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1

Comments regarding the binary power law for heterogeneity of disease incidence.

The binary power law (BPL) has been successfully used to characterize heterogeneity (overdispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial distribution over the range of incidence values, and the estimated scale (?) and slope (b) parameters provide information on the characteristics of aggregation. When b = 1, the interpretation is that the degree of aggregation remains constant over the range of incidence values observed; otherwise, aggregation is variable. In two articles published in this journal in 2009, Gosme and Lucas used their stochastic simulation model, Cascade, to show a multiphasic (split-line) relationship of the variances, with straight-line (linear) relationships on a log-log scale within each phase. In particular, they showed a strong break point in the lines at very low incidence, with b considerably >1 in the first line segment (corresponding to a range of incidence values usually not observed in the field), and b being ?1 in the next segment (corresponding to the range of incidence values usually observed). We evaluated their findings by utilizing a general spatially explicit stochastic simulator developed by Xu and Ridout in 1998, with a wide range of median dispersal distances for the contact distribution and number of plants in the sampling units (quadrats), and through an assessment of published BPL results. The simulation results showed that the split-line phenomenon can occur, with a break point at incidence values of ?0.01; however, the split is most obvious for short median dispersal distances and large quadrat sizes. However, values of b in the second phase were almost always >1, and only approached 1 with extremely short median dispersal distances and small quadrat sizes. An appraisal of published results showed no evidence of multiple phases (although the minimum incidence may generally be too high to observe the break), and estimates of b were almost always >1. Thus, it appears that the results from the Cascade simulation model represent a special epidemiological case, corresponding primarily to a roughly nearest-neighbor population-dynamic process. Implications of a multiphasic BPL property may be important and are discussed. PMID:21864088

Turechek, W W; Madden, L V; Gent, D H; Xu, X-M

2011-12-01

2

Since its introduction by Svensson in 1959, the power law curve y = axb (where x and y are horizontal and vertical direction, respectively) has been widely used in morphological analysis of glacial trough cross-profiles. The numerical constants a and b are obtained by a linear regression analysis of the logarithmic form of the power law curve (ln y =

Frank Pattyn; Wim van Huele

1998-01-01

3

NASA Astrophysics Data System (ADS)

We consider the scaling behaviors for fluctuations of the number of Korean firms bankrupted in the period from 1 August 2002 to 28 October 2003. We observe a power law for the distribution of the number of the bankrupted firms. The Pareto exponent is close to unity. We also consider the daily increments of the number of firms bankrupted. The probability distribution of the daily increments for the firms bankrupted follows the Gaussian distribution in central part and has a fat tail. The tail parts of the probability distribution of the daily increments for the firms bankrupted follow a power law.

Hong, Byoung Hee; Lee, Kyoung Eun; Lee, Jae Woo

2007-01-01

4

Power Laws in Firm Productivity

NASA Astrophysics Data System (ADS)

We estimate firm productivity for about 3.2 million firms from30 countries. We find that the distribution of firm productivity in each country, which is measured by total factor productivity (TFP), has a power law upper tail. However, the power law exponent of a TFP distribution in a country tends to be greater than that of a sales distribution in that country, indicating that the upper tail of a TFP distribution is less heavy compared to that of a sales distribution. We also find that the power law exponent of a TFP distribution tends to be greater than the power law exponents associated with the number of workers or tangible fixed assets. Given the idea that the sales of a firm is determined by the amount of various inputs employed by the firm (i.e., ``production function'' in the terminology of economics), these results suggest that the heavy tail of a sales distribution in a country comes not from the tail of a TFP distribution, but from the tail of the distribution of the number of workers or tangible fixed assets.

Mizuno, T.; Ishikawa, A.; Fujimoto, S.; Watanabe, T.

5

Quantum dissipation from power-law memory

NASA Astrophysics Data System (ADS)

A new quantum dissipation model based on memory mechanism is suggested. Dynamics of open and closed quantum systems with power-law memory is considered. The processes with power-law memory are described by using integration and differentiation of non-integer orders, by methods of fractional calculus. An example of quantum oscillator with linear friction and power-law memory is considered.

