Scaling laws of ambush predator 'waiting' behaviour are tuned to a common ecology

The decisions animals make about how long to wait between activities can determine the success of diverse behaviours such as foraging, group formation or risk avoidance. Remarkably, for diverse animal species, including humans, spontaneous patterns of waiting times show random ‘burstiness’ that appears scale-invariant across a broad set of scales. However, a general theory linking this phenomenon across the animal kingdom currently lacks an ecological basis. Here, we demonstrate from tracking the activities of 15 sympatric predator species (cephalopods, sharks, skates and teleosts) under natural and controlled conditions that bursty waiting times are an intrinsic spontaneous behaviour well approximated by heavy-tailed (power-law) models over data ranges up to four orders of magnitude. Scaling exponents quantifying ratios of frequent short to rare very long waits are species-specific, being determined by traits such as foraging mode (active versus ambush predation), body size and prey preference. A stochastic–deterministic decision model reproduced the empirical waiting time scaling and species-specific exponents, indicating that apparently complex scaling can emerge from simple decisions. Results indicate temporal power-law scaling is a behavioural ‘rule of thumb’ that is tuned to species’ ecological traits, implying a common pattern may have naturally evolved that optimizes move–wait decisions in less predictable natural environments.

Scaling of domain periodicity with thickness measured in BaTiO3 single crystal lamellae and comparison with other ferroics

The focused ion beam microscope has been used to cut parallel-sided {100}-oriented thin lamellae of single crystal barium titanate with controlled thicknesses, ranging from 530 nm to 70 nm. Scanning transmission electron microscopy has been used to examine domain configurations. In all cases, stripe domains were observed with {011}-type domain walls in perovskite unit-cell axes, suggesting 90 degrees domains with polarization in the plane of the lamellae. The domain widths were found to vary as the square root of the lamellar thickness, consistent with Kittel's law, and its later development by Mitsui and Furuichi and by Roytburd. An investigation into the manner in which domain period adapts to thickness gradient was undertaken on both wedge-shaped lamellae and lamellae with discrete terraces. It was found that when the thickness gradient was perpendicular to the domain walls, a continuous change in domain periodicity occurred, but if the thickness gradient was parallel to the domain walls, periodicity changes were accommodated through discrete domain bifurcation. Data were then compared with other work in literature, on both ferroelectric and ferromagnetic systems, from which conclusions on the widespread applicability of Kittel's law in ferroics were made.

Single-ionization of helium at Ti:sapphire wavelengths: rates and scaling laws

We present a numerical and theoretical study of intense-field single-electron ionization of helium at 390 nm and 780 nm. Accurate ionization rates (over an intensity range of (0.175-34) X10^14 W/ cm^2 at 390 nm, and (0.275 - 14.4) X 10^14 W /cm^2 at 780 nm) are obtained from full-dimensionality integrations of the time-dependent helium-laser Schroedinger equation. We show that the power law of lowest order perturbation theory, modified with a ponderomotive-shifted ionization potential, is capable of modelling the ionization rates over an intensity range that extends up to two orders of magnitude higher than that applicable to perturbation theory alone. Writing the modified perturbation theory in terms of scaled wavelength and intensity variables, we obtain to first approximation a single ionization law for both the 390 nm and 780 nm cases. To model the data in the high intensity limit as well as in the low, a new function is introduced for the rate. This function has, in part, a resemblance to that derived from tunnelling theory but, importantly, retains the correct frequency-dependence and scaling behaviour derived from the perturbative-like models at lower intensities. Comparison with the predictions of classical ADK tunnelling theory confirms that ADK performs poorly in the frequency and intensity domain treated here.

