Changes In Scaling Exponents Research Articles

Diffusive persistence on disordered lattices and random networks.

To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time t (or, in general, that the node remained active or inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law P(t,L)∼t^{-θ} with an exponent θ≃0.186, in the limit of large linear system size L. At the percolation threshold, however, the scaling exponent changes to θ≃0.141, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power law P(t,L)∼L^{-zθ} with z≃2.86 instead of the value of z=2 normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdős-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold.

Increase in light interception cost and metabolic mass component of leaves are coupled for efficient resource use in the high altitude vegetation

Global syntheses of leaf trait scaling relationships report an increase in light interception costs or ‘diminishing returns’ with increase in leaf area. However, variation in light interception costs across ecological gradients and plant strategies to cope up with these costs are not adequately understood. We analyzed leaf area (A) – leaf dry mass (M), leaf water mass (W) – M and W – A scaling relationships in plants occurring in a high altitude region of western Himalaya across environmental gradients to understand changes in light interception cost and metabolic mass component. M represents light interception cost, whereas, W is considered as a proxy of metabolic mass component for liquid phase being the ultimate source of metabolic activity. Trait values were measured from 9278 leaves belonging to 136 dominant species occurring at different sites, slope aspects, elevations and habitat types. Overall, light interception cost increased with increasing A (scaling exponent (α) < 1 in A–M relationship) and metabolic mass component increased disproportionately high with increasing M and A. We found significant differences in scaling exponents of leaf trait relationship between sites, elevations, slope aspects and habitat types, indicating that increase in light interception cost was more evident at higher elevations, southern slopes and open habitats. Further, with increase in light interception cost, metabolic mass component also increased (α > 1 in W–M and W–A relationships). The changes in scaling exponents of various leaf trait relationships across ecological gradients indicated that vegetation of different regions have differences in light interception cost and metabolic mass component. Moreover, increasing light interception cost (increase in mechanical and hydraulic tissues) with increasing A and increasing metabolic mass (leaf thickness) with increasing A and M are favored in high altitude vegetation. This could be a key strategy of high altitude plants for efficient resource capture and use in harsh environments.

Detection of future changes in trends and scaling exponents in extreme short-term rainfall at selected stations in Slovakia

Abstract This paper analyses projected changes in short-term rainfall events during the warm season (April – October) in an ensemble of 30 regional climate model (RCM) simulations. The analysis of trend changes and changes in scaling exponents was done for the Hurbanovo, Bratislava, Oravská Lesná, and Myjava stations in Slovakia. The characteristics of maximum rainfall events were analysed for two scenario periods, one past and one future (1960–2000 and 2070–2100) and compared to the characteristics of the actual observed events. The main findings from the analysis show that 60-min short-term events for most of the RCM simulations will either increase or remain constant. On the other hand, the depths and intensities of daily events are projected to increase significantly; in some cases they were found to be ten times larger. Trends in future events at the Hurbanovo station were found to be insignificant. In the other stations positive trends in future rainfall events prevail, except for daily rainfall at the Myjava station, which shows a negative trend. Using results from the selected simulations, the scaling exponents estimated are on average lower than the exponents of the data observed. On the other hand, due to the higher daily precipitation amounts in the future seen to all the scenarios, the downscaled values of short-term rainfall at all the stations analysed might be considerably higher in the future horizons, which could subsequently affect future design rainfall values for engineering designs.

Assessing changes in extreme river flow regulation from non-stationarity in hydrological scaling laws

Extreme flows are key components of river flow regimes that affect manifold hydrological, geomorphological and ecological processes with societal relevance. One fundamental characteristic of extreme flows in river basins is that they exhibit scaling properties which can be identified through scaling (power) laws. Understanding the physical mechanisms behind such scaling laws is a continuing challenge in hydrology, with potential implications for the prediction of river flow regimes in a changing environment and ungauged basins. After highlighting that the scaling properties are sensitive to environmental change, we develop a physical interpretation of how temporal changes in scaling exponents relate to the capacity of river basins to regulate extreme river flows. Regulation is defined here as the basins’ capacity to either dampen high flows or to enhance low flows. Further, we use this framework to infer temporal changes in the regulation capacity of five large basins in tropical South America. Our results indicate that, during the last few decades, the Amazon river basin has been reducing its capacity to enhance low flows, likely as a consequence of pronounced environmental change in its south and south-eastern sub-basins. The proposed framework is widely applicable to different basins, and provides foundations for using scaling laws as empirical tools for inferring temporal changes of hydrological regulation, particularly relevant for identifying and managing hydrological consequences of environmental change.