Tarasov, Vasily E.

2012-06-01

6

First law of mechanics for black hole binaries with spins

NASA Astrophysics Data System (ADS)

We use the canonical Hamiltonian formalism to generalize to spinning point particles the first law of mechanics established for binary systems of nonspinning point masses moving on circular orbits [A. Le Tiec, L. Blanchet, and B. F. Whiting, Phys. Rev. D 85, 064039 (2012)PRVDAQ1550-7998]. We find that the redshift observable of each particle is related in a very simple manner to the canonical Hamiltonian and, more generally, to a class of Fokker-type Hamiltonians. Our results are valid through linear order in the spin of each particle, but hold also for quadratic couplings between the spins of different particles. The knowledge of spin effects in the Hamiltonian allows us to compute spin-orbit terms in the redshift variable through 2.5PN order, for circular orbits and spins aligned or anti-aligned with the orbital angular momentum. To describe extended bodies such as black holes, we supplement the first law for spinning point-particle binaries with some “constitutive relations” that can be used for diagnosis of spin measurements in quasi-equilibrium initial data.

Blanchet, Luc; Buonanno, Alessandra; Le Tiec, Alexandre

2013-01-01

7

Power-law stellar distributions

NASA Astrophysics Data System (ADS)

The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power-law distribution suggested by the nonextensive kinetic theory. There are two different classes of solutions. The first class behaves like a subset of the polytropic Lane Emden spheres, whereas the second one corresponds to a transition between two different potytropic indices. Unlike the isothermal Maxwellian sphere, the total mass and sizes of both classes are finite for a large range of the nonextensive q-parameter.

Lima, J. A. S.; de Souza, R. E.

2005-05-01

8

Accretion-powered Compact Binaries

NASA Astrophysics Data System (ADS)

Preface; The workshop logo; A short history of the CV workshop F. A. Córdova; Part I. Observations: 1. Low mass x-ray binaries A. P. Cowley, P. C. Schmidtke, D. Crampton, J. B. Hutchings, C. A. Haswell, E. L. Robinson, K. D. Horne, H. M. Johnston, S. R. Kulkarni, S. Kitamoto, X. Han, R. M. Hjellming, R. M. Wagner, S. L. Morris, P. Hertz, A. N. Parmar, L. Stella, P. Giommi, P. J. Callanan, T. Naylor, P. A. Charles, C. D. Bailyn, J. N. Imamura, T. Steiman-Cameron, J. Kristian, J. Middleditch, L. Angelini and J. P. Noris; 2. Nonmagnetic cataclysmic variables R. S. Polidan, C. W. Mauche, R. A. Wade, R. H. Kaitchuck, E. M. Schlegel, P. A. Hantzios, R. C. Smith, J. H. Wood, F. Hessman, A. Fiedler, D. H. P. Jones, J. Casares, P. A. Charles, J. van Paradijs, E. Harlaftis, T. Naylor, G. Sonneborn, B. J. M. Hassall, K. Horne, C. A. la Dous, A. W. Shafter, N. A. Hawkins, D. A. H. Buckley, D. J. Sullivan, F. V. Hessman, V. S. Dhillon, T. R. Marsh, J. Singh, S. Seetha, F. Giovannelli, A. Bianchini, E. M. Sion, D. J. Mullan, H. L. Shipman, G. Machin, P. J. Callanan, S. B. Howell, P. Szkody, E. M. Schlegel and R. F. Webbink; 3. Magnetic cataclysmic variables C. Hellier, K. O. Mason, C. W. Mauche, G. S. Miller, J. C. Raymond, F. K. Lamb, J. Patterson, A. J. Norton, M. G. Watson, A. R. King, I. M. McHardy, H. Lehto, J. P. Osborne, E. L. Robinson, A. W. Shafter, S. Balachandran, S. R. Rosen, J. Krautter, W. Buchholz, D. A. H. Buckley, I. R. Tuoly, D. Crampton, B. Warner, R. M. Prestage, B. N. Ashoka, M. Mouchet, J. M. Bonnet-Bidaud, J. M. Hameury, P. Szkody, P. Garnavich, S. Howell, T. Kii, M. Cropper, K. Mason, J. Bailey, D. T. Wickramasinghe, L. Ferrario, K. Beuermann, A. D. Schwope, H.-C. Thomas, S. Jordan, J. Schachter, A. V. Filippenko, S. M. Kahn, F. B. S. Paerels, K. Mukai, M. L. Edgar, S. Larsson, R. F. Jameson, A. R. King, A. Silber, R. Remillard, H. Bradt, M. Ishida, T. Ohashi and G. D. Schmidt; Part II. Accretion Theory: 4. Nonmagnetic W. Kley, F. Geyer, H. Herold, H. Ruder, R. Whitehurst, A. King, J. C. Wheeler, S. Mineshige, M. Huang, S. W. Kim, Y. Tuchman, T. R. Kallman and J. A. Woods; 5. Magnetic M. T. Wolff, J. N. Imamura, K. S. Wood, J. H. Gardner, S. J. Litchfield, J. J. Brainerd, G. Chanmugan, K. Wu, J. Frank, T. Hanawa, K. Hirotani and N. Kawai; Part III. Novae S. Starrfield, R. M. Hjellming, A. B. Tomaney, A. W. Shafter, A. Cassatella, P. L. Selvelli, R. Gilmozzi, A. Bianchini, M. Friedjung, H. Ritter, M. J. Politano, M. Livio, R. F. Webbink, K. Horne, W. F. Welsh, R. A. Wade, J. Krauttler, M. A. J. Snijders, N. Vogt, L. H. Barrera, H. Barwig, K.-H Mantel, R. Gilmozzi, A. Shankar, A. Burkert, J. W. Truran and J. Hayes: Part IV. Evolution I. Iben Jr, M. S. Hjellming, R. E. Taam, M. Politano, F. D'Antona, I. Mazzitelli, H. Ritter, J. M. Hameury, A. R. King, J. P. Lasota, R. Popham, R. Narayan, J. Isern, J. Laybay, R. Canal, D. García, A. S. Fruchter, S. R. Kulkarni, R. W. Romani, A. Ray, W. Kluzniak, S. Miyaji and G. Chanmugam; Subject index; Star index.

