Corner contribution to cluster numbers in the Potts model

For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of Gamma. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.Comment: 9 pages, 6 figure

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random-cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector's problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process

Of the importance of a leaf: the ethnobotany of sarma in Turkey and the Balkans

BACKGROUND: Sarma - cooked leaves rolled around a filling made from rice and/or minced meat, possibly vegetables and seasoning plants - represents one of the most widespread feasting dishes of the Middle Eastern and South-Eastern European cuisines. Although cabbage and grape vine sarma is well-known worldwide, the use of alternative plant leaves remains largely unexplored. The aim of this research was to document all of the botanical taxa whose leaves are used for preparing sarma in the folk cuisines of Turkey and the Balkans. Methods: Field studies were conducted during broader ethnobotanical surveys, as well as during ad-hoc investigations between the years 2011 and 2014 that included diverse rural communities in Croatia, Bosnia and Herzegovina, Serbia, Kosovo, Albania, Macedonia, Bulgaria, Romania, and Turkey. Primary ethnobotanical and folkloric literatures in each country were also considered. Results: Eighty-seven botanical taxa, mainly wild, belonging to 50 genera and 27 families, were found to represent the bio-cultural heritage of sarma in Turkey and the Balkans. The greatest plant biodiversity in sarma was found in Turkey and, to less extent, in Bulgaria and Romania. The most commonly used leaves for preparing sarma were those of cabbage (both fresh and lacto-fermented), grape vine, beet, dock, sorrel, horseradish, lime tree, bean, and spinach. In a few cases, the leaves of endemic species (Centaurea haradjianii, Rumex gracilescens, and R. olympicus in Turkey) were recorded. Other uncommon sarma preparations were based on lightly toxic taxa, such as potato leaves in NE Albania, leaves of Arum, Convolvulus, and Smilax species in Turkey, of Phytolacca americana in Macedonia, and of Tussilago farfara in diverse countries. Moreover, the use of leaves of the introduced species Reynoutria japonica in Romania, Colocasia esculenta in Turkey, and Phytolacca americana in Macedonia shows the dynamic nature of folk cuisines. Conclusion: The rich ethnobotanical diversity of sarma confirms the urgent need to record folk culinary plant knowledge. The results presented here can be implemented into initiatives aimed at re-evaluating folk cuisines and niche food markets based on local neglected ingredients, and possibly also to foster trajectories of the avant-garde cuisines inspired by ethnobotanical knowledge

Use of an aminated Amberlite XAD-4 column coupled to flow injection cold vapour generation atomic absorption spectrometry for mercury speciation in water and fish tissue samples.

An aminated Amberlite XAD-resin as a solid phase extractant was tested for speciation of inorganic mercury, Hg(II) and methylmercury, MeHg(I) in water and fish tissue samples. It was found that Hg(II) and MeHg(I) ions could be simultaneously retained by a column filled with AAXAD-4 resin at pH 4 and the sequential quantitative elutions of Hg(II) and MeHg(I) were achieved using 10 mL of 0.1%(m/v) thiourea in 3%(v/v) HCl and 10 mL of 6 mol L(-1) HCl, respectively. Hg(II) in the eluent was directly determined and MeHg(I) in the second eluent is quantified using FI-CVG-AAS after its oxidative digestion with KMnO(4). The limits of detection for Hg(II) and MeHg(I) ions were found to be 0.148 and 0.157 µg L(-1), respectively. The method was validated by analysing a certified reference material. The relative errors for Hg(II), MeHg(I) and T-Hg were in range of -1.8% and -3.2%

Use of an aminated Amberlite XAD-4 column coupled to flow injection cold vapour generation atomic absorption spectrometry for mercury speciation in water and fish tissue samples

An aminated Amberlite XAD-resin as a solid phase extractant was tested for speciation of inorganic mercury, Hg(II) and methylmercury, MeHg(I) in water and fish tissue samples. It was found that Hg(II) and MeHg(I) ions could be simultaneously retained by a column filled with AAXAD-4 resin at pH 4 and the sequential quantitative elutions of Hg(II) and MeHg(I) were achieved using 10 mL of 0.1%(m/v) thiourea in 3%(v/v) HCl and 10 mL of 6 mol L−1 HCl, respectively. Hg(II) in the eluent was directly determined and MeHg(I) in the second eluent is quantified using FI-CVG-AAS after its oxidative digestion with KMnO4. The limits of detection for Hg(II) and MeHg(I) ions were found to be 0.148 and 0.157 µg L−1, respectively. The method was validated by analysing a certified reference material. The relative errors for Hg(II), MeHg(I) and T-Hg were in range of −1.8% and −3.2%. © 2018 Elsevier Lt

Ion pair-dispersive liquid-liquid microextraction coupled to microsample injection system-flame atomic absorption spectrometry for determination of gold at trace level in real samples

PubMed ID: 25830976A novel ion pair-dispersive liquid-liquid microextraction (IP-DLLME) of gold followed by its determination with microsample injection system - flame atomic absorption spectrometry (MIS-FAAS) was developed. The extraction method was based on the reaction of anionic tetrachloro gold(III) complex with the cationic form of Rhodamine B to give a violet ion pair complex, which is extracted from 1.0 mol L-1 HCl solution of 8.0 mL to fine droplets of chloroform of 500 µL. A Plackett-Burman experimental design of MINITAB statistical program was employed to optimize the influence of main parameters to be controlled in DLLME. After optimizing the extraction conditions, gold was quantitatively recovered by preconcentration factor 40, limit of detection (LOD) 1.8 µg L-1 and relative standard deviation less than 6.8%. The proposed method was successfully applied to the preconcentration and determination of gold in some samples such as tap water, waste water, copper electrolysis solution and copper wire coated with nickel

Development of 2-acetylpyridine-4-phenyl-3-thiosemicarbazone functionalized polymeric resin for the preconcentration of metal ions prior to their ultratrace determinations by MIS-FAAS

2-Acetylpyridine-4-phenyl-3-thiosemicarbazone (APPT) ligand was incorporated onto Amberlite XAD-2 resin through an azo spacer and characterized by FTIR spectroscopy, elemental analysis, TGA, and SEM analysis. The synthesized resin was used for the preconcentration of Pb(II), Zn(II), Co(II), Ni(II), Cu(II), and Cd(II) ions. The sorbed metal ions were eluted with 10 mL of 2.0 mol L-1 HCl and determined by microsample injection coupled flame atomic spectrometry (MIS-FAAS). The recoveries of studied metal ions were ≥ 95.1% with RSD ≥ 4.0% at optimum pH 8; resin amount, 300 mg; flow rates, 2.0 mL min-1 (of eluent) and 3.0 mL min-1 (sample solution). The limits of detection (LOD) and limits of quantifications (LOQ) of the studied metal ions were 0.11, 0.05, 0.07, 0.08, 0.09, and 0.03; and 0.37, 0.17, 0.21, 0.13, 0.31, and 0.10 μg L-1, respectively, with a preconcentration factor of 500 for the 6 studied metal ions. The total saturation capacity of the resin was 0.36, 1.20, 1.50, 1.61, 1.07, and 0.71 mmol g-1, respectively. © TÜBİTAK