Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.Comment: 5 pages, late

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

On the Potts model partition function in an external field

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial

Neighbourhood characteristics, social capital and self-rated health - A population-based survey in Sweden

<p>Abstract</p> <p>Background</p> <p>In previous public health surveys large differences in health have been shown between citizens living in different neighbourhoods in the Örebro municipality, which has about 125000 inhabitants. The aim of this study was to investigate the determinants of health with an emphasis on the importance of neighbourhood characteristics such as the influence of neighbourhood social cohesion and social capital. The point of departure in this study was a conceptual model inspired by the work of Carpiano, where different factors related to the neighbourhood have been used to find associations to individual self-rated health.</p> <p>Methods</p> <p>We used data from the survey 'Life & Health 2004' sent to inhabitants aged 18-84 years in Örebro municipality, Sweden. The respondents (n = 2346) answered a postal questionnaire about living conditions, housing conditions, health risk factors and individual health. The outcome variable was self-rated health. In the analysis we applied logistic regression modelling in various model steps following a conceptual model.</p> <p>Results</p> <p>The results show that poor self-rated health was associated with social capital, such as lack of personal support and no experience of being made proud even after controlling for strong factors related to health, such as age, disability pension, ethnicity and economic stress. Also the neighbourhood factors, housing area and residential stability were associated with self-rated health. Poor self-rated health was more common among people living in areas with predominately large blocks of flats or areas outside the city centre. Moreover, people who had lived in the same area 1-5 years reported poor health more frequently than those who had lived there longer.</p> <p>Conclusions</p> <p>The importance of the neighbourhood and social capital for individual health is confirmed in this study. The neighbourhoods could be emphasized as settings for health promotion. They can be constructed to promote social interaction which in turn supports the development of social networks, social support and social capital - all important determinants of health.</p

The potential contribution of disruptive low-carbon innovations to 1.5 °C climate mitigation

This paper investigates the potential for consumer-facing innovations to contribute emission reductions for limiting warming to 1.5 °C. First, we show that global integrated assessment models which characterise transformation pathways consistent with 1.5 °C mitigation are limited in their ability to analyse the emergence of novelty in energy end-use. Second, we introduce concepts of disruptive innovation which can be usefully applied to the challenge of 1.5 °C mitigation. Disruptive low-carbon innovations offer novel value propositions to consumers and can transform markets for energy-related goods and services while reducing emissions. Third, we identify 99 potentially disruptive low-carbon innovations relating to mobility, food, buildings and cities, and energy supply and distribution. Examples at the fringes of current markets include car clubs, mobility-as-a-service, prefabricated high-efficiency retrofits, internet of things, and urban farming. Each of these offers an alternative to mainstream consumer practices. Fourth, we assess the potential emission reductions from subsets of these disruptive low-carbon innovations using two methods: a survey eliciting experts’ perceptions and a quantitative scaling-up of evidence from early-adopting niches to matched segments of the UK population. We conclude that disruptive low-carbon innovations which appeal to consumers can help efforts to limit warming to 1.5 °C

Syngas Production, Storage, Compression and Use in Gas Turbines

This chapter analyses syngas production through pyrolysis and gasification, its compression and its use in gas turbines. Syngas compression can be performed during or after thermal treatment processes. Important points are discussed related to syngas ignition, syngas explosion limit at high temperatures and high pressures and syngas combustion kinetics. Kinetic aspects influence ignition and final emissions which are obtained at the completion of the combustion process. The chapter is organized into four subsections, dealing with (1) innovative syngas production plants, (2) syngas compressors and compression process, (3) syngas ignition in both heterogeneous and homogeneous systems and (4) syngas combustion kinetics and experimental methods. Particular attention is given to ignition regions that affect the kinetics, namely systems that operate at temperatures higher than 1000 K can have strong ignition, whereas those operating at lower temperatures have weak ignition. Keywords: Pyrogas Pyrolysis Ignition Syngas Compression GasificationacceptedVersio

A molecular-based identification resource for the arthropods of Finland

To associate specimens identified by molecular characters to other biological knowledge, we need reference sequences annotated by Linnaean taxonomy. In this study, we (1) report the creation of a comprehensive reference library of DNA barcodes for the arthropods of an entire country (Finland), (2) publish this library, and (3) deliver a new identification tool for insects and spiders, as based on this resource. The reference library contains mtDNA COI barcodes for 11,275 (43%) of 26,437 arthropod species known from Finland, including 10,811 (45%) of 23,956 insect species. To quantify the improvement in identification accuracy enabled by the current reference library, we ran 1000 Finnish insect and spider species through the Barcode of Life Data system (BOLD) identification engine. Of these, 91% were correctly assigned to a unique species when compared to the new reference library alone, 85% were correctly identified when compared to BOLD with the new material included, and 75% with the new material excluded. To capitalize on this resource, we used the new reference material to train a probabilistic taxonomic assignment tool, FinPROTAX, scoring high success. For the full-length barcode region, the accuracy of taxonomic assignments at the level of classes, orders, families, subfamilies, tribes, genera, and species reached 99.9%, 99.9%, 99.8%, 99.7%, 99.4%, 96.8%, and 88.5%, respectively. The FinBOL arthropod reference library and FinPROTAX are available through the Finnish Biodiversity Information Facility (www.laji.fi) at https://laji.fi/en/theme/protax. Overall, the FinBOL investment represents a massive capacity-transfer from the taxonomic community of Finland to all sectors of society.</p