Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time (MET) of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a prefactor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both two-state and three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

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.

O Modelo de Ising inomogêneo: uma interrupção contínua entre as redes quadrada e triangular.

The ferromagnetic and antiferromagnetic Ising model on a two dimensional inhomogeneous lattice characterized by two exchange constants (J1 and J2) is investigated. The lattice allows, in a continuous manner, the interpolation between the uniforme square (J2 = 0) and triangular (J2 = J1) lattices. By performing Monte Carlo simulation using the sequential Metropolis algorithm, we calculate the magnetization and the magnetic susceptibility on lattices of differents sizes. Applying the finite size scaling method through a data colappse, we obtained the critical temperatures as well as the critical exponents of the model for several values of the parameter α = J2 J1 in the [0, 1] range. The ferromagnetic case shows a linear increasing behavior of the critical temperature Tc for increasing values of α. Inwhich concerns the antiferromagnetic system, we observe a linear (decreasing) behavior of Tc, only for small values of α; in the range [0.6, 1], where frustrations effects are more pronunciated, the critical temperature Tc decays more quickly, possibly in a non-linear way, to the limiting value Tc = 0, cor-responding to the homogeneous fully frustrated antiferromagnetic triangular case.

Income and poverty in a developing economy

We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and investment. The income from personal effort alone is distributed about a mean, while the income from trade, which may be positive or negative, is proportional to the trader's income. These assumptions lead to a Langevin model with multiplicative noise, from which we derive a Fokker-Planck (FP) equation for the income probability density function (IPDF) and its variation in time. We find that high earners have a power law income distribution while the low-income groups have a Levy IPDF. Comparing our analysis with the Indian survey data (obtained from the world bank website: http://go.worldbank.org/SWGZB45DN0) taken over many years we obtain a near-perfect data collapse onto our model's equilibrium IPDF. Using survey data to relate the IPDF to actual food consumption we define a poverty index (Sen A. K., Econometrica., 44 (1976) 219; Kakwani N. C., Econometrica, 48 (1980) 437), which is consistent with traditional indices, but independent of an arbitrarily chosen "poverty line" and therefore less susceptible to manipulation. Copyright © EPLA, 2010.

Out-of-equilibrium dynamical fluctuations in glassy systems

"In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving "extreme value" distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma model approach."

Geodynamic evolution of the SW Variscides: Orogenic collapse shown by new tectonometamorphic and isotopic data from western Ossa-Morena Zone, SW Iberia

The pre-Mesozoic geodynamic evolution of SW Iberia has been investigated on the basis of detailed structural analysis, isotope dating, and petrologic study of high-pressure (HP) rocks, revealing the superposition of several tectonometamorphic events: (1) An HP event older than circa 358 Ma is recorded in basic rocks preserved inside marbles, which suggests subduction of a continental margin. The deformation associated with this stage is recorded by a refractory graphite fabric and noncoaxial mesoscopic structures found within the host metasediments. The sense of shear is top to south, revealing thrusting synthetic with subduction (underthrusting) to the north. (2) Recrystallization before circa 358 Ma is due to a regional-scale thermal episode and magmatism. (3) Noncoaxial deformation with top to north sense of shear in northward dipping large-scale shear zones is associated with pervasive hydration and metamorphic retrogression under mostly greenschist facies. This indicates exhumation by normal faulting in a detachment zone confined to the top to north and north dipping shear zones during postorogenic collapse soon after 358 Ma ago (inversion of earlier top to south thrusts). (4) Static recrystallization at circa 318 Ma is due to regional-scale granitic intrusions. Citation: Rosas, F. M., F. O. Marques, M. Ballevre, and C. Tassinari (2008), Geodynamic evolution of the SW Variscides: Orogenic collapse shown by new tectonometamorphic and isotopic data from western Ossa-Morena Zone, SW Iberia, Tectonics, 27, TC6008, doi:10.1029/2008TC002333.