Mauche, Christopher W.

2003-12-01

9

Power-Law Relaxation and Cumulative Information

NASA Astrophysics Data System (ADS)

We associate the cumulative information of a system relaxing towards equilibrium with a divergent integral when a power-law relaxation holds. We discuss and illustrate numerically how this implies that a system that relaxes to equilibrium through a power-law has a cumulative information content that progressively diverges from that of its equilibrium realization to which it is relaxing. Our findings shed light on some aspects of weak ergodicity breaking and suggest that power-laws imply a form of complexity that does not require dissipation or built-in disorder.

Di Porto, P.; Di Sabatino, S.; Crosignani, B.; DelRe, E.

2013-11-01

10

Power law inflation with electromagnetism

We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ?{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}?U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},?{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,?,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ?{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.

Luo, Xianghui; Isenberg, James, E-mail: isenberg@uoregon.edu

2013-07-15

11

The first and second laws of thermodynamics were used to analyze a novel thermodynamic cycle proposed by Goswami in 1995 that uses an ammonia–water binary mixture as the working fluid, while producing both power and refrigeration simultaneously. The thermodynamic performance of the cycle was optimized for maximum second law efficiency using a commercially available optimization program. A maximum second law

Afif Akel Hasan; D. Yogi Goswami; Sanjay Vijayaraghavan

2002-01-01

12

A probabilistic walk up power laws

NASA Astrophysics Data System (ADS)

We establish a path leading from Pareto’s law to anomalous diffusion, and present along the way a panoramic overview of power-law statistics. Pareto’s law is shown to universally emerge from “Central Limit Theorems” for rank distributions and exceedances, and is further shown to be a finite-dimensional projection of an infinite-dimensional underlying object - Pareto’s Poisson process. The fundamental importance and centrality of Pareto’s Poisson process is described, and we demonstrate how this process universally generates an array of anomalous diffusion statistics characterized by intrinsic power-law structures: sub-diffusion and super-diffusion, Lévy laws and the “Noah effect”, long-range dependence and the “Joseph effect”, 1/f noises, and anomalous relaxation.

