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PubMed2006

Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone.

Patterns of space-use by individuals are fundamental to the ecology of animal populations influencing their social organization, mating systems, demography and the spatial distribution of prey and competitors. To date, the principal method used to analyse the underlying determinants of animal home range patterns has been resource selection analysis (RSA), a spatially implicit approach that examines the relative frequencies of animal relocations in relation to landscape attributes. In this analysis, we adopt an alternative approach, using a series of mechanistic home range models to analyse observed patterns of territorial space-use by coyote packs in the heterogeneous landscape of Yellowstone National Park. Unlike RSAs, mechanistic home range models are derived from underlying correlated random walk models of individual movement behaviour, and yield spatially explicit predictions for patterns of space-use by individuals. As we show here, mechanistic home range models can be used to determine the underlying determinants of animal home range patterns, incorporating both movement responses to underlying landscape heterogeneities and the effects of behavioural interactions between individuals. Our analysis indicates that the spatial arrangement of coyote territories in Yellowstone is determined by the spatial distribution of prey resources and an avoidance response to the presence of neighbouring packs. We then show how the fitted mechanistic home range model can be used to correctly predict observed shifts in the patterns of coyote space-use in response to perturbation.

Animals↗
PubMed2006

Modelling dispersal of a temperate insect in a changing climate.

We construct a novel individual-based random-walk model to assess how predicted global climate change might affect the dispersal rates of a temperate insect. Using a novel approach we obtained accurate field measurements of daily movements for individuals over time to parameterize our model. Males were found to move significantly further on average than females. Significant variation in movement was evident among individuals; the most dispersive individuals moved up to five (females) and seven (males) times as far on average as the least dispersive individuals. Mean relative daily movement of both males and females were exponentially related to maximum daily temperature recorded within the grass sward. Variability, both within and among individuals, in relative daily movement was incorporated into the model using gamma probability distributions. Resultant dispersal functions for seasonal movement are predicted to be highly leptokurtic, which agrees well with observations from the field. Predictions of the model suggest that for populations at the polewards edge of the current range an increase of 3-5 degrees C in daily maximum temperature may increase the proportion of long-distance dispersers (those characterized as comprising the top 0.1% of furthest dispersing individuals under local conditions experienced during the 1963-1990 period) by up to 70%.

Animals↗
PubMed1999

Power-law distributions and Lévy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements.

A generic model of stochastic autocatalytic dynamics with many degrees of freedom w(i,) i=1, em leader,N, is studied using computer simulations. The time evolution of the w(i)'s combines a random multiplicative dynamics w(i)(t+1)=lambdaw(i)(t) at the individual level with a global coupling through a constraint which does not allow the w(i)'s to fall below a lower cutoff given by cw, where w is their momentary average and 0 infinity and the limit of decoupled free multiplicative random walks c-->0 do not commute: alpha(0,N)=0 for any finite N while alpha(c,infinity)>or=1 (which is the common range in empirical systems) for any positive c. The time evolution of w(t) exhibits intermittent fluctuations parametrized by a (truncated) Lévy-stable distribution L(alpha)(r) with the same index alpha. This nontrivial relation between the distribution of the wi's at a given time and the temporal fluctuations of their average is examined, and its relevance to empirical systems is discussed.

Journal Article↗
PubMed1999

Theta-point behavior of diluted polymer solutions: can one observe the universal logarithmic corrections predicted by field theory?

In recent large-scale Monte Carlo simulations of various models of Theta-point polymers in three dimensions Grassberger and Hegger found logarithmic corrections to mean field theory with amplitudes much larger than the universal amplitudes of the leading logarithmic corrections calculated by Duplantier in the framework of tricritical O(n) field theory. To resolve this issue we calculate the universal subleading correction of field theory, which turns out to be of the same order of magnitude as the leading correction for all chain lengths available in present day simulations. Borel resummation of the renormalization group flow equations also shows the presence of such large corrections. This suggests that the published simulations did not reach the asymptotic regime. To further support this view, we present results of Monte Carlo simulations on a Domb-Joyce-like model of weakly interacting random walks. Again the results cannot be explained by keeping only the leading corrections, but are in fair accordance with our full theoretical result. The corrections found for the Domb-Joyce model are much smaller than those for other models, which clearly shows that the effective corrections of are not yet in the asymptotic regime. Altogether, our findings show that the existing simulations of Theta polymers are compatible with tricritical field theory, since the crossover to the asymptotic regime is very slow. Similar results were found earlier for self-avoiding walks at their upper critical dimension d(c)=4.

Journal Article↗
PubMed1999

Critical behavior of roughening transitions in parity-conserving growth processes.

