Biomedical subjects

FG Mertens

Publications and source records attributed to FG Mertens.

12 recordsLinked to original sources

PubMed2000

Anomalous resonance phenomena of solitary waves with internal modes

We investigate the nonparametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency Omega(i). We show that the strongest resonance arises when the driving frequency delta = Omega(i)/2, whereas when delta = Omega(i) the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an indirect coupling to the internal mode due to its symmetry, we expect similar results for other systems.

Journal Article↗

PubMed2000

Solitons in anharmonic chains with ultra-long-range interatomic interactions

We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of pulse solitons coexist in a certain velocity interval: one type is unstable but the two others are stable. The high-energy stable soliton is broad and can be described in the quasicontinuum approximation. But the low-energy stable soliton consists of two components, short-range and long-range ones, and can be considered as a bound state of these components.

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PubMed2000

Resonances in the dynamics of straight phi(4) kinks perturbed by ac forces

We study the dynamics of straight phi(4) kinks perturbed by an ac force, both with and without damping. We address this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the kink center and width. We carry out a careful analysis of the corresponding ordinary differential equations, of Mathieu type in the undamped case, finding and characterizing the resonant frequencies and the regions of existence of resonant solutions. We verify the accuracy of our predictions by numerical simulation of the full partial differential equation, showing that the collective coordinate prediction is very accurate. Numerical simulations for the damped case establish that the strongest resonance is the one at half the frequency of the internal mode of the kink. In conclusion, we discuss the possible relevance of our results for other systems, especially the sine-Gordon equation. We also obtain additional results regarding the equivalence between different collective coordinate methods applied to this problem.

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PubMed2000

Existence of internal modes of sine-gordon kinks

We study whether or not sine-Gordon kinks exhibit internal modes or "quasimodes." By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor "quasimodes" exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the discretization of the system in the numerical simulations, thus confirming recent predictions.

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PubMed1995