The internal composition of proto-neutron stars under strong magnetic fields

In this work, we study the effects of magnetic fields and rotation on the structure and composition of proto-neutron stars (PNS's). A hadronic chiral SU(3) model is applied to cold neutron stars (NS) and proto-neutron stars with trapped neutrinos and at fixed entropy per baryon. We obtain general relativistic solutions for neutron and proto-neutron stars endowed with a poloidal magnetic field by solving Einstein-Maxwell field equations in a self-consistent way. As the neutrino chemical potential decreases in value over time, this alters the chemical equilibrium and the composition inside the star, leading to a change in the structure and in the particle population of these objects. We find that the magnetic field deforms the star and significantly alters the number of trapped neutrinos in the stellar interior, together with strangeness content and temperature in each evolution stage.Comment: Accepted for publication in PR

Balanced Boolean functions that can be evaluated so that every input bit is unlikely to be read

A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random inputs, no input bit is read with probability more than Theta(n^{-1/2} sqrt{log n}). We give a balanced monotone Boolean function for which the corresponding probability is Theta(n^{-1/3} log n). We then show that for any randomized algorithm for evaluating a balanced Boolean function, when the input bits are uniformly random, there is some input bit that is read with probability at least Theta(n^{-1/2}). For balanced monotone Boolean functions, there is some input bit that is read with probability at least Theta(n^{-1/3}).Comment: 11 page

Integral Launch and Reentry Vehicle - Executive Summary Final Report

Characteristics of integral launch and reentry vehicles - executive summar

Many-body forces in magnetic neutron stars

In this work, we study in detail the effects of many-body forces on the equation of state and the structure of magnetic neutron stars. The stellar matter is described within a relativistic mean field formalism that takes into account many-body forces by means of a non-linear meson field dependence on the nuclear interaction coupling constants. We assume that matter is at zero temperature, charge neutral, in beta-equilibrium, and populated by the baryon octet, electrons, and muons. In order to study the effects of different degrees of stiffness in the equation of state, we explore the parameter space of the model, which reproduces nuclear matter properties at saturation, as well as massive neutron stars. Magnetic field effects are introduced both in the equation of state and in the macroscopic structure of stars by the self-consistent solution of the Einstein-Maxwell equations. In addition, effects of poloidal magnetic fields on the global properties of stars, as well as density and magnetic field profiles are investigated. We find that not only different macroscopic magnetic field distributions, but also different parameterizations of the model for a fixed magnetic field distribution impact the gravitational mass, deformation and internal density profiles of stars. Finally, we also show that strong magnetic fields affect significantly the particle populations of starsComment: accepted by The Astrophysical Journa

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio