Critical manifold of the kagome-lattice Potts model

Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite subgraph B of G; we call B a basis of G. We introduce a two-parameter graph polynomial P_B(q,v) that depends on B and its embedding in G. The algebraic curve P_B(q,v) = 0 is shown to provide an approximation to the critical manifold of the q-state Potts model, with coupling v = exp(K)-1, defined on G. This curve predicts the phase diagram both in the ferromagnetic (v>0) and antiferromagnetic (v<0) regions. For larger bases B the approximations become increasingly accurate, and we conjecture that P_B(q,v) = 0 provides the exact critical manifold in the limit of infinite B. Furthermore, for some lattices G, or for the Ising model (q=2) on any G, P_B(q,v) factorises for any choice of B: the zero set of the recurrent factor then provides the exact critical manifold. In this sense, the computation of P_B(q,v) can be used to detect exact solvability of the Potts model on G. We illustrate the method for the square lattice, where the Potts model has been exactly solved, and the kagome lattice, where it has not. For the square lattice we correctly reproduce the known phase diagram, including the antiferromagnetic transition and the singularities in the Berker-Kadanoff phase. For the kagome lattice, taking the smallest basis with six edges we recover a well-known (but now refuted) conjecture of F.Y. Wu. Larger bases provide successive improvements on this formula, giving a natural extension of Wu's approach. The polynomial predictions are in excellent agreement with numerical computations. For v>0 the accuracy of the predicted critical coupling v_c is of the order 10^{-4} or 10^{-5} for the 6-edge basis, and improves to 10^{-6} or 10^{-7} for the largest basis studied (with 36 edges).Comment: 31 pages, 12 figure

Polynomial sequences for bond percolation critical thresholds

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4,6,12) and (3^4,6) lattices using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. P03021), implemented as a branching process of lattices. I find the estimates for the bond percolation thresholds, p_c(4,6,12)=0.69377849... and p_c(3^4,6)=0.43437077..., compared with Parviainen's numerical results of p_c \approx 0.69373383 and p_c \approx 0.43430621 . These deviations are of the order 10^{-5}, as is standard for this method, although they are outside Parviainen's typical standard error of 10^{-7}. Deriving thresholds in this way for a given lattice leads to a polynomial with integer coefficients, the root in [0,1] of which gives the estimate for the bond threshold. I show how the method can be refined, leading to a sequence of higher order polynomials making predictions that likely converge to the exact answer. Finally, I discuss how this fact hints that for certain graphs, such as the kagome lattice, the exact bond threshold may not be the root of any polynomial with integer coefficients.Comment: submitted to Journal of Statistical Mechanic

Development of Suitable CuO-Based Materials Supported on Al2O3, MgAl2O4, and ZrO2 for Ca/Cu H2 Production Process

Functional materials for the sorption enhanced reforming process for H2 production coupled to a Cu/CuO chemical loop have been synthesized. The performance of CuO-based materials supported on Al2O3, MgAl2O4, and ZrO2 and synthesized by different routes has been analyzed. Highly stable materials supported on Al2O3 or MgAl2O4 synthesized by coprecipitation and mechanical mixing with sufficient Cu loads (around 65% wt) have been successfully developed. However, it has been found that coprecipitation under these conditions is not a suitable route for ZrO2. Spray-drying and deposition precipitation did not provide the best chemical features to the materials. As the Ca/Cu process is operated in fixed bed reactors, the best candidates were pelletized and their stability was again assessed. Pellets with high chemical and mechanical stability, high oxygen transport capacity, and good mechanical properties have been finally obtained by coprecipitation. The good homogeneity that provides this route would allow an easy scaling up

The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices

We give a conditional derivation of the inhomogeneous critical percolation manifold of the bow-tie lattice with five different probabilities, a problem that does not appear at first to fall into any known solvable class. Although our argument is mathematically rigorous only on a region of the manifold, we conjecture that the formula is correct over its entire domain, and we provide a non-rigorous argument for this that employs the negative probability regime of the triangular lattice critical surface. We discuss how the rigorous portion of our result substantially broadens the range of lattices in the solvable class to include certain inhomogeneous and asymmetric bow-tie lattices, and that, if it could be put on a firm foundation, the negative probability portion of our method would extend this class to many further systems, including F Y Wu’s checkerboard formula for the square lattice. We conclude by showing that this latter problem can in fact be proved using a recent result of Grimmett and Manolescu for isoradial graphs, lending strong evidence in favor of our other conjectured results. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98528/1/1751-8121_45_49_494005.pd