Geotechnical Data and Numerical Analysis of Edifice Collapse and Related Hazards at Pacaya Volcano, Guatemala

The continual eruptive activity, occurrence of an ancestral catastrophic collapse, and inherent geologic features of Pacaya volcano (Guatemala) demands an evaluation of potential collapse hazards. This thesis merges techniques in the field and laboratory for a better rock mass characterization of volcanic slopes and slope stability evaluation. New field geological, structural, rock mechanical and geotechnical data on Pacaya is reported and is integrated with laboratory tests to better define the physical-mechanical rock mass properties. Additionally, this data is used in numerical models for the quantitative evaluation of lateral instability of large sector collapses and shallow landslides. Regional tectonics and local structures indicate that the local stress regime is transtensional, with an ENE-WSW sigma 3 stress component. Aligned features trending NNW-SSE can be considered as an expression of this weakness zone that favors magma upwelling to the surface. Numerical modeling suggests that a large-scale collapse could be triggered by reasonable ranges of magma pressure (greater than or equal to 7.7 MPa if constant along a central dyke) and seismic acceleration (greater than or equal to 460 cm/s2), and that a layer of pyroclastic deposits beneath the edifice could have been a factor which controlled the ancestral collapse. Finally, the formation of shear cracks within zones of maximum shear strain could provide conduits for lateral flow, which would account for long lava flows erupted at lower elevations.

Data analysis of collapse mechanisms of a 3D printed groin vault in shaking table testing

The aim of this novel experimental study is to investigate the behaviour of a 2m x 2m model of a masonry groin vault, which is built by the assembly of blocks made of a 3D-printed plastic skin filled with mortar. The choice of the groin vault is due to the large presence of this vulnerable roofing system in the historical heritage. Experimental tests on the shaking table are carried out to explore the vault response on two support boundary conditions, involving four lateral confinement modes. The data processing of markers displacement has allowed to examine the collapse mechanisms of the vault, based on the arches deformed shapes. There then follows a numerical evaluation, to provide the orders of magnitude of the displacements associated to the previous mechanisms. Given that these displacements are related to the arches shortening and elongation, the last objective is the definition of a critical elongation between two diagonal bricks and consequently of a diagonal portion. This study aims to continue the previous work and to take another step forward in the research of ground motion effects on masonry structures.

Historical overfishing and the recent collapse of coastal ecosystems

Ecological extinction caused by overfishing precedes all other pervasive human disturbance to coastal ecosystems, including pollution, degradation of water quality, and anthropogenic climate change. Historical abundances of large consumer species were fantastically large in comparison with recent observations. Paleoecological, archaeological, and historical data show that time lags of decades to centuries occurred between the onset of overfishing and consequent changes in ecological communities, because unfished species of similar trophic level assumed the ecological roles of overfished species until they too were overfished or died of epidemic diseases related to overcrowding. Retrospective data not only help to clarify underlying causes and rates of ecological change, but they also demonstrate achievable goals for restoration and management of coastal ecosystems that could not even be contemplated based on the limited perspective of recent observations alone.

Bedside estimation of recruitable alveolar collapse and hyperdistension by electrical impedance tomography

To present a novel algorithm for estimating recruitable alveolar collapse and hyperdistension based on electrical impedance tomography (EIT) during a decremental positive end-expiratory pressure (PEEP) titration. Technical note with illustrative case reports. Respiratory intensive care unit. Patients with acute respiratory distress syndrome. Lung recruitment and PEEP titration maneuver. Simultaneous acquisition of EIT and X-ray computerized tomography (CT) data. We found good agreement (in terms of amount and spatial location) between the collapse estimated by EIT and CT for all levels of PEEP. The optimal PEEP values detected by EIT for patients 1 and 2 (keeping lung collapse < 10%) were 19 and 17 cmH(2)O, respectively. Although pointing to the same non-dependent lung regions, EIT estimates of hyperdistension represent the functional deterioration of lung units, instead of their anatomical changes, and could not be compared directly with static CT estimates for hyperinflation. We described an EIT-based method for estimating recruitable alveolar collapse at the bedside, pointing out its regional distribution. Additionally, we proposed a measure of lung hyperdistension based on regional lung mechanics.

Reconstructing the architectural evolution of volcanic islands from combined K/AR, morphologic, tectonic, and magnetic data. The Faial Island exemple (Azores)

