Conditions for Phase Equilibrium in Supernovae, Proto-Neutron and Neutron Stars

We investigate the qualitative properties of phase transitions in a general way, if not the single particle numbers of the system but only some particular charges like e.g. baryon number are conserved. In addition to globally conserved charges we analyze the implications of locally conserved charge fractions, like e.g. local electric charge neutrality or locally fixed proton or lepton fractions. The conditions for phase equilibrium are derived and it is shown, that the properties of the phase transition do not depend on the locally conserved fractions. Finally, the general formalism is applied to the liquid-gas phase transition and the hadron-quark phase transition for typical astrophysical environments like in supernovae, proto-neutron or a neutron stars. We demonstrate that the Maxwell construction known from cold-deleptonized neutron star matter with two locally charge neutral phases requires modifications and further assumptions concerning the applicability for hot lepton-rich matter. All possible combinations of local and global conservation laws are analyzed, and the physical meaningful cases are identified. Several new kinds of mixed phases are presented, as e.g. a locally charge neutral mixed phase in proto-neutron stars which will disappear during the cooling and deleptonization of the proto-neutron star.Comment: 18 page

One-sided Heegaard splittings of RP^3

Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.Comment: This is the version published by Algebraic & Geometric Topology on 20 September 200

Dynamical Systems On Three Manifolds Part II: 3-Manifolds,Heegaard Splittings and Three-Dimensional Systems

The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neighbourhood of an operating point. Away from that point, the system may have totally different behaviour and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on 2- and 3- manifolds and show that it is possible to obtain systems with 'arbitrarily strange' behaviour, i.e., arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.Comment: 15 pages with 9 pictures. Accepted by Int. J. of Bifurcation and Chao

Finite-size effects in dynamics of zero-range processes

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluid-like behavior up to a density {\rho}c (L), which is the finite-size counterpart of the critical density {\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the cross-over behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster and correlations in its motion are studied.Comment: http://pre.aps.org/abstract/PRE/v82/i3/e03111

Mass, radius, and composition of the outer crust of nonaccreting cold neutron stars

The properties and composition of the outer crust of nonaccreting cold neutron stars are studied by applying the model of Baym, Pethick, and Sutherland, which was extended by including higher order corrections of the atomic binding, screening, exchange and zero-point energy. The most recent experimental nuclear data from the atomic mass table of Audi, Wapstra, and Thibault from 2003 is used. Extrapolation to the drip line is utilized by various state-of-the-art theoretical nuclear models (finite range droplet, relativistic nuclear field and non-relativistic Skyrme Hartree-Fock parameterizations). The different nuclear models are compared with respect to the mass and radius of the outer crust for different neutron star configurations and the nuclear compositions of the outer crust.Comment: 5 pages, 2 figures, submitted to J. Phys. G, part of the proceedings of the Nuclear Physics in Astrophysics III conference in Dresde

EROs found behind lensing clusters: II.Empirical properties, classification, and SED modelling based on multi-wavelength observations

We study the properties and nature of extremely red galaxies (ERO, R-K>5.6) found behind two lensing clusters and compare them with other known galaxy populations. New HST/ACS observations, Spitzer IRAC and MIPS, and Chandra/ACIS observations of the two lensing clusters Abell 1835 and AC114 contemplate our earlier optical and near-IR observations and have been used to study extremely red objects (EROs) in these deep fields. We have found 6 and 9 EROs in Abell 1835 and AC114. Several (7) of these objects are undetected up to the I and/or z band, and are hence ``optical'' drop-out sources. The photometric redshifts of most of our sources (80%) are z~0.7-1.5. According to simple colour-colour diagrams the majority of our objects would be classified as hosting old stellar populations. However, there are clear signs of dusty starbursts for several among them. These objects correspond to the most extreme ones in R-K colour. We estimate a surface density of (0.97+-0.31) arcmin-2 for EROs with (R-K>5.6) at K<20.5. Among our 15 EROs 6 (40 %) also classify as distant red galaxies (DRGs). 11 of 13 EROs with available IRAC photometry also fulfil the selection criteria for IRAC selected EROs (IEROs) of Yan et al. (2004). SED modelling shows that ~ 36 % of the IEROs in our sample are luminous or ultra-luminous infrared galaxies ((U)LIRG). Some very red DRGs are found to be very dusty starbursts, even (U)LIRGs, as also supported by their mid-IR photometry. No indication for AGNs is found, although faint activity cannot be excluded for all objects. From mid-IR and X-ray data 5 objects are clearly classified as starbursts. The derived properties are quite similar to those of DRGs and IEROs, except for 5 extreme objects in terms of colours, for which a very high extinction (Av>3) is found.Comment: 20 pages, 10 figures, accepted for publication in A&

A new possible quark-hadron mixed phase in protoneutron stars

The phase transition from hadronic matter to quark matter at high density might be a strong first order phase transition in presence of a large surface tension between the two phases. While this implies a constant-pressure mixed phase for cold and catalyzed matter this is not the case for the hot and lepton rich matter formed in a protoneutron star. We show that it is possible to obtain a mixed phase with non-constant pressure by considering the global conservation of lepton number during the stage of neutrino trapping. In turn, it allows for the appearance of a new kind of mixed phase as long as neutrinos are trapped and its gradual disappearance during deleptonization. This new mixed phase, being composed by two electric neutral phases, does not develop a Coulomb lattice and it is formed only by spherical structures, drops and bubbles, which can have macroscopic sizes. The disappearance of the mixed phase at the end of deleptonization might lead to a delayed collapse of the star into a more compact configuration containing a core of pure quark phase. In this scenario, a significant emission of neutrinos and, possibly, gravitational waves are expected.Comment: 4 pages, 4 figure

Cellular excitability and the regulation of functional neuronal identity: from gene expression to neuromodulation

The intrinsic properties of a neuron determine the translation of synaptic input to axonal output. It is this input– output relationship that is the heart of all nervous system activity. As such, the overall regulation of the intrinsic excitability of a neuron directly determines the output of that neuron at a given point in time, giving the cell a unique “functional identity.” To maintain this distinct functional output, neurons must adapt to changing patterns of synaptic excitation. These adaptations are essential to prevent neurons from either falling silent as synaptic excitation falls or becoming saturated as excitation increases. In the absence of stabilizing mechanisms, activity-dependent plasticity could drive neural activity to saturation or quiescence. Furthermore, as cells adapt to changing patterns of synaptic input, presumably the overall balance of intrinsic conductances of the cell must be maintained so that reliable output is achieved (Daoudal and Debanne, 2003; Turrigiano and Nelson, 2004; Frick and Johnston, 2005). Although these regulatory phenomena have been well documented, the molecular and physiological mechanisms involved are poorly understood

Triaxial nuclear models and the outer crust of nonaccreting cold neutron stars

The properties and composition of the outer crust of nonaccreting cold neutron stars are studied by applying the model of Baym, Pethick, and Sutherland (BPS) and taking into account for the first time triaxial deformations of nuclei. Two theoretical nuclear models, Hartree-Fock plus pairing in the BCS approximation (HF-BCS) with Skyrme SLy6 parametrization and Hartree-Fock-Bogolyubov (HFB) with Gogny D1S force, are used to calculate the nuclear masses. The two theoretical calculations are compared concerning their neutron drip line, binding energies, magic neutron numbers, and the sequence of nuclei in the outer crust of nonaccreting cold neutron stars, with special emphasis on the effect of triaxial deformations. The BPS model is extended by the higher-order corrections for the atomic binding, screening, exchange and zero-point energies. The influence of the higher-order corrections on the sequence of the outer crust is investigated.Comment: 7 page