Dynamical transitions in incommensurate systems

In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommensurate phase. This behavior is compared to the static version of the model. A remarkable difference is that, while in the static case the two regimes are separated by a single transition (the Aubry transition), in the dynamical case the transition is characterized by a critical region, in which different phenomena take place at different times. In this paper, the generalized angular momentum we have previously introduced, and the dynamical modulation function are used to begin a characterization of this critical region. We further elucidate the relation between these two quantities, and present preliminary results about the order of the dynamical transition.Comment: 7 pages, 6 figures, file 'epl.cls' necessary for compilation provided; subm. to Europhysics Letter

Anharmonic stacking in supercoiled DNA

Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conformation, show an energetic advantage against the overtwisted ones. Accordingly moderately untwisted helices better sustain local fluctuational openings and make more unlikely the thermally driven complete strand separation.Comment: In pres

Modelling DNA at the mesoscale: a challenge for nonlinear science?

Invited paper, in the series "Open Problems" of NonlinearityInternational audienceWhen it is viewed at the scale of a base pair, DNA appears as a nonlinear lattice. Modelling its properties is a fascinating goal. The detailed experiments that can be performed on this system impose constraints on the models and can be used as a guide to improve them. There are nevertheless many open problems, particularly to describe DNA at the scale of a few tens of base pairs, which is relevant for many biological phenomena

Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates

We predict a dynammical classical superfluid-insulator transition (CSIT) in a Bose-Einstein condensate (BEC) trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly-coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the BEC center of mass oscillates with the relative phases of neighbouring condensates locked at the same (oscillating) value. For large displacements, the BEC remains localized on the side of the harmonic trap. This is caused by a randomization of the relative phases, while the coherence of each individual condensate in the array is preserved. The CSIT is attributed to a discrete modulational instability, occurring when the BEC center of mass velocity is larger than a critical value, proportional to the tunneling rate between adjacent sites.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Mode-locking of incommensurate phase by quantum zero point energy in the Frenkel-Kontorova model

In this paper, it is shown that a configuration modulated system described by the Frenkel-Kontorova model can be locked at an incommensurate phase when the quantum zero point energy is taken into account. It is also found that the specific heat for an incommensurate phase shows different parameter-dependence in sliding phase and pinning phase. These findings provide a possible way for experimentalists to verify the phase transition by breaking of analyticity.Comment: 6 pages in Europhys style, 3 eps figure

Lengthscales and Cooperativity in DNA Bubble Formation

It appears that thermally activated DNA bubbles of different sizes play central roles in important genetic processes. Here we show that the probability for the formation of such bubbles is regulated by the number of soft AT pairs in specific regions with lengths which at physiological temperatures are of the order of (but not equal to) the size of the bubble. The analysis is based on the Peyrard- Bishop-Dauxois model, whose equilibrium statistical properties have been accurately calculated here with a transfer integral approach

Interaction of sine-Gordon kinks with defects: The two-bounce resonance

A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for weak defects. Matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem, which are then used to derive analytical formulas for the locations of the well known two- and three-bounce resonance windows, as well as several other phenomena seen in numerical simulations.Comment: 26 pages, 17 figure

Structural lubricity: Role of dimension and symmetry

When two chemically passivated solids are brought into contact, interfacial interactions between the solids compete with intrabulk elastic forces. The relative importance of these interactions, which are length-scale dependent, will be estimated using scaling arguments. If elastic interactions dominate on all length scales, solids will move as essentially rigid objects. This would imply superlow kinetic friction in UHV, provided wear was absent. The results of the scaling study depend on the symmetry of the surfaces and the dimensionalities of interface and solids. Some examples are discussed explicitly such as contacts between disordered three-dimensional solids and linear bearings realized from multiwall carbon nanotubes.Comment: 7 pages, 1 figur

Bubbles, clusters and denaturation in genomic DNA: modeling, parametrization, efficient computation

The paper uses mesoscopic, non-linear lattice dynamics based (Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long and short heterogeneous sequences are presented, using a recently introduced reparametrization of the PBD model, and critically discussed. The statistics of extended open bubbles and bound clusters is formulated and results are presented for selected examples.Comment: to appear in a special issue of the Journal of Nonlinear Mathematical Physics (ed. G. Gaeta

The kink Casimir energy in a lattice sine-Gordon model

The Casimir energy of quantum fluctuations about the classical kink configuration is computed numerically for a recently proposed lattice sine-Gordon model. This energy depends periodically on the kink position and is found to be approximately sinusoidal.Comment: 10 pages, 4 postscript figure