Scale-dependent Behavior Research Articles

Scale-Invariant or Scale-Dependent Behavior of the Link Density Property in Food Webs: A Matter of Sampling Effort?

Studies of initial compilations of food webs resulted in the intriguing generalization that the link density property, L/S (the number of trophic links L divided by the total number of species S in a web), may be scale invariant; that is, this ratio may remain constant across webs of

How Do Grazers Achieve Their Distribution? A Continuum of Models from Random Diffusion to the Ideal Free Distribution Using Biased Random Walks.

A conceptual model is described for generating distributions of grazing animals, according to their searching behavior, to investigate the mechanisms animals may use to achieve their distributions. The model simulates behaviors ranging from random diffusion, through taxis and cognitively aided navigation (i.e., using memory), to the optimization extreme of the Ideal Free Distribution. These behaviors are generated from simulation of biased diffusion that operates at multiple scales simultaneously, formalizing ideas of multiple-scale foraging behavior. It uses probabilistic bias to represent decisions, allowing multiple search goals to be combined (e.g., foraging and social goals) and the representation of suboptimal behavior. By allowing bias to arise at multiple scales within the environment, each weighted relative to the others, the model can represent different scales of simultaneous decision-making and scale-dependent behavior. The model also allows different constraints to be applied to the animal's ability (e.g., applying food-patch accessibility and information limits). Simulations show that foraging-decision randomness and spatial scale of decision bias have potentially profound effects on both animal intake rate and the distribution of resources in the environment. Spatial variograms show that foraging strategies can differentially change the spatial pattern of resource abundance in the environment to one characteristic of the foraging strategy.

Primary fracture propagation from circular cavities loaded in compression

When a brittle elastic material containing a cavity is loaded in uniaxial compression, fractures may form in three basic positions around the cavity; at the tensile stress concentration (primary fracture), at positions inside the material remote from the perimeter of the cavity, and at the compressive stress concentration. Granite blocks containing a circular cavity of radius between 2.5 mm and 50 mm were tested in uniaxial compression to collect data on primary fracture propagation. The laboratory results indicate that primary crack propagation is a stable process at small scales but approaches instability at large scales. A finite width crack model is presented which is able to capture this scale dependent behavior. The model illustrates that both tensile and compressive stresses play an important role in the primary fracture process.

A CHANNEL NETWORK MODEL FOR CHEMICAL MIGRATION IN SUBSURFACE MEDIA

We consider the migration of chemical species through saturated heterogeneous media, where the scale of the flow path geometry is large enough to invalidate a Fickian based, representative elementary volumes, approach to dispersal. Channel network models combine the effects of channeling over small spatial scales with network mixing which gives rise to an equivalent dispersion effect over large spatial scales. We extend equations and solutions given previously for ideal nonabsorbing tracers, to include the retardation of chemically active species. The primary aim is to derive explicit solutions for future calibration purposes, and illustrate scale dependent dispersive behavior with and without chemical absorption processes. In this paper we develop a twin channel model allowing for various specification of the retardation process. This allows the retardation to be either positively or negatively correlated with pathway apertures (which are in turn related directly to flow rates of the respective channels). We show that if absorption is controlled by specific surface area, then a scaling argument infers that highly transmissive paths are also less retarding. We illustrate the model’s applicability to such cases. We shall discuss the scale dependence of calculated (observed) equivalent dispersivities obtained by analyzing the moments of breakthrough curves at various distances. For a range of parameter values we exhibit scaling behavior similar to that observed in the field and laboratory. This does not necessarily imply any validity to the approach: it is a direct consequence of deferring the network — mixing effect to large length scales. An important point of consideration is that wherever conceptual model choices must be made, in modeling natural processes such as chemical migration, there is a possibility of biasing calculations by sole reliance on a particular approach. Channel network models marry channeling models and classical Fickian models. Thus in calibrating a model such as the Twin Channel model from given experimental behavior, we can immediately estimate over which scales channeling or Fickian dispersive effects are likely to be dominant.

Scale-dependent elastic response of closed phospholipid bilayers to transmembrane molecular pumping activity: a key for exo-endocytosis physiological process

The question is asked on the physiological role of the universal molecular biological function activity of lipid transmembrane translocation in living-cell membranes. The elastic response of closed bilayers to phospholipid translocation is theoretically found to be scale dependent, leading to vesiculation for plasma membrane characteristic-size bilayers (Rm≈10 μm), and to dilation strain for endocytic-vesicles characteristic-size bilayers (Rm≈0.1 μm). Both vesiculation and dilation effects are experimentally proved. On the basis of this scaledependent behaviour, it is argued that transmembrane pumping activity could control both the vesiculation and the fusion process in vivo, namely the exo-endocytic cellular-membrane traffic process itself.

