Hall drift of axisymmetric magnetic fields in solid neutron-star matter

Hall drift, i. e., transport of magnetic flux by the moving electrons giving rise to the electrical current, may be the dominant effect causing the evolution of the magnetic field in the solid crust of neutron stars. It is a nonlinear process that, despite a number of efforts, is still not fully understood. We use the Hall induction equation in axial symmetry to obtain some general properties of nonevolving fields, as well as analyzing the evolution of purely toroidal fields, their poloidal perturbations, and current-free, purely poloidal fields. We also analyze energy conservation in Hall instabilities and write down a variational principle for Hall equilibria. We show that the evolution of any toroidal magnetic field can be described by Burgers' equation, as previously found in plane-parallel geometry. It leads to sharp current sheets that dissipate on the Hall time scale, yielding a stationary field configuration that depends on a single, suitably defined coordinate. This field, however, is unstable to poloidal perturbations, which grow as their field lines are stretched by the background electron flow, as in instabilities earlier found numerically. On the other hand, current-free poloidal configurations are stable and could represent a long-lived crustal field supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction; accepted by Astronomy & Astrophysic

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Exact joint density-current probability function for the asymmetric exclusion process

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach, and by the introduction of new operators satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure

Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice, and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes. In the maximal current phase and on the coexistence line (between high/low density phases), the power spectrum displays algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the high/low density phases, we find pronounced \emph{oscillations}, which damp into power laws. This behavior can be understood in terms of driven biased diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure

Ellipticals at z=0 from Self-Consistent Hydrodynamical Simulations: Clues on Age Effects in their Stellar Populations

We present results of a study of the stellar age distributions in the sample of elliptical-like objects (ELOs) identified at z=0 in four simulations operating in the context of a concordance cosmological model. The simulations show that the formation of most stars in each ELO of the sample is a consequence of violent dynamical events, either fast multiclump collapse at high z, or mergers at lower z. This second way can explain the age spread as well as the dynamical peculiarities observed in some ellipticals, but its relative weight is never dominant and decreases as the ELO mass at the halo scale, $M_{vir}$, increases, to such an extent that some recent mergers contributing an important fraction to the total ELO mass can possibly contribute only a small fraction of new born stars. More massive objects have older means and narrower spreads in their stellar age distributions than less massive ones. The ELO sample shows also a tight correlation between $M_{vir}$ and the central stellar l.o.s. velocity dispersion, $\sigma_{los}$. This gives a trend of the means and spreads of ELO stellar populations with $\sigma_{los}$ that is consistent, even quantitatively, with the age effects observationally detected in the stellar populations of elliptical galaxies. Therefore, these effects can be explained as the observational manifestation of the intrinsic correlations found in the ELO sample between $M_{vir}$ and the properties of the stellar age distribution, on the one hand, and $M_{vir}$ and $\sigma_{los}$, on the other hand. These correlations hint, for the first time, at a possible way to reconcile age effects in ellipticals, and, particularly, the increase of $\alpha /$ ratios with $\sigma_{los}$, with the hierarchical clustering paradigm.Comment: 13 pages, 2 figures, accepted for publication in Astrophysical Journal Letter

Exact probability function for bulk density and current in the asymmetric exclusion process

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques, and by introducing a modified version of the original operator algebra. As a byproduct of these considerations we also arrive at a novel and very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure

The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension

We extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that the growth morphology can be interpreted in terms of dynamically evolving textures of localized growth modes with superimposed diffusive modes. In the Cole-Hopf representation the growth modes are static solutions to the diffusion equation and the nonlinear Schroedinger equation, subsequently boosted to finite velocity by a Galilei transformation. We discuss the dynamics of the pattern formation and, briefly, the superimposed linear modes. Implementing the stochastic interpretation we discuss kinetic transitions and in particular the properties in the pair mode or dipole sector. We find the Hurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipole sector. Finally, applying Derrick's theorem based on constrained minimization we show that the upper critical dimension is d=4 in the sense that growth modes cease to exist above this dimension.Comment: 27 pages, 19 eps figs, revte

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include

Merging and fragmentation in the Burgers dynamics

We explore the noiseless Burgers dynamics in the inviscid limit, the so-called ``adhesion model'' in cosmology, in a regime where (almost) all the fluid particles are embedded within point-like massive halos. Following previous works, we focus our investigations on a ``geometrical'' model, where the matter evolution within the shock manifold is defined from a geometrical construction. This hypothesis is at variance with the assumption that the usual continuity equation holds but, in the inviscid limit, both models agree in the regular regions. Taking advantage of the formulation of the dynamics of this ``geometrical model'' in terms of Legendre transforms and convex hulls, we study the evolution with time of the distribution of matter and the associated partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass distribution derives from a triangulation in Lagrangian space, while the dual Voronoi-like tessellation in Eulerian space gives the boundaries of empty regions with shock nodes at their vertices. We then emphasize that this dynamics actually leads to halo fragmentations for space dimensions greater or equal to 2 (for the inviscid limit studied in this article). This is most easily seen from the properties of the Lagrangian-space triangulation and we illustrate this process in the two-dimensional (2D) case. In particular, we explain how point-like halos only merge through three-body collisions while two-body collisions always give rise to two new massive shock nodes (in 2D). This generalizes to higher dimensions and we briefly illustrate the three-dimensional (3D) case. This leads to a specific picture for the continuous formation of massive halos through successive halo fragmentations and mergings.Comment: 21 pages, final version published in Phys.Rev.