We investigate a class of parity-conserving solid-on-solid models that describes the growth of an interface by the deposition and evaporation of dimers. As a key feature of the models, evaporation of dimers takes place only at the edges of terraces, leading to a roughening transition between a smooth and a rough phase. We consider several variants of growth models in order to identify universal and nonuniversal properties. Moreover, a parity-conserving polynuclear growth model is proposed. All variants display the same type of universal critical behavior at the roughening transition. Because of parity conservation, the critical behavior at the first few layers can be explained in terms of unidirectionally coupled branching annihilating random walks with an even number of offspring.

Journal Article↗
PubMed1999

Experimental evidence of power-law trapping-time distributions in porous media.

We present experimental results of solute transport in porous samples made of packings of activated carbon porous grains. Exchange experiments, where the tagged solution initially saturating the medium is replaced with the same solution without tracer, are accurately described by macroscopic transport equations. On the other hand, in desorption experiments, where the tagged solution is replaced by water, the solute concentration exhibits a power-law decay for long times, which requires a more detailed, mesoscopic description. We reproduce this behavior within a continuous-time random-walk approach, where the waiting time distribution is related to the desorption isotherm. Results are compatible with a power-law trapping time distribution with divergent first moment, characteristic of anomalous (sub)diffusion.

Journal Article↗
PubMed2000

Diffusion-mediated reactions with a time-dependent absorption rate

Diffusion-mediated reactions models are particularly useful for the characterization of physical, chemical, and biological problems. In this paper we present a theoretical study of the absorption probability density, survival probability, and reaction rate for diffusion-mediated reactions models with a time-dependent finite absorption rate (an extension of a model usually referred to as the "imperfect trap model"). The results are obtained by means of the formalism of continuous time random walk on a lattice and considering a general reaction dynamics upon encounter of the reactives. First jump probability densities are included to take initial conditions into account. Previous results presented by Collins and Kimball [J. Colloid. Sci. 4, 425 (1949)] and Noyes [J. Chem. Phys. 22, 1349 (1954)] are reobtained for the particular case of a time-independent absorptivity. Short and long time behaviors are analyzed resulting, in particular, in that the long time behavior of the absorption probability density exhibits the same time dependence as the first passage time density. The results obtained are illustrated by considering a one-dimensional model with consequent discussion.

Journal Article↗
PubMed2000

Surface critical behavior in systems with nonequilibrium phase transitions

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d(c), with d(c)=4 (DP) and d(c)=2 (BARW), we use mean field-theory to analyze the surface phase diagrams using the standard classification into ordinary, special, surface, and extraordinary transitions. For the case of BARW, at or below the upper critical dimension d</=d(c), we use field theoretic methods to study the effects of fluctuations. As in the bulk, the field-theory suffers from technical difficulties associated with the presence of a second critical dimension. However, we are still able to analyze the phase diagrams for BARW in d=1 and 2, which turn out to be very different from their mean field analog. Furthermore, for the case of BARW only (and not for DP), we find two independent surface beta(1) exponents in d=1, arising from two distinct definitions of the order parameter. Using an exact duality transformation on a lattice BARW model in d=1, we uncover a relationship between these two surface beta(1) exponents at the ordinary and special transitions. Many of our predictions are supported using Monte Carlo simulations of two different models belonging to the BARW universality class.

Journal Article↗
PubMed2000

Dynamic scaling approach to glass formation

Experimental data for the temperature dependence of relaxation times are used to argue that the dynamic scaling form, with relaxation time diverging at the critical temperature T(c) as (T-T(c))(-nuz), is superior to the classical Vogel form. This observation leads us to propose that glass formation can be described by a simple mean-field limit of a phase transition. The order parameter is the fraction of all space that has sufficient free volume to allow substantial motion, and grows logarithmically above T(c). Diffusion of this free volume creates random walk clusters that have cooperatively rearranged. We show that the distribution of cooperatively moving clusters must have a Fisher exponent tau=2. Dynamic scaling predicts a power law for the relaxation modulus G(t) approximately t(-2/z), where z is the dynamic critical exponent relating the relaxation time of a cluster to its size. Andrade creep, universally observed for all glass-forming materials, suggests z=6. Experimental data on the temperature dependence of viscosity and relaxation time of glass-forming liquids suggest that the exponent nu describing the correlation length divergence in this simple scaling picture is not always universal. Polymers appear to universally have nuz=9 (making nu=3 / 2). However, other glass-formers have unphysically large values of nuz, suggesting that the availability of free volume is a necessary, but not sufficient, condition for motion in these liquids. Such considerations lead us to assert that nuz=9 is in fact universal for all glass- forming liquids, but an energetic barrier to motion must also be overcome for strong glasses.

Journal Article↗
PubMed2000

Comment on "Walker diffusion method for calculation of transport properties of composite materials"

In a recent paper [C. DeW. Van Siclen, Phys. Rev. E 59, 2804 (1999)], a random-walk algorithm was proposed as the best method to calculate transport properties of composite materials. It was claimed that the method is applicable both to discrete and continuum systems. The limitations of the proposed algorithm are analyzed. We show that the algorithm does not capture the peculiarities of continuum systems (e.g., "necks" or "choke points") and we argue that it is the stochastic analog of the finite-difference method.

