Rigid ball-polyhedra in Euclidean 3-space

A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ball-polyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ball-polyhedron if its vertex-edge-face structure is a lattice (with respect to containment). To each edge of a ball-polyhedron one can assign an inner dihedral angle and say that the given ball-polyhedron is locally rigid with respect to its inner dihedral angles if the vertex-edge-face structure of the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron up to congruence locally. The main result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra stating that any simple and standard ball-polyhedron is locally rigid with respect to its inner dihedral angles.Comment: 11 pages, 2 figure

Magnetic relaxation in the Bianchi-I universe

Extended Einstein-Maxwell model and its application to the problem of evolution of magnetized Bianchi-I Universe are considered. The evolution of medium magnetization is governed by a relaxation type extended constitutive equation. The series of exact solutions to the extended master equations is obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is shown to become non-monotonic (accelerated/decelerated) in both principal directions (along the magnetic field and orthogonal to it). A specific type of expansion, the so-called evolution with hidden magnetic field, is shown to appear when the magnetization effectively screens the magnetic field and the latter disappears from the equations for gravitational field.Comment: 32 page

Pressure Training: From Research to Applied Practice

Pressure training (PT) strategically increases pressure during training to improve athletes’ abilities to cope with pressure in competition. Although evidence suggests that PT can improve performance under pressure, implementation of PT can be challenging in applied settings. The purpose of this article is to guide sport psychology practitioners and coaches in conducting PT at both elite and lower levels of sport. We first outline basics of PT, including who will benefit from the intervention and when to conduct it. We also clarify the purpose of PT and distinguish it from other forms of coaching that may seem similar. The next section includes steps for conducting PT effectively. Based on research and applied practice, these recommendations address how to create pressure and how to establish training environments that are conducive to PT. Each recommendation describes a principle that can guide practitioners and coaches as they tailor PT to specific sports and levels of competition. We argue that the use of negative consequences, an existing or “baseline” level of pressure, and involvement of coaches are key ingredients for conducting PT that promotes athletes’ development

On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, eg. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with the three dimensional experiment show that three and two dimensional approximations are in excellent agreement and one dimensional approximations are in good qualitative agreement. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.Comment: 24 pages, 28 figures, submitted to Phys Rev

Floquet theory of neutrino oscillations in the earth

We review the Floquet theory of linear differential equations with periodic coefficients and discuss its applications to neutrino oscillations in matter of periodically varying density. In particular, we consider parametric resonance in neutrino oscillations which can occur in such media, and discuss implications for oscillations of neutrinos traversing the earth and passing through the earth's core.Comment: LaTeX, 28 pages, 8 eps figures. Contribution to the special issue of Yad. Fiz. dedicated to the memory of A.B. Migda

The role and creation of pressure in training: Perspectives of athletes and sport psychologists

To prepare athletes for psychological pressure of competition, pressure training (PT) systematically applies pressure on athletes during training. This study explored how to create pressure for PT and how PT improves performance in competition. Specifically, it aimed to explore the views of sport psychologists and athletes on: (a) common properties of effective pressure manipulations, and (b) PT’s mechanisms for improving performance under pressure. Eight sport psychologists and eight international-level athletes participated in semi-structured interviews. Thematic analysis identified three properties of effective pressure manipulations: (a) extending the reach of consequences, (b) simulating psychological demands of competition, and (c) approximating, but not replicating, intensity of competition pressure. Analysis also produced three themes that described how PT benefits performance: (a) learn and practice coping skills, (b) “change the relationship” with pressure, and (c) increase the quality of training. Understanding these benefits can help communicate to athletes why they should participate in PT.  Lay summary: Pressure in training can help athletes adjust to pressure in competition, and this study found that practitioners can create pressure by applying psychological demands and consequences that have an extended impact on athletes. Athletes can then practice coping skills and learn that pressure does not have to hurt performance. • To create pressure in training, practitioners should implement pressure manipulations that increase the sense of importance to perform well. • These pressure manipulations include consequences that have extended reach or demands that emphasize psychological challenges of competition. • PT helps athletes train mental skills learned in workshops or one-on-one consulting

Following the signs: applying urban regime analysis to a UK case study

As the debate continues regarding the applicability of urban regime analysis in a UK context, three aspects stand out as highly significant: the target for analysis, the mode of scrutiny, and the context of local governing arrangements with its implications for interdependence as an impetus for co-operation. This article will examine urban regime analysis and the move from government to governance in order to answer why and how the private, voluntary and public sectors might be inclined to collaborate in regimes. In addition, the regime analysis will provide the parameters for examination whilst the issue of governance will afford context for local governing arrangements. Although some issues require slight reframing to reflect the UK context, the article will follow a rigorous framework for examination utilizing the full weight of regime analysis as articulated by Stone such that it could not be accused of “concept stretching.” Far from it: Through the examination of an informal partnership, a coalition of actors from the public, private, and voluntary sectors that has been in existence for more than 13 years, the article focuses, specifically, on the long-term, less visible aspects of local governance. As such, it is able to demonstrate how economic and political change can have a tangible effect on the manifestation of interdependence as an impetus for co-operation, not only for this specific locale but also for other cities facing similar challenges