Poisson actions up to homotopy and their quantization

Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are equivalent to Poisson principal bundles and describe their quantization to symmetries up to homotopy of the quantized algebras of functions.Comment: 8 page

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure, which enables us to derive an effective one-dimensional (1D) evolution equation, governing the 1D density of the particles in the channel. In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation, corrected by an effective diffusion coefficient D(x), depending on the longitudinal coordinate x. Our result is an approximate formula for D(x), involving also influence of the transverse force. Our calculations are verified on the stationary diffusion in a linear cone, which is exactly solvable.Comment: 10 pages, 7 figures, submitted in Phys. Rev.

The spectral properties of the Falicov-Kimball model in the weak-coupling limit

The $f$ and $d$ electron density of states of the one-dimensional Falicov-Kimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the $d$-electron gap ($\Delta_{d}$), the $f$-electron gap ($\Delta_{f}$), and the $fd$-electron gap ($\Delta_{fd}$) as functions of the $f$-level energy $E_f$ and hybridization $V$. It is shown that the spinless Falicov-Kimball model behaves fully differently for zero and finite hybridization between $f$ and $d$ states. At zero hybridization the energy gaps do not coincide ($\Delta_{d}\neq \Delta_{f} \neq \Delta_{fd}$), and the activation gap $\Delta_{fd}$ vanishes discontinuously at some critical value of the $f$-level energy $E_{fc}$. On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point $E_f=E_{fc}$. The importance of these results for a description of real materials is discussed.Comment: 10 pages, 7 figures, LaTe

Survival probability (heat content) and the lowest eigenvalue of Dirichlet Laplacian

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Pad\'e interpolation between the short-time and the long-time behavior of the survival probability, i.e. between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.Comment: Accepted in IJMP

Flare-induced changes of the photospheric magnetic field in a δ\delta-spot deduced from ground-based observations

Aims: Changes of the magnetic field and the line-of-sight velocities in the photosphere are being reported for an M-class flare that originated at a $\delta$-spot belonging to active region NOAA 11865. Methods: High-resolution ground-based near-infrared spectropolarimetric observations were acquired simultaneously in two photospheric spectral lines, Fe I 10783 \AA\ and Si I 10786 \AA, with the Tenerife Infrared Polarimeter at the Vacuum Tower Telescope (VTT) in Tenerife on 2013 October 15. The observations covered several stages of the M-class flare. Inversions of the full-Stokes vector of both lines were carried out and the results were put into context using (extreme)-ultraviolet filtergrams from the Solar Dynamics Observatory (SDO). Results: The active region showed high flaring activity during the whole observing period. After the M-class flare, the longitudinal magnetic field did not show significant changes along the polarity inversion line (PIL). However, an enhancement of the transverse magnetic field of approximately 550 G was found that bridges the PIL and connects umbrae of opposite polarities in the $\delta$-spot. At the same time, a newly formed system of loops appeared co-spatially in the corona as seen in 171 \AA\ filtergrams of the Atmospheric Imaging Assembly (AIA) on board SDO. However, we cannot exclude that the magnetic connection between the umbrae already existed in the upper atmosphere before the M-class flare and became visible only later when it was filled with hot plasma. The photospheric Doppler velocities show a persistent upflow pattern along the PIL without significant changes due to the flare. Conclusions: The increase of the transverse component of the magnetic field after the flare together with the newly formed loop system in the corona support recent predictions of flare models and flare observations.Comment: 8 pages, 9 figures. Accepted for publication in Astronomy & Astrophysic

Unconventional order/disorder behaviour in Al–Co–Cu–Fe–Ni multi-principal element alloys after casting and annealing

The effect of Cu concentration on the order/disorder behaviour of the AlCoCuxFeNi (x = 0.6 to 3.0) multi-principal element alloys was investigated. BCC and/or FCC phases were observed in the microstructures of the alloys after casting and annealing at 1050 ◦C followed by slow cooling. Interesting is that the alloys form ordered structures after casting and disordered structures after annealing and slow cooling, while the opposite would be expected. The ordering in the as-cast state is explained by the strong affinity of Al to transition metals, which results in the formation of supercell structures having sublattices occupied by certain elements only. Disordering after annealing has two reasons. Either the phase is composed of nearly pure element (Cu) and is disordered by default or it is composed of randomly distributed nano-segregated regions within a single phase resulting in a uniform distribution of all elements in the sublattices and therefore appearing to be macroscopically disordered. The reason for the formation of such nano-segregated areas might reside in the reduction of Gibbs free energy due to the annealing by the interplay between enthalpy and entropy

