arXiv subjects

Helge Frauenkron

Publications and source records attributed to Helge Frauenkron.

6 recordsLinked to original sources

arXiv1998

2-d Self-Avoiding Walks on a Cylinder

We present simulations of self-avoiding random walks on 2-d lattices with the topology of an infinitely long cylinder, in the limit where the cylinder circumference L is much smaller than the Flory radius. We study in particular the L-dependence of the size h parallel to the cylinder axis, the connectivity constant mu, the variance of the winding number around the cylinder, and the density of parallel contacts. While mu(L) and scale as as expected (in particular, \sim h/L), the number of parallel contacts decays as h/L^1.92, in striking contrast to recent predictions. These findings strongly speak against recent speculations that the critical exponent gamma of SAW's might be nonuniversal. Finally, we find that the amplitude for does not agree with naive expectations from conformal invariance.

cond-mat.stat-mech↗

arXiv1998

A New Monte Carlo Algorithm for Protein Folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to extremely efficient algorithms for the folding of simple model proteins. We test them on several models for lattice heteropolymers, and compare to published Monte Carlo studies. In all cases our algorithms are faster than all previous ones, and in several cases we find new minimal energy states. In addition to ground states, our algorithms give estimates for the partition sum at finite temperatures.

cond-mat.stat-mech↗

arXiv1997

Testing a new Monte Carlo Algorithm for Protein Folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P. Grassberger, Phys. Rev. E, in press (1997)) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences.

cond-mat.stat-mech↗

arXiv1996

Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation

The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient new integration scheme. Particular attention is paid to solutions with a non-zero phase gradient. For fixed control parameters, solutions with conserved average phase gradient $ν$ exist only for $|ν|$ less than some upper limit. The transition from phase to defect-turbulence happens when this limit becomes zero. A Lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient. For high values of the phase gradient a family of non-chaotic solutions of the CGLE is found. These solutions consist of spatially periodic or aperiodic waves travelling with constant velocity. They typically have incommensurate velocities for phase and amplitude propagation, showing thereby a novel type of quasiperiodic behavior. The main features of these travelling wave solutions can be explained through a modified Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the PT phase. The latter explains also the behavior of the maximal Lyapunov exponents of chaotic solutions.

chao-dyn↗

arXiv1995

A Novel Integration Scheme for Partial Differential Equations: an Application to the Complex Ginzburg-Landau Equation

A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and disturbance propagation in extended systems. An application to the complex Ginzburg-Landau equation shows the higher precision of this method with respect to spectral ones.

solv-int↗

arXiv1995

Interaction of Nonlinear Schrödinger Solitons with an External Potential

Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schrödinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an interface separating two regions of constant potential. We find that the soliton can break up into two solitons, eventually accompanied by radiation of non-solitary waves. Reflection coefficients and inelasticities are computed as functions of the height of the potential step and of its steepness.

chao-dyn↗