Mean and Transient Spectral Energy and Enstrophy Budgets

Abstract The scale-dependent behavior of atmospheric flow on the sphere is investigated in terms of the spectra and spectral budgets of enstrophy and kinetic and available potential energy. The decomposition into both the α = (n, m) and the more usual n-spectral forms is considered. Several novel spectral results are obtained. First, a direct test of the extent to which large-scale atmospheric flow satisfies the necessary and sufficient conditions for homogeneous and isotropic two-dimensional turbulent behavior is carried out by calculating “spectral teleconnections” from data. The conditions are satisfied for the higher wavenumber transient component of the flow. Second, the spectral budget equations are extended to include the decomposition into time mean and transient components, a method that, although common and straightforward in real-space calculations, is novel in the spectral domain. The terms in these budgets are evaluated from data. Finally, the flow of energy and enstrophy through α-spectral s...

Effects of finite-size joints on the deformability of jointed rock at the two-dimensional level

A numerical decomposition technique, which has resulted from a linking between joint-geometry modeling and generation schemes, and a distinct element code (UDEC), is used to study the effect of joint-geometry parameters of finite-size joints on the deformability properties of jointed rock at the two-dimensional (2D) level. The influence of joint-geometry parameters such as joint density, ratio of joint size to block size, and joint orientation on the deformability of jointed rock is shown. Relations are established between deformability properties of jointed rock and fracture-tensor parameters. An incrementally linear elastic, anisotropic constitutive model is developed to represent the prefailure mechanical behaviour of jointed rock at the 2D level. This constitutive model has captured the anisotropic, scale-dependent behaviour of jointed rock. In this model, the effect of the joint-geometry network in the rock mass is incorporated in terms of fracture-tensor components. Some insight is given related to estimation of representative elementary volumes for deformability properties of jointed rock. Key words : rock masses, deformability, distinct element method, fracture tensor, anisotropy, scale effects.

Effect of finite size joints on the deformability of jointed rock in three dimensions

A numerical decomposition technique, which has emerged from a linking between joint geometry modelling and generation schemes and a distinct element code (3DEC), is used to evaluate the effects of joint geometry parameters of finite size joints on the deformability properties of jointed rock at the three-dimensional (3-D) level. Variation of deformability parameters of jointed rock with joint geometry parameters such as joint density, joint size/block size and joint orientation, are shown through 3-D plots. Relations are developed between deformability properties of jointed rock and fracture tensor parameters. An incrementally linear elastic, orthotropic constitutive model is suggested to represent the pre-failure mechanical behaviour of jointed rock. This constitutive model has captured the anisotropic, scale-dependent behaviour of jointed rock. In this model, the effect of the joint geometry network in the rock mass is incorporated in terms of fracture tensor components. Some insight is given related to estimation of Representative Elementary Volumes (REVs) and REV property values with respect to deformability properties of jointed rock.

A Spectral Analysis of Predictability and Error in an Operational Forecast System

A spectral analysis of error at 24, 48 and 72 hours in an operational forecast system is carded out for a winter and a summer month. The scale-dependent behavior of the error and the several factors governing error growth, namely the nonlinear production term, the nonlinear transfer of energy between scales and the model-related error source term are evaluated. It is found that the largest errors occur at low wavenumbers where the amplitude of the flow is largest, while the largest relative errors occur at high wavenumbers when error is approaching saturation. Early in the forecast the growth of error is governed by the model error source term which supplies error at all scales. At later forecast times the nonlinear production and interaction terms become important. Error doubling times and the flux of error through wavenumber space are also calculated. The predictability of the flow resides in the low wavenumber region. The behavior of the error and its transient and stationary parts markedly with season at these scales.

Cabbeling at thermohaline fronts

A linear model with cabbeling dynamics is developed for a nonrotating, unstratified ocean and applied to observations of three medium‐ to large‐scale oceanic thermohaline (density balanced) fronts. The ability of the predicted cabbeling sinking and surface convergence rates to maintain a steady front against diffusion depends critically on the assumed values of horizontal and vertical eddy viscosities. There is good theoretical evidence for the existence of small‐scale (1 km), weak (surface currents 0.1 cm s−1) cabbeling fronts; however, the intensity and stability of such fronts will depend critically on the scale dependent behavior of dissipation processes.