Eliazar, Iddo; Klafter, Joseph

2012-02-01

13

Hierarchical networks, power laws, and neuronal avalanches

NASA Astrophysics Data System (ADS)

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions--even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.

Friedman, Eric J.; Landsberg, Adam S.

2013-03-01

14

Power Laws in Financial Time Series

We attempt empirical detection and characterization of power laws in financial time series. Fractional Brownian motion is defined. After testing for multifractality we calculate the multifractal spectrum of the series. The multifractal nature of stock prices leads to volatility clus- tering (conditional heteroscedasticity) and long memory (slowly decaying autocorrelation). Wavelet Transform Modulus Maxima approach to mul- tifractal spectrum estimation proved

Rossitsa Yalamova; Liu Qi; Yudong Chen; Chenwei Wang; Lin Wang; Qiao Wang

2007-01-01

15

Information Ranking and Power Laws on Trees

We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on trees; and the second one is based on a direct sample path large deviations analysis of weighted recursive random sums. We believe

Predrag R. Jelenkovic; Mariana Olvera-Cravioto

2009-01-01

16

Bach, breasts, and power-law processes

NASA Astrophysics Data System (ADS)

Both the natural and manmade worlds abound with processes that have power-law spectra of the form, P(f)equalsK/f(beta ). Statistical properties of such processes are dramatically different from those of smoothed Gaussian random processes. There is an extreme concentration of spectral power at low frequencies and a unique correlation distance does not exist. In addition, processes that do not have a low frequency cutoff have infinite (undefined) variance for infinite data sets. The fact that mammographic structure has a power-law spectrum does not tell one a great deal about the underlying process that generated the structure. Many different processes can have the same second order statistics, example classes are: deterministic, stochastic, self-similar, self-affine, and chaotic. It will be necessary to develop or adapt a variety of analytical techniques to investigate the nature of mammographic statistics. Some examples of power-law processes will be described and some statistical properties of mammograms will be presented.

Burgess, Arthur E.

2001-06-01

17

Laws of power industry development: Elusory essence

NASA Astrophysics Data System (ADS)

Ideas, hopes, and disappointments related to a quarter-century research into the laws of power industry development and its relations with society are reviewed; new hypotheses concerning the character and characteristics of these relations are formulated, and some preliminary results of the quantitative verification of these hypotheses are presented. The scope of future investigations is outlined and difficulties encountered in the attempts to collect the necessary retrospective information are considered.

Makarov, Aleksei A.; Makarov, Aleksandr A.

2010-12-01

18

Gibbsian Theory of Power-Law Distributions

It is shown that power-law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium, which are expected to occur in collisionless plasmas containing fully developed quasistationary turbulence. Gibbsian theory is extended on the fundamental level to statistically dependent subsystems introducing an 'ordering parameter' {kappa}. Particular forms for the entropy and partition functions are derived with superadditive (nonextensive) entropy, and a redefinition of temperature in such systems is given.

Treumann, R. A. [Department of Geophysics and Environmental Sciences, Munich University, D-80333 Munich (Germany); Department of Physics, Dartmouth College, Hanover, New Hampshire 03755 (United States); Jaroschek, C. H. [Department Earth and Planetary Science, University of Tokyo, Tokyo (Japan)

2008-04-18

19

Power-law distributions from additive preferential redistributions

NASA Astrophysics Data System (ADS)

We introduce a nongrowth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed N -particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.

Ree, Suhan

2006-02-01

20

Power law distributions of seismic rates

NASA Astrophysics Data System (ADS)

We report an empirical determination of the probability density functions Pdata( r) of the number r of earthquakes in finite space-time windows for the California catalog for different space (5 × 5 to 50 × 50 km 2) and time intervals (0.1 to 1000 days). The data can be represented by asymptotic power law tails together with several cross-overs reasonably explained by one of the most used reference model in seismology (ETAS), which assumes that each earthquake can trigger other earthquakes according to complex cascades. These results are useful to constrain the physics of earthquakes and to estimate the performance of forecasting models of seismicity.

