Biomedical subjects

F G Mertens

Publications and source records attributed to F G Mertens.

4 recordsLinked to original sources

PubMed2006

Persistent breathers in long-ranged discrete nonlinear Schrödinger models.

The DNLS model including Kac-Baker long-range interactions and nonlinear damping exhibits prominent effects in computer simulations. The combination of long-range forces and damping yields a periodic pattern of stationary breathers from an originally uniformly distributed background. The inverse interaction radius determines the periodicity which can be understood in the quasicontinuum approximation of the system. For the undamped system, we investigate the impact of the long-range interactions on the transition to the persistent-breather phase, which only depends on the energy and the norm of the DNLS. Using Monte Carlo techniques, we can monitor the localization strength as a function of the the long-range radius and the system temperature, which is formally negative in the persistent-breather phase.

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PubMed2006

Envelope solitons on anharmonic damped atomic chains.

We investigate the influence of dissipation on envelope solitons on anharmonic chains. We consider both Stokes and hydrodynamical damping and derive the evolution equations for the envelope in both the continuum and the quasi-continuum approximation of the chain. We introduce an appropriate collective variable ansatz for the envelope in order to describe the effect of damping on the soliton shape. We derive ordinary differential equations for the evolution of the three collective variables amplitude, width, and chirp which describe the spatial modulation of the envelope. The analytical results are in good agreement with the simulations of the discrete system for high-energy excitations on the chain. Our results derived from the quasi-continuum approximation show significant improvements compared to the continuum approximation.

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PubMed2001

Anomalies of ac driven solitary waves with internal modes: nonparametric resonances induced by parametric forces.

We study the dynamics of kinks in the straight phi(4) model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a nonparametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for nonparametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.

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PubMed1999

Overdamped sine-Gordon kink in a thermal bath.

We study sine-Gordon kink diffusion at finite temperature in the overdamped limit. By means of a general perturbative approach, we calculate the first- and second-order (in temperature) contributions to the diffusion coefficient. We compare our analytical predictions with numerical simulations. The good agreement allows us to conclude that, up to temperatures where kink-antikink nucleation processes cannot be neglected, a diffusion constant linear and quadratic in temperature gives a very accurate description of the diffusive motion of the kink. The quadratic temperature dependence is shown to stem from the interaction with the phonons. In addition, we calculate and compute the average value < phi(x,t)> of the wave function as a function of time, and show that its width grows with square root of t. We discuss the interpretation of this finding and show that it arises from the dispersion of the kink center positions of individual realizations which all keep their width.

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