Equilibrium glassy phase in a polydisperse hard sphere system

The phase diagram of a polydisperse hard sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears and the glass becomes the equilibrium phase beyond a "terminal" value of the polydispersity. A crystal to glass transition is also observed as the density is increased at high polydispersity. The phase diagram obtained in our study is qualitatively similar to that of hard spheres in a quenched random potential.Comment: 4 pages, 4 figure

Laser induced reentrant freezing in two-dimensional attractive colloidal systems

The effects of an externally applied one-dimensional periodic potential on the freezing/melting behaviour of two-dimensional systems of colloidal particles with a short-range attractive interaction are studied using Monte Carlo simulations. In such systems, incommensuration results when the periodicity of the external potential does not match the length-scale at which the minimum of the attractive potential occurs. To study the effects of this incommensuration, we consider two different models for the system. Our simulations for both these models show the phenomenon of reentrant freezing as the strength of the periodic potential is varied. Our simulations also show that different exotic phases can form when the strength of the periodic potential is high, depending on the length-scale at which the minimum of the attractive pair-potential occurs.Comment: 24 pages (including figures) in preprint forma

Large-amplitude chirped coherent phonons in tellurium mediated by ultrafast photoexcited carrier diffusion

We report femtosecond time-resolved reflectivity measurements of coherent phonons in tellurium performed over a wide range of temperatures (3K to 296K) and pump laser intensities. A totally symmetric A$_{1}$ coherent phonon at 3.6 THz responsible for the oscillations in the reflectivity data is observed to be strongly positively chirped (i.e, phonon time period decreases at longer pump-probe delay times) with increasing photoexcited carrier density, more so at lower temperatures. We show for the first time that the temperature dependence of the coherent phonon frequency is anomalous (i.e, increasing with increasing temperature) at high photoexcited carrier density due to electron-phonon interaction. At the highest photoexcited carrier density of $\sim$ 1.4 $\times$ 10$^{21}$cm$^{-3}$ and the sample temperature of 3K, the lattice displacement of the coherent phonon mode is estimated to be as high as $\sim$ 0.24 \AA. Numerical simulations based on coupled effects of optical absorption and carrier diffusion reveal that the diffusion of carriers dominates the non-oscillatory electronic part of the time-resolved reflectivity. Finally, using the pump-probe experiments at low carrier density of 6 $\times$ 10$^{18}$ cm$^{-3}$, we separate the phonon anharmonicity to obtain the electron-phonon coupling contribution to the phonon frequency and linewidth.Comment: 22 pages, 6 figures, submitted to PR

The Interacting Branching Process as a Simple Model of Innovation

We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/\tau at each generation. In contrast to mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For \tau = \infty, surviving processes exhibit a bottleneck before exploding super-exponentially - a growth consistent with a law of accelerating returns. This behavior persists for finite \tau. We analyze, in detail, the asymptotic behavior as p \to 0.Comment: 4 pages, 4 figure

Pulse Wave Velocity and Electroneurophysiological Evaluation in patients of Rheumatoid Arthritis

Rheumatoid arthritis is a chronic systemic inflammatory disease of undetermined etiology involving the synovial membranes and articular structures of multiple joints and is also associated with carditis, pleuritis, hepatitis, peripheral neuropathy and vasculitis. The present study was undertaken to investigate arterial stiffness using carotid-radial and femoral-dorsalis pedis pulse wave velocity measurements and electrophysiological tests for peripheral nervous system involvement. 25 patients (aged between 20-60 years) with rheumatoid arthritis according to the criteria of the American College of Rheumatology and 25 control subjects of the same age and sex were recruited. In the motor conduction studies, out of 25 patients of Rheumatoid arthritis, 6 had clinical evidence of peripheral neuropathy. 11 patients showed pure sensory neuropathy (44%), 10 showed mixed sensory motor neuropathy (40%) while 4 showed normal motor and sensory conduction velocity. Two patients (8%) showed features of entrapment neuropathy of median nerve i.e. feature of Carpal tunnel syndrome. In the pulse wave velocity evaluation statistically significant increase in pulse wave velocity between femoral-dorsalis pedis and carotid-radial artery segments was observed in Rheumatoid arthritis patients as compared to the control group. Measurement of carotid-radial and femoral-dorsalis pedis PWV may provide a simple and non-invasive technique for identifying patients at increased risk of vascular disease in Rheumatoid arthritis

Random sampling vs. exact enumeration of attractors in random Boolean networks

We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure cycle lengths of attractors and sizes of basins of attraction in RBNs using exact enumeration of the state space. In general, the distribution of attractor lengths differs markedly from that obtained by randomly choosing an initial state and following the dynamics to reach an attractor. Our results indicate that the former distribution decays as a power-law with exponent 1 for all connectivities $K>1$ in the infinite system size limit. In contrast, the latter distribution decays as a power law only for K=2. This is because the mean basin size grows linearly with the attractor cycle length for $K>2$, and is statistically independent of the cycle length for K=2. We also find that the histograms of basin sizes are strongly peaked at integer multiples of powers of two for $K<3$