9 research outputs found
Sine-Gordon ratchets with general periodic, additive, and parametric driving forces
We study the soliton ratchets in the damped sine-Gordon equation with periodic nonsinusoidal, additive, and parametric driving forces. By means of symmetry analysis of this system we show that the net motion of the kink is not possible if the frequencies of both forces satisfy a certain relationship. Using a collective coordinate theory with two degrees of freedom, we show that the ratchet motion of kinks appears as a consequence of a resonance between the oscillations of the momentum and the width of the kink. We show that the equations of motion that fulfill these collective coordinates follow from the corresponding symmetry properties of the original systems. As a further application of the collective coordinate technique we obtain another relationship between the frequencies of the parametric and additive drivers that suppresses the ratchetlike motion of the kink. We check all these results by means of numerical simulations of the originaMEC, (Spain) and by DAAD (Germany) through “Acciones Integradas Hispano-Alemanas” HA2004-0034—D/04/39957MEC Grant No. FIS2005-973Junta de Andalucía under Projects No. 00481, No. P06-FQM-01735, and No. FQM-020
Ratchet effect in a damped sine-Gordon system with additive and parametric ac driving forces
We study in detail the damped sine-Gordon equation, driven by two ac forces (one is added as a parametric perturbation and the other one in an additive way), as an example of soliton ratchets. By means of a collective coordinate approach we derive an analytical expression for the average velocity of the soliton, which allows us to show that this mechanism of transport requires certain relationships both between the frequencies and between the initial phases of the two ac forces. The control of the velocity by the damping coefficient and parameters of the ac forces is also presented and discussed. All these results are subsequently checked by means of simulations for the driven and damped sine-Gordon equation that we have studied.Ministerio de Educación y Ciencia (MEC, Spain) Grant No. HA2004-0034-D/04/39957Ministerio de Educación y Ciencia (MEC, Spain) Grant No. FIS2005-973Junta de Andalucía Project No. 00481Junta de Andalucía Project No. FQM-020
Efficient characterization of high-dimensional parameter spaces for systems biology
BACKGROUND: A biological system's robustness to mutations and its evolution are influenced by the structure of its viable space, the region of its space of biochemical parameters where it can exert its function. In systems with a large number of biochemical parameters, viable regions with potentially complex geometries fill a tiny fraction of the whole parameter space. This hampers explorations of the viable space based on "brute force" or Gaussian sampling. RESULTS: We here propose a novel algorithm to characterize viable spaces efficiently. The algorithm combines global and local explorations of a parameter space. The global exploration involves an out-of-equilibrium adaptive Metropolis Monte Carlo method aimed at identifying poorly connected viable regions. The local exploration then samples these regions in detail by a method we call multiple ellipsoid-based sampling. Our algorithm explores efficiently nonconvex and poorly connected viable regions of different test-problems. Most importantly, its computational effort scales linearly with the number of dimensions, in contrast to "brute force" sampling that shows an exponential dependence on the number of dimensions. We also apply this algorithm to a simplified model of a biochemical oscillator with positive and negative feedback loops. A detailed characterization of the model's viable space captures well known structural properties of circadian oscillators. Concretely, we find that model topologies with an essential negative feedback loop and a nonessential positive feedback loop provide the most robust fixed period oscillations. Moreover, the connectedness of the model's viable space suggests that biochemical oscillators with varying topologies can evolve from one another. CONCLUSIONS: Our algorithm permits an efficient analysis of high-dimensional, nonconvex, and poorly connected viable spaces characteristic of complex biological circuitry. It allows a systematic use of robustness as a tool for model discrimination
Domain wall dynamics in expanding spaces
We study the effects on the dynamics of kinks due to expansions and
contractions of the space. We show that the propagation velocity of the kink
can be adiabatically tuned through slow expansions/contractions, while its
width is given as a function of the velocity. We also analyze the case of fast
expansions/contractions, where we are no longer on the adiabatic regime. In
this case the kink moves more slowly after an expansion-contraction cycle as a
consequence of loss of energy through radiation. All these effects are
numerically studied in the nonlinear Klein-Gordon equations (both for the
sine-Gordon and for the phi^4 potential), and they are also studied within the
framework of the collective coordinate evolution equations for the width and
the center of mass of the kink. These collective coordinate evolution equations
are obtained with a procedure that allows us to consider even the case of large
expansions/contractions.Comment: LaTeX, 18 pages, 2 figures, improved version to appear in Phys Rev
Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations
We develop an alternative approach to study the effect of the generic
perturbation (in addition to explicitly considering the loss term) in the
nonlinear Klein-Gordon equations. By a change of the variables that cancel the
dissipation term we are able to write the Lagrangian density and then,
calculate the Lagrangian as a function of collective variables. We use the
Lagrangian formalism together with the Rice {\it Ansatz} to derive the
equations of motion of the collective coordinates (CCs) for the perturbed
sine-Gordon (sG) and systems. For the collective coordinates,
regardless of the {\it Ansatz} used, we show that, for the nonlinear
Klein-Gordon equations, this approach is equivalent to the {\it Generalized
Traveling Wave Ansatz} ({\it GTWA})Comment: 9 page
¿Puede apararecer el efecto ratchet en sistemas simétricos?
Organizado por GENOFOL y la Universidad de Granada