arXiv subjects

V. L. Golo

Publications and source records attributed to V. L. Golo.

17 recordsLinked to original sources

arXiv2013

Topological metastability of textures in biaxial nematics

We consider textures of biaxial nematics confined between two parallel plates. The boundary conformations at the bordering plates are supposed to be identical, the gradients of the order parameter being generally nonzero. We claim that for any texture (including stable uniform order parameter alignment) there exists its counterpart texture which is also a minimum of the gradient elastic energy. Our arguments are based on the topological analysis of the conformation of the order parameter.

cond-mat.soft↗

arXiv2013

Twisted quasiperiodic textures of biaxial nematics

Textures (i.e., smooth space non-uniform distributions of the order parameter) in biaxial nematics turned out to be much more difficult 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.

cond-mat.soft↗

arXiv2012

Localization of water monomers inside ice-like clusters

On the basis of the experimental data we suggest that water monomers could be trapped in channels running through ice-like clusters in water. Our argument relies on a simple model that describes the motion of a dipole particle inside a channel in the presence of an electric field with linear gradient. The model admits of both finite and infinite regimes of motion so that the finite one could correspond to the particle being confined to a channel.

cond-mat.soft↗

arXiv2011

Maxwell viscoelastic dynamics of the DNA in the THz range

The attenuation of phonon modes of the DNA is due to the exchange of water molecules adsorbed by a molecule of DNA and the bulk solvent. Using Maxwell's mechanism of relaxation and a simple lattice model of the DNA, we show that the attenuation tends to a constant value for phonon frequencies larger than the inverse residence time of water molecules. We come to the conclusion that in the THz range the attenuation could be small enough to allow the propagation of the phonon modes.

cond-mat.soft↗

arXiv2009

Hyper-sound as a means for generating inter-strand defects in a duplex of the DNA

The formation of bubble defects of the double stranded DNA is treated according to the Lifshits theory of disordered chains. A molecule of the DNA is modelled on a harmonic lattice with nearest neighbour interaction, elastic constants being randomly distributed. The helicoidal symmetry is accommodated through a chiral field at sites of the lattice. The number of sites varies from 100 to 300, corresponding to DNA segmnets of persistence length. We find the spectra of elastic eigen-modes that mimic inter-strand excitations of the duplex. The frequency distribution shows peaks and valleys at the high-frequency end of the spectra, in accord with the general theory. External excitations may lead to a parametric resonance that can generate localized modes of the lattice. In real life pumping hyper-sound may generate a resonance similar to that studied in this paper, and thus result in excitation of inter-strand modes and possible formation of bubbles, in the duplex of the DNA.

cond-mat.soft↗

arXiv2008

Pyrophosphate Groups in Liquid Crystalline Phases of the DNA

We study electrostatic interaction between molecules of the DNA 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 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 potential $U$. The symmetries form a noncommutative group of 8-th order, ${\cal S}$. Using the group ${\cal S}$ we suggest a classification of liquid crystalline phases of the DNA, which allows of several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the part played by charges in its liquid crystalline phases, and make for experimental research, important for nano-technological and bio-medical applications.

cond-mat.soft↗

arXiv2008

Elastic and Proton Dynamics of the DNA

The subject of this report is the dynamics of elastic system in conjunction with hydrogen bonds of the DNA. We draw attention to the draw-back of the familiar rod model of the DNA, and make a case of constructing models that could accommodate the intrinsic structure of the DNA. In this respect studying the interplay among the elastic system and the protons of the DNA, is of interest, for it could accommodate the inter-strand as well as the tunneling modes of protons. Following this direction, we come to the conclusion that the elastic-proton dynamics may have a bearing on biophysics of the DNA. The phenomenon of point mutations is discussed within this framework.

cond-mat.soft↗

arXiv2005

Asymptotic Hamiltonian reduction for the dynamics of a particle on a surface

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a subsidiary Hamiltonian system that has the form of equations for the top with a 4-th order Hamiltonian, and provides the detailed asymptotic description of the particle's motion in terms of graphs on the standard sphere.

math-ph↗

arXiv2005

Geodetic Coils on Deformed Sphere

We study geodetic lines on a surface generated by a small deformation of the standard 2D-sphere. We construct an auxiliary hamiltonian system with the view of describing geodetic coils and almost closed geodesics, by using the fact that loops of the coil can be well approximated by great circles of the sphere. The phase space of the auxiliary system is determined by the graph generated by separatrixes of its solutions, the vertices of the graph corresponding to almost closed geodesics and the edges to the geodetic coils joining them. Topological types of the graph depend on the parameters determining the deformation. Using the method of averaging in conjunction with the computer modelling of the auxiliary system, we obtain a fairly detailed visualization of geodesics on the deformed sphere.

