Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.Comment: 6 pages, 4 figures, final published versio

A symmetry invariant integral on kappa-deformed spacetime

In this note we present an approach using both constructive and Hopf algebraic methods to contribute to the not yet fully satisfactory definition of an integral on kappa-deformed spacetime. The integral presented here is based on the inner product of differential forms and it is shown that this integral is explicitly invariant under the deformed symmetry structure.Comment: 16 page

Computerized visual feedback: an adjunct to robotic-assisted gait training

BACKGROUND AND PURPOSE: Robotic devices for walking rehabilitation allow new possibilities for providing performance-related information to patients during gait training. Based on motor learning principles, augmented feedback during robotic-assisted gait training might improve the rehabilitation process used to regain walking function. This report presents a method to provide visual feedback implemented in a driven gait orthosis (DGO). The purpose of the study was to compare the immediate effect on motor output in subjects during robotic-assisted gait training when they used computerized visual feedback and when they followed verbal instructions of a physical therapist. SUBJECTS: Twelve people with neurological gait disorders due to incomplete spinal cord injury participated. METHODS: Subjects were instructed to walk within the DGO in 2 different conditions. They were asked to increase their motor output by following the instructions of a therapist and by observing visual feedback. In addition, the subjects' opinions about using visual feedback were investigated by a questionnaire. RESULTS: Computerized visual feedback and verbal instructions by the therapist were observed to result in a similar change in motor output in subjects when walking within the DGO. Subjects reported that they were more motivated and concentrated on their movements when using computerized visual feedback compared with when no form of feedback was provided. DISCUSSION AND CONCLUSION: Computerized visual feedback is a valuable adjunct to robotic-assisted gait training. It represents a relevant tool to increase patients' motor output, involvement, and motivation during gait training, similar to verbal instructions by a therapist

Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-G\'omez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.Comment: 15 pages, 3 figures; Contribution to Juergen Ehlers Memorial Issue (GeRG journal

Influence of vestibular and visual stimulation on split-belt walking

We investigated the influence of vestibular (caloric ear irrigation) and visual (optokinetic) stimulation on slow and fast split-belt walking. The velocity of one belt was fixed (1.5 or 5.0-6.0km/h) and subjects (N=8 for vestibular and N=6 for visual experiments) were asked to adjust the velocity of the other belt to a level at which they perceived the velocity of both the belts as equal. Throughout all experiments, subjects bimanually held on to the space-fixed handles along the treadmill, which provided haptic information on body orientation. While the optokinetic stimulus (displayed on face-mounted virtual reality goggles) had no effect on belt velocity adjustments compared to control trials, cold-water ear irrigation during slow (but not fast) walking effectively influenced belt velocity adjustments in seven of eight subjects. Only two of these subjects decreased the velocity of the ipsilateral belt, consistent with the ipsilateral turning toward the irrigated ear in the Fukuda stepping test. The other five subjects, however, increased the velocity of the ipsilateral belt. A straight-ahead sense mechanism can explain both decreased and increased velocity adjustments. Subjects decrease or increase ipsilateral belt velocity depending on whether the vestibular stimulus is interpreted as an indicator of the straight-ahead direction (decreased velocity) or as an error signal relative to the straight-ahead direction provided by the haptic input from the space-fixed handles along the treadmill (increased velocity). The missing effect during fast walking corroborates the findings by others that the influence of vestibular tone asymmetry on locomotion decreases at higher gait velocitie

Evidence for Neutrinoless Double Beta Decay

The data of the Heidelberg-Moscow double beta decay experiment for the measuring period August 1990 - May 2000 (54.9813 kg y or 723.44 molyears), published recently, are analyzed using the potential of the Bayesian method for low counting rates. First evidence for neutrinoless double beta decay is observed giving first evidence for lepton number violation. The evidence for this decay mode is 97% (2.2\sigma) with the Bayesian method, and 99.8% c.l. (3.1\sigma) with the method recommended by the Particle Data Group. The half-life of the process is found with the Bayesian method to be T_{1/2}^{0\nu} = (0.8 - 18.3) x 10^{25} y (95% c.l.) with a best value of 1.5 x 10^{25} y. The deduced value of the effective neutrino mass is, with the nuclear matrix elements from [Sta90,Tom91] = (0.11 - 0.56) eV (95% c.l.), with a best value of 0.39 eV. Uncertainties in the nuclear matrix elements may widen the range given for the effective neutrino mass by at most a factor 2. Our observation which at the same time means evidence that the neutrino is a Majorana particle, will be of fundamental importance for neutrino physics. PACS. 14.69.Pq Neutrino mass and mixing; 23.40.Bw Weak-interaction and lepton (including neutrino) aspects 23.40.-s Beta decay; double beta decay; electron and muon capture.Comment: 14 pages, psfile, 7 figures, Published in Modern Physics Letters A, Vol. 16, No. 37 (2001) 2409-2420, World Scientific Publishing Company, Home Page: http://ejournals.wspc.com.sg/mpla/16/1637/S0217732301005825.html, Home Page of Heidelberg Non-Accelerator Particle Physics Group: http://www.mpi-hd.mpg.de/non_acc

In search of virus carriers of the 1988 and 2002 phocine distemper virus outbreaks in European harbour seals

European harbour seal (Phoca vitulina) populations decreased substantially during the phocine distemper virus (PDV) outbreaks of 1988 and 2002. Different hypotheses have stated that various seals and terrestrial carnivore species might be the source of infection. To further analyse these hypotheses, grey (Halichoerus grypus) and ringed (Phoca hispida) seals, polar bears (Ursus maritimus) and minks (Mustela lutreola) were sampled from the North Sea and East Greenland coasts between 1988 and 2004 and investigated by RT-PCR using a panmorbillivirus primer pair. However, all samples were negative for morbillivirus nucleic acid

Generalized Killing equations and Taub-NUT spinning space

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional euclidean Taub-NUT manifold.Comment: 10 pages, late

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size