The morpho-structural evolution of oceanic islands results from competition between volcano growth and partial destruction by mass-wasting processes. We present here a multi-disciplinary study of the successive stages of development of Faial (Azores) during the last 1 Myr. Using high-resolution digital elevation model (DEM), and new K/Ar, tectonic, and magnetic data, we reconstruct the rapidly evolving topography at successive stages, in response to complex interactions between volcanic construction and mass wasting, including the development of a graben. We show that: (1) sub-aerial evolution of the island first involved the rapid growth of a large elongated volcano at ca. 0.85 Ma, followed by its partial destruction over half a million years; (2) beginning about 360 ka a new small edifice grew on the NE of the island, and was subsequently cut by normal faults responsible for initiation of the graben; (3) after an apparent pause of ca. 250 kyr, the large Central Volcano (CV) developed on the western side of the island at ca 120 ka, accumulating a thick pile of lava flows in less than 20 kyr, which were partly channelized within the graben; (4) the period between 120 ka and 40 ka is marked by widespread deformation at the island scale, including westward propagation of faulting and associated erosion of the graben walls, which produced sedimentary deposits; subsequent growth of the CV at 40 ka was then constrained within the graben, with lava flowing onto the sediments up to the eastern shore; (5) the island evolution during the Holocene involves basaltic volcanic activity along the main southern faults and pyroclastic eruptions associated with the formation of a caldera volcano-tectonic depression. We conclude that the whole evolution of Faial Island has been characterized by successive short volcanic pulses probably controlled by brief episodes of regional deformation. Each pulse has been separated by considerable periods of volcanic inactivity during which the Faial graben gradually developed. We propose that the volume loss associated with sudden magma extraction from a shallow reservoir in different episodes triggered incremental downward graben movement, as observed historically, when immediate vertical collapse of up to 2 m was observed along the western segments of the graben at the end of the Capelinhos eruptive crises (1957-58).

Technical note: Implementation of a geodatabase of published and unpublished data on the catastrophic Vaiont landslide

On 9 October 1963 a catastrophic landslide suddenly occurred on the southern slope of the Vaiont dam reservoir. A mass of approximately 270 million m3 collapsed into the reservoir generating a wave that overtopped the dam and hit the town of Longarone and other villages nearby. Several investigations and interpretations of the slope collapse have been carried out during the last 45 years, however, a comprehensive explanation of both the triggering and the dynamics of the phenomenon has yet to be provided. In order to re-evaluate the currently existing information on the slide, an electronic bibliographic database and an ESRI-geodatabase have been developed. The chronology of the collected documentation showed that most of the studies for re-evaluating the failure mechanisms were conducted in the last decade, as a consequence of knowledge, methods and techniques recently acquired. The current contents of the geodatabase will improve definition of the structural setting that influenced the slide and led to the the propagation of the displaced rock mass. The objectives, structure and contents of the e-bibliography and Geodatabase are indicated, together with a brief description on the possible use of the alphanumeric and spatial contents of the databases.

Prevention of Caval Collapse During Venous Drainage for CPB.

A new plastic self-expanding Smartcanula (Smartcanula LLC, Lausanne, Switzerland) is designed for central insertion and prevention of caval collapse. The objective of our work is to assess the influence of the new design on atrial chatter. Caval collapse over the entire caval axis, right atrial, hepatic, renal vein, and iliac vein is realized in drainage tubes with holes at 5 cm distance intervals. Smartcanulas with various lengths (26 cm [= right atrial], 34 cm [= hepatic], 43 cm [= renal], and 53 cm [= iliac]) versus two-stage cannulas are compared. Pressure drop (ΔP) is measured using Millar pressure-transducers. Flow rate (Q) is measured using an ultrasonic flow meter. Cannula resistance is defined as the ΔP/Q ratio. Data display and recording are controlled using LabView virtual instruments. At an 88 cm height differential, Q values are 8.69 and 6.8 l/min, and ΔP/Q ratios are 0.63 and 1.28 for the 26-cm Smartcanula and the reference cannula, respectively. The 34-cm Smartcanula showed 8.89 l/min and 0.6 ΔP/Q ratio vs. 7.59 l/min and 0.9 for the control cannula (P < 0.05). The 43-cm and 53-cm Smartcanulas showed Q values of 9.04 and 8.81 l/min, respectively, and ΔP/Q2 ratio of 0.6. The Smartcanula outperforms the two-stage cannula, and direct cannula insertion without guide wire is effective.

Sex ratio bias, male aggression, and population collapse in lizards.

The adult sex ratio (ASR) is a key parameter of the demography of human and other animal populations, yet the causes of variation in ASR, how individuals respond to this variation, and how their response feeds back into population dynamics remain poorly understood. A prevalent hypothesis is that ASR is regulated by intrasexual competition, which would cause more mortality or emigration in the sex of increasing frequency. Our experimental manipulation of populations of the common lizard (Lacerta vivipara) shows the opposite effect. Male mortality and emigration are not higher under male-biased ASR. Rather, an excess of adult males begets aggression toward adult females, whose survival and fecundity drop, along with their emigration rate. The ensuing prediction that adult male skew should be amplified and total population size should decline is supported by long-term data. Numerical projections show that this amplifying effect causes a major risk of population extinction. In general, such an "evolutionary trap" toward extinction threatens populations in which there is a substantial mating cost for females, and environmental changes or management practices skew the ASR toward males.