Branched Polymers on the Given-Mandelbrot family of fractals

We study the average number A_n per site of the number of different configurations of a branched polymer of n bonds on the Given-Mandelbrot family of fractals using exact real-space renormalization. Different members of the family are characterized by an integer parameter b, b > 1. The fractal dimension varies from $log_{_2} 3$ to 2 as b is varied from 2 to infinity. We find that for all b > 2, A_n varies as $\lambda^n exp(b n ^{\psi})$, where $\lambda$ and $b$ are some constants, and $0 < \psi <1$. We determine the exponent $\psi$, and the size exponent $\nu$ (average diameter of polymer varies as $n^\nu$), exactly for all b > 2. This generalizes the earlier results of Knezevic and Vannimenus for b = 3 [Phys. Rev {\bf B 35} (1987) 4988].Comment: 24 pages, 8 figure

Radiative capture of polarized neutrons by polarized protons

A model-independent irreducible tensor approach to p(n,gamma)d is presented and an explicit form for the spin-structure of the matrix for the reaction is obtained in terms of the Pauli spin-matrices for the neutron and the proton. Expressing the multipole amplitudes in terms of the triplet --> triplet and singlet --> triplet transitions, we point out how the initial singlet and triplet contributions to the differential cross section can be determined empirically.Comment: Revised version; typeset using RevTeX4; 6 pages, no figure

Generating entanglement between quantum dots with different resonant frequencies based on Dipole Induced Transparency

We describe a method for generating entanglement between two spatially separated dipoles coupled to optical micro-cavities. The protocol works even when the dipoles have different resonant frequencies and radiative lifetimes. This method is particularly important for solid-state emitters, such as quantum dots, which suffer from large inhomogeneous broadening. We show that high fidelities can be obtained over a large dipole detuning range without significant loss of efficiency. We analyze the impact of higher order photon number states and cavity resonance mismatch on the performance of the protocol

Crossover from hydrodynamic to acoustic drag on quartz tuning forks in normal and superfluid 4He

We present measurements of the drag forces on quartz tuning forks oscillating at low velocities in normal and superfluid 4He. We have investigated the dissipative drag over a wide range of frequencies, from 6.5 to 600 kHz, by using arrays of forks with varying prong lengths and by exciting the forks in their fundamental and first overtone modes. At low frequencies the behavior is dominated by laminar hydrodynamic drag, governed by the fluid viscosity. At higher frequencies acoustic drag is dominant and is described well by a three-dimensional model of sound emission

Transition from confined to bulk dynamics in symmetric star-linear polymer mixtures

We report on the linear viscoelastic properties of mixtures comprising multiarm star (as model soft colloids) and long linear chain homopolymers in a good solvent. In contrast to earlier works, we investigated symmetric mixtures (with a size ratio of 1) and showed that the polymeric and colloidal responses can be decoupled. The adopted experimental protocol involved probing the linear chain dynamics in different star environments. To this end, we studied mixtures with different star mass fraction, which was kept constant while linear chains were added and their entanglement plateau modulus ($G_p$) and terminal relaxation time ($\tau_d$) were measured as functions of their concentration. Two distinct scaling regimes were observed for both $G_p$ and $\tau_d$: at low linear polymer concentrations, a weak concentration dependence was observed, that became even weaker as the fraction of stars in the mixtures increased into the star glassy regime. On the other hand, at higher linear polymer concentrations, the classical entangled polymer scaling was recovered. Simple scaling arguments show that the threshold crossover concentration between the two regimes corresponds to the maximum osmotic star compression and signals the transition from confined to bulk dynamics. These results provide the needed ingredients to complete the state diagram of soft colloid-polymer mixtures and investigate their dynamics at large polymer-colloid size ratios. They also offer an alternative way to explore aspects of the colloidal glass transition and the polymer dynamics in confinement. Finally, they provide a new avenue to tailor the rheology of soft composites.Comment: 9 Figure

Drift and trapping in biased diffusion on disordered lattices

We reexamine the theory of transition from drift to no-drift in biased diffusion on percolation networks. We argue that for the bias field B equal to the critical value B_c, the average velocity at large times t decreases to zero as 1/log(t). For B < B_c, the time required to reach the steady-state velocity diverges as exp(const/|B_c-B|). We propose an extrapolation form that describes the behavior of average velocity as a function of time at intermediate time scales. This form is found to have a very good agreement with the results of extensive Monte Carlo simulations on a 3-dimensional site-percolation network and moderate bias.Comment: 4 pages, RevTex, 3 figures, To appear in International Journal of Modern Physics C, vol.

Probability distribution of residence times of grains in models of ricepiles

We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different ricepile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size $L$, the probabilities that the residence time at a site or the total residence time is greater than $t$, both decay as $1/t(\ln t)^x$ for $L^{\omega} \ll t \ll \exp(L^{\gamma})$ where $\gamma$ is an exponent $\ge 1$, and values of $x$ and $\omega$ in the two cases are different. In the Oslo ricepile model we find that the probability that the residence time $T_i$ at a site $i$ being greater than or equal to $t$, is a non-monotonic function of $L$ for a fixed $t$ and does not obey simple scaling. For model in $d$ dimensions, we show that the probability of minimum slope configuration in the steady state, for large $L$, varies as $\exp(-\kappa L^{d+2})$ where $\kappa$ is a constant, and hence $\gamma = d+2$.Comment: 13 pages, 23 figures, Submitted to Phys. Rev.