arXiv subjects

Guenter Wunner

Publications and source records attributed to Guenter Wunner.

4 recordsLinked to original sources

arXiv2020

Magnetic effect on the rotational frequency of a neutron star

A neutron star contains regions with particles which exhibit magnetic moments, which, in turn, generate respective magnetizations. By magnetoelastic interactions between the magnetization and the matter there arises a magnetostriction. The magnetostriction changes the mass density of the neutron star and hence its inertia tensor, and as a result it changes the rotation frequency of the star. We also sketch how the calculation of the magnetostriction in the different inner regions of the neutron star has to proceed, and which parameter inputs are needed.

astro-ph.HE↗

arXiv2017

Neural network approach to time-dependent dividing surfaces in classical reaction dynamics

In a dynamical system, the transition between reactants and products is typically mediated by an energy barrier whose properties determine the corresponding pathways and rates. The latter is the flux through a dividing surface (DS) between the two corresponding regions and it is exact only if it is free of recrossings. For time-independent barriers, the DS can be attached to the top of the corresponding saddle point of the potential energy surface, and in time-dependent systems, the DS is a moving object. The precise determination of reaction rates, eg using transition state theory, requires the actual construction of a DS for a given saddle geometry which is in general a demanding methodical and computational task, especially in high-dimensional systems. In this paper, we demonstrate how such time-dependent, global, and recrossing-free DSs can be constructed using neural networks. In our approach, the neural network uses the bath coordinates and time as input and it is trained in a way that its output provides the position of the DS along the reaction coordinate. An advantage of this procedure is that, once the neural network is trained, the complete information about the dynamical phase space separation is stored in the network's parameters, and a precise distinction between reactants and products can be made for all possible system configurations, all times, and with little computational effort. We demonstrate this general method for two- and three-dimensional systems, and explain its straightforward extension to even more degrees of freedom.

physics.chem-ph↗

arXiv2007

Synergetic Analysis of the Haeussler-von der Malsburg Equations for Manifolds of Arbitrary Geometry

We generalize a model of Haeussler and von der Malsburg which describes the self-organized generation of retinotopic projections between two one-dimensional discrete cell arrays on the basis of cooperative and competitive interactions of the individual synaptic contacts. Our generalized model is independent of the special geometry of the cell arrays and describes the temporal evolution of the connection weights between cells on different manifolds. By linearizing the equations of evolution around the stationary uniform state we determine the critical global growth rate for synapses onto the tectum where an instability arises. Within a nonlinear analysis we use then the methods of synergetics to adiabatically eliminate the stable modes near the instability. The resulting order parameter equations describe the emergence of retinotopic projections from initially undifferentiated mappings independent of dimension and geometry.

physics.bio-ph↗

arXiv2007

Solutions of the Haeussler-von der Malsburg Equations in Manifolds with Constant Curvatures

We apply generic order parameter equations for the emergence of retinotopy between manifolds of different geometry to one- and two-dimensional Euclidean and spherical manifolds. To this end we elaborate both a linear and a nonlinear synergetic analysis which results in order parameter equations for the dynamics of connection weights between two cell sheets. Our results for strings are analogous to those for discrete linear chains obtained previously by Haeussler and von der Malsburg. The case of planes turns out to be more involved as the two dimensions do not decouple in a trivial way. However, superimposing two modes under suitable conditions provides a state with a pronounced retinotopic character. In the case of spherical manifolds we show that the order parameter equations provide stable stationary solutions which correspond to retinotopic modes. A further analysis of higher modes furnishes proof that our model describes the emergence of a perfect one-to-one retinotopy between two spheres.

physics.bio-ph↗