A particle system with explosions: law of large numbers for the density of particles and the blow-up time

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If f(u)=u^p, 1<p \le 3, we also obtain a law of large numbers for the explosion time

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Pattern formation and selection in quasi-static fracture

Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model produces cellular, hierarchical patterns of cracks, characterized by a mean fragment size linear in the layer thickness, in agreement with experiments. The selection of a stationary fragment size is explained by exploiting the correlations prior to cracking. A scaling behavior associated with the thickness and substrate coupling, derived and confirmed by simulations, suggests why patterns have similar morphology despite their disparity in scales.Comment: 4 pages, RevTeX, two-column, 5 PS figures include

A framework for bounding nonlocality of state discrimination

We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl

Reanalysis Data Underestimate Significant Changes in Growing Season Weather in Kazakhstan

We present time series analyses of recently compiled climate station data which allowed us to assess contemporary trends in growing season weather across Kazakhstan as drivers of a significant decline in growing season normalized difference vegetation index (NDVI) recently observed by satellite remote sensing across much of Central Asia. We used a robust nonparametric time series analysis method, the seasonal Kendall trend test to analyze georeferenced time series of accumulated growing season precipitation (APPT) and accumulated growing degree-days (AGDD). Over the period 2000–2006 we found geographically extensive, statistically significant (p \u3c 0.05) decreasing trends in APPT and increasing trends in AGDD. The temperature trends were especially apparent during the warm season and coincided with precipitation decreases in northwest Kazakhstan, indicating that pervasive drought conditions and higher temperature excursions were the likely drivers of NDVI declines observed in Kazakhstan over the same period. We also compared the APPT and AGDD trends at individual stations with results from trend analysis of gridded monthly precipitation data from the Global Precipitation Climatology Centre (GPCC) Full Data Reanalysis v4 and gridded daily near surface air temperature from the National Centers for Climate Prediction Reanalysis v2 (NCEP R2). We found substantial deviation between the station and the reanalysis trends, suggesting that GPCC and NCEP data substantially underestimate the geographic extent of recent drought in Kazakhstan. Although gridded climate products offer many advantages in ease of use and complete coverage, our findings for Kazakhstan should serve as a caveat against uncritical use of GPCC and NCEP reanalysis data and demonstrate the importance of compiling and standardizing daily climate data from data-sparse regions like Central Asia

Development and geometry of isotropic and directional shrinkage crack patterns

We have studied shrinkage crack patterns which form when a thin layer of an alumina/water slurry dries. Both isotropic and directional drying were studied. The dynamics of the pattern formation process and the geometric properties of the isotropic crack patterns are similar to what is expected from recent models, assuming weak disorder. There is some evidence for a gradual increase in disorder as the drying layer become thinner, but no sudden transition, in contrast to what has been seen in previous experiments. The morphology of the crack patterns is influenced by drying gradients and front propagation effects, with sharp gradients having a strong orienting and ordering effect.Comment: 8 pages, 11 figures, 8 in jpg format, 3 in postscript. See also http://mobydick.physics.utoronto.ca/mud.htm

The International Surface Pressure Databank version 2

The International Surface Pressure Databank (ISPD) is the world's largest collection of global surface and sea-level pressure observations. It was developed by extracting observations from established international archives, through international cooperation with data recovery facilitated by the Atmospheric Circulation Reconstructions over the Earth (ACRE) initiative, and directly by contributing universities, organizations, and countries. The dataset period is currently 1768–2012 and consists of three data components: observations from land stations, marine observing systems, and tropical cyclone best track pressure reports. Version 2 of the ISPD (ISPDv2) was created to be observational input for the Twentieth Century Reanalysis Project (20CR) and contains the quality control and assimilation feedback metadata from the 20CR. Since then, it has been used for various general climate and weather studies, and an updated version 3 (ISPDv3) has been used in the ERA-20C reanalysis in connection with the European Reanalysis of Global Climate Observations project (ERA-CLIM). The focus of this paper is on the ISPDv2 and the inclusion of the 20CR feedback metadata. The Research Data Archive at the National Center for Atmospheric Research provides data collection and access for the ISPDv2, and will provide access to future versions

Modulation of Localized States in Electroconvection

We report on the effects of temporal modulation of the driving force on a particular class of localized states, known as worms, that have been observed in electroconvection in nematic liquid crystals. The worms consist of the superposition of traveling waves and have been observed to have unique, small widths, but to vary in length. The transition from the pure conduction state to worms occurs via a backward bifurcation. A possible explanation of the formation of the worms has been given in terms of coupled amplitude equations. Because the worms consist of the superposition of traveling waves, temporal modulation of the control parameter is a useful probe of the dynamics of the system. We observe that temporal modulation increases the average length of the worms and stabilizes worms below the transition point in the absence of modulation.Comment: 4 pages, 4 figure

Global impacts of the 1980s regime shift

Despite evidence from a number of Earth systems that abrupt temporal changes known as regime shifts are important, their nature, scale and mechanisms remain poorly documented and understood. Applying principal component analysis, change-point analysis and a sequential t-test analysis of regime shifts to 72 time series, we confirm that the 1980s regime shift represented a major change in the Earth's biophysical systems from the upper atmosphere to the depths of the ocean and from the Arctic to the Antarctic, and occurred at slightly different times around the world. Using historical climate model simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and statistical modelling of historical temperatures, we then demonstrate that this event was triggered by rapid global warming from anthropogenic plus natural forcing, the latter associated with the recovery from the El Chichón volcanic eruption. The shift in temperature that occurred at this time is hypothesized as the main forcing for a cascade of abrupt environmental changes. Within the context of the last century or more, the 1980s event was unique in terms of its global scope and scale; our observed consequences imply that if unavoidable natural events such as major volcanic eruptions interact with anthropogenic warming unforeseen multiplier effects may occur

Defining the Plasticity of Transcription Factor Binding Sites by Deconstructing DNA Consensus Sequences: The PhoP-Binding Sites among Gamma/Enterobacteria

Transcriptional regulators recognize specific DNA sequences. Because these sequences are embedded in the background of genomic DNA, it is hard to identify the key cis-regulatory elements that determine disparate patterns of gene expression. The detection of the intra- and inter-species differences among these sequences is crucial for understanding the molecular basis of both differential gene expression and evolution. Here, we address this problem by investigating the target promoters controlled by the DNA-binding PhoP protein, which governs virulence and Mg2+ homeostasis in several bacterial species. PhoP is particularly interesting; it is highly conserved in different gamma/enterobacteria, regulating not only ancestral genes but also governing the expression of dozens of horizontally acquired genes that differ from species to species. Our approach consists of decomposing the DNA binding site sequences for a given regulator into families of motifs (i.e., termed submotifs) using a machine learning method inspired by the “Divide & Conquer” strategy. By partitioning a motif into sub-patterns, computational advantages for classification were produced, resulting in the discovery of new members of a regulon, and alleviating the problem of distinguishing functional sites in chromatin immunoprecipitation and DNA microarray genome-wide analysis. Moreover, we found that certain partitions were useful in revealing biological properties of binding site sequences, including modular gains and losses of PhoP binding sites through evolutionary turnover events, as well as conservation in distant species. The high conservation of PhoP submotifs within gamma/enterobacteria, as well as the regulatory protein that recognizes them, suggests that the major cause of divergence between related species is not due to the binding sites, as was previously suggested for other regulators. Instead, the divergence may be attributed to the fast evolution of orthologous target genes and/or the promoter architectures resulting from the interaction of those binding sites with the RNA polymerase