DETECTING CHANGES IN TRENDS AND SCALING EXPONENTS OF SHORT TERM RAINFALL: CASE STUDY FOR THE ORAVSKÁ LESNÁ STATION

The aim of this study was to test the rainfall trend and scaling exponent changes of different duration at the Oravská Lesná climatological station during the observation period 1964 to 2009. Trends of rainfall intensities were tested for the durations of 5, 10, 15, 30, 40, 50, 60, 120, 180, 240 and 1440 minutes from April till October and for the whole warm period. To analyze the significance of rainfall trends Mann-Kendall trend test (Kendall, 1975) was used. Trend analysis of the short-term rainfall was performed for 90% significance. In the next step, the simple scaling methodology was applied to derive scaling exponents and compared changes in their values in different observation periods. Finally, the impact of changes in trends on scaling exponents at the selected station in Slovakia was discussed.

Power Laws in Cone Production of Longleaf Pine across Its Native Range in the United States

Longleaf pine (Pinus palustris Mill.) forests in the southeastern United States are considered endangered ecosystems, because of their dramatic decrease in area since European colonization and poor rates of recovery related to episodic natural regeneration. Sporadic seed production constrains restoration efforts and complicates sustainable management of this species. Previous studies of other tree species found invariant scaling properties in seed output. Here, using long-term monitoring data for cone production at seven sites across the native range of longleaf pine, we tested the possible presence of two types of power laws. Findings indicate that (i) the frequency distribution of cone production at seven sites, from 1958 to 2014, follows power law relationships with high level of significance; (ii) although there is no general trend in the dynamics of scaling exponents among all sites, there are dynamics of scaling exponents at each site, with sudden changes in scaling exponents generally corresponding to the years of higher or lower cone production; and (iii) Taylor’s power laws explain cone production at different locations, but the scaling exponents vary among these. Results from this computational approach provide new insight into the irregular cone production of longleaf pine at spatial and temporal scales. Integrated ecosystem monitoring will be necessary to more fully understand future changes in cone production.

Thermal conductivity in porous media: Percolation‐based effective‐medium approximation

AbstractKnowledge of porosity and saturation‐dependent thermal conductivities is necessary to investigate heat and water transfer in natural porous media such as rocks and soils. Thermal conductivity in a porous medium is affected by the complicated relationship between the topology and geometry of the pore space and the solid matrix. However, as water content increases from completely dry to fully saturated, the effect of the liquid phase on thermal conductivity may increase substantially. Although various methods have been proposed to model the porosity and saturation dependence of thermal conductivity, most are empirical or quasiphysical. In this study, we present a theoretical upscaling framework from percolation theory and the effective‐medium approximation, which is called percolation‐based effective‐medium approximation (P‐EMA). The proposed model predicts the thermal conductivity in porous media from endmember properties (e.g., air, solid matrix, and saturating fluid thermal conductivities), a scaling exponent, and a percolation threshold. In order to evaluate our porosity and saturation‐dependent models, we compare our theory with 193 porosity‐dependent thermal conductivity measurements and 25 saturation‐dependent thermal conductivity data sets and find excellent match. We also find values for the scaling exponent different than the universal value of 2, in insulator‐conductor systems, and also different from 0.76, the exponent in conductor‐superconductor mixtures, in three dimensions. These results indicate that the thermal conductivity under fully and partially saturated conditions conforms to nonuniversal behavior. This means the value of the scaling exponent changes from medium to medium and depends not only on structural and geometrical properties of the medium but also characteristics (e.g., wetting or nonwetting) of the saturating fluid.

Competition between Primary Nucleation and Autocatalysis in Amyloid Fibril Self-Assembly

Kinetic measurements of the self-assembly of proteins into amyloid fibrils are often used to make inferences about molecular mechanisms. In particular, the lag time—the quiescent period before aggregates are detected—is often found to scale with the protein concentration as a power law, whose exponent has been used to infer the presence or absence of autocatalytic growth processes such as fibril fragmentation. Here we show that experimental data for lag time versus protein concentration can show signs of kinks: clear changes in scaling exponent, indicating changes in the dominant molecular mechanism determining the lag time. Classical models for the kinetics of fibril assembly suggest that at least two mechanisms are at play during the lag time: primary nucleation and autocatalytic growth. Using computer simulations and theoretical calculations, we investigate whether the competition between these two processes can account for the kinks which we observe in our and others’ experimental data. We derive theoretical conditions for the crossover between nucleation-dominated and growth-dominated regimes, and analyze their dependence on system volume and autocatalysis mechanism. Comparing these predictions to the data, we find that the experimentally observed kinks cannot be explained by a simple crossover between nucleation-dominated and autocatalytic growth regimes. Our results show that existing kinetic models fail to explain detailed features of lag time versus concentration curves, suggesting that new mechanistic understanding is needed. More broadly, our work demonstrates that care is needed in interpreting lag-time scaling exponents from protein assembly data.

Permeability of Pore Networks Under Compaction

The characteristic pore length fixes the scale of permeability of a porous medium. For pore networks undergoing strong random compaction, this length becomes singular at transition porosities, revealing a change in the microstructure of the porespace controlling the transport. Nodal balances and lattice Boltzmann simulations of flow in pore networks under compaction show that the scaling between permeability and porosity changes near the transition porosities. Simulation results are compared with experimental permeability data from transparent two-dimensional micromodels of networks decorated with the same pore size distribution. Permeability–porosity data of media undergoing smooth compaction is well described by a single power law. Under strong compaction, however, the scaling between permeability and porosity is possible by traits only, the scaling exponent changes notably at given transition porosities. These behaviors are common to a wealth of permeability–porosity data thus far unexplained.

A scaling exponent-based detector of chaos in oscillatory circuits

In this paper, a scaling exponent based approach is proposed to determine the state of chaotic circuits, and the scaling exponent is calculated using detrended fluctuation analysis (DFA). The corresponding detector is designed using the fact that the scaling exponent changes for various states of chaotic circuits. Simulation examples in this paper are performed for Chua’s circuit and other chaotic systems and compared with the state-of-the-art in the field. The proposed detector outperforms existing techniques in ability to distinguish the chaotic and periodic states in the circuits for relatively high noise.

Adaptive time-varying detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a technique commonly used to assess and quantify the presence of long-range temporal correlations (LRTCs) in neurophysiological time series. Convergence of the method is asymptotic only and therefore its application assumes a constant scaling exponent. However, most neurophysiological data are likely to involve either spontaneous or experimentally induced scaling exponent changes. We present a novel extension of the DFA method that permits the characterisation of time-varying scaling exponents. The effectiveness of the methodology in recovering known changes in scaling exponents is demonstrated through its application to synthetic data. The dependence of the method on its free parameters is systematically explored. Finally, application of the methodology to neurophysiological data demonstrates that it provides experimenters with a way to identify previously un-recognised changes in the scaling exponent in the data. We suggest that this methodology will make it possible to go beyond a simple demonstration of the presence of scaling to an appreciation of how it may vary in response to either intrinsic changes or experimental perturbations.

Effects of landscape constraints on street patterns in cities: Examples from Khorramabad, Iran

The development of street patterns within cities is partly related to internal, social factors and partly to external, primarily landscape factors. Here we explore the effects of landscape constraints on the street pattern in the city of Khorramabad (population 334 thousand), West Iran. The city is located in a valley whose comparatively wide north and south parts are connected by a narrow (1-km-wide) pass. The surrounding mountains rise 400–900 m above the valley floor. These landscape constraints result in a crescent-shaped city. A total of 8481 street trends and lengths were measured, as well as the street spacing (the distance between adjacent streets), in five subareas/subsets of the city. The streets have two main trends, one perpendicular and one parallel with the city boundaries. The street-length distributions are generally power laws. On log–log plots, the distributions show abrupt changes in scaling exponent at lengths of 120 ± 20 m, suggesting different street populations. In the narrow pass between the mountains the average street spacing is much less (and the street density thus much higher) than in the other parts of the city. Using the Gibbs formula, the entropies of street populations were calculated and compared with their scaling exponents and length ranges (differences between the longest and the shortest streets). The entropies show a strong linear correlation with the scaling exponents (R2 = 0.9916) and with the length ranges (R2 = 0.8886).

