Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions

We have studied the spin ordering of a dilute classical Heisenberg model with spin concentration $x$, and with ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic next-nearest-neighbor interaction $J_2$. Magnetic phases at absolute zero temperature $T = 0$ are determined examining the stiffness of the ground state, and those at finite temperatures $T \neq 0$ are determined calculating the Binder parameter $g_L$ and the spin correlation length $\xi_L$. Three ordered phases appear in the $x-T$ phase diagram: (i) the ferromagnetic (FM) phase; (ii) the spin glass (SG) phase; and (iii) the mixed (M) phase of the FM and the SG. Near below the ferromagnetic threshold $x_{\rm F}$, a reentrant SG transition occurs. That is, as the temperature is decreased from a high temperature, the FM phase, the M phase and the SG phase appear successively. The magnetization which grows in the FM phase disappears in the SG phase. The SG phase is suggested to be characterized by ferromagnetic clusters. We conclude, hence, that this model could reproduce experimental phase diagrams of dilute ferromagnets Fe$_x$Au$_{1-x}$ and Eu$_x$Sr$_{1-x}$S.Comment: 9 pages, 23 figure

The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section

Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions

We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the representations considered correspond to a different set of weighted lattice paths which, when summed over, give the stationary state probability distribution. We show that all three sets of paths are combinatorially related via sequences of bijections and sign reversing involutions.Comment: 28 page

Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions

We consider the Potts model and the related bond, site, and mixed site-bond percolation problems on triangular-type and kagome-type lattices, and derive closed-form expressions for the critical frontier. For triangular-type lattices the critical frontier is known, usually derived from a duality consideration in conjunction with the assumption of a unique transition. Our analysis, however, is rigorous and based on an established result without the need of a uniqueness assumption, thus firmly establishing all derived results. For kagome-type lattices the exact critical frontier is not known. We derive a closed-form expression for the Potts critical frontier by making use of a homogeneity assumption. The closed-form expression is new, and we apply it to a host of problems including site, bond, and mixed site-bond percolation on various lattices. It yields exact thresholds for site percolation on kagome, martini, and other lattices, and is highly accurate numerically in other applications when compared to numerical determination.Comment: 22 pages, 13 figure

Optimum Selection of a Sustainable Lighting System for a University Class Room in Saudi Arabia

Sustainability assessment is highly critical to the success of a construction project that are to be classified as sustainable building or green buildings, by either using the Leadership in Energy and Environmental Design (LEED) rating tools as in my case or using BRE Environmental Assessment Method (BREEAM) and other rating systems. This paper will involve on developing a decision support system (DSS) following the (LEED® ) rating system requirements to; Improved health and well being of building users, Reduced operating costs and energy consumption and lastly to increase the lighting efficiency of the Classroom there by improving the building/student performance. This was carried out by selecting an appropriate energy efficient artificial lighting system for indoor comfort ability, in which case (03) lamps ( Incandescent, Compact Fluorescent and LED )were, ran in a simulation program (Dialux 4.10) and also designing for best Natural lighting to improve the performance of University Classroom. The DSS we developed was based on; functional requirement of the space on the aspect of both Natural lighting and also on the users characteristic where by the DF (daylight factor) was used as a parameter and Artificial Lighting where by energy and cost was used as baseline for selection. Base on our criterion for analysis, the LED lamp was found to be more energy efficient and cost effective within a long duration while for the Natural lighting, our design of window gave us a minimum Day Light Factor of 2.2 which was satisfactory according to the LEED requirement. Keywords: Sustainable lighting, building performance, LEED rating system

Structural behaviour of ferrocement channels slabs for low cost housing

This paper presents a new pre cast U-shape ferrocement forms reinforced with various types of metallic and non-metallic mesh reinforcement. This research was designed to investigate the feasibility and effectiveness of employing various types of reinforcing meshes in the construction of structural slabs incorporating permanent U-shape ferrocement forms as a viable alternative for conventional reinforced concrete slabs. Fiber glass meshes reinforcement was used for durability and protection against corrosion of reinforcing steel. To accomplish this objective, an experimental program was conducted. The experimental program comprised casting and testing ten slabs having the total dimensions of 500x100x2500 mm incorporating 40 mm thick U-shape permanent ferrocement forms. Series A consists of two conventionally reinforced concrete slabs were cast and tested and used as control slab without fibers and with fibers, volume fraction, 2.05 % and 2.177 %. Series B comprises of two slabs reinforced with one and two layers of expanded steel mesh, volume fraction 2.09 and 2.42% respectively. Series C comprises two slabs reinforced with two and four layers of welded galvanized steel mesh, having volume fraction 2.05 and 2.189% respectively. Series D Consists of two slabs reinforced with one layer and two layers of fiber glass meshes, having volume fraction 2.107 and 2.277% respectively. Series E comprises two slabs reinforced with 2 layers expanded steel mesh and one layer expanded steel mesh, having volume fraction 1.357 and 2.750 % respectively. The test specimens were tested as simple slabs under four-line loadings condition on a span of 2300mm. The performance of the test slabs in terms of strength, stiffness, strains, cracking behavior, ductility, and energy absorption properties was investigated. The behavior of the developed slabs was compared to that of the control slabs. The experimental results showed that high ultimate and serviceability loads, better crack resistance control, high ductility, and good energy absorption properties could be achieved by using the proposed slabs and low cost compared with control specimen

Precise calculation of the threshold of various directed percolation models on a square lattice

Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of connectivity. We conjecture that $p_{c}$ decays exactly as the inverse of the coodination number.Comment: 2 pages, 2 figures and 1 tabl