相关论文: Two-state dynamics for replicating two-strand syst…

This paper is concerned with a lattice model which is suited to square-rectangle transformations characterized by two strain components. The microscopic model involves nonlinear and competing interactions, which play a key role in the…

We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties…

The folding dynamics of small single-domain proteins is a current focus of simulations and experiments. Many of these proteins are 'two-state folders', i.e. proteins that fold rather directly from the denatured state to the native state,…

We develop a framework to solve a large class of linearly driven non-Hermitian quantum systems. Such a class of models in the Hermitian scenario is commonly known as multi-state Landau-Zener models. The non-hermiticity is due to the…

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time…

We use the two-time scale subordination in order to describe dynamical processes in continuous media with a long-term memory. Our consideration touches two physical examples in detail. First we study a temporal evolution of the species…

Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…

We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…

We propose that semiflexible polymers in poor solvent collapse in two stages. The first stage is the well known formation of a dense toroidal aggregate. However, if the solvent is sufficiently poor, the condensate will undergo a second…

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…

A simple Langevin approach is used to study stationary properties of the Peyrard-Bishop-Dauxois model for DNA, allowing known properties to be recovered in an easy way. Results are shown for the denaturation transition in homogeneous…

A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…

It has been recently discovered that exceptional families of Sturm-Liouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of…

On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…

Nonlinear dynamics of two biomolecules is studied. These are a microtubule and DNA molecule. Two mathematical procedures are explained, yielding to three kinds of solitary waves moving through the systems. These waves are kinks, modulated…

This paper presents the study of a DNA replication model grounded in the biochemical kinetics of DNA polymerases, which copy each DNA strand into a complementary strand, except for rare point-like mutations caused by nucleotide substitution…

Intracellular positive ions neutralise negative charges on the phosphates of a DNA strand conferring greater strength on the hydrogen bonds that connect complementary strands into a double helix and so confer enhanced stability. Beyond a…

The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous…

We construct a Darboux transformation of a general $su(3)$-valued spin system called the $\Gamma$-spin system. Using this Darboux transformation we derive a recursive formula for the soliton solutions of this spin system. Then using these…

We derive for the first time fundamental equations that describe soliton spatial profiles consisting of two-photon mode fields and macroscopic polarization of medium. Numerical solutions of this basic equation are presented to give single…