A proposed generalized constitutive equation for nonlinear para-isotropic materials

Finite element models of varying complexities were used to solve problems in solid mechanics. Particular emphasis was given to concrete which is nonisotropic at any level of deformation and is also nonlinear in terms of stress-strain relationships

Exact Ampitude Ratio and Finite-Size Corrections for the M x N Square Lattice Ising Model The :

Let f, U and C represent, respectively, the free energy, the internal energy and the specific heat of the critical Ising model on the square M x N lattice with periodic boundary conditions. We find that N f and U are well-defined odd function of 1/N. We also find that ratios of subdominant (N^(-2 i - 1)) finite-size corrections amplitudes for the internal energy and the specific heat are constant. The free energy and the internal energy at the critical point are calculated asymtotically up to N^(-5) order, and the specific heat up to N^(-3) order.Comment: 18 pages, 4 figures, to be published in Phys. Rev. E 65, 1 February 200

Assessment of different urban traffic control strategy impacts on vehicle emissions

This paper investigates the influence of traffic signal control strategy on vehicle emissions, vehicle journey time and total throughput flow within a single isolated four-armed junction. Two pre-timed signal plans are considered, one with two-stages involving permissive-only opposing turns and the other with four-stages which has no conflicting traffic. Additionally, the increase in efficiency by utilising actuated signal timing where green time is re-optimised as flow values vary is investigated. A microscopic traffic simulation model is used to model flows and AIRE (Analysis of Instantaneous Road Emissions) microscopic emissions model is utilised to out- put emission levels from the flow data. A simple junction model shows that the two-stage signal plan is more efficient in both emis- sions and journey time. However, as the level of opposed turning vehicles and conflicting movement increases, the two-stage model moves to being the inferior signal plan choice and the four-stage plan outputs fewer emissions than the two-stage plan. A real-world example of a four-armed junction has been used in this study and from the traffic survey data and existing junction layout; it is rec- ommended that a two-stage plan is used as it produces lower amounts of emissions and shorter journey times compared to a four-stage plan. The results also show that nitrogen oxides (NOx) are the most sensitive to changes in flow followed by carbon dioxide (CO2), Black Carbon and then particulate matter (PM10)

Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime

A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes. This explanation is based on the hypothesis that samples which show this behavior contain density inhomogeneities. Theory then relates the non-universal conductance peak-heights to the ``number of alternating percolation clusters'' of a continuum percolation model defined on the spatially-varying local carrier density. We discuss the statistical properties of the number of alternating percolation clusters for Corbino disc samples characterized by random density fluctuations which have a correlation length small compared to the sample size. This allows a determination of the statistical properties of the low-temperature conductance peak-heights of such samples. We focus on a range of filling fraction at the center of the plateau transition for which the percolation model may be considered to be critical. We appeal to conformal invariance of critical percolation and argue that the properties of interest are directly related to the corresponding quantities calculated numerically for bond-percolation on a cylinder. Our results allow a lower bound to be placed on the non-universal conductance peak-heights, and we compare these results with recent experimental measurements.Comment: 7 pages, 4 postscript figures included. Revtex with epsf.tex and multicol.sty. The revised version contains some additional discussion of the theory and slightly improved numerical result

Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle

We study the finite-size scaling properties of the Ising model on the Moebius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function $p(m)$ for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at $T=T_c$ for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.Comment: 4 pages including 5 eps figures, RevTex, to appear in Phys. Rev. Let

Bicritical and tetracritical phenomena and scaling properties of the SO(5) theory

By large scale Monte Carlo simulations it is shown that the stable fixed point of the SO(5) theory is either bicritical or tetracritical depending on the effective interaction between the antiferromagnetism and superconductivity orders. There are no fluctuation-induced first-order transitions suggested by epsilon expansions. Bicritical and tetracritical scaling functions are derived for the first time and critical exponents are evaluated with high accuracy. Suggestions on experiments are given.Comment: 11 pages, 8 postscript figures, Revtex, revised versio

Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters

Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $_{n}$ ($_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $_{n}$ ($_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure

Probability-Changing Cluster Algorithm for Potts Models

We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, $p = 1 - e^{- J/ k_BT}$, in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.Comment: 4 pages including 5 eps figures, RevTeX, to appear in Phys. Rev. Let