Biomedical subjects

Lorenz Kramer

Publications and source records attributed to Lorenz Kramer.

10 recordsLinked to original sources

PubMed2006

Role of initial conditions in the decay of spatially periodic patterns in a nematic liquid crystal.

The decay of stripe patterns in planarly aligned nematic liquid crystals has been studied experimentally and theoretically. The initial patterns have been generated by the electrohydrodynamic instability and a light diffraction technique has been used to monitor their decay. In our experiments different decay rates have been observed as a function of the pattern wave number. According to our theoretical analysis they belong to a spectrum of decay modes and are individually selected in dependence on the initial conditions. Additional insight has emerged from a refined physical optical description of the diffraction intensity. The results compare well with experiments, which include also controlled modifications of the initial conditions to assess different decay modes.

Journal Article↗

PubMed2006

Effect of axial growth on Turing pattern formation.

We have performed one-dimensional and two-dimensional experiments and simulations to study the formation of patterns in a system that grows continuously in one direction. Depending on the growth velocity, three basic spatial configurations can be obtained: stripes that are parallel, oblique, or perpendicular to the growth direction. The dependence of the wavelength on the growth velocity has also been observed. Our results illustrate the importance of these growth mechanisms in determining the final configuration of chemical and biological pattern-forming processes.

Chlorine Compounds↗

PubMed2006

A normal form for excitable media.

We present a normal form for traveling waves in one-dimensional excitable media in the form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behavior of single pulses in a periodic domain and also the richer behavior of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle node in a Bogdanov-Takens point, and a symmetry-breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.

Action Potentials↗

PubMed2005

Transformation from walls to disclination lines: statics and dynamics of the pincement transition.

We present an experimental and theoretical study of the pincement phenomenon-transformation of a wall associated with the Fréedericksz transition into a pair of disclination lines. We measure the velocity of the boundary (front) between the two states as a function of the voltage. Experimental results are recovered by numerical simulations based on the nematic tensor order parameter, which also reveal the detailed three-dimensional structure of the front. By introducing reduced models we obtain approximate expressions for the two-state coexistence voltage and the front velocity. We find a bifurcation scenario incorporating a pair of saddle nodes at which the wall and disclination solutions appear or disappear.

Journal Article↗

PubMed2004

Decay of spatially periodic patterns in a nematic liquid crystal.

A detailed theoretical and experimental analysis of the decay of electroconvection patterns is presented in a planarly aligned nematic liquid crystal. The relaxation time is measured as a function of the wave number of the pattern using a light diffraction technique. A theoretical analysis exhibits a rich structure of the dispersion curves for the decay rates. An interesting relation between the realistic case of no-slip boundary conditions and the simpler free-slip case is found. The experimentally determined relaxation rates for both "conductive" and "dielectric" initial patterns follow the theoretical solution with subsequent jumps between branches when the wave number is increased.

Journal Article↗

PubMed2004

Retracting fronts induce spatiotemporal intermittency.

The intermittent route to spatiotemporal complexity is analyzed in simple models which display a subcritical bifurcation without hysteresis. A new type of spatiotemporal complex behavior is found, induced by fronts which "clean" the perturbations around an unstable state. The mechanism which generates these "retracting fronts" through nonlinear dispersion is analyzed in the frame of the complex Ginzburg-Landau equation. For sufficiently strong nonlinear dispersion the effects also occur for a supercritical bifurcation.

Journal Article↗

PubMed2004

On propagation failure in one- and two-dimensional excitable media.

We present a nonperturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behavior of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity, and scaling behavior. The results are compared with numerical simulations and show good agreement.

Arrhythmias, Cardiac↗

PubMed2003

Mechanism of standing wave patterns in cardiac muscle.

Recent experiments [R. A. Gray, Phys. Rev. Lett. 87, 168104 (2001)]] have revealed striking standing wave patterns in cardiac muscle. In excitable media, such as cardiac tissue where colliding waves annihilate, standing wave patterns result from a fully nonlinear mechanism. We present a possible physical mechanism explaining these patterns. The phenomenon does not depend on the precise excitable model chosen. Analogies are drawn with weak links in superconductors, and phase-slip solutions in the Ginzburg-Landau equations.

Computer Simulation↗

PubMed2002

Magnetic field effect on the thresholds of a sequence of transitions in the electroconvection of a homeotropic nematic liquid crystal.

We present a detailed analysis of the characteristics of electroconvection patterns in a homeotropic nematic liquid crystal under the influence of a variable magnetic field. An unambiguous observation of low frequency "reentrant" normal rolls and a nonmonotonic magnetic field dependence of the threshold voltages is reported. The effect of the magnetic field on the normal roll-abnormal roll transition is determined, which is in good agreement with theoretical predictions of the weakly nonlinear analysis.

Journal Article↗

PubMed2000

Persistence of zero velocity fronts in reaction diffusion systems.

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics.

Journal Article↗