Temperature and Water Vapor Variance Scaling in Global Models: Comparisons to Satellite and Aircraft Data

AbstractObservations of the scale dependence of height-resolved temperature T and water vapor q variability are valuable for improved subgrid-scale climate model parameterizations and model evaluation. Variance spectral benchmarks for T and q obtained from the Atmospheric Infrared Sounder (AIRS) are compared to those generated by state-of-the-art numerical weather prediction “analyses” and “free-running” climate model simulations with spatial resolution comparable to AIRS. The T and q spectra from both types of models are generally too steep, with small-scale variance up to several factors smaller than AIRS. However, the two model analyses more closely resemble AIRS than the two free-running model simulations. Scaling exponents obtained for AIRS column water vapor (CWV) and height-resolved layers of q are also compared to the superparameterized Community Atmospheric Model (SP-CAM), highlighting large differences in the magnitude of CWV variance and the relative flatness of height-resolved q scaling in SP-CAM. Height-resolved q spectra obtained from aircraft observations during the Variability of the American Monsoon Systems Ocean–Cloud–Atmosphere–Land Study Regional Experiment (VOCALS-REx) demonstrate changes in scaling exponents that depend on the observations’ proximity to the base of the subsidence inversion with scale breaks that occur at approximately the dominant cloud scale (~10–30 km). This suggests that finer spatial resolution requirements must be considered for future satellite observations of T and q than those currently planned for infrared and microwave satellite sounders.

Wavelet based multiscale analysis of geophysical downhole measurements: Application to a clayey siliclastic sequence

In order to reveal the structural properties at small scale within a geological unit apparently homogeneous at large scale, we explore the stochastic components of petrophysical measurements recorded in a borehole drilled through the Cretaceous siliclastic units of the South-eastern Basin of France. First, we analyse the instantaneous fluctuations of gamma ray log measurements searching for scaling laws in its power spectrum. Power spectra indicate a scaling behaviour with average exponent βa values mostly falling in the range 1 < βa < 3, a typical fingerprint of fractional Brownian motion. We show that the changes in scaling exponents extracted from the natural gamma ray measurement by a Continuous Wavelet Transform present a close correlation with the stochastic behaviour of radioactive decay processes described by the Poisson's law. Secondly, we investigate the stochastic component of three different electrical resistivity logs. In the space/frequency domain explored by a Continuous Wavelet Transform, their local spectral densities show self-affine proprieties. An integrated statistical analysis of the local variations of the three pseudo-logs extracted from these measurements allows to point out new petrophysical heterogeneity within the silty unit.

Fractal Analyses of Steady Infiltration and Terrain on an Undulating Agricultural Field

Analysis of spatially distributed quasi‐steady infiltration measurements is important because of the effects of infiltration capacity on spatial patterns of soil water, nutrients, and plant development and production. We explored fractal models of quasi‐steady infiltration rates, emphasizing apparent changes in scaling exponents with domain size. Quasi‐steady infiltration rates were measured using single‐ring (0.30‐m‐diameter) constant‐head infiltrometers at 150 locations over 10 landscape positions (30 by 30 m, or approximately 0.1 ha) across a field (approximately 100 ha). At each landscape position, 15 rings were distributed randomly in nested patterns. The field in northeastern Colorado comprises undulating agricultural terrain cropped with dryland winter wheat (Triticum aestivum L.) under conventional tillage. Data were analyzed for multifractal and monofractal behavior. A monofractal model fit the infiltration data best, while terrain attributes other than elevation deviated from monofractals to different degrees. The Hurst exponent (H) was estimated by fitting power‐law variograms at different scales across the field. Values of H changed with the maximum lag distance, peaking near H = 0.9 at approximately 200 m, which represents a typical hillslope length. Spatial persistence in steady infiltration was not observed at long distances (&gt;300 m). Using dense and sparsely sampled terrain attributes as proxy data indicated that the observed spatial scaling of infiltration was not solely due to the clustering of infiltration measurements. These results shed new light on research needed to address spatial variability of soil hydraulic properties, with implications for hillslope process interactions between land areas when modeling distributed infiltration, runoff and run‐on, and plant water use.

