Singular lagrangians: some geometric structures along the Legendre map

New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the computation of the kernel of the presymplectic form of lagrangian formalism, the construction of the lagrangian dynamical vector fields, and the characterisation of dynamical symmetries.Comment: 27 pages; minor changes, a reference update

The Emotional Self-Efficacy Scale: Adaptation and Validation for Young Adolescents

Emotional self-efficacy (ESE) is an important aspect of emotional functioning, with current measures for children and adolescents focused on the measurement of self-beliefs in relation to the management of emotions. In the present study, we report the psychometric properties of the first adaptation of the Emotional Self-Efficacy Scale for youth (Youth-ESES) that measures additional aspects of ESE, such as perceiving and understanding emotions and helping others modulate their emotions. Participants were 192 young adolescents aged 11 to 13 years from a U.K. state school. They completed the Youth-ESES and measures of ability emotional intelligence (EI) and cognitive ability. Results support the same four-factor structure that has been previously documented using the adult version of the ESES, with the four subscales being largely independent from cognitive ability and only moderately related to ability EI. However, the four subscales were less differentiated in the present study compared with adult data previously published, suggesting that there is a strong general factor underlying young adolescents’ ESE scores. Overall, the results suggest that the adapted Youth-ESES can be reliably used with youth, and that confidence in how a young person feels about his or her emotional functioning remains distinct from emotional skill

A white dwarf-neutron star relativistic binary model for soft gamma-ray repeaters

A scenario for SGRs is introduced in which gravitational radiation reaction effects drive the dynamics of an ultrashort orbital period X-ray binary embracing a high-mass donor white dwarf (WD) to a rapidly rotating low magnetised massive neutron star (NS) surrounded by a thick, dense and massive accretion torus. Driven by GR reaction, sparsely, the binary separation reduces, the WD overflows its Roche lobe and the mass transfer drives unstable the accretion disk around the NS. As the binary circular orbital period is a multiple integer number ($m$) of the period of the WD fundamental mode (Pons et al. 2002), the WD is since long pulsating at its fundamental mode; and most of its harmonics, due to the tidal interaction with its NS orbital companion. Hence, when the powerful irradiation glows onto the WD; from the fireball ejected as part of the disk matter slumps onto the NS, it is partially absorbed. This huge energy excites other WD radial ($p$-mode) pulsations (Podsiadlowski 1991,1995). After each mass-transfer episode the binary separation (and orbital period) is augmented significantly (Deloye & Bildsten 2003; Al\'ecyan & Morsink 2004) due to the binary's angular momentum redistribution. Thus a new adiabatic inspiral phase driven by GR reaction starts which brings the binary close again, and the process repeats. This model allows to explain most of SGRs observational features: their recurrent activity, energetics of giant superoutbursts and quiescent stages, and particularly the intriguing subpulses discovered by BeppoSAX (Feroci et al. 1999), which are suggested here to be {\it overtones} of the WD radial fundamental mode (see the accompanying paper: Mosquera Cuesta 2004b).Comment: This paper was submitted as a "Letter to the Editor" of MNRAS in July 17/2004. Since that time no answer or referee report was provided to the Author [MNRAS publication policy limits reviewal process no longer than one month (+/- half more) for the reviewal of this kind of submission). I hope this contribution is not receiving a similar "peer-reviewing" as given to the A. Dar and A. De Rujula's "Cannonball model for gamma-ray bursts", or to the R.K. Williams' "Penrose process for energy extraction from rotating black holes". The author welcomes criticisms and suggestions on this pape

Feedback control of unstable cellular solidification fronts

We present a numerical and experimental study of feedback control of unstable cellular patterns in directional solidification (DS). The sample, a dilute binary alloy, solidifies in a 2D geometry under a control scheme which applies local heating close to the cell tips which protrude ahead of the other. For the experiments, we use a real-time image processing algorithm to track cell tips, coupled with a movable laser spot array device, to heat locally. We show, numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable, and the spacing becomes uniform through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl

Canonical Gravity, Diffeomorphisms and Objective Histories

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by constraints on the phase space so that a) The algebra of the generators reflects the algebra of the diffeomorphism group. b) The Poisson brackets of the basic fields with the generators reflects the space-time transformation properties of these basic fields. This suggests that in a purely Hamiltonian approach the requirement of diffeomorphism invariance should be interpreted to include b) and not just a) as one might naively suppose. Giving up b) amounts to giving up objective histories, even at the classical level. This observation has implications for Loop Quantum Gravity which are spelled out in a companion paper. We also describe an analogy between canonical gravity and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees' comments, accepted for publication in Classical and Quantum Gravit

Hamiltonian Noether theorem for gauge systems and two time physics

The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al. model and, with special emphasis, to two time physics.Comment: 20 pages, Latex, references added, the "massless" sense of (87) is clarifie

Cooling of Neutron Stars: Two Types of Triplet Neutron Pairing

We consider cooling of neutron stars (NSs) with superfluid cores composed of neutrons, protons, and electrons (assuming singlet-state pairing of protons, and triplet-state pairing of neutrons). We mainly focus on (nonstandard) triplet-state pairing of neutrons with the $|m_J| = 2$ projection of the total angular momentum of Cooper pairs onto quantization axis. The specific feature of this pairing is that it leads to a power-law (nonexponential) reduction of the emissivity of the main neutrino processes by neutron superfluidity. For a wide range of neutron critical temperatures $T_{cn}$, the cooling of NSs with the $|m_J| = 2$ superfluidity is either the same as the cooling with the $m_J = 0$ superfluidity, considered in the majority of papers, or much faster. The cooling of NSs with density dependent critical temperatures $T_{cn}(\rho)$ and $T_{cp}(\rho)$ can be imitated by the cooling of the NSs with some effective critical temperatures $T_{cn}$ and $T_{cp}$ constant over NS cores. The hypothesis of strong neutron superfluidity with $|m_J| = 2$ is inconsistent with current observations of thermal emission from NSs, but the hypothesis of weak neutron superfluidity of any type does not contradict to observations.Comment: 10 pages, 6 figure

Evidence for Heating of Neutron Stars by Magnetic Field Decay

We show the existence of a strong trend between neutron star surface temperature and the dipolar component of the magnetic field extending through three orders of field magnitude, a range that includes magnetars, radio-quiet isolated neutron stars, and many ordinary radio pulsars. We suggest that this trend can be explained by the decay of currents in the crust over a time scale of few Myr. We estimate the minimum temperature that a NS with a given magnetic field can reach in this interpretation.Comment: 4 pages, 1 figures, version accepted for publication in Phys. Rev. Let