Susceptible-infected-recovered and susceptible-exposed-infected models

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b(c) = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p(c) = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1) b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

Oriented Percolation in One-dimensional 1/vertical bar x-y vertical bar(2) Percolation Models

We consider independent edge percolation models on Z, with edge occupation probabilities. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104: 547, 1986). The proof is based on multi-scale analysis.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Complexity and anisotropy in host morphology make populations less susceptible to epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to separately analyse the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.

Elastomeric Composites Based on Ethylene-Propylene-Diene Monomer Rubber and Conducting Polymer-Modified Carbon Black

Thermally stable elastomeric composites based on ethylene-propylene-diene monomer (EPDM) and conducting polymer-modified carbon black (CPMCB) additives were produced by casting and crosslinked by compression molding. CPMCB represent a novel thermally stable conductive compound made via ""in situ"" deposition of intrinsically conducting polymers (ICP) such as polyaniline or polypyrrole on carbon black particles. Thermogravimetric analysis showed that the composites are thermally stable with no appreciable degradation at ca. 300 degrees C. Incorporating CPMCB has been found to be advantageous to the processing of composites, as the presence of ICP lead to a better distribution of the filler within the rubber matrix, as confirmed by morphological analysis. These materials have a percolation threshold range of 5-10 phr depending on the formulation and electrical dc conductivity values in the range of 1 x 10(-3) to 1 x 10(-2) S cm(-1) above the percolation threshold. A less pronounced reinforcing effect was observed in composites produced with ICP-modified additives in relation to those produced only with carbon black. The results obtained in this study show the feasibility of this method for producing stable, electrically conducting composites with elastomeric characteristics. POLYM. COMPOS., 30:897-906, 2009. (C) 2008 Society of Plastics Engineers

Fluoride in the groundwater of the Tubarao and Crystaline aquifers, Salto-Indaiatuba region (SP)

Anomalous concentrations of fluoride in groundwater were identified in 19 drilling wells in the Salto-Indaiatuba region, Sao Paulo State, with an average concentration of 3.03 mg dm(-3) and a maximum of 6.95 mg dm(-3), which constitute a restriction for the water`s usage in terms of human consumption. The wells exploit water from the Tubarao Aquifer (sedimentary, granular) and Crystalline Aquifer (granitic, fractured), used for sanitary or industrial purposes. These groundwaters are typically HCO(3) and HCO(3)-SO(4) types, with high concentrations of HCO(3) -and Na(+) and high pH-values between 7.5 and 10.0. The highest concentrations of F-are associated to the Tubarao and Tubarao/Crystalline aquifer drilling wells. The presence of F-in groundwater is controlled by these high pH-values, alkalinity, and fluorine availability. The source of fluoride in the Tubarao and Crystalline Aquifers can be related to the percolation of hydrothermal fluids associated with Mesozoic lava flow, emplaced due to the opening of Atlantic Ocean and/or hydrolysis of fluorine-rich minerals and clay minerals.

The number of open paths in an oriented rho-percolation model

We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Coating of Cotton Yarn with Poly(vinyl alcohol) and Poly(N-vinyl-2-pyrrolidone) Crosslinked via Ultraviolet Radiation

The coating of cotton fiber is used in the textile industry to increase the mechanical resistance of the yarn and their resistance to vibration, friction, impact, and elongation, which are some of the forces to which the yarn is subjected during the weaving process. The main objective of this study was to investigate the use of synthetic hydrophilic polymers, poly(vinyl alcohol) (PVA), and poly(N-vinyl-2-pyrrolidone) (PVP) to coat 100% cotton textile fiber, with the aim of giving the fiber temporary mechanical resistance. For the fixation of the polymer on the fiber, UV-C radiation was used as the crosslinking process. The influence of the crosslinking process was determined through tensile testing of the coated fibers. The results indicated that UV-C radiation increased the mechanical resistance of the yarn coated with PVP by up to 44% and the yarn coated with PVA by up to 67% compared with the pure cotton yarn, that is, without polymeric coating and crosslinking. This study is of great relevance, and it is important to consider that UV-C radiation dispenses with the use of chemical substances and prevents the generation of toxic waste at the end of the process. (C) 2010 Wiley Periodicals, Inc. J Appl Polym Sci 119: 2560-2567, 2011

Tribological Testing of Some Potential PVD and CVD Coatings for Steel Wire Drawing Dies

