Potts Models with (17) Invisible States on Thin Graphs

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.Comment: (2) Minor typos corrected, references update

The Gonihedric Ising Model and Glassiness

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum. In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to investigation of the non-equilibrium, glassy behaviour of the model.Comment: To appear as Chapter 7 in Rugged Free-Energy Landscapes - An Introduction, Springer Lecture Notes in Physics, 736, ed. W. Janke, (2008

(Four) Dual Plaquette 3D Ising Models

A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3d plaquette Ising and the X-Cube model is similar to that between the 2d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.Comment: Reviews results in arXiv:1106.0325 and arXiv:1106.4664 in light of more recent simulations and fracton literature. Published in special issue of Entropy dedicated to the memory of Professor Ian Campbel

Extending coupling volume theory to analyse small loop antennas for UHF RFID applications

Copyright © 2006 IEEEPeter H. Cole, Damith Chinthana Ranasingh

Development of combustion models for RANS and LES applications in SI engines

Prediction of flow and combustion in IC engines remains a challenging task. Traditional Reynolds Averaged Navier Stokes (RANS) methods and emerging Large Eddy Simulation (LES) techniques are being used as reliable mathematical tools for such predictions. However, RANS models have to be further refined to make them more predictive by eliminating or reducing the requirement for application based fine tuning. LES holds a great potential for more accurate predictions in engine related unsteady combustion and associated cycle-tocycle variations. Accordingly, in the present work, new advanced CFD based flow models were developed and validated for RANS and LES modelling of turbulent premixed combustion in SI engines. In the research undertaken for RANS modelling, theoretical and experimental based modifications have been investigated, such that the Bray-Moss-Libby (BML) model can be applied to wall-bounded combustion modelling, eliminating its inherent wall flame acceleration problem. Estimation of integral length scale of turbulence has been made dynamic providing allowances for spatial inhomogeneity of turbulence. A new dynamic formulation has been proposed to evaluate the mean flame wrinkling scale based on the Kolmogorov Pertovsky Piskunow (KPP) analysis and fractal geometry. In addition, a novel empirical correlation to quantify the quenching rates in the influenced zone of the quenching region near solid boundaries has been derived based on experimentally estimated flame image data. Moreover, to model the spark ignition and early stage of flame kernel formation, an improved version of the Discrete Particle Ignition Kernel (DPIK) model was developed, accounting for local bulk flow convection effects. These models were first verified against published benchmark test cases. Subsequently, full cycle combustion in a Ricardo E6 engine for different operating conditions was simulated. An experimental programme was conducted to obtain engine data and operating conditions of the Ricardo E6 engine and the formulated model was validated using the obtained experimental data. Results show that, the present improvements have been successful in eliminating the wall flame acceleration problem, while accurately predicting the in-cylinder pressure rise and flame propagation characteristics throughout the combustion period. In the LES work carried out in this research, the KIVA-4 RANS code was modified to incorporate the LES capability. Various turbulence models were implemented and validated in engine applications. The flame surface density approach was implemented to model the combustion process. A new ignition and flame kernel formation model was also developed to simulate the early stage of flame propagation in the context of LES. A dynamic procedure was formulated, where all model coefficients were locally evaluated using the resolved and test filtered flow properties during the fully turbulent phase of combustion. A test filtering technique was adopted to use in wall bounded systems. The developed methodology was then applied to simulate the combustion and associated unsteady effects in Ricardo E6 spark ignition engine at different operating conditions. Results show that, present LES model has been able to resolve the evolution of a large number of in-cylinder flow structures, which are more influential for engine performance. Predicted heat release rates, flame propagation characteristics, in-cylinder pressure rise and their cyclic variations are also in good agreement with measurements

Building an Efficient Content Based Image Retrieval System by Changing the Database Structure

Content Based Image Retrieval (CBIR) is still a major research area due to its complexity and the growth of the image databases. Color Based Image Retrieval is one of the major retrieval methods in Content Based Image Retrieval systems. At present, researchers combine image retrieval techniques to get more accurate results. With the large image databases, image retrieval is still a challenging area and the efficiency of the image retrieval techniques still need to be considered. For this purpose, a comparative study of image retrieval techniques has been discussed in this paper. In addition, an efficient method is presented which aids to retrieve images by storing an intermediate result of the process in the database. To compare the query image and the images in the database, Euclidean distance, Normalized Cross Correlation distance and Histogram Intersection distance are taken as distance measures. Experimental results demonstrate Histogram Intersection distance is better than the other two methods. The intermediate result was stored using an event in the system. By making minor modifications to the proposed system, it creates a possibility for the user to add images to the database just by clicking on a button. Thus, the user can expand his/her database on his/her own will. Results show a significant improvement of performance in the proposed method

An improved formulation of the Bray-Moss-Libby (BML) model for SI engine combustion modelling

In this paper an improved version of the BML model has been developed so that it could be applied to wall-bounded combustion modelling, eliminating the wall flame acceleration problem. Based on the Kolmogorov-Petrovski-Piskunov (KPP) analysis and fractal theory, a new dynamic formulation has been proposed to evaluate the mean flame wrinkling scale making necessary allowance for spatial inhomogeneity of turbulence. A novel empirical correlation has been derived based on experimentally estimated flame image data to quantify the quenching rates near solid boundaries. The proposed modifications were then applied to simulate premixed combustion in two spark ignition engines with different operating conditions. Results show that the present improvements have been successful in eliminating the wall flame acceleration problem found with the original BML model, while accurately predicting the in-cylinder pressure rise, mass burn rates and heat release rates

Simulation of engine combustion with ethanol as a renewable fuel

Ethanol as a fuel is an important bio-fuel for future energy needs. In this work the combustion process of gasoline-ethanol blends in spark ignition engines was investigated using computational fluid dynamics and turbulent combustion modeling. A modified flame surface density approach developed for gasoline engine combustion was adapted to calculate fuel-burning rate of the blend. The rise in in-cylinder peak pressure and temperature for blends up to E20 was found relatively small compared to E00. A significant reduction of CO and an increment of NOx were observed for optimized combustion with adjusted ignition timing