Power laws, Discontinuities and Regional City Size Distributions

Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classics in the city size distributions are snapshots of stable states within urban systems in flux.

Generalized scaling of misorientation angle distributions at meso-scale in deformed materials

Scaling behaviour has been observed at mesoscopic level irrespective of crystal structure, type of boundary and operative micro-mechanisms like slip and twinning. The presence of scaling at the meso-scale accompanied with that at the nano-scale clearly demonstrates the intrinsic spanning for different deformation processes and a true universal nature of scaling. The origin of a 1/2 power law in deformation of crystalline materials in terms of misorientation proportional to square root of strain is attributed to importance of interfaces in deformation processes. It is proposed that materials existing in three dimensional Euclidean spaces accommodate plastic deformation by one dimensional dislocations and their interaction with two dimensional interfaces at different length scales. This gives rise to a 1/2 power law scaling in materials. This intrinsic relationship can be incorporated in crystal plasticity models that aim to span different length and time scales to predict the deformation response of crystalline materials accurately.

Kinetics and Statistical Distributions of Single-Molecule Conformational Dynamics

We developed a coarse-grained yet microscopic detailed model to study the statistical fluctuations of single-molecule protein conformational dynamics of adenylate kinase. We explored the underlying conformational energy landscape and found that the system has two basins of attractions, open and closed conformations connected by two separate pathways. The kinetics is found to be nonexponential, consistent with single-molecule conformational dynamics experiments. Furthermore, we found that the statistical distribution of the kinetic times for the conformational transition has a long power law tail, reflecting the exponential density of state of the underlying landscape. We also studied the joint distribution of the two pathways and found memory effects.

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Are power laws that estimate fractal dimension a good descriptor of soil structure and its link to soil biological properties?

The study of interrelationships between soil structure and its functional properties is complicated by the fact that the quantitative description of soil structure is challenging. Soil scientists have tackled this challenge by taking advantage of approaches such as fractal geometry, which describes soil architectural complexity through a scaling exponent (D) relating mass and numbers of particles/aggregates to particle/aggregate size. Typically, soil biologists use empirical indices such as mean weight diameters (MWD) and percent of water stable aggregates (WSA), or the entire size distribution, and they have successfully related these indices to key soil features such as C and N dynamics and biological promoters of soil structure. Here, we focused on D, WSA and MWD and we tested whether: D estimated by the exponent of the power law of number-size distributions is a good and consistent correlate of MWD and WSA; D carries information that differs from MWD and WSA; the fraction of variation in D that is uncorrelated with MWD and WSA is related to soil chemical and biological properties that are thought to establish interdependence with soil structure (e.g., organic C, N, arbuscular mycorrhizal fungi). We analysed observational data from a broad scale field study and results from a greenhouse experiment where arbuscular mycorrhizal fungi (AMF) and collembola altered soil structure. We were able to develop empirical models that account for a highly significant and large portion of the correlation observed between WSA and MWD but we did not uncover the mechanisms that underlie this correlation. We conclude that most of the covariance between D and soil biotic (AMF, plant roots) and abiotic (C. N) properties can be accounted for by WSA and MWD. This result implies that the ecological effects of the fragmentation properties described by D and generally discussed under the framework of fractal models can be interpreted under the intuitive perspective of simpler indices and we suggest that the biotic components mostly impacted the largest size fractions, which dominate MWD, WSA and the scaling exponent ruling number-size distributions. (C) 2010 Elsevier Ltd. All rights reserved.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Size frequency distributions of β-amyloid (Aβ) deposits:a comparative study of four neurodegenerative disorders

Deposition of ß-amyloid (Aß ), a 'signature' pathological lesion of Alzheimer's disease (AD), is also characteristic of Down's syndrome (DS), and has been observed in dementia with Lewy bodies (DLB) and corticobasal degeneration (CBD). To determine whether the growth of Aß deposits was similar in these disorders, the size frequency distributions of the diffuse ('pre-amyloid'), primitive ('neuritic'), and classic ('dense-cored') A ß deposits were compared in AD, DS, DLB, and CBD. All size distributions had essentially the same shape, i.e., they were unimodal and positively skewed. Mean size of Aß deposits, however, varied between disorders. Mean diameters of the diffuse, primitive, and classic deposits were greatest in DS, DS and CBD, and DS, respectively, while the smallest deposits, on average, were recorded in DLB. Although the shape of the frequency distributions was approximately log-normal, the model underestimated the frequency of smaller deposits and overestimated the frequency of larger deposits in all disorders. A 'power-law' model fitted the size distributions of the primitive deposits in AD, DS, and DLB, and the diffuse deposits in AD. The data suggest: (1) similarities in size distributions of Aß deposits among disorders, (2) growth of deposits varies with subtype and disorder, (3) different factors are involved in the growth of the diffuse/primitive and classic deposits, and (4) log-normal and power-law models do not completely account for the size frequency distributions.