Scaling of Food-Web Properties with Diversity and Complexity Across Ecosystems

Trophic scaling models describe how topological food-web properties such as the number of predator prey links scale with species richness of the community. Early models predicted that either the link density (i.e. the number of links per species) or the connectance (i.e. the linkage probability between any pair of species) is constant across communities. More recent analyses, however, suggest that both these scaling models have to be rejected, and we discuss several hypotheses that aim to explain the scale dependence of these complexity parameters. Based on a recent, highly resolved food-web compilation, we analysed the scaling behaviour of 16 topological parameters and found significant power law scaling relationships with diversity (i.e. species richness) and complexity (i.e. connectance) for most of them. These results illustrate the lack of universal constants in food-web ecology as a function of diversity or complexity. Nonetheless, our power law scaling relationships suggest that fundamental processes determine food-web topology, and subsequent analyses demonstrated that ecosystem-specific differences in these relationships were of minor importance. As such, these newly described scaling relationships provide robust and testable cornerstones for future structural food-web models.

A scaling method for modelling the crashworthiness of novel roadside barrier designs

In this paper, a novel method for modelling a scaled vehicle–barrier crash test similar to the 20◦ angled barrier test specified in EN 1317 is reported. The intended application is for proof-of-concept evaluation of novel roadside barrier designs, and as a cost-effective precursor to full-scale testing or detailed computational modelling. The method is based on the combination of the conservation of energy law and the equation of motion of a spring mass system representing the impact, and shows, for the first time, the feasibility of applying classical scaling theories to evaluation of roadside barrier design. The scaling method is used to set the initial velocity of the vehicle in the scaled test and to provide scaling factors to convert the measured vehicle accelerations in the scaled test to predicted full-scale accelerations. These values can then be used to calculate the Acceleration Severity Index score of the barrier for a full-scale test. The theoretical validity of the method is demonstrated by comparison to numerical simulations of scaled and full-scale angled barrier impacts using multibody analysis implemented in the crash simulation software MADYMO. Results show a maximum error of 0.3% ascribable to the scaling method.

One size fits all: stability of metabolic scaling under warming and ocean acidification in echinoderms

Responses by marine species to ocean acidification (OA) have recently been shown to be modulated by external factors including temperature, food supply and salinity. However the role of a fundamental biological parameter relevant to all organisms, that of body size, in governing responses to multiple stressors has been almost entirely overlooked. Recent consensus suggests allometric scaling of metabolism with body size differs between species, the commonly cited 'universal' mass scaling exponent (b) of A3/4 representing an average of exponents that naturally vary. One model, the Metabolic-Level Boundaries hypothesis, provides a testable prediction: that b will decrease within species under increasing temperature. However, no previous studies have examined how metabolic scaling may be directly affected by OA. We acclimated a wide body-mass range of three common NE Atlantic echinoderms (the sea star Asterias rubens, the brittlestars Ophiothrix fragilis and Amphiura filiformis) to two levels of pCO(2) and three temperatures, and metabolic rates were determined using closed-chamber respirometry. The results show that contrary to some models these echinoderm species possess a notable degree of stability in metabolic scaling under different abiotic conditions; the mass scaling exponent (b) varied in value between species, but not within species under different conditions. Additionally, we found no effect of OA on metabolic rates in any species. These data suggest responses to abiotic stressors are not modulated by body size in these species, as reflected in the stability of the metabolic scaling relationship. Such equivalence in response across ontogenetic size ranges has important implications for the stability of ecological food webs.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Generic Finite Element Model for Mechanically Consistent Scaling of Composite Beam-to-column Joint with Welded Connection

To study the behaviour of beam-to-column composite connection more sophisticated finite element models is required, since component model has some severe limitations. In this research a generic finite element model for composite beam-to-column joint with welded connections is developed using current state of the art local modelling. Applying mechanically consistent scaling method, it can provide the constitutive relationship for a plane rectangular macro element with beam-type boundaries. Then, this defined macro element, which preserves local behaviour and allows for the transfer of five independent states between local and global models, can be implemented in high-accuracy frame analysis with the possibility of limit state checks. In order that macro element for scaling method can be used in practical manner, a generic geometry program as a new idea proposed in this study is also developed for this finite element model. With generic programming a set of global geometric variables can be input to generate a specific instance of the connection without much effort. The proposed finite element model generated by this generic programming is validated against testing results from University of Kaiserslautern. Finally, two illustrative examples for applying this macro element approach are presented. In the first example how to obtain the constitutive relationships of macro element is demonstrated. With certain assumptions for typical composite frame the constitutive relationships can be represented by bilinear laws for the macro bending and shear states that are then coupled by a two-dimensional surface law with yield and failure surfaces. In second example a scaling concept that combines sophisticated local models with a frame analysis using a macro element approach is presented as a practical application of this numerical model.

