Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions

Turbulent Rayleigh-Benard convection with phase changes in an extended layer between two parallel impermeable planes is studied by means of three-dimensional direct numerical simulations for Rayleigh numbers between 10^4 and 1.5\times 10^7 and for Prandtl number Pr=0.7. Two different sets of boundary conditions of temperature and total water content are compared: imposed constant amplitudes which translate into Dirichlet boundary conditions for the scalar field fluctuations about the quiescent diffusive equilibrium and constant imposed flux boundary conditions that result in Neumann boundary conditions. Moist turbulent convection is in the conditionally unstable regime throughout this study for which unsaturated air parcels are stably and saturated air parcels unstably stratified. A direct comparison of both sets of boundary conditions with the same parameters requires to start the turbulence simulations out of differently saturated equilibrium states. Similar to dry Rayleigh-Benard convection the differences in the turbulent velocity fluctuations, the cloud cover and the convective buoyancy flux decrease across the layer with increasing Rayleigh number. At the highest Rayleigh numbers the system is found in a two-layer regime, a dry cloudless and stably stratified layer with low turbulence level below a fully saturated and cloudy turbulent one which equals classical Rayleigh-Benard convection layer. Both are separated by a strong inversion that gets increasingly narrower for growing Rayleigh number.Comment: 19 pages, 13 Postscript figures, Figures 10,11,12,13, in reduced qualit

A measure of centrality based on the spectrum of the Laplacian

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table

Polar middle atmosphere temperature climatology from Rayleigh lidar measurements at ALOMAR (69° N)

Rayleigh lidar temperature profiles have been derived in the polar middle atmosphere from 834 measurements with the ALOMAR Rayleigh/Mie/Raman lidar (69.3° N, 16.0° E) in the years 1997–2005. Since our instrument is able to operate under full daylight conditions, the unique data set presented here extends over the entire year and covers the altitude region 30 km–85 km in winter and 30 km–65 km in summer. Comparisons of our lidar data set to reference atmospheres and ECMWF analyses show agreement within a few Kelvin in summer but in winter higher temperatures below 55 km and lower temperatures above by as much as 25 K, due likely to superior resolution of stratospheric warming and associated mesospheric cooling events. We also present a temperature climatology for the entire lower and middle atmosphere at 69° N obtained from a combination of lidar measurements, falling sphere measurements and ECMWF analyses. Day to day temperature variability in the lidar data is found to be largest in winter and smallest in summer

Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation

The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an information-theoretic description of the process of coding inter- and intra-community transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original Map coding scheme, which is both block-averaged and one-step, neglects the internal structure of the communities and introduces an upper scale, the `field-of-view' limit, in the communities it can detect. As a consequence, Map is well tuned to detect clique-like communities but can lead to undesirable overpartitioning when communities are far from clique-like. We show that a signature of this behavior is a large compression gap: the Map description length is far from its ideal limit. To address this issue, we propose a simple dynamic approach that introduces time explicitly into the Map coding through the analysis of the weighted adjacency matrix of the time-dependent multistep transition matrix of the Markov process. The resulting Markov time sweeping induces a dynamical zooming across scales that can reveal (potentially multiscale) community structure above the field-of-view limit, with the relevant partitions indicated by a small compression gap.Comment: 10 pages, 6 figure

Influence of Sensory Dependence on Postural Control

The current project is part of an NSBRI funded project, "Development of Countermeasures to Aid Functional Egress from the Crew Exploration Vehicle Following Long-Duration Spaceflight." The development of this countermeasure is based on the use of imperceptible levels of electrical stimulation to the balance organs of the inner ear to assist and enhance the response of a person s sensorimotor function. These countermeasures could be used to increase an astronaut s re-adaptation rate to Earth s gravity following long-duration space flight. The focus of my project is to evaluate and examine the correlation of sensory preferences for vision and vestibular systems. Disruption of the sensorimotor functions following space flight affects posture, locomotion and spatial orientation tasks in astronauts. The Group Embedded Figures Test (GEFT), the Rod and Frame Test (RFT) and the Computerized Dynamic Posturography Test (CDP) are measurements used to examine subjects visual and vestibular sensory preferences. The analysis of data from these tasks will assist in relating the visual dependence measures recognized in the GEFT and RFT with vestibular dependence measures recognized in the stability measures obtained during CDP. Studying the impact of sensory dependence on the performance in varied tasks will help in the development of targeted countermeasures to help astronauts readapt to gravitational changes after long duration space flight

Concept of an efficient self-startup voltage converter with dynamic maximum power point tracking for microscale thermoelectric generators

Microscale Thermoelectric Generators (microTEGs) have a high application potential for energy harvesting for autonomous microsystems. In contrast to conventional thermoelectric generators, microTEGs can only supply small output-voltages. Therefore, voltage converters are required to provide supply-voltages that are sufficiently high to power microelectronics. However, for high conversion efficiency, voltage converters need to be optimized for the limited input voltage range and the typically high internal resistance of microTEGs. To overcome the limitations of conventional voltage converters we present an optimized self-startup voltage converter with dynamic maximum power point tracking. The performance potential of our concept is theoretically and experimentally analyzed. The voltage conversion interface demonstrates energy harvesting from open-circuit voltages as low as 30.7 mV, and enables independent and full start-up from 131 mV. No additional external power supply is required at any time during operation. It can be operated with a wide range of internal resistances from 20.6 to − 4 kΩ with a conversation efficiency between η = 68–79%

On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase

Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of system with one fast rotating phase lead to a situation of such kind: numerical solution demonstrate phenomenon of scattering on resonances that is absent in the original system.Comment: 10 pages, 5 figure