Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process

We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebra. We construct all finite dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.Comment: 18 pages, Latex, 1 EPS figur

Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the average density profile is computed in the thermodynamic limit. The phase diagram for the correlation length, which was conjectured in the previous work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.Comment: 24 pages, 6 figure

Electronic correlation effects and the Coulomb gap at finite temperature

We have investigated the effect of the long-range Coulomb interaction on the one-particle excitation spectrum of n-type Germanium, using tunneling spectroscopy on mechanically controllable break junctions. The tunnel conductance was measured as a function of energy and temperature. At low temperatures, the spectra reveal a minimum at zero bias voltage due to the Coulomb gap. In the temperature range above 1 K the Coulomb gap is filled by thermal excitations. This behavior is reflected in the temperature dependence of the variable-range hopping resitivity measured on the same samples: Up to a few degrees Kelvin the Efros-Shkovskii ln$R \propto T^{-1/2}$ law is obeyed, whereas at higher temperatures deviations from this law are observed, indicating a cross-over to Mott's ln$R \propto T^{-1/4}$ law. The mechanism of this cross-over is different from that considered previously in the literature.Comment: 3 pages, 3 figure

Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability

The reaction process $A+B->C$ is modelled for ballistic reactants on an infinite line with particle velocities $v_A=c$ and $v_B=-c$ and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of the origin. Previous, models of ballistic annihilation have particles that always react on contact, i.e. pair-reaction probability $p=1$. The evolution of such systems are wholly determined by the initial distribution of particles and therefore do not have a stochastic dynamics. However, in this paper the generalisation is made to $p<1$, allowing particles to pass through each other without necessarily reacting. In this way, the A and B particle domains overlap to form a fluctuating, finite-sized reaction zone where the product C is created. Fluctuations are also included in the currents of A and B particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by the `intrinsic reaction rate', seen in a single system, and the `extrinsic reaction rate', seen in an average over many systems. The intrinsic and extrinsic behaviours are examined and compared to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte

On Matrix Product Ground States for Reaction-Diffusion Models

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation-decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of $n$-point correlation functions at the phase transition.Comment: LaTeX source, 7 pages, no figure

Adelaide in-depth accident study 1975-1979. Part 5: Commercial vehicle accidents

This report deals with accidents involving trucks, vans, buses and multi-purpose vehicles, not all of which were being used as commercial vehicles. There were relatively few single vehicle accidents, apart from those involving pedestrians, and the reluctance of semitrailer drivers to brake hard at s~gnalisedin tersections and insecure loads of some heavy vehicles distinguished these accidents from those involving only passenger cars. All but one of the drivers of these commercial vehicles were males, most of whom were aged between 20 and 50 years. None of these drivers were affected by alcohol intoxication to a significant degree, nor was fatigue a factor in any of these accidents. Although none of the commercial vehicle occupants was severely injured, the provision and use of seat belts may have avoided many of the injuries which did occur. Some multi-purpose passenger vehicles are deficient, when compared to passenger cars, in terms of protecting their occupants from injury in a crash.A.J. Mclean, H.S. Aust, B.L. Sando

Adelaide in-depth accident study 1975-1979. Part 2: Pedestrian accidents

This report contains descriptions of the causes and consequences of the pedestrian accidents contained in a representative sample of road traffic accidents to which an ambulance was called in metropolitan Adelaide. Reviews of the relevant characteristics of the pedestrians and drivers, the vehicles, and the road and traffic environment are also included. All but one of these 40 accidents occurred on busy roads. Some measures designed to increase the rate of flow of vehicular traffic are detrimental to the safety of the pedestrian, to the extent that some urban arterial roads are very hazardous for some pedestrians, particularly children and the elderly. The pedestrian was more likely to have been careless, or to have made a mistake, than was the driver, but alcohol intoxication was less apparent as a causal factor in these pedestrian accidents than in other types of accidents covered by this survey. The injuries sustained by the pedestrians were much more likely to be dangerous to life than were the injuries sustained by other road users involved in other types of accident. The front of the striking car, including the upper surface of the bonnet, accounted for more than half of the injuries. A number of possible countermeasures and topics worthy of further investigation are listed at the end of the report.A.J. McLean, N.D.Brewer, B.L. Sando

Adelaide in-depth accident study 1975-1979. Part 3: Pedal cycle accidents.

This report contains descriptions of the causes and consequences of the pedal cycle accidents contained in a representative sample of road traffic accidents to which an ambulance was called in metropolitan Adelaide. Reviews of the relevant characteristics of the cyclists and drivers, the vehicles, and the road and traffic environment are also included. One-third of these 22 accidents involved a child cyclist who was riding carelessly on a residential street. The other two-thirds mostly involved adult cyclists on arterial roads, and were a consequence of errors made equally by the cyclists and the drivers. Alcohol intoxication was not a significant factor in any of these accidents. Almost all of the cyclists were injured, and their injuries were often very severe. The front of the striking car caused two-thirds of the severe injuries. A number of possible countermeasures and topics worthy of further investigation are listed at the end of the report.A.J. McLean, N.D. Brewer, B.L. Sando

Adelaide in-depth accident study 1975-1979. Part 3: Pedal cycle accidents.

This report contains descriptions of the causes and consequences of the pedal cycle accidents contained in a representative sample of road traffic accidents to which an ambulance was called in metropolitan Adelaide. Reviews of the relevant characteristics of the cyclists and drivers, the vehicles, and the road and traffic environment are also included. One-third of these 22 accidents involved a child cyclist who was riding carelessly on a residential street. The other two-thirds mostly involved adult cyclists on arterial roads, and were a consequence of errors made equally by the cyclists and the drivers. Alcohol intoxication was not a significant factor in any of these accidents. Almost all of the cyclists were injured, and their injuries were often very severe. The front of the striking car caused two-thirds of the severe injuries. A number of possible countermeasures and topics worthy of further investigation are listed at the end of the report.A.J. McLean, N.D. Brewer, B.L. Sando

Applying psychological type theory to cathedral visitors : a case study of two cathedrals in England and Wales

This study employs Jungian psychological type theory to profile visitors to Chester Cathedral in England and St Davids Cathedral in Wales. Psychological type theory offers a fourfold psychographic segmentation of visitors, distinguishing between introversion and extraversion, sensing and intuition, thinking and feeling, and judging and perceiving. New data provided by 157 visitors to Chester Cathedral (considered alongside previously published data provided by 381 visitors to St Davids Cathedral) demonstrated that these two cathedrals attract more introverts than extraverts, more sensers than intuitives, and more judgers than perceivers, but equal proportions of thinkers and feelers. Comparison with the population norms demonstrated that extraverts and perceivers are significantly under-represented among visitors to these two cathedrals. The implications of these findings are discussed both for maximising the visitor experiences of those already attracted to these cathedrals and for discovering ways of attracting more extraverts and more perceivers to explore these cathedrals