V. Muto

Thermally generated solitons in a toda lattice model of DNA

Abstract Here we calculate the thermal equilibrium number of solitons in DNA as a function of absolute temperature and the number of base pairs. This calculation is effected by modeling DNA as a Toda lattice with parameters chosen to match experimentally measured properties of DNA. We find that a significant number of solitons is generated at physiological temperature (310 K).

On a Toda lattice model with a transversal degree of freedom

A transversal degree of freedom is introduced in the Toda lattice. For different orders of magnitude of the longitudinal and transversal strains, coupled and uncoupled equations for these fields are derived in the discrete case as well as the continuum limit. Travelling wave solutions of the system are obtained and compared to numerical solutions. Standing waves, obtained by separation of variables, exhibit blow-up in finite time as well as bounded behaviour.

Solitons in DNA.

DNA is modeled as a homogeneous, cylindrical rod with nonlinear elasticity using the Ostrovskii-Sutin equation (OSE) with periodic boundary conditions. This equation predicts that longitudinal sound waves will be concentrated into packets called solitons. From a study of the damped OSE, we conclude that decay time is almost independent of the solitonic character of the solution. For the damped, driven OSE, on the other hand, we find that spectral features (such as absorption line widths and fine structure) are strongly influenced by the presence of anharmonicity. This effect is enhanced as the length of the DNA is increased.

A Toda lattice model for DNA: thermally generated solitons

In this paper we calculate the thermal equilibrium number of solitons in DNA as a function of absolute temperature and the number of base pairs. These calculations are effected by modeling DNA as a Toda lattice with parameters chosen to match experimentally measured properties of DNA. We find that a significant number of solitons is generated at physiological temperature (310 K). Moreover at low temperature, the dependence of the number of solitons on the temperature follows a T13 law.

Nonlinear models of DNA dynamics

Abstract The effect of nonlinearity in models of DNA with homogeneous and inhomogeneous strands is investigated. Numbers of solitons and numbers of long-lived open states as function of temperature are computed.

Solitary wave solutions to a system of Boussinesq-like equations

Abstract A set of coupled Boussinesq-like equations arise in the continuum limit of a Toda lattice performing longitudinal and transversal motion. The cases of quartic and cubic approximations of the Toda potential are considered. In the latter case new solitary wave solutions are obtained by means of a generalized ansatz concerning the coupling between the two fields.

Induced anisotropy and magnetoelastic properties in Fe-rich metallic glasses

Abstract Magnetoelastic measurements have been performed on metallic glasses of composition ( Fe 0.79 Co 0.21 ) 75+x Si 15−1.4x B 10+0.4x (x=0,2,4,6,8) by using the resonance–antiresonance method. Samples were obtained in the form of ribbons and annealed under applied field in such a way that a transverse and homogeneous anisotropy was induced in all compositions. The measured magnetoelastic coupling coefficients (k) are about 0.8 in the annealed samples. The quantity E0/ES, that is the initial to saturation Youngs modulus ratio, is close to 1 for all compositions, and is an indicator of the colinearity of the magnetic moments around the direction of the induced easy axis. The dependence of Youngs modulus on the applied magnetic field (or ΔE effect) has also been simulated following a phenomenological model. There is agreement between experimental data and simulation as far as the canting of the magnetic moments is a distributed function around the mean induced easy axis direction, for each sample, is taken into account.

Solitary Waves on Nonlinear Elastic Rods

Acoustic waves on elastic rods with circular cross section are governed by so-called improved Boussinesq equations when transverse motion and nonlinearity in the medium are taken into account. Solitary waves to these equations are shown to possess soliton-like properties in agreement with the fact that the impro ed Boussinesq equations are nearly integrable. Numerical investigations of blow up (in finite time), reflection and fission of solitary waves are presented in the cases of ending rods and rods with varying cross-section. The results are applied in a model for DNA-molecules in aqueous solution which is capable to predict the influence of anharmonicity on the spectral properties of this important molecule.

Local denaturation in DNA molecules

A two-dimensional anharmonic model, the so-called Toda-Lennard-Jones model, is considered in order to investigate the problems related to the lifetime of the open states precursors to full denaturation, in inhomogeneous ring-shaped DNA molecules. It is found that a transition from double-stranded to single-stranded DNA occurs locally around physiological temperature. Moreover, the presence of inhomogeneities enhances the hydrogen bond breaking.

Chaotic behaviour of a pendulum with variable length

SummaryThe Melnikov function for the prediction of Smale horseshoe chaos is applied to a driven damped pendulum with variable length. Depending on the parameters, it is shown that this dynamical system undertakes heteroclinic bifurcations which are the source of the unstable chaotic motion. The analytical results are illustrated by new numerical simulations. Furthermore, using the averaging theorem, the stability of the subharmonics is studied.RiassuntoIn questo articolo si applica la teoria di Melnikov per predire analiticamente la presenza di caos (Smale-horseshoe) in un pendolo con lunghezza variabile in presenza di dissipazione e di un termine forzante. Si mostra che tale sistema dinamico presenta una cascata di biforcazioni eterocliniche quando i parametri che entrano nell’equazione differenziale che lo descrive sono variati. La presenza di queste biforcazioni è la sorgente del moto caotico. Si studia inoltre la stabilità delle subarmoniche facendo uso del teorema della media temporale.