100 research outputs found
Aging phenomena in nonlinear dissipative chains: Application to polymer
We study energy relaxation in a phenomenological model for polymer built from
rheological considerations: a one dimensional nonlinear lattice with
dissipative couplings. These couplings are well known in polymer's community to
be possibly responsible of beta-relaxation (as in Burger's model). After
thermalisation of this system, the extremities of the chain are put in contact
with a zero-temperature reservoir, showing the existence of surprising
quasi-stationary states with non zero energy when the dissipative coupling is
high. This strange behavior, due to long-lived nonlinear localized modes,
induces stretched exponential laws. Furthermore, we observe a strong dependence
on the waiting time tw after the quench of the two-time intermediate
correlation function C(tw+t,tw). This function can be scaled onto a master
curve, similar to the case of spin or Lennard-Jones glasses.Comment: 8 pages, 10 figure
Disorder and fluctuations in nonlinear excitations in DNA
We study the effects of the sequence on the propagation of nonlinear
excitations in simple models of DNA, and how those effects are modified by
noise. Starting from previous results on soliton dynamics on lattices defined
by aperiodic potentials, [F. Dom\'\i nguez-Adame {\em et al.}, Phys. Rev. E
{\bf 52}, 2183 (1995)], we analyze the behavior of lattices built from real DNA
sequences obtained from human genome data. We confirm the existence of
threshold forces, already found in Fibonacci sequences, and of stop positions
highly dependent on the specific sequence. Another relevant conclusion is that
the effective potential, a collective coordinate formalism introduced by
Salerno and Kivshar [Phys. Lett. A {\bf 193}, 263 (1994)] is a useful tool to
identify key regions that control the behaviour of a larger sequence. We then
study how the fluctuations can assist the propagation process by helping the
excitations to escape the stop positions. Our conclusions point out to
improvements of the model which look promising to describe mechanical
denaturation of DNA. Finally, we also consider how randomly distributed energy
focus on the chain as a function of the sequence.Comment: 14 pages, final version, accepted in Fluctuation and Noise Letters,
scheduled to apper in vol. 4, issue 3 (2004
Discrete Breathers in a Realistic Coarse-Grained Model of Proteins
We report the results of molecular dynamics simulations of an off-lattice
protein model featuring a physical force-field and amino-acid sequence. We show
that localized modes of nonlinear origin (discrete breathers) emerge naturally
as continuations of a subset of high-frequency normal modes residing at
specific sites dictated by the native fold. In the case of the small
-barrel structure that we consider, localization occurs on the turns
connecting the strands. At high energies, discrete breathers stabilize the
structure by concentrating energy on few sites, while their collapse marks the
onset of large-amplitude fluctuations of the protein. Furthermore, we show how
breathers develop as energy-accumulating centres following perturbations even
at distant locations, thus mediating efficient and irreversible energy
transfers. Remarkably, due to the presence of angular potentials, the breather
induces a local static distortion of the native fold. Altogether, the
combination of this two nonlinear effects may provide a ready means for
remotely controlling local conformational changes in proteins.Comment: Submitted to Physical Biolog
Breathers in oscillator chains with Hertzian interactions
We prove nonexistence of breathers (spatially localized and time-periodic
oscillations) for a class of Fermi-Pasta-Ulam lattices representing an
uncompressed chain of beads interacting via Hertz's contact forces. We then
consider the setting in which an additional on-site potential is present,
motivated by the Newton's cradle under the effect of gravity. Using both direct
numerical computations and a simplified asymptotic model of the oscillator
chain, the so-called discrete p-Schr\"odinger (DpS) equation, we show the
existence of discrete breathers and study their spectral properties and
mobility. Due to the fully nonlinear character of Hertzian interactions,
breathers are found to be much more localized than in classical nonlinear
lattices and their motion occurs with less dispersion. In addition, we study
numerically the excitation of a traveling breather after an impact at one end
of a semi-infinite chain. This case is well described by the DpS equation when
local oscillations are faster than binary collisions, a situation occuring e.g.
in chains of stiff cantilevers decorated by spherical beads. When a hard
anharmonic part is added to the local potential, a new type of traveling
breather emerges, showing spontaneous direction-reversing in a spatially
homogeneous system. Finally, the interaction of a moving breather with a point
defect is also considered in the cradle system. Almost total breather
reflections are observed at sufficiently high defect sizes, suggesting
potential applications of such systems as shock wave reflectors
Discrete localized modes supported by an inhomogeneous defocusing nonlinearity
We report that infinite and semi-infinite lattices with spatially
inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength
increases rapidly enough toward the lattice periphery, support stable
unstaggered (UnST) discrete bright solitons, which do not exist in lattices
with the spatially uniform SDF nonlinearity. The UnST solitons coexist with
stable staggered (ST) localized modes, which are always possible under the
defocusing onsite nonlinearity. The results are obtained in a numerical form,
and also by means of variational approximation (VA). In the semi-infinite
(truncated) system, some solutions for the UnST surface solitons are produced
in an exact form. On the contrary to surface discrete solitons in uniform
truncated lattices, the threshold value of the norm vanishes for the UnST
solitons in the present system. Stability regions for the novel UnST solitons
are identified. The same results imply the existence of ST discrete solitons in
lattices with the spatially growing self-focusing nonlinearity, where such
solitons cannot exist either if the nonlinearity is homogeneous. In addition, a
lattice with the uniform onsite SDF nonlinearity and exponentially decaying
inter-site coupling is introduced and briefly considered too. Via a similar
mechanism, it may also support UnST discrete solitons, under the action of the
SDF nonlinearity. The results may be realized in arrayed optical waveguides and
collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical
lattices. A generalization for a two-dimensional system is briefly considered
too.Comment: 14 pages, 7 figures, accepted for publication in PR
Nonlinear waves in Newton's cradle and the discrete p-Schroedinger equation
We study nonlinear waves in Newton's cradle, a classical mechanical system
consisting of a chain of beads attached to linear pendula and interacting
nonlinearly via Hertz's contact forces. We formally derive a spatially discrete
modulation equation, for small amplitude nonlinear waves consisting of slow
modulations of time-periodic linear oscillations. The fully-nonlinear and
unilateral interactions between beads yield a nonstandard modulation equation
that we call the discrete p-Schroedinger (DpS) equation. It consists of a
spatial discretization of a generalized Schroedinger equation with p-Laplacian,
with fractional p>2 depending on the exponent of Hertz's contact force. We show
that the DpS equation admits explicit periodic travelling wave solutions, and
numerically find a plethora of standing wave solutions given by the orbits of a
discrete map, in particular spatially localized breather solutions. Using a
modified Lyapunov-Schmidt technique, we prove the existence of exact periodic
travelling waves in the chain of beads, close to the small amplitude modulated
waves given by the DpS equation. Using numerical simulations, we show that the
DpS equation captures several other important features of the dynamics in the
weakly nonlinear regime, namely modulational instabilities, the existence of
static and travelling breathers, and repulsive or attractive interactions of
these localized structures
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