Saichev, A.; Sornette, D.

2007-02-01

21

Anisotropic power-law k-inflation

NASA Astrophysics Data System (ADS)

It is known that power-law k-inflation can be realized for the Lagrangian P=Xg(Y), where X=-(??)2/2 is the kinetic energy of a scalar field ? and g is an arbitrary function in terms of Y=Xe??/Mpl (? is a constant and Mpl is the reduced Planck mass). In the presence of a vector field coupled to the inflaton with an exponential coupling f(?)?e??/Mpl, we show that the models with the Lagrangian P=Xg(Y) generally give rise to anisotropic inflationary solutions with ?/H=constant, where ? is an anisotropic shear and H is an isotropic expansion rate. Provided these anisotropic solutions exist in the regime where the ratio ?/H is much smaller than 1, they are stable attractors irrespective of the forms of g(Y). We apply our results to concrete models of k-inflation such as the generalized dilatonic ghost condensate and the Dirac-Born-Infeld model and we numerically show that the solutions with different initial conditions converge to the anisotropic power-law inflationary attractors. Even in the de Sitter limit (??0) such solutions can exist, but in this case the null energy condition is generally violated. The latter property is consistent with the Wald’s cosmic conjecture stating that the anisotropic hair does not survive on the de Sitter background in the presence of matter respecting the dominant/strong energy conditions.

Ohashi, Junko; Soda, Jiro; Tsujikawa, Shinji

2013-11-01

22

Finite disks with power-law potentials

NASA Astrophysics Data System (ADS)

We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, cutoff at some radius R0. First we discuss circular disks whose circular rotation speed upsilon proportional to ralpha, with any alpha greater than -1/2. The surface-density of the disks is expressed in terms of hypergeometric functions of the radius. The disk then has the same rotation curve as the sphere within the cutoff radius (up to a constant factor). We give expressions for the full three-dimensional potentials in terms of hypergeometric functions of two variables. We express the potential and acceleration in the plane at r greater than R0, and along the rotation axis, in terms of simple hypergeometric functions. All the multipoles of the disk are given. We then generalize to nonaxisymmetric disks with midplane axis ratio p less than 1. The potential in the midplane is given by psi(r, phi)proportional to r2 alphaF1(alpha + 1/2 - alpha, alpha + 1/2, alpha + 1; tau sin2 phi, tau) + c, where F1 is the hypergeometric function of two variables, and tau = 1 - p2. For integer values of 2 alpha the above quantities are given in more elementary terms. All these results follow straightforwardly from formulae we derive for the general, cutoff, power-law, triaxial ellipsoid. Linear combinations of our single-power disks are also useful. In particular, we describe such disks whose surface density vanishes at the edge more smoothly.

Brada, Rafael; Milgrom, Mordehai

1995-05-01

23

Fractional power-law spatial dispersion in electrodynamics

NASA Astrophysics Data System (ADS)

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb's law and Debye's screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type.

Tarasov, Vasily E.; Trujillo, Juan J.

2013-07-01

24

In the crystallization of highly diluted macroscopic binary solid solutions in the region of low supercooling in each layer of the transition region in practice only one spontaneous thermal equilibrium fluctuation is possible and, as a result, the concentration of particles in the solid state takes the mean value of the concentration calculated for the case of the corresponding binary microsystems. The growth kinetics of crystals of highly diluted macroscopic binary solid solutions (a particular form of binary metallic macrosystems) in the region of low supercooling of the system binary melt-crystal are described by the normal law (v = K ..delta..T) due to the action of the mechanism of spontaneous fluctuations with a limited spectrum of changes in the concentration of solid particles in the layers of the two-phase transition zone. An expression is obtained for the kinetic coefficient of the normal law of crystallization in the case of highly diluted macroscopic binary solid solutions.

Baikov, Yu.A.; Zelenev, Yu.V.

1987-03-01

25

Fractional power-law spatial dispersion in electrodynamics

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media.

