Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices

We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse matrices, each of dimension ~ 3^m, where m is the number of lattice spacings across the strip. As a specific application, we obtain the large-q series of the bulk, surface and corner free energies of the chromatic polynomial. This extends the existing series for the square lattice by 32 terms, to order q^{-79}. On the triangular lattice, we verify Baxter's analytical expression for the bulk free energy (to order q^{-40}), and we are able to conjecture exact product formulae for the surface and corner free energies.Comment: 17 pages. Version 2: added 4 further term to the serie

Experimental and Theoretical Evidence for Nitrogen-Fluorine Halogen Bonding in Silver-Initiated Radical Fluorinations

We report experimental and computational evidence for nitrogen–fluorine halogen bonding in Ag­(I)-initiated radical C–H fluorinations. Simple pyridines form [N–F–N]+ halogen bonds with Selectfluor to facilitate single-electron reduction by catalytic Ag­(I). Pyridine electronics affect the extent of halogen bonding, leading to significant differences in selectivity between mono- and difluorinated products. Electronic structure calculations show that halogen bonding to various pyridines alters the single-electron reduction potential of Selectfluor, which is consistent with experimental electrochemical analysis. Multinuclear correlation NMR also provides spectroscopic evidence for pyridine halogen bonding to Selectfluor under ambient conditions

Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions

We address the general problem of hard objects on random lattices, and emphasize the crucial role played by the colorability of the lattices to ensure the existence of a crystallization transition. We first solve explicitly the naive (colorless) random-lattice version of the hard-square model and find that the only matter critical point is the non-unitary Lee-Yang edge singularity. We then show how to restore the crystallization transition of the hard-square model by considering the same model on bicolored random lattices. Solving this model exactly, we show moreover that the crystallization transition point lies in the universality class of the Ising model coupled to 2D quantum gravity. We finally extend our analysis to a new two-particle exclusion model, whose regular lattice version involves hard squares of two different sizes. The exact solution of this model on bicolorable random lattices displays a phase diagram with two (continuous and discontinuous) crystallization transition lines meeting at a higher order critical point, in the universality class of the tricritical Ising model coupled to 2D quantum gravity.Comment: 48 pages, 13 figures, tex, harvmac, eps

The application of the global isomorphism to the surface tension of the liquid-vapor interface of the Lennard-Jones fluids

In this communication we show that the surface tension of the real fluids of the Lennard-Jones type can be obtained from the surface tension of the lattice gas (Ising model) on the basis of the global isomorphism approach developed earlier for the bulk properties.Comment: 8 pages, 6 figure

Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagom\'e lattice.Comment: 33 pages, Latex, 9 encapsulated postscript figures, J. Phys. A, in pres

Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter Δ=1/2\Delta = {1/2}

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter $\Delta = {1/2}$ corresponding to $q^3 = -1$.Comment: 6 page

Statistical mechanical aspects of joint source-channel coding

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented with the following main results: (a) for a binary symmetric channel the threshold, $f_c$, is extrapolated for infinite messages using the scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$; (b) a degradation in the threshold is observed as the correlations are enhanced; (c) for a given set of autocorrelations the performance is enhanced as $q$ is increased; (d) the efficiency of the DBP joint source-channel coding is slightly better than the standard gzip compression method; (e) for a given entropy, the performance of the DBP algorithm is a function of the decay of the correlation function over large distances.Comment: 6 page

Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem

We prove that the $q$-state Potts antiferromagnet on a lattice of maximum coordination number $r$ exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever $q > 2r$. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for $q \ge 7$), triangular lattice ($q \ge 11$), hexagonal lattice ($q \ge 4$), and Kagom\'e lattice ($q \ge 6$). The proofs are based on the Dobrushin uniqueness theorem.Comment: 32 pages including 3 figures. Self-unpacking file containing the tex file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and eqsection.sty) and the 3 ps file

Design of a high efficiency cyclone for collection of rare and low concentration airborne pathogens

Recent serious outbreaks of pathogens such as Chalara Fraxinea, (Ash Dieback) demonstrate the vulnerability of UK’s forests, woods, and trees. Early detection of threats is critical in the fight against such tree pests and pathogens. This requires a process for collecting and analysing the spores which is robust, flexible and can be deployed rapidly, but which also has sufficient sensitivity to detect the earliest precursors. The work presented here describes a newly-developed high-efficiency detection apparatus and is part of an ongoing BBRSC project to improve the UK’s biosecurity. Our automatic spore system is capable of collecting and analysing Chalara Fraxinea using a novel cyclonic pathogen collector. Cyclones are an effective way to separate small particles (spores) from large quantities of surrounding air and store them for analysis. Our system incorporates a purpose-designed high efficiency cyclone directly integrated with a low power custom impeller to maximise volumetric air sampling while minimising the power requirement. 3D printing was used extensively to validate theoretical models and the particle collection and retention capability of this series of prototypes was evaluated experimentally within our Aerosol test chamber. We found that we could collect greater than 90% of particulate in the target size range, thus providing a front-end to a detection platform. Our system is capable of operating autonomously and at low power, with a high sensitivity to ambient particles. The final system design incorporates the use of multiple cyclone storage vessels ensuring complete isolation of each sample, eradicating cross-contamination, and facilitating automated handling of the sample inside the same apparatus. COTS – commercial off the shelf components were incorporated into the cyclone to make a series of cost effective collection vessels. Early collection and detection of pathogens in-situ represents a considerable advance in surveillance and monitoring of pathogens strengthening UK biosecurity for the future

Development of an automated smart trap for wheat pathogens

National surveys show fungicide use on wheat continues to increase despite fluctuations in disease pressure, reaching a 30 year high in 2012 (Defra). Septoria tritici is the most significant foliar disease in UK wheat causing between £43M to £53M in yield losses annually; Yellow and brown rust are more sporadic but have caused significant losses during high disease years. In all cases control is by fungicide application costing £82M annually (GFK Kynetec 2013). Effective disease management relies on either prophylactic pesticide use or significant manual intervention and time consuming assessment of crop disease indicators by farmers and agronomists. Furthermore indications are that current levels of pesticide use could lead to increased risk of pesticide resistance, if this should occur it is estimated that wheat yields could reduce by up to 20%. To address this we have developed a prototype integrated and automated spore detection system, designed for unattended field application, to monitor and identify the presence of Septoria, brown and yellow rust. The prototype system incorporates novel cyclonic pathogen collection, on-board sample processing and isothermal DNA amplification chemistry (LAMP). We present the engineering design, optimisation and evaluation of our prototype system reporting on successfully completed laboratory testing and initial field trial results. This prototype will be the basis for the development of a commercially available system which, in addition to inoculum detection, will be capable of providing growers/agronomists with real-time information on inoculum moving into a crop enabling more effective timing and selection of fungicide application, and thus better control, increased yield, and improved environmental stewardship