Stress correlations in glasses

We rigorously establish that, in disordered three-dimensional (3D) isotropic solids, the stress autocorrelation function presents anisotropic terms that decay as $1/r^3$ at long-range, with $r$ the distance, as soon as either pressure or shear stress fluctuations are normal. By normal, we mean that the fluctuations of stress, as averaged over spherical domains, decay as the inverse domain volume. Since this property is required for macroscopic stress to be self-averaging, it is expected to hold generically in all glasses and we thus conclude that the presence of $1/r^3$ stress correlation tails is the rule in these systems. Our proof follows from the observation that, in an infinite medium, when both material isotropy and mechanical balance hold, (i) the stress autocorrelation matrix is completely fixed by just two radial functions: the pressure autocorrelation and the trace of the autocorrelation of stress deviators; furthermore, these two functions (ii) fix the decay of the fluctuations of sphere-averaged pressure and deviatoric stresses for windows of increasing volume. Our conclusion is reached because, due to the precise analytic relation (i) fixed by isotropy and mechanical balance, the constraints arising via (ii) from the normality of stress fluctuations demand the spatially anisotropic stress correlation terms to decay as $1/r^3$ at long-range. For the sake of generality, we also examine situations when stress fluctuations are not normal

A finite difference scheme for the equilibrium equations of elastic bodies

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques

A compact finite difference scheme for div(Rho grad u) - q2u = 0

A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation

Time evolution of the Partridge-Barton Model

The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for the time dependence of the mean survival probabilities are derived. Using the fact that the asymptotic behavior for large time $t$ is controlled by the largest matrix eigenvalue, we obtain the steady state values for the mean survival probabilities and the Malthusian growth exponent. The mean age of the population exhibits a $t^{-1}$ power law decayment. Some Monte Carlo simulations were also performed and they corroborated our theoretical results.Comment: 10 pages, Latex, 1 postscript figure, published in Phys. Rev. E 61, 5664 (2000

A Solution of the Maxwell-Dirac Equations in 3+1 Dimensions

We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced electric field.Comment: 12 pages, revtex, 2 figure

Supporting reflection and creative thinking by carers of older people with dementia

This vision paper frames requirements engineering as a creative problem solving process. Its purpose is to enable requirements researchers and practitioners to recruit relevant theories, models, techniques and tools from creative problem solving to understand and support requirements processes more effectively. It uses 4 drivers to motivate the case for requirements engineering as a creative problem solving process. It then maps established requirements activities onto one of the longest-established creative problem solving processes, and uses these mappings to locate opportunities for the application of creative problem solving in requirements engineering. The second half of the paper describes selected creativity theories, techniques, software tools and training that can be adopted to improve requirements engineering research and practice. The focus is on support for problem and idea finding - two creative problem solving processes that our investigation revealed are poorly supported in requirements engineering. The paper ends with a research agenda to incorporate creative processes, techniques, training and tools in requirements projects

Introducing creativity techniques and software apps to the care of people with dementia

This poster reports research to introduce creative problem solving techniques and software to the care for people with dementia in residential homes

Multi-Objective Optimisation of CNC Milling Process for Al 6061 using Modified NSGA-II

Computer numerical controlled (CNC) growth has revolutionised the manufacturing sectors by changing the way people work. In milling process, it has contributed to the higher productivity and better quality of the products. Although a lot of researches have been done on how to improve the process, the process improvement does not stop there because of evolving materials, methods and technologies. This paper presents a multi-objective optimisation of CNC milling process in order to achieve desired surface roughness and minimise machining time for Al 6061. A full factorial experiment has been conducted to model surface roughness by controlling three variables; spindle speed, feed rate and depth of cut. Multi-objective optimisation has been performed using modified Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) with two levels crossover. The optimisation result concluded that the modified NSGA-II was able to converge to Pareto-optimal, but having difficulties to spread solutions in wider range

HST and Spitzer point source detection and optical extinction in powerful narrow-line radio galaxies

We present the analysis of infrared HST and Spitzer data for a sample of 13 FRII radio galaxies at 0.03<z<0.11 that are classified as narrow-line radio galaxies (NLRG). In the context of the unified schemes for active galactic nuclei (AGN), our direct view of the AGN in NLRG is impeded by a parsec-scale dusty torus structure. Our high resolution infrared observations provide new information about the degree of extinction induced by the torus, and the incidence of obscured AGN in NLRG. We find that the point-like nucleus detection rate increases from 25 per cent at 1.025$\mu$m, to 80 per cent at 2.05$\mu$m, and to 100 per cent at 8.0$\mu$m. This supports the idea that most NLRG host an obscured AGN in their centre. We estimate the extinction from the obscuring structures using X-ray, near-IR and mid-IR data. We find that the optical extinction derived from the 9.7$\mu$m silicate absorption feature is consistently lower than the extinction derived using other techniques. This discrepancy challenges the assumption that all the mid-infrared emission of NLRG is extinguished by a simple screen of dust at larger radii. This disagreement can be explained in terms of either weakening of the silicate absorption feature by (i) thermal mid-IR emission from the narrow-line region, (ii) non-thermal emission from the base of the radio jets, or (iii) by direct warm dust emission that leaks through a clumpy torus without suffering major attenuation.Comment: 18 pages, 7 figures, 8 tables, accepted for publication in MNRA

Limits on entanglement in rotationally-invariant scattering of spin systems

This paper investigates the dynamical generation of entanglement in scattering systems, in particular two spin systems that interact via rotationally-invariant scattering. The spin degrees of freedom of the in-states are assumed to be in unentangled, pure states, as defined by the entropy of entanglement. Because of the restriction of rotationally-symmetric interactions, perfectly-entangling S-matrices, i.e. those that lead to a maximally entangled out-state, only exist for a certain class of separable in-states. Using Clebsch-Gordan coefficients for the rotation group, the scattering phases that determine the S-matrix are determined for the case of spin systems with $\sigma = 1/2$, 1, and 3/2.Comment: 6 pages, no figures; v.2: sections added, edited for clarity, conclusions and calculation unchanged, typos corrected; v.3: new abstrct, revised first two sections, added reference