Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

Defect formation and local gauge invariance

We propose a new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry. This mechanism leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global theories. We confirm these predictions in numerical simulations, and they can also be tested in superconductor experiments. We believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and the equations of motion added. To appear in PRL (http://prl.aps.org/

Critical Collapse of an Ultrarelativistic Fluid in the Γ→1\Gamma\to 1 Limit

In this paper we investigate the critical collapse of an ultrarelativistic perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of $\Gamma\to 1$. We calculate the limiting continuously self similar (CSS) solution and the limiting scaling exponent by exploiting self-similarity of the solution. We also solve the complete set of equations governing the gravitational collapse numerically for $(\Gamma-1) = 10^{-2},...,10^{-6}$ and compare them with the CSS solutions. We also investigate the supercritical regime and discuss the hypothesis of naked singularity formation in a generic gravitational collapse. The numerical calculations make use of advanced methods such as high resolution shock capturing evolution scheme for the matter evolution, adaptive mesh refinement, and quadruple precision arithmetic. The treatment of vacuum is also non standard. We were able to tune the critical parameter up to 30 significant digits and to calculate the scaling exponents accurately. The numerical results agree very well with those calculated using the CSS ansatz. The analysis of the collapse in the supercritical regime supports the hypothesis of the existence of naked singularities formed during a generic gravitational collapse.Comment: 23 pages, 16 figures, revised version, added new results of investigation of a supercritical collapse and the existence of naked singularities in generic gravitational collaps

Anti-Proton Evolution in Little Bangs and Big Bang

The abundances of anti-protons and protons are considered within momentum-integrated Boltzmann equations describing Little Bangs, i.e., fireballs created in relativistic heavy-ion collisions. Despite of a large anti-proton annihilation cross section we find a small drop of the ratio of anti-protons to protons from 170 MeV (chemical freeze-out temperature) till 100 MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus corroborating the solution of the previously exposed "ani-proton puzzle". In contrast, the Big Bang evolves so slowly that the anti-baryons are kept for a long time in equilibrium resulting in an exceedingly small fraction. The adiabatic path of cosmic matter in the phase diagram of strongly interacting matter is mapped out

Cosmic String Formation from Correlated Fields

We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum $P(k) \propto k^n$, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over previous simulations: we include a non-zero random background field in our box to simulate the effect of long-wavelength modes, and we examine the effects of smoothing the field on small scales. The inclusion of the background field significantly reduces the fraction of length in infinite strings for $n < -2$. Our results are consistent with the possibility that infinite strings disappear at some $n = n_c$ in the range $-3 \le n_c < -2.2$, although we cannot rule out $n_c = -3$, in which case infinite strings would disappear only at the point where the mean string density goes to zero. We present an analytic argument which suggests the latter case. Smoothing on small scales eliminates closed loops on the order of the lattice cell size and leads to a ``lattice-free" estimate of the infinite string fraction. As expected, this fraction depends on the type of window function used for smoothing.Comment: 24 pages, latex, 10 figures, submitted to Phys Rev

Numerical simulations of string networks in the Abelian-Higgs model

We present the results of a field theory simulation of networks of strings in the Abelian Higgs model. Starting from a random initial configuration we show that the resulting vortex tangle approaches a self-similar regime in which the length density of lines of zeros of $\phi$ reduces as $t^{-2}$. We demonstrate that the network loses energy directly into scalar and gauge radiation. These results support a recent claim that particle production, and not gravitational radiation, is the dominant energy loss mechanism for cosmic strings. This means that cosmic strings in Grand Unified Theories are severely constrained by high energy cosmic ray fluxes: either they are ruled out, or an implausibly small fraction of their energy ends up in quarks and leptons.Comment: 4pp RevTeX, 3 eps figures, clarifications and new results included, to be published in Phys. Rev. Let

Defect formation in superconducting rings: external fields and finite-size effects

Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields. Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform large-scale 3D simulations of quenches of small, thin rings of various geometries with fully dynamical electromagnetic fields, at nonzero externally applied magnetic flux. We find that the outcomes are, in practice, indistinguishable from those of much simpler Gaussian analytical approximations in which the rings are treated as one-dimensional systems and the magnetic field fluctuation-free.Comment: 10 pages, 3 figures, presentation at QFS2012, to appear in JLT

Estimation of vortex density after superconducting film quench

This paper addresses the problem of vortex formation during a rapid quench in a superconducting film. It builds on previous work showing that in a local gauge theory there are two distinct mechanisms of defect formation, based on fluctuations of the scalar and gauge fields, respectively. We show how vortex formation in a thin film differs from the fully two-dimensional case, on which most theoretical studies have focused. We discuss ways of testing theoretical predictions in superconductor experiments and analyse the results of recent experiments in this light.Comment: 7 pages, no figure

The evolution of a network of cosmic string loops

We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly from existing ones. We describe the average properties of the network in terms of the distribution function n(l,t) dl, the average number of loops per unit volume with physical length between l and l + dl at time t. The dynamical processes which change the length of loops are then estimated and an equation, which we call the `rate equation', is derived for (dn/dt). In a non-expanding universe, the loops should reach the equilibrium distribution predicted by string statistical mechanics. Analysis of the rate equation gives results consistent with this. We then study the rate equation in an expanding universe and suggest that three different final states are possible for the evolving loop network, each of which may well be realised for some initial conditions. If the initial energy density in loops in the radiation era is low, then the loops rapidly disappear. For large initial energy densities, we expect that either infinite strings are formed or that the loops tend towards a scaling solution in the radiation era and then rapidly disappear in the matter era. Such a scenario may be relevant given recent work highlighting the problems with structure formation from the standard cosmic string scenario.Comment: LaTeX, 27 pages, 10 figures included as .eps file

The relationship between sticky spots and radar reflectivity beneath an active West Antarctic ice stream

Isolated areas of high basal drag, or ‘sticky spots’, are important and poorly understood features in the force balance and dynamics of West Antarctic ice streams. Characterizing sticky spots formed by thin or drying subglacial till using ice-penetrating radar is theoretically possible, as high radar bed-returned power (BRP) is commonly related to an abundance of free water at the ice/bed interface, provided losses from englacial attenuation can be estimated. In this study we use airborne radar data collected over Evans Ice Stream to extract BRP profiles and test the sensitivity of BRP to the adopted englacial attenuation correction. We analyse 11 �20km profiles in four fast-flow areas where sticky spots have been inferred to exist on the basis of model and surface data inversions. In the majority of profiles we note that the increase in basal drag is accompanied by a decrease in BRP and suggest that this is evidence both for the presence of a sticky spot in those locations and that local variations in subglacial hydrology are responsible for their existence. A comparison is made between empirical and numerical modelling approaches for deriving englacial attenuation, and our findings generally support previous studies that advocate a modelling approach