Cemented carbide is today the most frequently used drawing die material in steel wire drawing applications. This is mainly due to the possibility to obtain a broad combination of hardness and toughness thus meeting the requirements concerning strength, crack resistance and wear resistance set by the wire drawing process. However, the increasing cost of cemented carbide in combination with the possibility to increase the wear resistance of steel through the deposition of wear resistant CVD and PVD coatings have enhanced the interest to replace cemented carbide drawing dies with CVD and PVD coated steel wire drawing dies. In the present study, the possibility to replace cemented carbide wire drawing dies with CVD and PVD coated steel drawing dies have been investigated by tribological characterisation, i.e. pin-on-disc and scratch testing, in combination with post-test observations of the tribo surfaces using scanning electron microscopy, energy dispersive X-ray spectroscopy and 3D surface profilometry. Based on the results obtained, CVD and PVD coatings aimed to provide improved tribological performance of steel wire drawing dies should display a smooth surface topography, a high wear resistance, a high fracture toughness (i.e. a high cracking and chipping resistance) and intrinsic low friction properties in contact with the wire material. Also, the steel substrate used must display a sufficient load carrying capacity and resistance to thermal softening. Of the CVD and PVD coatings evaluated in the tribological tests, a CVD TiC and a PVD CrC/C coating displayed the most promising results.

Design and validation of a sheet metal shearing experimental procedure

Throughout the industrial processes of sheet metal manufacturing and refining, shear cutting is widely used for its speed and cost advantages over competing cutting methods. Industrial shears may include some force measurement possibilities, but the force is most likely influenced by friction losses between shear tool and the point of measurement, and are in general not showing the actual force applied to the sheet. Well defined shears and accurate measurements of force and shear tool position are important for understanding the influence of shear parameters. Accurate experimental data are also necessary for calibration of numerical shear models. Here, a dedicated laboratory set-up with well defined geometry and movement in the shear, and high measurability in terms of force and geometry is designed, built and verified. Parameters important to the shear process are studied with perturbation analysis techniques and requirements on input parameter accuracy are formulated to meet experimental output demands. Input parameters in shearing are mostly geometric parameters, but also material properties and contact conditions. Based on the accuracy requirements, a symmetric experiment with internal balancing of forces is constructed to avoid guides and corresponding friction losses. Finally, the experimental procedure is validated through shearing of a medium grade steel. With the obtained experimental set-up performance, force changes as result of changes in studied input parameters are distinguishable down to a level of 1%.

Limited memory and the essentiality of money

This paper investigates the relationship between memory and the essentiality of money. We consider a random matching economy with a large finite population in which commitment is not possible and memory is limited in the sense that only a fraction m E(0; 1) of the population has publicly observable histories. We show that no matter how limited memory is, there exists a social norm that achieves the first best regardless of the population size. In other words, money can fail to be essential irrespective of the amount of memory in the economy. This suggests that the emphasis on limited memory as a fundamental friction for money to be essential deserves a deeper examination.

Estimation and evaluation of dynamic properties as indicators of changes on soil structure in sugarcane fields of São Paulo State - Brazil

The indiscriminate management and use of soils without moisture control has changed the structure of it due to the increment of the traffic by agricultural machines through the years, causing in consequence, a soil compaction and yield reduction in the areas of intensive traffic. The purpose of this work was to estimate and to evaluate the performance of preconsolidation pressure of the soil and shear stress as indicators of changes on soil structure in fields cropped with sugarcane, as well as the impact of management processes in an Eutrorthox soil structure located in São Paulo State. The experimental field was located in Piracicaba's rural area (São Paulo State, Brazil) and has been cropped with sugarcane, in the second harvest cycle. The soil was classified by Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA) [Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA), 1999. Centro Nacional de Pesquisa de Solos. Sistema Brasileiro de Classificao de Solos, Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA), Brasilia, 412 pp.] as an Eutrorthox. Undisturbed samples were collected and georeferenced in a grid of 60 m x 60 m from two depths: 0-0.10 m (superficial layer - SL) and in the layer of greatest mechanical resistance (LGMR), previously identified by cone index (CI). The investigated variables were pressure preconsolidation (sigma(p)), apparent cohesion (c) and internal friction angle (phi). The conclusions from the results were that the SLSC was predicted satisfactorily from up as a function of soil moisture; thus, decisions about machinery size and loading (contact pressures) can be taken. Apparent cohesion (c), internal friction angle (phi) and the Coulomb equation were significantly altered by traffic intensity. The sigma(p), c and phi maps were shown to be important tools to localize and visualize soil compaction and mechanical resistance zones. They constitute a valuable resource to evaluate the traffic impact in areas cropped with sugarcane in State of São Paulo, Brazil. (C) 2008 Elsevier B.V. All rights reserved.