122 research outputs found
Pulse interaction via gain and loss dynamics in passive mode-locking
We study theoretically the effects of pulse interactions mediated by the gain and absorber dynamics in a passively mode-locked laser containing a slow saturable absorber, and operating in a regime with several pulses coexisting in the cavity
Hopf bifurcations in time-delay systems with band-limited feedback
We investigate the steady-state solution and its bifurcations in time-delay
systems with band-limited feedback. This is a first step in a rigorous study
concerning the effects of AC-coupled components in nonlinear devices with
time-delayed feedback. We show that the steady state is globally stable for
small feedback gain and that local stability is lost, generically, through a
Hopf bifurcation for larger feedback gain. We provide simple criteria that
determine whether the Hopf bifurcation is supercritical or subcritical based on
the knowledge of the first three terms in the Taylor-expansion of the
nonlinearity. Furthermore, the presence of double-Hopf bifurcations of the
steady state is shown, which indicates possible quasiperiodic and chaotic
dynamics in these systems. As a result of this investigation, we find that
AC-coupling introduces fundamental differences to systems of Ikeda-type [Ikeda
et al., Physica D 29 (1987) 223-235] already at the level of steady-state
bifurcations, e.g. bifurcations exist in which limit cycles are created with
periods other than the fundamental ``period-2'' mode found in Ikeda-type
systems.Comment: 32 pages, 5 figures, accepted for publication in Physica D: Nonlinear
Phenomen
Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams
Although acoustics is one of the disciplines of mechanics, its
"geometrization" is still limited to a few areas. As shown in the work on
nonlinear propagation in Reissner beams, it seems that an interpretation of the
theories of acoustics through the concepts of differential geometry can help to
address the non-linear phenomena in their intrinsic qualities. This results in
a field of research aimed at establishing and solving dynamic models purged of
any artificial nonlinearity by taking advantage of symmetry properties
underlying the use of Lie groups. The geometric constructions needed for
reduction are presented in the context of the "covariant" approach.Comment: Submitted to GSI2013 - Geometric Science of Informatio
Nucleosome repositioning via loop formation
Active (catalysed) and passive (intrinsic) nucleosome repositioning is known
to be a crucial event during the transcriptional activation of certain
eucaryotic genes. Here we consider theoretically the intrinsic mechanism and
study in detail the energetics and dynamics of DNA-loop-mediated nucleosome
repositioning, as previously proposed by Schiessel et al. (H. Schiessel, J.
Widom, R. F. Bruinsma, and W. M. Gelbart. 2001. {\it Phys. Rev. Lett.}
86:4414-4417). The surprising outcome of the present study is the inherent
nonlocality of nucleosome motion within this model -- being a direct physical
consequence of the loop mechanism. On long enough DNA templates the longer
jumps dominate over the previously predicted local motion, a fact that
contrasts simple diffusive mechanisms considered before. The possible
experimental outcome resulting from the considered mechanism is predicted,
discussed and compared to existing experimental findings
Resonant helical deformations in nonhomogeneous Kirchhoff filaments
We study the three-dimensional static configurations of nonhomogeneous
Kirchhoff filaments with periodically varying Young's modulus. This type of
variation may occur in long tandemly repeated sequences of DNA. We analyse the
effects of the Young's modulus frequence and amplitude of oscillation in the
stroboscopic maps, and in the regular (non chaotic) spatial configurations of
the filaments. Our analysis shows that the tridimensional conformations of long
filaments may depend critically on the Young's modulus frequence in case of
resonance with other natural frequencies of the filament. As expected, far from
resonance the shape of the solutions remain very close to that of the
homogeneous case. In the case of biomolecules, it is well known that various
other elements, besides sequence-dependent effects, combine to determine their
conformation, like self-contact, salt concentration, thermal fluctuations,
anisotropy and interaction with proteins. Our results show that
sequence-dependent effects alone may have a significant influence on the shape
of these molecules, including DNA. This could, therefore, be a possible
mechanical function of the ``junk'' sequences.Comment: 18 pages (twocolumn), 5 figures Revised manuscrip
Frequency locking of modulated waves
We consider the behavior of a modulated wave solution to an
-equivariant autonomous system of differential equations under an
external forcing of modulated wave type. The modulation frequency of the
forcing is assumed to be close to the modulation frequency of the modulated
wave solution, while the wave frequency of the forcing is supposed to be far
from that of the modulated wave solution. We describe the domain in the
three-dimensional control parameter space (of frequencies and amplitude of the
forcing) where stable locking of the modulation frequencies of the forcing and
the modulated wave solution occurs.
Our system is a simplest case scenario for the behavior of self-pulsating
lasers under the influence of external periodically modulated optical signals
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