Fredericks transitions in biaxial nematics.

Much of our understanding (and applications) of biaxial nematic liquid crystals requires the study of the textural transformations in external electric or magnetic fields. To that end, one should employ theoretical approaches which could have bearing on the minimization problem of the multi-parametric free energy. The immediate shortcoming of the direct free-energy minimization (widely used for uniaxial nematics) is the need to resolve several non-linear constraints. To overcome this difficulty, in what follows we shall use the "angular velocity", which describes space rotations of the order parameter, and is in fact a vector internal curvature of the texture. This method provides a means to resolve the constraints imposed on the order parameter. Thus, we have obtained the set of equations to find all possible one-dimensional textures of biaxial nematics in the external field. To illustrate our method, we calculate the critical fields corresponding to some basic configurations for textural transitions in the biaxial nematics. We feel that this result could be useful to determine the intrinsic degree of biaxiality for liquid crystalline materials.

Twisted quasiperiodic textures of biaxial nematic liquid crystals.

Textures (i.e., smooth space nonuniform distributions of the order parameter) in biaxial nematics turned out to be much more complex and interesting than expected. Scanning the literature we find only a very few publications on this topic. Thus, the immediate motivation of the present paper is to develop a systematic procedure to study, classify, and visualize possible textures in biaxial nematics. Based on the elastic energy of a biaxial nematic (written in the most simple form that involves the least number of phenomenological parameters) we derive and solve numerically the Lagrange equations of the first kind. It allows one to visualize the solutions and offers a deep insight into their geometrical and topological features. Performing Fourier analysis we find some particular textures possessing two or more characteristic space periods (we term such solutions quasiperiodic ones because the periods are not necessarily commensurate). The problem is not only of intellectual interest but also of relevance to optical characteristics of the liquid-crystalline textures.

Acoustic spectroscopy of DNA in the gigahertz range.

We find a parametric resonance in the gigahertz range of DNA dynamics, generated by pumping hypersound. The resonance may be accompanied by the formation of localized phonon modes due to the random structure of elastic modulii of DNA.

Symmetry of electrostatic interaction between pyrophosphate DNA molecules.

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.

Harmonic oscillators in the Nosé-Hoover environment.

We study the dynamics of an ensemble of noninteracting harmonic oscillators in a nonlinear dissipative environment described by the Nosé-Hoover model, and find the histogram for energy regions of phase space against visiting time by employing numerical simulation. The results agree with the analysis of the Nosé-Hoover equations effected with the method of averaging for small values of the dissipative parameter alpha of the thermostat. We find oscillations at frequencies proportional to sqrt[alpha/m ], m being the characteristic mass of the particle, about the stationary state corresponding to equilibrium, for sufficiently small alpha . In this region of alpha the histogram does not correspond to Gibbs' canonical distribution. For larger values of alpha the motion becomes irregular. The phenomena could have an important bearing upon simulating molecular dynamics in the Nosé-Hoover thermostat.

[Dynamic attractor for the Berendsen thermostat an the slow dynamics of biomacromolecules]. / Dinamicheskii attraktor v termostate Berendsena i medlennaia dinamika biomakromolekul.

It was shown that the nonlinear relaxation of a model system confined to the Berendsen's thermostat is determined by an attractor regime. The latter does not correspond generally to the true thermodynamic state of the system. Therefore, the use of the Berendsen's thermostat for molecular dynamics simulations, even in the case of large protein molecules at trajectory lengths of more than 10 ns, can lead to wrong conclusions. Our results agree with the concept of slow dynamics for macroscopic systems considered within the framework of the topological approach to stochastic dynamics.

Novel Cholesteric Phase in Dispersions of Nucleic Acids due to Polymeric Chelate Bridges.

Physics, Moscow, RussiaWe consider cholesteric liquid-crystalline DNA dispersions, and show thatpolymeric (Dau-Cu) complexes, the so-called bridges, between pairs of DNA molecules may generate a super liquid-crystalline structure (BR-phase), charachterized by a soliton lattice of the spatial distribution of theorder parameter. The BR-phase could have a layered spatial structure andan abnormal optical activity that could have a bearing upon the intenseCD-band observed in DNA-dispersions.

["Phantom" structure of solvents and packing of dual-chain nucleic acid molecules in liquid crystal dispersion particles]. / "Fantomnaia" struktura rastvoritelia i upakovka dvukhtsepochechnykh molekul nukleinovykh kislot v chastitsakh zhidkokristallicheskikh dispersii.

The properties of mesomorphic dispersions of double-stranded nucleic acids were studied. A comparison of these properties indicates that their diversity cannot be explained unambiguously in terms of the conception of Van-der-Waals interactions in particles of mesomorphic dispersions without regard for the specific properties of the solvent, water, in the vicinity of adjacent nucleic acid molecules. It was assumed that, with small distances between the molecules of nucleic acids, a specific "phantom" structure of the solvent appears in their vicinity, which acts as an elastic medium that modifies the interactions between nucleic acid molecules and as a medium in which a collective tunneling of protons can occur. The combination of the two effects determines the "recognition" of nucliec acid molecules and the stabilization of the cholesteric structure of mesomorphic dispersions of nucleic acids.

Toroidal structures due to anisotropy of DNA-like molecules.

We suggest that toroidal structures in the state of psi-condensation of DNA may be caused by anisotropy on a meso-scale of several thousand A, the conformation of a DNA-molecule being determined by its elasticity and neutralization of phosphate charge. We model a molecule of B-DNA on an anisotropic elastic rod subject to a torque, and make the numerical simulation of the model that reveals that under appropriate conditions, which may be effected in experimental setting by changing the concentration of polymeric solutions, there are toroidal structures having the size of a few persistence lengths, in agreement with the experimental data. On changing the elastic modulii or characteristics of the counterion layer, we see the toroidal structures turn into the spherical ones. To understand the function of anisotropy it would be interesting to investigate the Z-DNA as regards psi-condensation.