Colloidal dynamics on disordered substrates.

Using Langevin simulations, we examine driven colloids interacting with quenched disorder. For weak substrates the colloids form an ordered state and depin elastically. For increasing substrate strength, we find a sharp crossover to inhomogeneous depinning and a substantial increase in the depinning force, analogous to the peak effect in superconductors. The velocity versus driving force curve shows criticality at depinning, with a change in scaling exponent occurring at the order to disorder crossover. Upon application of a sudden pulse of driving force, pronounced transients appear in the disordered regime which are due to the formation of long-lived colloidal flow channels.

A Small-Angle Scattering Study of the Bulk Structure of a Symmetric Diblock Copolymer System

The bulk structure of a homologous series of symmetric polystyrene-polybutadiene (SB) diblock copolymers is investigated using small-angle X-ray and neutron scattering (SANS). The study focuses on the lamellar thickness, the lamellar correlation length and the concentration profile as a function of the chain length and the preparation method applied. The characteristic length, D, scales with the chain length, N, in the whole range studied, but with a clear change in scaling exponent near X N = 29, in accordance with theoretical predictions of a crossover from an Intermediate-Segregation Regime (ISR) to the Strong-Segregation Limit (SSL). In the ISR ( X N≃5 - 29), D is found to scale like D N 0.83 and in the SSL (XN > 29) like D N 0.61 . The temperature dependence of the SANS spectra is studied for a low molar mass sample in an interval around the order-disorder transition temperature (T ODT ). The peak position is found to vary more strongly with temperature than expected for Gaussian chains. Only a weak discontinuity of the peak position at T ODT is observed. In summary, the phase behavior of symmetric SB diblock copolymers in the bulk spans three regimes: the Gaussian regime in the region X N 29.

Structure function as a tool in AE and Dst time series analysis

A new method to analyse the structure function (SF) has been constructed and used in the analysis of the AE time series for the years 1978–85 and Dst time series for 1957–84. It is shown that this SF analysis makes a clear distinction between affine and periodicity dominated time series, and it displays the essential periodicities of the series in a range relevant to its characteristic time scale. The AE time series is found to be affine such that the scaling exponent changes at a time scale of 113 (±9) minutes. On the other hand, in the SF function analysis, the Dst data are dominated by the 24‐hour and 27‐day periods. The 27‐day period is modulated by the annual variation.

Properties of AE data and bicolored noise

A detailed analysis has been made of 13 periods of 20 days of the AE data. The average correlation dimension is found to be 3.4, and the calculated dimension is found to depend on the magnetospheric activity such that more active periods have smaller dimensions. This apparent correlation dimension does not, however, imply that the magnetospheric system behind the AE data is low‐dimensional. On the contrary, bicolored noise is shown to share many properties with the AE data. The AE time series is also found to be self‐affine such that the scaling exponent changes at the time scale of about 2 hours. This same time scale is suggested to appear as a spectral break at about 1/(5 hours) in the power spectrum of the AE data.

Characteristic time scale of auroral electrojet data

The structure function of the AE time series shows that the AE time series is self‐affine such that the scaling exponent changes at the time scale of approximately 113 (±9) minutes. Autocorrelation function is shown to have scaling properties similar to those of the structure function. From this result it can be deduced that the time scale at which the scaling properties of the AE data change should equal the typical autocorrelation time of these data. We find the typical autocorrelation time of the AE data is 118 (±9) minutes. The characteristic time scale of the AE data appears as a spectral break in their power spectrum at a period of about twice the autocorrelation time.