Synchronization of unidirectional time delay chaotic networks and the greatest common divisor

We present the interplay between synchronization of unidirectional coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the oriented graph. In the weak chaos region and for GCD=1 the network is in chaotic zero-lag synchronization, whereas for GCD=m>1 synchronization of m-sublattices emerges. Complete synchronization can be achieved when all chaotic nodes are influenced by an identical set of delays and in particular for the limiting case of homogeneous delays. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.Comment: 7 pages, 5 figure

Utilization rates of hip arthroplasty in OECD countries

SummaryBackgroundHip arthroplasty and revision surgery is growing exponentially in OECD countries, but rates vary between countries.MethodsWe extracted economic data and utilization rates data about hip arthroplasty done in OECD countries between 1990 and 2011. Absolute number of implantations and compound annual growth rates were computed per 100,000 population and for patients aged 65 years old and over and for patients aged 64 years and younger.ResultsIn the majority of OECD countries, there has been a significant increase in the utilization of total hip arthroplasty in the last 10 years, but rates vary to a great extent: In the United States, Switzerland, and Germany the utilization rate exceeds 200/100,000 population whereas in Spain and Mexico rates are 102 and 8, respectively. There is a strong correlation between gross domestic product (GDP) and health care expenditures per capita with utilization rate. Utilization rates in all age groups have continued to rise up to present day. A seven fold higher growth rate was seen in patients aged 64 years and younger as compared to older patients.ConclusionWe observed a 38-fold variation in the utilization of hip arthroplasty among OECD countries, correlating with GDP and health care expenditures. Over recent years, there has been an increase in the utilization rate in most countries. This was particularly evident in the younger patients. Due to increasing life expectancy and the disproportionally high use of arthroplasty in younger patients we expect an exponential increase of revision rate in the future

The limits of filopodium stability

Filopodia are long, finger-like membrane tubes supported by cytoskeletal filaments. Their shape is determined by the stiffness of the actin filament bundles found inside them and by the interplay between the surface tension and bending rigidity of the membrane. Although one might expect the Euler buckling instability to limit the length of filopodia, we show through simple energetic considerations that this is in general not the case. By further analyzing the statics of filaments inside membrane tubes, and through computer simulations that capture membrane and filament fluctuations, we show under which conditions filopodia of arbitrary lengths are stable. We discuss several in vitro experiments where this kind of stability has already been observed. Furthermore, we predict that the filaments in long, stable filopodia adopt a helical shape

Effective Invariant Theory of Permutation Groups using Representation Theory

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at http://www.springer.com

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid

We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations, and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically, and verify this prediction numerically. In addition, we find that the characteristic relaxation time of the model is a non-monotonic function of attraction strength, again in agreement with numerical results.Comment: 10 page

Consequences of local inter-strand dehybridization for large-amplitude bending fluctuations of double-stranded DNA

The wormlike chain (WLC) model of DNA bending accurately reproduces single-molecule force-extension profiles of long (kilobase) chains. These bending statistics over large scales do not, however, establish a unique microscopic model for elasticity at the 1-10 bp scale, which holds particular interest in biological contexts. Here we examine a class of microscopic models which allow for disruption of base pairing (i.e., a `melt' or `kink', generically an `excitation') and consequently enhanced local flexibility. We first analyze the effect on the excitation free energy of integrating out the spatial degrees of freedom in a wormlike chain. Based on this analysis, we present a formulation of these models that ensures consistency with the well-established thermodynamics of melting in long chains. Using a new method to calculate cyclization statistics of short chains from enhanced-sampling Monte Carlo simulations, we compute J-factors of a meltable wormlike chain (MWLC) over a broad range of chain lengths, including very short molecules (30 bp) that have not yet been explored experimentally. For chains longer than about 120 bp, including most molecules studied to date in the laboratory, we find that melting excitations have little impact on cyclization kinetics. Strong signatures of melting, which might be resolved within typical experimental scatter, emerge only for shorter chains.Comment: 13 pages, 5 figure

Catastrophic stress corrosion failure of Zr-base bulk metallic glass through hydrogen embrittlement

Zr-base bulk metallic glasses (BMG) are prone to pitting corrosion in halide containing solutions and also stress corrosion cracking (SCC) is often interpreted in this context. This work presents in situ SCC experiments on notched Zr52.5Cu17.9Ni14.6Al10Ti5 (at.%) BMG bars under 3-point bending in dilute NaCl solution. They show that pitting corrosion is only the initiating process. The pitted areas have a lower local corrosion potential and the reaction of Zr4+ to zirconyl ions in solution produces H+ that can be reduced and absorbed in the local acidic environment. So, hydrogen embrittlement causes the observed catastrophic failure and peculiar fracture surface characteristics. © 2019 The Author

Loki, Io: New groundbased observations and a model describing the change from periodic overturn

Loki Patera is the most powerful volcano in the solar system. We have obtained measurements of Loki's 3.5 micron brightness from NASA's Infrared Telescope Facility (IRTF) and have witnessed a change from the periodic behavior previously noted. While Loki brightened by a factor of several every 540 days prior to 2001, from 2001 through 2004 Loki remained at a constant, medium brightness. We have constructed a quantitative model of Loki as a basaltic lava lake whose solidified crust overturns when it becomes buoyantly unstable. By altering the speed at which the overturn propagates across the patera, we can match our groundbased brightness data. In addition, we can match other data taken at other times and wavelengths. By slowing the propagation speed dramatically, we can match the observations from 2001-2004. This slowing may be due to a small change in volatile content in the magma

The magmatic system beneath the Tristan da Cunha Island: Insights from thermobarometry, melting models and geophysics

This study provides new insights on the conditions of melt generation and of magma transport and storage beneath Tristan da Cunha Island in the South Atlantic. Situated at the seaward end of the Walvis Ridge-guyot hotspot track, this island is related to the evolving magmatic system of the Tristan plume. Much is known about the geochemical and isotopic composition of the alkaline lavas on Tristan, but the pressure-temperature conditions of the hotspot magmas are under-explored. This contribution reports new data from a suite of 10 samples collected during a geologic-geophysical expedition in 2012. The focus of this study is on the least-evolved, phenocryst-rich basanite lavas but we also included a sample of trachyandesite lava erupted in 1961. Mineral-melt equilibrium thermobarometry uses the composition of olivine, clinopyroxene and plagioclase phenocrysts. In addition to bulk-rock data we also analysed olivine-hosted melt inclusions for the P-T calculations. The results for olivine-melt and clinopyroxene-melt calculations suggest crystallization conditions of around 1200-1250. °C and 0.8-1.3. GPa for the least-evolved magmas (ankaramitic basanites). Combined with seismological evidence for a Moho depth of about 19. km, these results imply magma storage and partial crystallization of Tristan magmas in the uppermost mantle and at Moho level. The trachyandesite yielded values of about 1000. °C and 0.2-0.3. GPa (6 to 10. km depth), indicating further crystallization within the crust.Constraints on the depth and degree of melting at the source of Tristan basanites were derived from REE inverse modelling using our new trace element data. The model predicts 5% melt generation from a melting column with its base at 80-100. km and a top at 60. km, which is consistent with the lithospheric thickness resulting from cooling models and seismological observations. The thermobarometry and melting models combined suggest a mantle potential temperature of about 1360. °C for the Tristan hotspot