Scale-up of CLC oxygen carriers for gaseous fuels

Chemical Looping Combustion, CLC, is one of the most promising processes to capture CO2 at a low cost. It is based on the transfer of the oxygen from air to the fuel by using a solid oxygen carrier that circulates in dual fluidized bed systems. The CO2 capture is inherent to this process, as the air does not get mixed with the fuel. However, the CLC process is still under development waiting for a large scale demonstration experience. The key issue in the system performance is the oxygen carrier material. The oxygen carrier must fulfil several characteristics such as high reactivity and good fluidization properties, that will rely on their redox system and the support. Therefore, the identification of raw materials, available at multi-tonn scale at a competitive price, is one of requirements for the success of the technology. Promising impregnated oxygen carriers, based on copper and iron, have been developed to perform well for gaseous fuels (CH4, syngas , LHC..), although they were prepared from not commercially scalable production supports. In this work, the performance of different impregnated materials, prepared with commercial-scale supports, was analyzed during methane combustion in a continuous 500 Wth CLC unit to identify the best material based on reactivity, attrition resistance and sulfur tolerance. A copper-based material with improved performance than the reference material was identified and therefore proposed as the best oxygen carrier for scale-up CLC technology for gaseous fuels

Classical phase transitions in a one-dimensional short-range spin model

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure

Assessing Order Effects in Online Community-based Health Forums

Measuring the quality of health content in online health forums is a challenging task. The majority of the existing measures are based on evaluations of forum users and may not be reliable. We employed machine learning techniques, text mining methods, and Big Data platforms to construct four measures of textual quality to automatically determine the similarity of a given answer to professional answers. We then used them to assess the quality of 66,888 answers posted on Yahoo! Answers Health section. All four measures of textual quality revealed a higher quality for asker-selected best answers indicating that askers, to some extent, have a proper judgment to select the best answers. We also studied the presence of order effects in online health forums. Our results suggest that the textual quality of the first answer positively influences the mean textual quality of the subsequent answers and negatively influences the quantity of subsequent answers

Incidence of cancer and overall risk of mortality in individuals treated with raltegravir-based and non-raltegravir-based combination antiretroviral therapy regimens

Objectives: There are currently few data on the long-term risk of cancer and death in individuals taking raltegravir (RAL). The aim of this analysis was to evaluate whether there is evidence for an association. Methods: The EuroSIDA cohort was divided into three groups: those starting RAL-based combination antiretroviral therapy (cART) on or after 21 December 2007 (RAL); a historical cohort (HIST) of individuals adding a new antiretroviral (ARV) drug (not RAL) to their cART between 1 January 2005 and 20 December 2007, and a concurrent cohort (CONC) of individuals adding a new ARV drug (not RAL) to their cART on or after 21 December 2007. Baseline characteristics were compared using logistic regression. The incidences of newly diagnosed malignancies and death were compared using Poisson regression. Results: The RAL cohort included 1470 individuals [with 4058 person-years of follow-up (PYFU)] compared with 3787 (4472 PYFU) and 4467 (10 691 PYFU) in the HIST and CONC cohorts, respectively. The prevalence of non-AIDS-related malignancies prior to baseline tended to be higher in the RAL cohort vs. the HIST cohort [adjusted odds ratio (aOR) 1.31; 95% confidence interval (CI) 0.95–1.80] and vs. the CONC cohort (aOR 1.89; 95% CI 1.37–2.61). In intention-to-treat (ITT) analysis (events: RAL, 50; HIST, 45; CONC, 127), the incidence of all new malignancies was 1.11 (95% CI 0.84–1.46) per 100 PYFU in the RAL cohort vs. 1.20 (95% CI 0.90–1.61) and 0.83 (95% CI 0.70–0.99) in the HIST and CONC cohorts, respectively. After adjustment, there was no evidence for a difference in the risk of malignancies [adjusted rate ratio (RR) 0.73; 95% CI 0.47–1.14 for RALvs. HIST; RR 0.95; 95% CI 0.65–1.39 for RALvs. CONC] or mortality (adjusted RR 0.87; 95% CI 0.53–1.43 for RALvs. HIST; RR 1.14; 95% CI 0.76–1.72 for RALvs. CONC). Conclusions: We found no evidence for an oncogenic risk or poorer survival associated with using RAL compared with control groups.Peer reviewe