Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent $\Theta$ and the exponent $lambda$ characterising the two-time autocorrelation function of the total magnetization under non-equilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.Comment: 6 pages, Latex, postscript figures include

Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

Corrections to Scaling in Phase-Ordering Kinetics

The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a characteristic length scale extracted from the energy. The correction-to-scaling exponent \omega has the value \omega=4 for the d=1 Glauber model, the n-vector model with n=\infty, and the approximate theory of Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st

Policy and regulatory barriers to local energy markets in Great Britain

EPG Working Paper: EPG 1801The requirement to decarbonise the GB electricity system, alongside the falling costs of renewable technologies and developments in IT capabilities, provides GB with an opportunity for systemic change in the way that electricity is produced and sold, with the potential to enable flexibility markets at the local level given the correct regulatory conditions. The report highlights a range of regulatory and policy barriers to the Local Energy Market (LEM) approach

A Remark on Boundary Effects in Static Vacuum Initial Data sets

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that the boundary of (M, g) has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that the boundary has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the area and mean curvature of the boundary. Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit

Mechanism for the failure of the Edwards hypothesis in the SK spin glass

The dynamics of the SK model at T=0 starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, $p(\lambda)$, is small at $\lambda=0$. Since virtually all metastable states have a much larger $p(0)$, this behavior demonstrates a qualitative failure of the Edwards hypothesis. We look for its origins by modelling the changes in the site energies during the dynamics as a Markov process. We show how the small $p(0)$ arises from features of the Markov process that have a clear physical basis in the spin-glass, and hence explain the failure of the Edwards hypothesis.Comment: 5 pages, new title, modified text, additional reference

Self Consistent Screening Approximation For Critical Dynamics

We generalise Bray's self-consistent screening approximation to describe the critical dynamics of the $\phi^4$ theory. In order to obtain the dynamical exponent $z$, we have to make an ansatz for the form of the scaling functions, which fortunately can be much constrained by general arguments. Numerical values of $z$ for $d=3$, and $n=1,...,10$ are obtained using two different ans\"atze, and differ by a very small amount. In particular, the value of $z \simeq 2.115$ obtained for the 3-d Ising model agrees well with recent Monte-Carlo simulations.Comment: 21 pages, LaTeX file + 4 (EPS) figure

Growth Laws for Phase Ordering

We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by comparing the global rate of energy change to the energy dissipation from the local evolution of the order parameter. We derive growth laws for O(n) models, and our results can be applied to other systems with similar defect structures.Comment: 12 pages, LaTeX, second tr

Diffusion of particles in an expanding sphere with an absorbing boundary

We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material undergoing grain growth. We solve the time dependent diffusion equation for particles in a d-dimensional expanding sphere to obtain the particle density function (function of space and time). The survival rate or the total number of particles per unit volume as a function of time is evaluated. We have obtained particular solutions exactly for the case where d=3 and a parabolic growth of the sphere. Asymptotic solutions for the particle density when the sphere growth rate is small relative to particle diffusivity and vice versa are derived.Comment: 12 pages. To appear in J. Phys. A: Math. Theor. 41 (2008

Medium-term performance and maintenance of SUDS:a case-study of Hopwood Park Motorway Service Area, UK

One of the main barriers to implementing SUDS is concern about performance and maintenance costs since there are few well-documented case-studies. This paper summarizes studies conducted between 2000 and 2008 of the performance and maintenance of four SUDS management trains constructed in 1999 at the Hopwood Park Motorway Service Area, central England. Assessments were made of the wildlife value and sedimentation in the SUDS ponds, the hydraulic performance of the coach park management train, water quality in all management trains, and soil/sediment composition in the grass filter strip, interceptor and ponds. Maintenance procedures and costs were also reviewed. Results demonstrate the benefits of a management train approach over individual SUDS units for flow attenuation, water treatment, spillage containment and maintenance. Peak flows, pond sediment depth and contaminant concentrations in sediment and water decreased through the coach park management train. Of the 2007 annual landscape budget of £15,000 for the whole site, the maintenance costs for SUDS only accounted for £2,500 compared to £4,000 for conventional drainage structures. Furthermore, since sediment has been attenuated in the management trains, the cost of sediment removal after the recommended period of three years was only £554 and, if the design is not compromised, less frequent removal will be required in future