Antarctic icebergs distributions 1992-2014

Basal melting of floating ice shelves and iceberg calving constitute the two almost equal paths of freshwater flux between the Antarctic ice cap and the Southern Ocean. The largest icebergs (>100 km2) transport most of the ice volume but their basal melting is small compared to their breaking into smaller icebergs that constitute thus the major vector of freshwater. The archives of nine altimeters have been processed to create a database of small icebergs (<8 km2) within open water containing the positions, sizes, and volumes spanning the 1992–2014 period. The intercalibrated monthly ice volumes from the different altimeters have been merged in a homogeneous 23 year climatology. The iceberg size distribution, covering the 0.1–10,000 km2 range, estimated by combining small and large icebergs size measurements follows well a power law of slope −1.52 ± 0.32 close to the −3/2 laws observed and modeled for brittle fragmentation. The global volume of ice and its distribution between the ocean basins present a very strong interannual variability only partially explained by the number of large icebergs. Indeed, vast zones of the Southern Ocean free of large icebergs are largely populated by small iceberg drifting over thousands of kilometers. The correlation between the global small and large icebergs volumes shows that small icebergs are mainly generated by large ones breaking. Drifting and trapping by sea ice can transport small icebergs for long period and distances. Small icebergs act as an ice diffuse process along large icebergs trajectories while sea ice trapping acts as a buffer delaying melting.

The constitutional power to make war: domestic legal issues raised by Australia's action in Iraq

The legal power to declare war has traditionally been a part of a prerogative to be exercised solely on advice that passed from the King to the Governor-General no later than 1942. In 2003, the Governor- General was not involved in the decision by the Prime Minister and Cabinet to commit Australian troops to the invasion of Iraq. The authors explore the alternative legal means by which Australia can go to war - means the government in fact used in 2003 - and the constitutional basis of those means. While the prerogative power can be regulated and/or devolved by legislation, and just possibly by practice, there does not seem to be a sound legal basis to assert that the power has been devolved to any other person. It appears that in 2003 the Defence Minister used his legal powers under the Defence Act 1903 (Cth) (as amended in 1975) to give instructions to the service head(s). A powerful argument could be made that the relevant sections of the Defence Act were not intended to be used for the decision to go to war, and that such instructions are for peacetime or in bello decisions. If so, the power to make war remains within the prerogative to be exercised on advice. Interviews with the then Governor-General indicate that Prime Minister Howard had planned to take the matter to the Federal Executive Council 'for noting', but did not do so after the Governor-General sought the views of the then Attorney-General about relevant issues of international law. The exchange raises many issues, but those of interest concern the kinds of questions the Governor-General could and should ask about proposed international action and whether they in any way mirror the assurances that are uncontroversially required for domestic action. In 2003, the Governor-General's scrutiny was the only independent scrutiny available because the legality of the decision to go to war was not a matter that could be determined in the High Court, and the federal government had taken action in March 2002 that effectively prevented the matter coming before the International Court of Justice

Characteristics of airborne ultrafine and coarse particles during the Australian dust storm of 23 September 2009

Particle number concentrations and size distributions, visibility and particulate mass concentrations and weather parameters were monitored in Brisbane, Australia, on 23 September 2009, during the passage of a dust storm that originated 1400 km away in the dry continental interior. The dust concentration peaked at about mid-day when the hourly average PM2.5 and PM10 values reached 814 and 6460 µg m-3, respectively, with a sharp drop in atmospheric visibility. A linear regression analysis showed a good correlation between the coefficient of light scattering by particles (Bsp) and both PM10 and PM2.5. The particle number in the size range 0.5-20 µm exhibited a lognormal size distribution with modal and geometrical mean diameters of 1.6 and 1.9 µm, respectively. The modal mass was around 10 µm with less than 10% of the mass carried by particles smaller than 2.5 µm. The PM10 fraction accounted for about 68% of the total mass. By mid-day, as the dust began to increase sharply, the ultrafine particle number concentration fell from about 6x103 cm-3 to 3x103 cm-3 and then continued to decrease to less than 1x103 cm-3 by 14h, showing a power-law decrease with Bsp with an R2 value of 0.77 (p<0.01). Ultrafine particle size distributions also showed a significant decrease in number during the dust storm. This is the first scientific study of particle size distributions in an Australian dust storm.

Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion

Small-angle and ultra-small-angle neutron scattering (SANS and USANS), low-pressure adsorption (N2 and CO2), and high-pressure mercury intrusion measurements were performed on a suite of North American shale reservoir samples providing the first ever comparison of all these techniques for characterizing the complex pore structure of shales. The techniques were used to gain insight into the nature of the pore structure including pore geometry, pore size distribution and accessible versus inaccessible porosity. Reservoir samples for analysis were taken from currently-active shale gas plays including the Barnett, Marcellus, Haynesville, Eagle Ford, Woodford, Muskwa, and Duvernay shales. Low-pressure adsorption revealed strong differences in BET surface area and pore volumes for the sample suite, consistent with variability in composition of the samples. The combination of CO2 and N2 adsorption data allowed pore size distributions to be created for micro–meso–macroporosity up to a limit of �1000 Å. Pore size distributions are either uni- or multi-modal. The adsorption-derived pore size distributions for some samples are inconsistent with mercury intrusion data, likely owing to a combination of grain compression during high-pressure intrusion, and the fact that mercury intrusion yields information about pore throat rather than pore body distributions. SANS/USANS scattering data indicate a fractal geometry (power-law scattering) for a wide range of pore sizes and provide evidence that nanometer-scale spatial ordering occurs in lower mesopore–micropore range for some samples, which may be associated with inter-layer spacing in clay minerals. SANS/USANS pore radius distributions were converted to pore volume distributions for direct comparison with adsorption data. For the overlap region between the two methods, the agreement is quite good. Accessible porosity in the pore size (radius) range 5 nm–10 lm was determined for a Barnett shale sample using the contrast matching method with pressurized deuterated methane fluid. The results demonstrate that accessible porosity is pore-size dependent.

Non-Newtonian mixed convection flow from a horizontal circular cylinder with uniform surface heat flux

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.