Proportion of Unaffected Sites in a Reaction-Diffusion Process

We consider the probability $P(t)$ that a given site remains unvisited by any of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$ when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a universal exponent \theta=\ffrac12-O(\epsilon) for $d=2-\epsilon$, while, for $d>2$, $\theta$ is non-universal and depends on the reaction rate. The analysis, which uses field-theoretic renormalisation group methods, is also applied to the reaction $kA\to0$ with $k>2$. In this case, a stretched exponential behaviour is found for all $d\geq1$, except in the case $k=3$, $d=1$, where P(t)\sim {\rm e}^{-\const (\ln t)^{3/2}}.Comment: 10 pages, (revised version with abstract included) OUTP-94-35

Boundary Condition of Polyelectrolyte Adsorption

The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.Comment: 4 page

Effective Edwards-Wilkinson equation for single-file diffusion

In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles. The effective equation gives a description of single-file diffusion using the global roughness of the system of particles, which presents three characteristic regimes, namely normal diffusion, subdiffusion and saturation, separated by two crossover times. We show how these regimes scale with the parameters of the original system. Additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms. Finally, we show that the roughness distribution can be well characterized by the Edwards-Wilkinson universal form for the different single-file diffusion processes studied here.Comment: 9 pages, 9 figure

Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems

We study kinetics of single species reactions ("A+A -> 0") for general local reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above the critical value d_c=z, kinetics are always mean field (MF). Below d_c, the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~ n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q<Qstar, MF kinetics persist, with n_t ~ 1/Qt. In all cases n_t ~ 1/x_t^d at the longest times. Our analysis avoids decoupling approximations by instead postulating weak physically motivated bounds on correlation functions.Comment: 10 pages, 1 figure, uses bulk2.sty, minor changes, submitted to Europhysics Letter

Topological versus rheological entanglement length in primitive path analysis protocols

Primitive path analysis algorithms are now routinely employed to analyze entanglements in computer simulations of polymeric systems, but different analysis protocols result in different estimates of the entanglement length, N_e. Here we argue that standard PPA measures the rheological entanglement length, typically employed by tube models and relevant to quantitative comparisons with experiment, while codes like Z or CReTA also determine the topological entanglement length. For loosely entangled systems, a simple analogy between between phantom networks and the mesh of entangled primitive paths suggests a factor of two between the two numbers. This result is in excellent agreement with reported values for poly-ethylene, poly-butadiene and bead-spring polymer melts.Comment: 3 pages, no figure

Swimmers in thin films: from swarming to hydrodynamic instabilities

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses (force dipoles or quadrupoles) on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behaviour. In contrast, for quadrupolar swimmers, our analysis shows that detailed features of the internal dynamics play an important role in determining the bulk behaviour. In the broken symmetry phases, we investigate fluctuations of hydrodynamic variables of the system and find that these destabilize order. Interestingly, this instability is not generic and depends on length-scale.Comment: 4 pages, 2 figures, references added, typos corrected, new introductio

Stretching An Anisotropic DNA

We present a perturbation theory to find the response of an anisotropic DNA to the external tension. It is shown that the anisotropy has a nonzero but small contribution to the force-extension curve of the DNA. Thus an anisotropic DNA behaves like an isotropic one with an effective bending constant equal to the harmonic average of its soft and hard bending constants.Comment: 29 pages and 4 figure. To appear in J. Chem. Phy

A multi-wavelength view of galaxy evolution with AKARI

AKARI's all-sky survey resolves the far-infrared emission in many thousands of nearby galaxies, providing essential local benchmarks against which the evolution of high-redshift populations can be measured. This review presents some recent results in the resolved galaxy populations, covering some well-known nearby targets, as well as samples from major legacy surveys such as the Herschel Reference Survey and the JCMT Nearby Galaxies Survey. This review also discusses the prospects for higher redshifts surveys, including strong gravitational lens clusters and the AKARI NEP field.Comment: Accepted for Publications of the Korean Astronomical Society (September 30, 2012 issue, volume 27, No. 3), Proceedings of the Second AKARI conference, Legacy of AKARI: A Panoramic View of the Dusty Universe. 6 page

Scoping a public health impact assessment of aquaculture with particular reference to tilapia in the UK

Background. The paper explores shaping public health impact assessment tools for tilapia, a novel emergent aquaculture sector in the UK. This Research Council’s UK Rural Economy and Land Use project embraces technical, public health, and marketing perspectives scoping tools to assess possible impacts of the activity. Globally, aquaculture produced over 65 million tonnes of food in 2008 and will grow significantly requiring apposite global public health impact assessment tools.&lt;p&gt;&lt;/p&gt; Methods. Quantitative and qualitative methods incorporated data from a tridisciplinary literature. Holistic tools scoped tilapia farming impact assessments. Laboratory-based tilapia production generated data on impacts in UK and Thailand along with 11 UK focus groups involving 90 consumers, 30 interviews and site visits, 9 visits to UK tilapia growers and 2 in The Netherlands.&lt;p&gt;&lt;/p&gt; Results. The feasibility, challenges, strengths, and weaknesses of creating a tilapia Public Health Impact Assessment are analysed. Occupational and environmental health benefits and risks attached to tilapia production were identified.&lt;p&gt;&lt;/p&gt; Conclusions. Scoping public health impacts of tilapia production is possible at different levels and forms for producers, retailers, consumers, civil society and governmental bodies that may contribute to complex and interrelated public health assessments of aquaculture projects. Our assessment framework constitutes an innovatory perspective in the field

Shear-stress controlled dynamics of nematic complex fluids

Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $\sigma_{\mathrm{xy}}$ (rather than the usual shear rate, $\dot\gamma$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dot\gamma$, which then becomes time-dependent. Shearing the system from an isotropic state, the stress- controlled flow properties turn out to be essentially identical to those at fixed $\dot\gamma$. Pronounced differences when the equilibrium state is nematic. Here, shearing at controlled $\dot\gamma$ yields several non-equilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the $\sigma_{\mathrm{xy}}$-$\dot\gamma$ plane turns out to be tunable by the delay time entering our control scheme for $\sigma_{\mathrm{xy}}$. Moreover, a sudden change of the control method can {\it stabilize} the chaotic states appearing at fixed $\dot\gamma$.Comment: 10 pages, 11 figure