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation); Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain); Trujillo, Juan J., E-mail: jtrujill@ullmat.es [Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain)

2013-07-15

26

A (varying power)-law modified gravity

NASA Astrophysics Data System (ADS)

In the present paper, we analyze a toy model for f(? ,R) gravity which has the form of a power-law modified gravity in which the exponent is space-time dependent. Namely, we investigate the effects of adding to the Hilbert-Einstein action an R? term. We present possible equivalences of the model with known models of modified gravity theories and examine the problem of matter stability in this model. Like f(R)-gravity toy models, the present one offers the possibility of unifying the early- and the late-time evolution of the Universe. We show that the behavior of the scalar field depends globally on the size of the Universe and locally on the surrounding environment. For the early Universe a huge cosmological constant appears that might drive inflation. For the late times a tiny cosmological constant appears globally.

Hammad, Fayçal

2014-02-01

27

Power Law Mapping in Human Area Perception

NASA Astrophysics Data System (ADS)

We investigate how humans visually perceive and approximate area or space allocation through visual area experiments. The participants are asked to draw a circle concentric to the reference circle on the monitor screen using a computer mouse with area measurements relative to the area of the reference circle. The activity is repeated for triangle, square and hexagon. The area estimated corresponds to the area estimates of a participant (perceived) for a corresponding requested area to be drawn (stimulus). The area estimated fits very well (goodness of fit R2 > 0.97) to a power law given by r2? where r is the radius of the circle or the distance of the edge for triangle, square and hexagon. The power law fit demonstrates that for all shapes sampled, participants underestimated area for stimulus that are less than ~100% of the reference area and overestimated area for stimulus greater than ~100% of the reference area. The value of ? is smallest for the circle (?? ? 1.33) and largest for triangle (?? ? 1.56) indicating that in the presence of a reference area with the same shape, circle is perceived to be smallest among the figures considered when drawn bigger than the reference area, but largest when drawn smaller than the reference area. We also conducted experiments on length estimation and consistent with the results of Dehaene et al., Science 2008, we recover a linear relationship between the perceived length and the stimulus. We show that contrary to number mapping into space and/or length perception, human's perception of area is not corrected by the introduction of cultural interventions such as formal education.

Longjas, Anthony; Legara, Erika Fille; Monterola, Christopher

28

Power-law creep model for densification of powder compacts

Densification behaviour of powder compacts by power-law creep during pressure-assisted compaction at an elevated temperature was investigated. A constitutive model was proposed for the densification behavior of powder compacts under a power-law creep situation based on the plastic deformation theory for porous materials which satisfies the uniaxial stress condition. The proposed power-law creep model is compared with Shima and Oyane’s

Hyoung Seop Kim; Dong Nyung Lee

1999-01-01

29

Power-law spatial dispersion from fractional Liouville equation

NASA Astrophysics Data System (ADS)

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

Tarasov, Vasily E.

2013-10-01

30

Power-law spatial dispersion from fractional Liouville equation

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)] [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

2013-10-15

31

Stochastic model of Zipf's law and the universality of the power-law exponent

NASA Astrophysics Data System (ADS)

We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.

Yamamoto, Ken

2014-04-01

32

Equipment of the binary-cycle geothermal power unit at the Pauzhet geothermal power station

NASA Astrophysics Data System (ADS)

The equipment of and technological processes in the pilot industrial model of the domestically produced binary-cycle geothermal power unit operating on the discharge separate at the Pauzhet geothermal power station are considered. The development principles, the design and operational features, and the data on selecting the metal in manufacturing the main equipment of the 2.5-MW binary power unit of the geothermal power station are described.

Tomarov, G. V.; Nikol'skii, A. I.; Semenov, V. N.; Shipkov, A. A.

