Generalized Hawking-Page Phase Transition

The issue of radiant spherical black holes being in stable thermal equilibrium with their radiation bath is reconsidered. Using a simple equilibrium statistical mechanical analysis incorporating Gaussian thermal fluctuations in a canonical ensemble of isolated horizons, the heat capacity is shown to diverge at a critical value of the classical mass of the isolated horizon, given (in Planckian units) by the {\it microcanonical} entropy calculated using Loop Quantum Gravity. The analysis reproduces the Hawking-Page phase transition discerned for anti-de Sitter black holes and generalizes it in the sense that nowhere is any classical metric made use of.Comment: 9 Pages, Latex with 2 eps figure

Persistence in higher dimensions : a finite size scaling study

We show that the persistence probability $P(t,L)$, in a coarsening system of linear size $L$ at a time $t$, has the finite size scaling form $P(t,L)\sim L^{-z\theta}f(\frac{t}{L^{z}})$ where $\theta$ is the persistence exponent and $z$ is the coarsening exponent. The scaling function $f(x)\sim x^{-\theta}$ for $x \ll 1$ and is constant for large $x$. The scaling form implies a fractal distribution of persistent sites with power-law spatial correlations. We study the scaling numerically for Glauber-Ising model at dimension $d = 1$ to 4 and extend the study to the diffusion problem. Our finite size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent $\theta$.Comment: 4 pages in RevTeX with 6 figures. To appear in Phys. Rev.

Extremal statistics of curved growing interfaces in 1+1 dimensions

We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1 dimensions. We obtain exact results for the closely related problem of p non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M) where \tau_M is there the time at which the maximal height M is reached. Our analytical results, in the limit p \to \infty, become exact for the interface problem in the growth regime. We show that our results, for moderate values of p \sim 10 describe accurately our numerical data of a prototype of these systems, the polynuclear growth model in droplet geometry. We also discuss applications of our results to the ground state configuration of the directed polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics Letters. New results added for non-intersecting excursion

Area Distribution of Elastic Brownian Motion

We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will stress on the power of self adjoint extension to investigate different possible boundary conditions for the stochastic processes.Comment: 18 pages, published versio

Time dependent spectral modeling of Markarian 421 during a violent outburst in 2010

We present the results of extensive modeling of the spectral energy distributions (SEDs) of the closest blazar (z=0.031) Markarian 421 (Mrk 421) during a giant outburst in February 2010. The source underwent rapid flux variations in both X-rays and very high energy (VHE) gamma-rays as it evolved from a low-flux state on 2010 February 13-15 to a high-flux state on 2010 February 17. During this period, the source exhibited significant spectral hardening from X-rays to VHE gamma-rays while exhibiting a "harder when brighter" behavior in these energy bands. We reproduce the broadband SED using a time-dependent multi-zone leptonic jet model with radiation feedback. We find that an injection of the leptonic particle population with a single power-law energy distribution at shock fronts followed by energy losses in an inhomogeneous emission region is suitable for explaining the evolution of Mrk 421 from low- to high-flux state in February 2010. The spectral states are successfully reproduced by a combination of a few key physical parameters, such as the maximum $\&$ minimum cutoffs and power-law slope of the electron injection energies, magnetic field strength, and bulk Lorentz factor of the emission region. The simulated light curves and spectral evolution of Mrk 421 during this period imply an almost linear correlation between X-ray flux at 1-10 keV energies and VHE gamma-ray flux above 200 GeV, as has been previously exhibited by this source. Through this study, a general trend that has emerged for the role of physical parameters is that, as the flare evolves from a low- to a high-flux state, higher bulk kinetic energy is injected into the system with a harder particle population and a lower magnetic field strength.Comment: 13 pages, 5 figures, accepted for publication in MNRA

The effect of shear on persistence in coarsening systems

We analytically study the effect of a uniform shear flow on the persistence properties of coarsening systems. The study is carried out within the anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with nonconserved scalar order parameter. We find that the persistence exponent theta has a non-trivial value: theta = 0.5034... in space dimension d=3, and theta = 0.2406... for d=2, the latter being exactly twice the value found for the unsheared system in d=1. We also find that the autocorrelation exponent lambda is affected by shear in d=3 but not in d=2.Comment: 6 page

Classification of unit-vector fields in convex polyhedra with tangent boundary conditions

A unit-vector field n on a convex three-dimensional polyhedron P is tangent if, on the faces of P, n is tangent to the faces. A homotopy classification of tangent unit-vector fields continuous away from the vertices of P is given. The classification is determined by certain invariants, namely edge orientations (values of n on the edges of P), kink numbers (relative winding numbers of n between edges on the faces of P), and wrapping numbers (relative degrees of n on surfaces separating the vertices of P), which are subject to certain sum rules. Another invariant, the trapped area, is expressed in terms of these. One motivation for this study comes from liquid crystal physics; tangent unit-vector fields describe the orientation of liquid crystals in certain polyhedral cells.Comment: 21 pages, 2 figure

Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models

We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via a gauge transformation raises an interesting new question for a generic finite sized spin glass model: at a given temperature, what is the distribution (over disorder) of the thermally averaged number of spins that are aligned to their local fields? We show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the Sherrington-Kirkpatrick model with Gaussian disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included

Biomathematical Study of the Kinetics of Energy Output During Physical Exercise

The kinetics of energy production during different grades of activity has been described in terms of rate constant and workload for submaximal, maximal and supermaximal exercises. Equations have been derived for the aerobic and anaerobic components of energy production for the three cases. The theoretical approach has been validated with the available experimental data

Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries

Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0<H<1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion, while for H unequal 1/2, x(t) is a non-Markovian process. Here we study x(t) in presence of an absorbing boundary at the origin and focus on the probability density P(x,t) for the process to arrive at x at time t, starting near the origin at time 0, given that it has never crossed the origin. It has a scaling form P(x,t) ~ R(x/t^H)/t^H. Our objective is to compute the scaling function R(y), which up to now was only known for the Markov case H=1/2. We develop a systematic perturbation theory around this limit, setting H = 1/2 + epsilon, to calculate the scaling function R(y) to first order in epsilon. We find that R(y) behaves as R(y) ~ y^phi as y -> 0 (near the absorbing boundary), while R(y) ~ y^gamma exp(-y^2/2) as y -> oo, with phi = 1 - 4 epsilon + O(epsilon^2) and gamma = 1 - 2 epsilon + O(epsilon^2). Our epsilon-expansion result confirms the scaling relation phi = (1-H)/H proposed in Ref. [28]. We verify our findings via numerical simulations for H = 2/3. The tools developed here are versatile, powerful, and adaptable to different situations.Comment: 16 pages, 8 figures; revised version 2 adds discussion on spatial small-distance cutof