Evolution equations of curvature tensors along the hyperbolic geometric flow

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature tensors along the hyperbolic geometric flow. The method and results are computed and written in global tensor form, different from the local normal coordinate method in [DKL1]. In addition, we further show that any solution to the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.Comment: 15 page

Time-Periodic Solutions of the Einstein's Field Equations II

In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively. The singularities of these new time-periodic solutions are investigated and some new physical phenomena are found. The applications of these solutions in modern cosmology and general relativity can be expected.Comment: 10 pages, 1 figur

New Results for Diffusion in Lorentz Lattice Gas Cellular Automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported, of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the super diffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits with {\em universal} exponents ${\displaystyle{d_f = \frac{7}{4}}}$ and ${\displaystyle{\tau = \frac{15}{7}}}$. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem, and of the dynamical significance of hyperscaling.Comment: 52 pages, including 18 figures on the last 22 pages, email: [email protected]

Radiative corrections to the Casimir force and effective field theories

Radiative corrections to the Casimir force between two parallel plates are considered in both scalar field theory of one massless and one massive field and in QED. Full calculations are contrasted with calculations based on employing ``boundary-free'' effective field theories. The difference between two previous results on QED radiative corrections to the Casimir force between two parallel plates is clarified and the low-energy effective field theory for the Casimir effect in QED is constructed.Comment: 17 pages, revte

The sidewall-localized mode in a resonant precessing cylinder

ArticleWe investigate, via direct numerical simulation using a finite-element method, the precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. Our numerical simulation, after validating with the asymptotic analytical solution for a weakly precessing cylinder and with the constructed exact solution for the strongly nonlinear problem, focuses on the strongly precessing flow at asymptotically small Ekman numbers. An unusual form of the resonant precessing flow is found when the precessing rate is sufficiently large and the corresponding nonlinearity is sufficiently strong. The nonlinear precessing flow is marked by a sidewall-localized non-axisymmetric traveling wave and a wall-localized axisymmetric shear together with an overwhelmingly dominant interior rigid-body rotation whose direction and magnitude substantially reduce the angular momentum of the rotating fluid system.K.Z. is supported by grants from UK Science and Technology Facilities Council and Natural Environment Research Council. X.L. is supported by National Natural Science Foundation of China/11133004 and Chinese Academy of Sciences under Grant Nos. KZZD-EW-01-3 and XDB09000000

A web system trace model and its application to web design

Traceability analysis is crucial to the development of web-centric systems, particularly those with frequent system changes, fine-grained evolution and maintenance, and high level of requirements uncertainty. A trace model at the level of the web system architecture is presented in this paper to address the specific challenges of developing web-centric systems. The trace model separates the concerns of different stakeholders in the web development life cycle into viewpoints; and classifies each viewpoint into structure and behaviour. Tracing relationships are presented along two dimensions: within viewpoints; and among viewpoints. Examples of tracing relationships are presented using UML. This trace model is demonstrated through its application to the design of a commercial web project using a web-design process. The design artifacts in each activity are transformed based on the artifacts tracing relationship in the trace model. The model provides mechanisms for verification of consistency, completeness and coverage within each viewpoint and the connectedness across viewpoints

Using synchronized lightweight state observers to minimise wireless sensor resource utilisation

A major trend in the evolution of the Web is the rapidly growing numbers of web-enabled sensors which provide a rich ability to monitor and control our physical environment. The devices are often cheap, lightweight, rapidly deployed and densely interconnected. The current dominant models of Web-based data monitoring are not well-adapted to the operational needs of these devices, particularly in terms of resource utilization. In this paper we describe an approach to the optimization of the resources utilized by these devices based on the use of synchronized state-observers. By embedding state observers with a minimized footprint into both the sensors and the monitoring Web client, we show that it is possible to minimize the utilization of limited sensor resources such as power and bandwidth, and hence to improve the performance and potential applications of these devices

Separation of concerns: A web application architecture framework

Architecture frameworks have been extensively developed and described within the literature. These frameworks typically support and guide organisations during system planning, design, building, deployment and maintenance. Their main pupose is to provide clarity to the different modelling perspectives, abstractions, and domains of consideration within system development. In dpoing so they allow improved clarity with regard to the connections between the different models, and the selection of models tht are most likely to capture salient features of the system. In this paper we present an Architectural Framework which takes into account the specific characteristics of web systems. The framework is based around a two dimensional matrix. One dimension separates the concerns of different participants of the web system into perspectives. The second dimension classifies each perspective into development abstractions: structure (what), behaviour (how), location (where) and pattern. The framework is illustrated through examples from the development of a commercial web application