2014-06-01

33

Low Power Reversible Parallel Binary Adder\\/Subtractor

In recent years, Reversible Logic is becoming more and more prominent technology having its applications in Low Power CMOS, Quantum Computing, Nanotechnology, and Optical Computing. Reversibility plays an important role when energy efficient computations are considered. In this paper, Reversible eight-bit Parallel Binary Adder\\/Subtractor with Design I, Design II and Design III are proposed. In all the three design approaches,

H G Rangaraju; U. Venugopal; K N Muralidhara; K B Raja

2010-01-01

34

Double power laws in income and wealth distributions

NASA Astrophysics Data System (ADS)

Close examination of wealth distributions reveal the existence of two distinct power law regimes. The Pareto exponents of the super-rich, identified, for example in rich lists such as provided by Forbes, are smaller than the Pareto exponents obtained for top earners in income data sets. Our extension of the Slanina model of wealth is able to reproduce these double power law features.

Coelho, Ricardo; Richmond, Peter; Barry, Joseph; Hutzler, Stefan

2008-06-01

35

Functionality, power-laws and defect evolution in software systems

In a previous paper, an intimate link between power-law distri- bution of component sizes and defect growth in maturing software systems, independently of their representation language, was revealed by the use of a variational method built on statistical mechanical ar- guments. Building on the above work, this paper first of all demonstrates ex- perimentally that power-law behaviour in component sizes

Les Hatton

36

Distortion of power law blinking with binning and thresholding

NASA Astrophysics Data System (ADS)

Fluorescence intermittency is a random switching between emitting (on) and non-emitting (off) periods found for many single chromophores such as semiconductor quantum dots and organic molecules. The statistics of the duration of on- and off-periods are commonly determined by thresholding the emission time trace of a single chromophore and appear to be power law distributed. Here we test with the help of simulations if the experimentally determined power law distributions can actually reflect the underlying statistics. We find that with the experimentally limited time resolution real power law statistics with exponents ?on/off ? 1.6, especially if ?on ? ?off would not be observed as such in the experimental data after binning and thresholding. Instead, a power law appearance could simply be obtained from the continuous distribution of intermediate intensity levels. This challenges much of the obtained data and the models describing the so-called power law blinking.

Amecke, Nicole; Heber, André; Cichos, Frank

2014-03-01

37

Resurrecting power law inflation in the light of Planck results

NASA Astrophysics Data System (ADS)

It is well known that a canonical scalar field with an exponential potential can drive power law inflation (PLI). However, the tensor-to-scalar ratio in such models turns out to be larger than the stringent limit set by recent Planck results. We propose a new model of power law inflation for which the scalar spectra index, the tensor-to-scalar ratio and the non-gaussianity parameter fNLequil are in excellent agreement with Planck results. Inflation, in this model, is driven by a non-canonical scalar field with an inverse power law potential. The Lagrangian for our model is structurally similar to that of a canonical scalar field and has a power law form for the kinetic term. A simple extension of our model resolves the graceful exit problem which usually afflicts models of power law inflation.

Unnikrishnan, Sanil; Sahni, Varun

2013-10-01

38

Do wealth distributions follow power laws? Evidence from ‘rich lists’

NASA Astrophysics Data System (ADS)

We use data on the wealth of the richest persons taken from the ‘rich lists’ provided by business magazines like Forbes to verify if the upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover the world’s richest persons over 1996-2012, the richest Americans over 1988-2012, the richest Chinese over 2006-2012, and the richest Russians over 2004-2011. Using a recently introduced comprehensive empirical methodology for detecting power laws, which allows for testing the goodness of fit as well as for comparing the power-law model with rival distributions, we find that a power-law model is consistent with data only in 35% of the analysed data sets. Moreover, even if wealth data are consistent with the power-law model, they are usually also consistent with some rivals like the log-normal or stretched exponential distributions.

Brzezinski, Michal

2014-07-01

39

Distortion of power law blinking with binning and thresholding.

Fluorescence intermittency is a random switching between emitting (on) and non-emitting (off) periods found for many single chromophores such as semiconductor quantum dots and organic molecules. The statistics of the duration of on- and off-periods are commonly determined by thresholding the emission time trace of a single chromophore and appear to be power law distributed. Here we test with the help of simulations if the experimentally determined power law distributions can actually reflect the underlying statistics. We find that with the experimentally limited time resolution real power law statistics with exponents ?(on/off) ? 1.6, especially if ?(on) ? ?(off) would not be observed as such in the experimental data after binning and thresholding. Instead, a power law appearance could simply be obtained from the continuous distribution of intermediate intensity levels. This challenges much of the obtained data and the models describing the so-called power law blinking. PMID:24655179

