent finite-difference calculations.

Nebulized heparin and anabolic steroid in the prevention of postoperative deep vein thrombosis following elective abdominal surgery.

One hundred eighty three patients, all over 40 years old, who underwent major abdominal surgery, were randomized into 3 groups: Group I received a single dose of nebulized heparin (800 IU per kg b.w.) administered by inhalation one day prior to surgery. Group II besides the above, also received a single injection of 50 mg of long acting anabolic steroid (nandrolone phenylpropionate) intramuscularly. Group III received 5000 IU heparin subcutaneously on hr prior to surgery as well as every 12 h for the next 5 postoperative days. Postoperatively the patients were evaluated for deep vein thrombosis (DVT) using the 125-I-fibrinogen test. The occurrence of DVT was determined as: in Group I--16%, in Group II--7.9%, in Group III--7.8%. Haemorrhagic complications (clinically important) were observed in 7.8% of patients from Group III, but only in 1.7% of patients in Group I and 1.6% in Group II. For DVT prophylaxis following abdominal surgery a single application of nebulized heparin and long acting anabolic steroid is as effective as conventional low-dose subcutaneous heparin administration, but gives less haemorrhagic complications. This method is also more advantagenous in term of acceptance by the patients and represents considerable saving of nursing time.