Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model

The conjectured exact percolation thresholds of the Fortuin-Kasteleyn cluster for the +-J Ising spin glass model are theoretically shown based on a conjecture. It is pointed out that the percolation transition of the Fortuin-Kasteleyn cluster for the spin glass model is related to a dynamical transition for the freezing of spins. The present results are obtained as locations of points on the so-called Nishimori line, which is a special line in the phase diagram. We obtain TFK = 2 / ln [z / (z - 2)] and pFK = z / [2 (z - 1)] for the Bethe lattice, TFK -> infinity and pFK -> 1 / 2 for the infinite-range model, TFK = 2 / ln 3 and pFK = 3 / 4 for the square lattice, TFK ~ 3.9347 and pFK ~ 0.62441 for the simple cubic lattice, TFK ~ 6.191 and pFK ~ 0.5801 for the 4-dimensional hypercubic lattice, and TFK = 2 / ln {[1 + 2 sin (pi / 18)] / [1 - 2 sin (pi / 18) ]} and pFK = [1 + 2 sin (pi / 18) ] / 2 for the triangular lattice, when J / kB = 1, where z is the coordination number, J is the strength of the exchange interaction between spins, kB is the Boltzmann constant, TFK is the temperature at the percolation transition point, and pFK is the probability, that the interaction is ferromagnetic, at the percolation transition point.Comment: 10 pages, 1 figure. v8: this is the final versio

Gutenberg-Richter’s law in sliding friction of gels

We report on experimental studies of spatio-temporally heterogeneous stick-slip motions in the sliding friction between a hard polymethyl methacrylate (PMMA, plexiglass) block and a soft poly-dimethyl siloxane (PDMS, silicone) gel plate. We perform experiments on two PDMS gels with different viscoelastic properties. For the less viscous gel, large and rapid events are preceded by an alternation of active and less active periods. For the more viscous gel, successive slow slip events take place continuously. The probability distributions of the force drop, a quantity analogous to seismic moment, obey a power law similar to Gutenberg-Richter's empirical law for the frequency-size statistics of earthquakes, and the exponents of the power law vary with the plate velocity and the viscosity of the gel. We propose a simple model to explain the dependence of the power law exponent on the plate velocity, which agrees with experimental results

Element Stratification in the Middle-Aged Type Ia Supernova Remnant G344.7-0.1

Despite their importance, a detailed understanding of Type Ia supernovae (SNe Ia) remains elusive. X-ray measurements of the element distributions in supernova remnants (SNRs) offer important clues for understanding the explosion and nucleosynthesis mechanisms for SNe Ia. However, it is challenging to observe the entire ejecta mass in X-rays for young SNRs, because the central ejecta may not have been heated by the reverse shock yet. Here we present over 200 kilosecond Chandra observations of the Type Ia SNR G344.7-0.1, whose age is old enough for the reverse shock to have reached the SNR center, providing an opportunity to investigate the distribution of the entire ejecta mass. We reveal a clear stratification of heavy elements with a centrally peaked distribution of the Fe ejecta surrounded by intermediate-mass elements (IMEs: Si, S, Ar Ca) with an arc-like structure. The centroid energy of the Fe K emission is marginally lower in the central Fe-rich region than in the outer IME-rich regions, suggesting that the Fe ejecta were shock-heated more recently. These results are consistent with the prediction for standard SN Ia models, where the heavier elements are synthesized in the interior of an exploding white dwarf. We find, however, that the peak location of the Fe K emission is slightly offset to the west with respect to the geometric center of the SNR. This apparent asymmetry is likely due to the inhomogeneous density distribution of the ambient medium, consistent with our radio observations of the ambient molecular and neutral gas.Comment: 16 pages, 10 figures, Accepted for publication in Astrophysical Journa

Is individualization of sodium bicarbonate ingestion based on time to peak necessary?

Purpose: To describe the reliability of blood bicarbonate pharmacokinetics in response to sodium bicarbonate (SB) supplementation across multiple occasions and assess, using putative thresholds, whether individual variation indicated a need for individualised ingestion timings. Methods: Thirteen men (age 27±5 y; body mass (BM) 77.4±10.5 kg; height 1.75±0.06 m) ingested 0.3 g·kg-1BM SB in gelatine capsules on 3 occasions. One hour after a standardised meal, venous blood was obtained before and every 10 min following ingestion for 3 h, then every 20 min for a further hour. Time-to-peak (Tmax), absolute-peak (Cmax), absolute-peak-change (ΔCmax) and area under the curve (AUC) were analysed using mixed models, intraclass correlation coefficient (ICC), coefficient of variation (CV) and typical error. Individual variation in pharmacokinetic responses was assessed using Bayesian simulation with multilevel models with random intercepts. Results: No significant differences between sessions were shown for blood bicarbonate regarding Cmax, ΔCmax or AUC (p>0.05), although Tmax occurred earlier in SB2 (127±36 min) than in SB1 (169±54 min, p=0.0088) and SB3 (159±42 min, p=0.05). ICC, CV and typical error showed moderate to poor reliability. Bayesian modelling estimated that >80% of individuals from the population experience elevated blood bicarbonate levels above + 5 mmol∙L-1 between 75-240 min after ingestion, and between 90-225 min above +6 mmol∙L-1. Conclusion: Assessing SB supplementation using discrete values showed only moderate reliability at the group level, and poor reliability at the individual level, while Tmax was not reproducible. However, when analysed as modelled curves, a 0.3 g·kg-1BM dose was shown to create a long-lasting window of ergogenic potential, challenging the notion that SB ingestion individualised to time-to-peak is a necessary strategy, at least when SB is ingested in capsules