282 research outputs found
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
- …