math.DS↗

arXiv2005

Chaotic Tunneling in a Laser Field

We study the driven tunneling of a one-dimensional charged particle confined to a rectangular double-well. The numerical simulation of the Schrödinger equation based on the Cranck-Nicholson finite-difference scheme, shows that the modulation of the amplitude of the external field may result in the parametric resonance. The latter is accompanied by the breakdown of the quasi-periodic motion characteristic of the usual driven tunneling, and the emergence of an irregular dynamics. We describe the above breakdown with the occupation probability for the ground state of the unperturbed system, and make the visualization of the irregular dynamics with the help of Shaw-Takens' reconstruction of the state-space. Both approaches agree as to the values of the resonant frequency for the parametric excitation. Our results indicate that the shape of the laser pulse could be essential for generating chaotic tunneling.

quant-ph↗

arXiv2004

Harmonic oscillators in the Nosé - Hoover thermostat

We study the dynamics of an ensemble of non-interacting harmonic oscillators in a nonlinear dissipative environment described by the Nosé - Hoover model. Using numerical simulation we find the histogram for total energy, which agrees with the analysis of the Nosé - Hoover equations effected with the method of averaging. The histogram does not correspond to Gibbs' canonical distribution. We have found oscillations at frequency proportional to $\sqrt{α/m}$, $α$ the dissipative parameter of thermostat and $m$ the characteristic mass of particle, about the stationary state corresponding to equilibrium. The oscillations could have an important bearing upon the analysis of simulating molecular dynamics in the Nosé - Hoover thermostat.

cond-mat.other↗

arXiv2001

Nonlinear Regimes in Thermostats of Berendsen's Type

We consider the models of relaxational dynamics within the framework of Berendsen's and Nose-Hoover's thermostats. On studying the crucial case of ideal gas we come to the conclusion that both models mentioned above do not allow for describing the true thermodynamical equilibrium.

cond-mat.stat-mech↗

arXiv2001

Tautomeric Transitions in DNA

We study the tautomeric transitions in base pairs of DNA considering elastic properties of DNA as classical and tunneling of protons as quantum, and show that the dynamics of the transitions admits of soliton like solutions whose shape and size strongly depend on the structure of the double helix. In particular, we have found that the set of discrete breathers can be drastically modified by the interplay of the torsional and elastic constants. Our results may have a bearing upon substitution mutagenesis within the framework of Watson-Crick's approach, and in this respect the breather soliton could describe conformations corresponding to point mutations. The numerical simulation of soliton dynamics suggests that an initial distribution of base pairs with low probability of mutation per pair but of a sufficiently large number of base pairs involved, could move and gather around a site so as to form a set of base pairs with high probability of mutation, for a period of time approximately 1 musec. We suggest that the irradiation of DNA at frequencies of the proton tunneling, that is in infra-red region, could cause mutations.

cond-mat.soft↗

arXiv2001

Concerted motion of protons in hydrogen bonds of DNA-type molecules

We study the dynamical behaviour of the proton transfer in the hydrogen bonds in the base-pairs of the double helices of the DNA type. Under the assumption that the elastic and the tunnelling degrees of freedom may be coupled, we derive a non-linear and non-local Schrodinger equation (SNLNL) that describes the concerted motion of the proton tunnelling. Rough estimates of the solutions to the SNLNL show an intimate interplay between the concerted tunnelling of protons and the symmetry of double helix.

cond-mat.soft↗

arXiv2000

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

We consider cholesteric liquid-crystalline DNA dispersions, and show that polymeric (Dau-Cu) complexes, the so-called bridges, between pairs of DNA molecules may generate a super liquid-crystalline structure (BR-phase). The latter could have a layered spatial structure and an abnormal optical activity that could have a bearing upon the intense CD-band observed in DNA-dispersions.

cond-mat.soft↗

arXiv2000

Network of Hydrogen Bonds as a Medium for DNA Interaction in Solvents

We suggest that the DNA molecules could form the cholesteric phase owing to an interaction mediated by the network of the hydrogen bonds (H-network) in the solvent. The model admits of the dependence of the optical activity of the solution on the concentration of the PEG, and the change in the sense of the cholesteric twist due to the intercalation by the daunomicyn. Using the experimental data for the cholesteric phase of the DNA dispersion, we obtain a rough estimate for the energy given by our model, and show that it should be taken into account as well as the energy due to the steric repulsion, van der Waals, and electrostatic forces, generally used for studying the DNA molecules. The elastic constant of the H-network generating the interaction between the DNA molecules is determined by the energy due to the proton's vibration in the hydrogen bonds.

cond-mat.soft↗

arXiv1999

A Model for Double-Stranded Excitations of DNA

We calculate the spectrum of torsional vibrations of a double-stranded structure that models the double helix of the DNA. We come to the conclusion that within the framework of the model elementary excitations may display an asymmetry as regards their winding and direction of the propagation, depending on initial polarization. The asymmetry could have a bearing on processes that take place in molecules of the DNA.

cond-mat.soft↗