Journal Article↗
PubMed2000

Integrated approach to the assessment of long range correlation in time series data

To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results. We thus advocate an integrated approach which requires the use of both methods in a consistent fashion. We provide the theoretical foundation of this approach and illustrate the main ideas using examples. The second objective relates to the observation of long range anticorrelation (Hurst exponent H < 1/2) in real world time series data. The very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur. Using examples, we discuss the possible factors that could contribute to the false claim of long range anticorrelations, and demonstrate the particular importance of the integrated approach in this case.

Journal Article↗
PubMed2000

Multifractal behavior of linear polymers in disordered media.

The scaling behavior of linear polymers in disordered media modeled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p(c) is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior; i.e., different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers mu(q) and enhancement exponents gamma(q), which depend on q. Our numerical results suggest that the relation mu(1)=p(c)mu between the first moment mu(1) and its regular lattice counterpart mu is valid.

Journal Article↗
PubMed2000

Inverse cascade avalanche model with limit cycle exhibiting period doubling, intermittency, and self-similarity

A one-dimensional avalanche "sandpile" algorithm is presented for transport in a driven dissipative confinement system. Sand is added at the closed inflow boundary and redistributed when the local gradient exceeds a threshold. The redistribution rule is conservative, nonlocal, and linear and is chosen to mimic fluid flow. Potential energy is dissipated by avalanches that also expel matter at the open outflow boundary. The system then evolves through an inverse cascade. A "fluidization" parameter L(f) specifies the length scale over which the algorithm operates. The limiting case of L(f)=1 cell and L(f)=N, the system size, are analytically soluble. For other values of L(f) the emergent, large-scale dynamics of the system shows a variety of behavior including a limit cycle that has a period-doubling sequence, intermittency, and a random walk.

Journal Article↗
PubMed2000

Generalized chapman-kolmogorov equation: A unifying approach to the description of anomalous transport in external fields

The generalized Chapman-Kolmogorov equation [V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973)] is discussed. It is demonstrated that this equation unifies recently proposed kinetic equations of fractional order that describe anomalous transport in external fields, as well as continuous time random walks. The conditions under which the individual models can be established are discussed.

Journal Article↗
PubMed2000

Scaling behaviors of branched polymers

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions for branched polymers are given by those for straight phi(3) theory with a single mass insertion, not those for the straight phi(3) theory themselves. In particular, the two-point function behaves as 1/p(4), not as 1/p(2), in the scaling region. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is 4. In the appendixes we derive the exact two-point correlation function at finite (but large) system size N, which is consistent with the analysis in the body of the paper.

Journal Article↗
PubMed2000

Collective response of an array of rotating particles to fluctuating confining forces

We study the influence of fluctuations of confining forces on the rotation patterns in a dense array of cylinders. Our theoretical studies are motivated by new results from detailed time-resolved experimental measurements. In order to calculate the system's evolution in time at each moment, a molecular-dynamics code adapted to the system is developed. The numerical procedure is tested by a comparison with rigorous predictions derived analytically. The chain's reaction on oscillating confining forces is analyzed numerically for different typical cases. Our theoretical results reproduce the striking features of the experimental data. A quantitative analysis of the experimental data is performed by a computation of their power spectrum and of spatial and temporal correlation functions. From our comparison of the theoretical and experimental results we conclude that the experimental rotation patterns result of random superpositions of different steady-state patterns ("collective random walk").

Journal Article↗
PubMed2000

Biased diffusion in anisotropic disordered systems

We investigate a diffusion process into an anisotropic disordered medium in the presence of a bias. The medium is modeled by a two-dimensional square lattice in which the anisotropic disorder is represented by a bond percolation model with different occupation probabilities on each direction. The biased diffusion process is mapped by a random walk with unequal transition probabilities along and against the field (in the [1,1] direction) by performing Monte Carlo simulations. We observe a transition from pure to drift diffusion when the bias reaches a threshold B(c). In order to estimate this B(c), an effective exponentis used to characterize the diffusion process. This B(c) is also compared with another estimation for the critical field.

Journal Article↗
PubMed2000

Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels.

Intrinsic noise and random synaptic inputs generate a fluctuating current across neuron membranes. We determine the statistics of the output spike train of a biophysical model neuron as a function of the mean and variance of the fluctuating current, when the current is white noise, or when it derives from Poisson trains of excitatory and inhibitory postsynaptic conductances. In the first case, the firing rate increases with increasing variance of the current, whereas in the latter case it decreases. In contrast, the firing rate is independent of variance (for constant mean) in the commonly used random walk, and perfect integrate-and-fire models for spike generation. The model neuron can be in the current-dominated state, representative of neurons in the in vitro slice preparation, or in the fluctuation-dominated state, representative of in vivo neurons. We discuss the functional relevance of these states to cortical information processing.

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