The dispersive self-dual Einstein equations and the Toda lattice

The Boyer-Finley equation, or $SU(\infty)$-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionlesslimit of the $2d$-Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is studied in this paper. The results are achieved by using a deformation, based on an associative $\star$-product, of the algebra $sdiff(\Sigma^2)$ used in the study of the undeformed, or dispersionless, equations.Comment: 11 pages, LaTeX. To appear: J. Phys.

Molecular dynamics simulations of oxide memory resistors (memristors)

Reversible bipolar nano-switches that can be set and read electronically in a solid-state two-terminal device are very promising for applications. We have performed molecular-dynamics simulations that mimic systems with oxygen vacancies interacting via realistic potentials and driven by an external bias voltage. The competing short- and long-range interactions among charged mobile vacancies lead to density fluctuations and short-range ordering, while illustrating some aspects of observed experimental behavior, such as memristor polarity inversion.Comment: 15 pages, 5 figure

Effective temperatures in a simple model of non-equilibrium, non-Markovian dynamics

The concept of effective temperatures in nonequilibrium systems is studied within an exactly solvable model of non-Markovian diffusion. The system is coupled to two heat baths which are kept at different temperatures: one ('fast') bath associated with an uncorrelated Gaussian noise and a second ('slow') bath with an exponential memory kernel. Various definitions of effective temperatures proposed in the literature are evaluated and compared. The range of validity of these definitions is discussed. It is shown in particular, that the effective temperature defined from the fluctuation-dissipation relation mirrors the temperature of the slow bath in parameter regions corresponding to a separation of time scales. On the contrary, quasi-static and thermodynamic definitions of an effective temperature are found to display the temperature of the fast bath in most parameter regions

The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies

The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields. This symmetry enables formulae normally given implicitly in terms of residues, such as conserved charges and fluxes, to be calculated explicitly. As a corollary of these results the equivalence of the Benney and Toda hierarchies is established. It is further shown that such quantities may be expressed in terms of generalized hypergeometric functions, the simplest example involving Legendre polynomials. These results are then extended to systems derived from a rational Lax function and a logarithmic function. Various reductions are also studied.Comment: 29 pages, LaTe

Non equilibrium effects in fragmentation

We study, using molecular dynamics techniques, how boundary conditions affect the process of fragmentation of finite, highly excited, Lennard-Jones systems. We analyze the behavior of the caloric curves (CC), the associated thermal response functions (TRF) and cluster mass distributions for constrained and unconstrained hot drops. It is shown that the resulting CC's for the constrained case differ from the one in the unconstrained case, mainly in the presence of a ``vapor branch''. This branch is absent in the free expanding case even at high energies . This effect is traced to the role played by the collective expansion motion. On the other hand, we found that the recently proposed characteristic features of a first order phase transition taking place in a finite isolated system, i.e. abnormally large kinetic energy fluctuations and a negative branch in the TRF, are present for the constrained (dilute) as well the unconstrained case. The microscopic origin of this behavior is also analyzed.Comment: 21 pages, 11 figure

The Moyal bracket and the dispersionless limit of the KP hierarchy

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is particularly simple.Comment: 9 pages, LaTe

Interaction of vortices in thin superconducting films and Berezinskii-Kosterlitz-Thouless transition

The precondition for the BKT transition in thin superconducting films, the logarithmic intervortex interaction, is satisfied at distances short relative to $\Lambda=2\lambda^2/d$, $\lambda$ is the London penetration depth of the bulk material and $d$ is the film thickness. For this reason, the search for the transition has been conducted in samples of the size $L<\Lambda$. It is argued below that film edges turn the interaction into near exponential (short-range) thus making the BKT transition impossible. If however the substrate is superconducting and separated from the film by an insulated layer, the logarithmic intervortex interaction is recovered and the BKT transition should be observable.Comment: 4 pages, no figure

Developmental contexts and features of elite academy football players: Coach and player perspectives

Player profiling can reap many benefits; through reflective coach-athlete dialogue that produces a profile the athlete has a raised awareness of their own development, while the coach has an opportunity to understand the athlete's viewpoint. In this study, we explored how coaches and players perceived the development features of an elite academy footballer and the contexts in which these features are revealed, in order to develop a player profile to be used for mentoring players. Using a Delphi polling technique, coaches and players experienced a number of 'rounds' of expressing their opinions regarding player development contexts and features, ultimately reduced into a consensus. Players and coaches had differing priorities on the key contexts of player development. These contexts, when they reflect the consensus between players and coaches were heavily dominated by ability within the game and training. Personal, social, school, and lifestyle contexts featured less prominently. Although 'discipline' was frequently mentioned as an important player development feature, coaches and players disagreed on the importance of 'training'

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page

An exploration of gene-environment interaction and asthma in a large sample of 5-year-old Dutch twins.

A consistent finding from twin studies is that the environment shared by family members does not contribute to the variation in susceptibility to asthma. At the same time, it is known that environmental risk factors that are shared by family members are associated with the liability for asthma. We hypothesize that the absence of a main effect of shared environmental factors in twin studies can be explained by gene-environment interaction, that is, that the effect of an environmental factor shared by family members depends on the genotype of the individual. We explore this hypothesis by modeling the resemblance in asthma liability in twin pairs as a function of various environmental risk factors and test for gene-environment interaction. Asthma data were obtained by parental report for nearly 12,000 5-year-old twin pairs. A series of environmental risk factors was examined: birth cohort, gestational age, time spent in incubator, breastfeeding, maternal educational level, maternal smoking during pregnancy, current smoking of parents, having older siblings, and amount of child care outside home. Results revealed that being a boy, born in the 1990s, premature birth, longer incubator time, and child care outside home increased the risk for asthma. With the exception of premature birth, however, none of these factors modified the genetic effects on asthma. In very premature children shared environmental influences were important. In children born after a gestation of 32 weeks or more only genetic factors were important to explain familial resemblance for asthma