Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps

We calculate the survival probability P_S(t) up to time t of a tracer particle moving along a deterministic trajectory in a continuous d-dimensional space in the presence of diffusing but mutually noninteracting traps. In particular, for a tracer particle moving ballistically with a constant velocity c, we obtain an exact expression for P_S(t), valid for all t, for d<2. For d \geq 2, we obtain the leading asymptotic behavior of P_S(t) for large t. In all cases, P_S(t) decays exponentially for large t, P_S(t) \sim \exp(-\theta t). We provide an explicit exact expression for the exponent \theta in dimensions d \leq 2, and for the physically relevant case, d=3, as a function of the system parameters.Comment: RevTeX, 4 page

Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps

The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and lower bounds for the probability Q(t) (averaged over all particle and trap trajectories) that the particle survives up to time t. We show that, for 1<=d<2, the bounds converge asymptotically to give $Q(t) \sim exp(-\lambda_d t^{d/2})$ where $\lambda_d = (2/\pi d) sin(\pi d/2) (4\pi D)^{d/2} \rho$ and D is the diffusion constant of the traps, and that $Q(t) \sim exp(- 4\pi\rho D t/ln t)$ for d=2. For d>2 bounds can still be derived, but they no longer converge for large t. For 1<=d<=2, these asymptotic form are independent of the diffusion constant of the particle. The results are compared with simulation results obtained using a new algorithm [V. Mehra and P. Grassberger, Phys. Rev. E v65 050101 (2002)] which is described in detail. Deviations from the predicted asymptotic forms are found to be large even for very small values of Q(t), indicating slowly decaying corrections whose form is consistent with the bounds. We also present results in d=1 for the case where the trap densities on either side of the particle are different. For this case we can still obtain exact bounds but they no longer converge.Comment: 13 pages, RevTeX4, 6 figures. Figures and references updated; equations corrected; discussion clarifie

A Singular Perturbation Analysis for \\Unstable Systems with Convective Nonlinearity

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this method, developed by Kawasaki, Yalabik and Gunton for the time-dependant Ginzburg-Landau equation and used successfully on other NCOP systems, breaks down for our system when the strength of bias/convection gets large enough.Comment: 5 pages, PostScript forma

Collaborating with the enemy? A view from Down Under on GM research partnerships

Abstract This chapter explores the distribution of funding and approvals for GM crops in Australia in order to determine if private interests dominate public research in agricultural biotechnology and if public interests can be served by collaborations with private organizations. Although a highly detailed analysis is not possible given the available data, it is contended that the Australian setting provides a different perspective on the potential for various forms of public-private collaborations in GM research, as well as an excellent test bed for assessing effects of diverse types of funding and institutional arrangements. Three brief GM case studies from the Australian context are presented to explore key issues arising and underlying complexities associated with GM research: (i) drought-tolerant wheat; (ii) high-amylose wheat; and (iii) Vitamin A-enhanced 'super banana'.Rachel A. Ankeny, Heather J. Bray, Kelly A. McKinle

Dynamical Scaling: the Two-Dimensional XY Model Following a Quench

To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly compare various length-scales. All of our results are consistent with dynamical scaling and an asymptotic growth law $L \sim (t/\ln[t/t_0])^{1/2}$, though with a time-scale $t_0$ that depends on the length-scale in question. We then reconstruct correlations from the minimal-energy configuration consistent with the vortex positions, and find them significantly different from the ``natural'' correlations --- though both scale with $L$. This indicates that both topological (vortex) and non-topological (``spin-wave'') contributions to correlations are relevant arbitrarily late after the quench. We also present a consistent definition of dynamical scaling applicable more generally, and emphasize how to generalize our approach to other quenched systems where dynamical scaling is in question. Our approach directly applies to planar liquid-crystal systems.Comment: 10 pages, 10 figure

Ferals or food? Does hunting have a role in ethical food consumption in Australia?

Although hunting is pursued by relatively few people in Australia, increasing attention to ‘ethical’ consumption is renewing interest in hunting as a source of ‘ethical’ meat and complicating our views about it as a leisure activity. Most scholarly attention about hunting practices has been focused in Europe and North America, and we argue that Australia provides a unique context for exploring hunting and its association with ethical consumption because of attitudes to native versus introduced animals and gun ownership. With increasing public attention to both animal welfare and ethical consumption, it is timely to revisit public attitudes to hunting as a leisure activity in Australia and explore the values and motivations of recreational hunters.Rachel Ankeny & Heather Bra

Mean-field analysis of the q-voter model on networks

We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.Comment: 20 pages, 10 figure

Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG

Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass (SG) in a field), in the universal regime of a large Imry Ma length so that coarsening of domains after a quench occurs over large scales. Two types of domain walls diffuse in opposite Sinai random potentials and mutually annihilate. The domain walls converge rapidly to a set of system-specific time-dependent positions {\it independent of the initial conditions}. We obtain the time dependent energy, magnetization and domain size distribution (statistically independent). The equilibrium limits agree with known exact results. We obtain exact scaling forms for two-point equal time correlation and two-time autocorrelations. We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the spin glass are obtained. We compute the two-point two-time correlation which can be measured by experiments on spin-glass like systems. Thermal fluctuations are found to be dominated by rare events; all moments of truncated correlations are computed. The response to a small field applied after waiting time $t_w$, as measured in aging experiments, and the fluctuation-dissipation ratio $X(t,t_w)$ are computed. For $(t-t_w) \sim t_w^{\hat{\alpha}}$, $\hat{\alpha} <1$, it equals its equilibrium value X=1, though time translational invariance fails. It exhibits for $t-t_w \sim t_w$ aging regime with non-trivial $X=X(t/t_w) \neq 1$, different from mean field.Comment: 55 pages, 9 figures, revte

Randomly dilute Ising model: A nonperturbative approach

The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical physics between two and four dimensions. We give the critical exponents for the three-dimensional randomly dilute Ising model which are in good agreement with experimental and numerical data. The relevance of the cubic anisotropy in the O(N) model is also treated.Comment: 4 pages, published versio

Critical structure factor in Ising systems

We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L^3 with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernicke expression of Puglielli and Ford.Comment: 16 page