Base pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium

We study the nonlinear dynamics of a protein-DNA molecular system by treating DNA as a set of two coupled linear chains and protein in the form of a single linear chain sliding along the DNA at the physiological temperature in a viscous medium. The nonlinear dynamics of the above molecular system in general is governed by a perturbed nonlinear Schr\"{o}dinger equation. In the non-viscous limit, the equation reduces to the completely integrable nonlinear Schr\"{o}dinger (NLS) equation which admits N-soliton solutions. The soliton excitations of the DNA bases make localized base pair opening and travel along the DNA chain in the form of a bubble. This may represent the bubble generated during the transcription process when an RNA-polymerase binds to a promoter site in the DNA double helical chain. The perturbed NLS equation is solved using a perturbation theory by treating the viscous effect due to surrounding as a weak perturbation and the results show that the viscosity of the solvent in the surrounding damps out the amplitude of the soliton.Comment: 4. Submitted to Phys. Rev.

Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and Astrophysic

Level-rank duality via tensor categories

We give a new way to derive branching rules for the conformal embedding (\asl_n)_m\oplus(\asl_m)_n\subset(\asl_{nm})_1. In addition, we show that the category \Cc(\asl_n)_m^0 of degree zero integrable highest weight (\asl_n)_m-representations is braided equivalent to \Cc(\asl_m)_n^0 with the reversed braiding.Comment: 16 pages, to appear in Communications in Mathematical Physics. Version 2 changes: Proof of main theorem made explicit, example 4.11 removed, references update

Floristic diversity of steppe territories near Poltava town (Ukraine)

Current progress in botany requires new claims for floristic research. Now the latter is not a simple species inventory of a separate local or regional flora but it needs coordination with recent results of critical taxonomic, nomenclatural and molecular phylogenetic investigations. Based on the fact that detailed research on steppes as a zonal type of vegetation in the Forest-Steppe zone of Ukraine is very important for preservation of current steppe territories, the authors studied several territories with steppe vegetation near Poltava town (Poltava region, Ukraine). The key steppe territories found are situated near Abazivka, Rozhayivka, Kostochky, Buhayivka, Machukhy, Ivonchentsi and Zhuky villages. Data about steppe flora from only the first territory located between Abazivka and Rozhayivka villages including “Rozhayivskyi” local botanical reserve were early reported in literature sources while data about steppe vegetation of the other areas has never been published in detail. The full list of 401 vascular plant species found on these steppe territories with the frequency of distribution, major synonym names and references to current taxonomic papers for separate species are proposed. One of these species (Hemerocallis fulva (L.) L.) is a new alien for Poltava region. Taxonomy for all species was critically revised, nomenclature of several taxa (Dichoropetalum carvifolia (Vill.) Pimenov & Kljuykov, Erophila verna (L.) DC., Campanula canescens (Waldst. & Kit.) Roth) is discussed in detail. The name “Dichoropetalum carvifolium-chabraei (Crantz) Soldano et al.” is an invalid designation based on trinominal and must be rejected. The names Selinum chabraei Jacq. ex Murray, Peucedanum euphimiae Kotov and Hemerocallis lilio-asphodelus var. fulva L. were lectotypified. The studied steppe territories have the great significance in the sozological aspect, they include 32 rare steppe plant species (seven from the Red Data Book of Ukraine and 25 from the list of locally rare plants within Poltava region) so the primary task for further research is to organize their protection as the most valuable steppe areas and the monitoring of their condition in the future

Microscopic derivation of Frenkel excitons in second quantization

Starting from the microscopic hamiltonian describing free electrons in a periodic lattice, we derive the hamiltonian appropriate to Frenkel excitons. This is done through a grouping of terms different from the one leading to Wannier excitons. This grouping makes appearing the atomic states as a relevant basis to describe Frenkel excitons in the second quantization. Using them, we derive the Frenkel exciton creation operators as well as the commutators which rule these operators and which make the Frenkel excitons differing from elementary bosons. The main goal of the present paper is to provide the necessary grounds for future works on Frenkel exciton many-body effects, with the composite nature of these particles treated exactly through a procedure similar to the one we have recently developed for Wannier excitons.Comment: 16 pages, 4 figure

Adiabatic-Nonadiabatic Transition in the Diffusive Hamiltonian Dynamics of a Classical Holstein Polaron

We study the Hamiltonian dynamics of a free particle injected onto a chain containing a periodic array of harmonic oscillators in thermal equilibrium. The particle interacts locally with each oscillator, with an interaction that is linear in the oscillator coordinate and independent of the particle's position when it is within a finite interaction range. At long times the particle exhibits diffusive motion, with an ensemble averaged mean-squared displacement that is linear in time. The diffusion constant at high temperatures follows a power law D ~ T^{5/2} for all parameter values studied. At low temperatures particle motion changes to a hopping process in which the particle is bound for considerable periods of time to a single oscillator before it is able to escape and explore the rest of the chain. A different power law, D ~ T^{3/4}, emerges in this limit. A thermal distribution of particles exhibits thermally activated diffusion at low temperatures as a result of classically self-trapped polaronic states.Comment: 15 pages, 4 figures Submitted to Physical Review

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure