Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.     

Maturation of auditory temporal integration and inhibition assessed with event-related potentials (ERPs)

Background

We examined development of auditory temporal integration and inhibition by assessing electrophysiological responses to tone pairs separated by interstimulus intervals (ISIs) of 25, 50, 100, 200, 400, and 800 ms in 28 children aged 7 to 9 years, and 15 adults.

Results

In adults a distinct neural response was elicited to tones presented at ISIs of 25 ms or longer, whereas in children this was only seen in response to tones presented at ISIs above 100 ms. In adults, late N1 amplitude was larger for the second tone of the tone pair when separated by ISIs as short as 100 ms, consistent with the perceptual integration of successive stimuli within the temporal window of integration. In contrast, children showed enhanced negativity only when tone pairs were separated by ISIs of 200 ms. In children, the amplitude of the P1 component was attenuated at ISIs below 200 ms, consistent with a refractory process.

Conclusions

These results indicate that adults integrate sequential auditory information into smaller temporal segments than children. These results suggest that there are marked maturational changes from childhood to adulthood in the perceptual processes underpinning the grouping of incoming auditory sensory information, and that electrophysiological measures provide a sensitive, non-invasive method allowing further examination of these changes.     

Coexistence of two colloidal crystals at the nematic-liquid-crystal-air interface

Glycerol droplets at a nematic-liquid-crystal-air interface form two different lattices--hexagonal and dense quasihexagonal--which are separated by the energy barrier and can coexist. Director distortions around each droplet form an elastic dipole. The first order transition between the two lattices is driven by a reduction of the dipole-dipole repulsion through reorientation of these dipoles. The elastic-capillary attraction is essential for the both lattices. The effect has a many-body origin.     

Kinetic energy of flexible aggregates and universal power-law behavior of self-assembling in a thermal bath

I am drawing the readers’ attention to the importance of the kinetic energy contribution which has been systematically ignored in the partition functions of worm-like objects in a thermal bath. The kinetic energy of linear aggregates is shown to play a unique role when they are reversibly assembled from solute molecules in a solvent. The kinetic energy contribution to the partition function of an n-mer is modeled by the term n ^q , where q is determined by the persistence lengths of different translation-rotation modes (e.g., q = 5 for a rigid rod and q ≈ 0 for a very flexible chain). The model gives rise to different aggregation regimes for lower and higher solute concentration. The concentrations of different n-mers and total aggregate concentration, which is the main order parameter of the system, are found to depend on the solute concentration via its powers that are different in different regimes, but are always determined solely by the parameter q. The approximate analytical and numerical solutions of the model are in quantitative agreement and clearly show the universal power-law q dependencies. At the same time, it is imposible to express the exact analytical solution in a simple form. The model is pertinent to self-assemblies of plank-like dye molecules dissolved in an isotropic solvent (related to lyotropic chromonic liquid crystals).     

Aggregation of Anthraquinone Dye Molecules in a Nematic Liquid Crystal

We report an experimental evidence that molecules of anthraquinone dye aggregate in an anisotropic solvent, a nematic liquid crystal (NLC). We observe strong nonlinear dependencies of the dielectric permittivity and anisotropy of light absorption on the dye concentration c. Moreover, the data suggest that the aggregates are linear, but, in contrast to the isotropic case, their formation in a NLC undergoes two different concentration regimes with a well pronounced crossover. These effects are explained by the interplay between the aggregates’ lengths and their orientational ordering due to the interaction with the nematic director.