Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction

The additivity principle allows to compute the current distribution in many one-dimensional (1D) nonequilibrium systems. Using simulations, we confirm this conjecture in the 1D Kipnis-Marchioro-Presutti model of heat conduction for a wide current interval. The current distribution shows both Gaussian and non-Gaussian regimes, and obeys the Gallavotti-Cohen fluctuation theorem. We verify the existence of a well-defined temperature profile associated to a given current fluctuation. This profile is independent of the sign of the current, and this symmetry extends to higher-order profiles and spatial correlations. We also show that finite-time joint fluctuations of the current and the profile are described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.Comment: 4 pages, 4 figure

Virtual reality learning resources in building pathology

Building surveying students must be capable of analysing the condition of buildings and their components and, where this falls below an agreed standard, make recommendations for their repair. Hence university courses must provide opportunities for students to learn about the main causes of deterioration. Fieldwork exercises are essential but there are often problems locating appropriate buildings, programming visits to satisfy course timetables and complying with health and safety requirements. Whilst virtual surveys of existing buildings are not considered to be a substitute for real-life educational visits, this paper critically examines the development of a novel building pathology educational resource. Alternative technologies for creating digital panoramas are examined, prior to the development of an interactive case study, which enables students to conduct an on-line survey of a Grade 1 listed 16th Century hunting lodge. 360 degree panoramic scenes are linked with hot spots to create an interactive virtual tour of the building. The paper considers how virtual resources can be embedded within the curriculum, gauges tutor reaction to case study materials and identifies opportunities for the development of a suite of building pathology educational media-rich learning materials

Unification Bounds on the Possible N=2 Supersymmetry Breaking Scale

In this letter, the possible appearance of N=2 supersymmetry at a low energy scale is investigated in the context of unified theories. Introducing mirror particles for all the gauge and matter multiplets of the Minimal Supersymmetric extension of the Standard Model (MSSM), the measured values of sin^2 \theta_W and \alpha_3(M_Z) indicate that the N=2 threshold scale M_{S_2} cannot be lower than \sim 10^{14}GeV. If the U(1) normalization coefficient k is treated as a free parameter, M_{S_2} can be as low as 10^9 GeV. On the other hand, if mirror quarks and leptons are absent and a non-standard value for k is used, N=2 supersymmetry breaking could in principle occur at the electroweak scale.Comment: 10 pages, LATEX, 2 eps figure

Evaluations of topological Tutte polynomials

We find new properties of the topological transition polynomial of embedded graphs, $Q(G)$. We use these properties to explain the striking similarities between certain evaluations of Bollob\'as and Riordan's ribbon graph polynomial, $R(G)$, and the topological Penrose polynomial, $P(G)$. The general framework provided by $Q(G)$ also leads to several other combinatorial interpretations these polynomials. In particular, we express $P(G)$, $R(G)$, and the Tutte polynomial, $T(G)$, as sums of chromatic polynomials of graphs derived from $G$; show that these polynomials count $k$-valuations of medial graphs; show that $R(G)$ counts edge 3-colourings; and reformulate the Four Colour Theorem in terms of $R(G)$. We conclude with a reduction formula for the transition polynomial of the tensor product of two embedded graphs, showing that it leads to additional relations among these polynomials and to further combinatorial interpretations of $P(G)$ and $R(G)$.Comment: V2: major revision, several new results, and improved expositio

The implementation and evaluation of an undergraduate virtual reality surveying application

Multi-media applications are increasingly being used to enhance the delivery of on-site and distance learning teaching material. However, production costs are often prohibitive, both in terms of capital investment and development time. Hence it is surprising that authors comment on the failure to adequately evaluate new educational software applications. This paper evaluates an interactive multi-media levelling resource, which comprises text-based guides, video instruction, photo-realistic panoramic scenes and multi-row object movies. Students explore 360 degree images of building sites, using traditional computer input devices, and click on hot spots to gather detailed information about the position of the optical level and staff. Readings are taken directly from the staff and students record backsights and foresights as various change points are introduced. On completion of the levelling exercise, 192 first year undergraduate students completed an evaluation based upon a series of statements drawn from technology-based training literature. The findings suggest that the exercise complements traditional learning approaches, maintains student interest, and reinforces understanding. However, significant differences in student ratings for part-time and full-time cohorts emphasise the importance of designing resources that accommodate the needs of varying student profiles. Suggestions for enhanced interactivity are offered and new areas for development allied to construction technology are identified

Low-Energy Theorems for QCD at Finite Temperature and Chemical Potential

The low-energy theorems for QCD are generalized to finite temperature. and chemical potential, including non-zero quark masses.Comment: 6 pages late