High school students' attitudes towards spiders: a cross-cultural comparison

Spiders are traditionally considered to be among the least popular of animals. Current evidence suggests that a negative attitude towards spiders could be influenced by both cultural and evolutionary pressures. Some researchers suggest that science education activities could positively influence students' perceptions of spiders. Their evidence is, however, ambivalent. Using a five-point score Likert-type questionnaire in which the items were developed in a similar way to four of Keller’s categories of attitude (scientistic, negativistic, naturalistic, and ecologistic) towards invertebrates, we compared the level of knowledge of and attitudes towards spiders of high school students from two countries, Slovakia (n = 354) and South Africa (n = 382). The students represented different cultures and followed dissimilar science education curricula. Only among the Slovakian students there was a statistically significant, but low correlation between knowledge and attitude (r = .30). The Slovakian students had less fear of spiders. The South African students scored higher in the categories of scientistic, naturalistic and ecologistic attitudes. Comparison of attitude towards spiders of indigenous Africans from coeducational Catholic schools revealed that, South African students have greater fear of spiders than Slovakian students, supporting the biological preparedness hypothesis. This hypothesis predicts a greater fear of spiders in South Africa than in Europe since several South African spiders possess venoms that are dangerous to humans. The results of this study are discussed from science education, cultural and evolutionary perspectives

Response Time is More Important than Walking Speed for the Ability of Older Adults to Avoid a Fall after a Trip

We previously reported that the probability of an older adult recovering from a forward trip and using a “lowering” strategy increases with decreased walking velocity and faster response time. To determine the within-subject interaction of these variables we asked three questions: (1) Is the body orientation at the time that the recovery foot is lowered to the ground (“tilt angle”) critical for successful recovery? (2) Can a simple inverted pendulum model, using subject-specific walking velocity and response time as input variables, predict this body orientation, and thus success of recovery? (3) Is slower walking velocity or faster response time more effective in preventing a fall after a trip? Tilt angle was a perfect predictor of a successful recovery step, indicating that the recovery foot placement must occur before the tilt angle exceeds a critical value of between 23° and 26° from vertical. The inverted pendulum model predicted the tilt angle from walking velocity and response time with an error of 0.4±2.2° and a correlation coefficient of 0.93. The model predicted that faster response time was more important than slower walking velocity for successful recovery. In a typical individual who is at risk for falling, we predicted that a reduction of response time to a normal value allows a 77% increase in safe walking velocity. The mathematical model produced patient-specific recommendations for fall prevention, and suggested the importance of directing therapeutic interventions toward improving the response time of older adults

Interval-Like Graphs and Digraphs

We unify several seemingly different graph and digraph classes under one umbrella. These classes are all, broadly speaking, different generalizations of interval graphs, and include, in addition to interval graphs, adjusted interval digraphs, threshold graphs, complements of threshold tolerance graphs (known as `co-TT\u27 graphs), bipartite interval containment graphs, bipartite co-circular arc graphs, and two-directional orthogonal ray graphs. (The last three classes coincide, but have been investigated in different contexts.) This common view is made possible by introducing reflexive relationships (loops) into the analysis. We also show that all the above classes are united by a common ordering characterization, the existence of a min ordering. We propose a common generalization of all these graph and digraph classes, namely signed-interval digraphs, and show that they are precisely the digraphs that are characterized by the existence of a min ordering. We also offer an alternative geometric characterization of these digraphs. For most of the above graph and digraph classes, we show that they are exactly those signed-interval digraphs that satisfy a suitable natural restriction on the digraph, like having a loop on every vertex, or having a symmetric edge-set, or being bipartite. For instance, co-TT graphs are precisely those signed-interval digraphs that have each edge symmetric. We also offer some discussion of future work on recognition algorithms and characterizations