Phase Transitions in Lyotropic Nematic Gels

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur.Comment: 13 pages Revtex, 10 figures, submitted to EPJ

On the Canonical Reduction of Spherically Symmetric Gravity

In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity. The essential technical ingredient in Kuchar's analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter $M_{S}$, expressed in terms of what are essentially Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we discuss the geometric interpretation of Kuchar's canonical transformation in terms of the theory of quasilocal energy-momentum in general relativity given by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent boost to the rest frame," where the ``rest frame'' is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kucha\v{r}'s original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten-black-hole geometrodynamics.Comment: Revtex, 35 pages, no figure

New variables, the gravitational action, and boosted quasilocal stress-energy-momentum

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covariant action principle for the Ashtekar variables. As such, the theory presented here is an Ashtekar-variable reformulation of the metric theory of quasilocal stress-energy-momentum originally due to Brown and York. This work also investigates how the quasilocal densities behave under generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is shown that under such boosts the densities behave in a manner which is similar to the simple boost law for energy-momentum four-vectors in special relativity. The developed formalism is used to obtain a collection of two-surface or boost invariants. With these invariants, one may ``build" several different mass definitions in general relativity, such as the Hawking expression. Also discussed in detail in this paper is the canonical action principle as applied to bounded spacetime regions with ``sharp corners."Comment: Revtex, 41 Pages, 4 figures added. Final version has been revised and improved quite a bit. To appear in Classical and Quantum Gravit

Entanglement and the nonlinear elastic behavior of forests of coiled carbon nanotubes

Helical or coiled nanostructures have been object of intense experimental and theoretical studies due to their special electronic and mechanical properties. Recently, it was experimentally reported that the dynamical response of foamlike forest of coiled carbon nanotubes under mechanical impact exhibits a nonlinear, non-Hertzian behavior, with no trace of plastic deformation. The physical origin of this unusual behavior is not yet fully understood. In this work, based on analytical models, we show that the entanglement among neighboring coils in the superior part of the forest surface must be taken into account for a full description of the strongly nonlinear behavior of the impact response of a drop-ball onto a forest of coiled carbon nanotubes.Comment: 4 pages, 3 figure

Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary

A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.Comment: 17 pages, 3 figures. Typos correcte

Single polaron properties of the breathing-mode Hamiltonian

We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave-functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron Greens function. We contrast these results with results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings the breathing-mode polaron dispersion has non-monotonic dependence on the polaron momentum k. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation

Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy

We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system $\Sigma$ contained within a finite topologically spherical boundary $B = \partial \Sigma$. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values.Comment: REVTEX, 16 pages, 1 figur

The relation between gas density and velocity power spectra in galaxy clusters: qualitative treatment and cosmological simulations

We address the problem of evaluating the power spectrum of the velocity field of the ICM using only information on the plasma density fluctuations, which can be measured today by Chandra and XMM-Newton observatories. We argue that for relaxed clusters there is a linear relation between the rms density and velocity fluctuations across a range of scales, from the largest ones, where motions are dominated by buoyancy, down to small, turbulent scales: $(\delta\rho_k/\rho)^2 = \eta_1^2 (V_{1,k}/c_s)^2$, where $\delta\rho_k/\rho$ is the spectral amplitude of the density perturbations at wave number $k$, $V_{1,k}^2=V_k^2/3$ is the mean square component of the velocity field, $c_s$ is the sound speed, and $\eta_1$ is a dimensionless constant of order unity. Using cosmological simulations of relaxed galaxy clusters, we calibrate this relation and find $\eta_1\approx 1 \pm 0.3$. We argue that this value is set at large scales by buoyancy physics, while at small scales the density and velocity power spectra are proportional because the former are a passive scalar advected by the latter. This opens an interesting possibility to use gas density power spectra as a proxy for the velocity power spectra in relaxed clusters, across a wide range of scales.Comment: 6 pages, 3 figures, submitted to ApJ Letter

Absolute conservation law for black holes

In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as determining the initial value together with the initial values for the matter field. We discuss this for spherically reduced Einstein-gravity in a diagonal metric and in a Bondi-Sachs metric using the first order formulation of spherically reduced gravity, which allows easy and direct fixations of any type of gauge. The relation of our conserved quantity to the ADM and Bondi mass is investigated. Further possible applications (ideal fluid, black holes in higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.

Phase transitions near black hole horizons

The Reissner-Nordstrom black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field. New stable black hole solutions then exist with greater entropy for fixed mass and charge than the Reissner-Nordstrom solution. In these new solutions, the scalar condenses to a non-zero value near the horizon. Various generalizations of these hairy black holes are discussed, and an attempt is made to characterize when black hole hair can occur.Comment: 30 pages, 6 figures. v2: minor corrections, references adde