Phylogeny and metabolic scaling in mammals

The scaling of metabolic rates to body size is widely considered to be of great biological and ecological importance, and much attention has been devoted to determining its theoretical and empirical value. Most debate centers on whether the underlying power law describing metabolic rates is 2/3 (as predicted by scaling of surface area/volume relationships) or 3/4 ("Kleiber's law"). Although recent evidence suggests that empirically derived exponents vary among clades with radically different metabolic strategies, such as ectotherms and endotherms, models, such as the metabolic theory of ecology, depend on the assumption that there is at least a predominant, if not universal, metabolic scaling exponent. Most analyses claimed to support the predictions of general models, however, failed to control for phylogeny. We used phylogenetic generalized least-squares models to estimate allometric slopes for both basal metabolic rate (BMR) and field metabolic rate (FMR) in mammals. Metabolic rate scaling conformed to no single theoretical prediction, but varied significantly among phylogenetic lineages. In some lineages we found a 3/4 exponent, in others a 2/3 exponent, and in yet others exponents differed significantly from both theoretical values. Analysis of the phylogenetic signal in the data indicated that the assumptions of neither species-level analysis nor independent contrasts were met. Analyses that assumed no phylogenetic signal in the data (species-level analysis) or a strong phylogenetic signal (independent contrasts), therefore, returned estimates of allometric slopes that were erroneous in 30% and 50% of cases, respectively. Hence, quantitative estimation of the phylogenetic signal is essential for determining scaling exponents. The lack of evidence for a predominant scaling exponent in these analyses suggests that general models of metabolic scaling, and macro-ecological theories that depend on them, have little explanatory power.

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Dynamic Scaling and Growth Kinetics of 3-Glycidoxypropyltrimethoxysilane-Derived Organic/Silica Hybrids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogels

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Power-law distribution in a learning process: competition, learning and natural selection

In the present work, we propose a model for the statistical distribution of people versus number of steps acquired by them in a learning process, based on competition, learning and natural selection. We consider that learning ability is normally distributed. We found that the number of people versus step acquired by them in a learning process is given through a power law. As competition, learning and selection is also at the core of all economical and social systems, we consider that power-law scaling is a quantitative description of this process in social systems. This gives an alternative thinking in holistic properties of complex systems. (C) 2004 Elsevier B.V. All rights reserved.

Quantum critical scaling at a Bose-glass/superfluid transition: Theory and experiment for a model quantum magnet

In this paper we investigate the quantum phase transition from magnetic Bose Glass to magnetic Bose-Einstein condensation induced by amagnetic field in NiCl2 center dot 4SC(NH2)(2) (dichloro-tetrakis-thiourea-nickel, or DTN), doped with Br (Br-DTN) or site diluted. Quantum Monte Carlo simulations for the quantum phase transition of the model Hamiltonian for Br-DTN, as well as for site-diluted DTN, are consistent with conventional scaling at the quantum critical point and with a critical exponent z verifying the prediction z = d; moreover the correlation length exponent is found to be nu = 0.75(10), and the order parameter exponent to be beta = 0.95(10). We investigate the low-temperature thermodynamics at the quantum critical field of Br-DTN both numerically and experimentally, and extract the power-law behavior of the magnetization and of the specific heat. Our results for the exponents of the power laws, as well as previous results for the scaling of the critical temperature to magnetic ordering with the applied field, are incompatible with the conventional crossover-scaling Ansatz proposed by Fisher et al. [Phys. Rev. B 40, 546 (1989)]. However they can all be reconciled within a phenomenological Ansatz in the presence of a dangerously irrelevant operator.