Amecke, Nicole; Heber, André; Cichos, Frank

2014-03-21

40

Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to ?1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling (“finite size” effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to ?1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

41

Power-law decreasing in solutions of the Boltzmann equation

NASA Astrophysics Data System (ADS)

We analyze the evolution of distribution functions with a power-law decrease at large energies. We apply the temperature transform approach and show that these decays correspond to branch points of the transformed function. For the very hard particle (VHP) model we find that an initial condition with power-law decrease relaxes to an exponential one immediately for t > 0. For Maxwell models we study the displacement of the branch points and find that the power-law decrease is preserved as time elapses.

Zanette, D.; Garibotti, C. R.; Barrachina, R. O.

1987-02-01

42

A Cosmic Coincidence: The Power-law Galaxy Correlation Function

NASA Astrophysics Data System (ADS)

We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of ?(r), the galaxy two-point correlation function. While ?(r) at large scales is set by primordial fluctuations, departures from a power law are governed by galaxy pair counts at small scales, subject to nonlinear dynamics. We assume that galaxies reside within dark matter halos and subhalos. Therefore, the shape of the correlation function at small scales depends on the amount of halo substructure. We use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal mass loss and, to a lesser extent, dynamical friction dramatically deplete the number of subhalos within larger host halos over time, resulting in a ~90% reduction by z = 0 compared to the number of distinct mergers that occur during the assembly of a host halo. We show that these nonlinear processes resulting in this depletion are essential for achieving a power law ?(r). We investigate how the shape of ?(r) depends on subhalo mass (or luminosity) and redshift. We find that ?(r) breaks from a power law at high masses, implying that only galaxies of luminosities <~ L * should exhibit power-law clustering. Moreover, we demonstrate that ?(r) evolves from being far from a power law at high redshift, toward a near power-law shape at z = 0. We argue that ?(r) will once again evolve away from a power law in the future. This is in large part caused by the evolving competition between the accretion and destruction rates of subhalos over time, which happen to strike just the right balance at z ? 0. We then investigate the conditions required for ?(r) to be a power law in a general context. We use the halo model, along with simple parameterizations of the halo occupation distribution, to probe galaxy occupation at various masses and redshifts. We show that the key ingredients determining the shape of ?(r) are the fraction of galaxies that are satellites, the relative difference in mass between the halos of isolated galaxies and halos that contain a single satellite on average, and the rareness of halos that host galaxies. These pieces are intertwined and we find no simple, universal rule for which a power law ?(r) will occur. However, we do show that the physics responsible for setting the galaxy content of halos do not care about the conditions needed to achieve a power law ?(r) and that these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of ?(r) for L * and fainter galaxy samples at low redshift is a cosmic coincidence.

Watson, Douglas F.; Berlind, Andreas A.; Zentner, Andrew R.

2011-09-01

43

Power-law distribution of family names in Japanese societies

NASA Astrophysics Data System (ADS)

We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total number of different family names in a society scales as a power law of the population, (ii) the total number of family names of the same size decreases as the size increases with a power law and (iii) the relation between size and rank of a family name also shows a power law. These scaling properties are found to be consistent for five different regional communities in Japan.

Miyazima, Sasuke; Lee, Youngki; Nagamine, Tomomasa; Miyajima, Hiroaki

2000-04-01

44

Power-law inflation from the rolling tachyon

Modeling the potential by an inverse square law in terms of the tachyon field [V(T)=betaT-2] we find an exact solution for a spatially flat isotropic universe. We show that for beta>2(3)\\/3 the model undergoes power-law inflation. A way to construct other exact solutions is specified and exemplified.

Alexander Feinstein; F ´ õsica Teorica

2002-01-01

45

Low Power Reversible Parallel Binary Adder\\/Subtractor

In recent years, Reversible Logic is becoming more and more prominent\\u000atechnology having its applications in Low Power CMOS, Quantum Computing,\\u000aNanotechnology, and Optical Computing. Reversibility plays an important role\\u000awhen energy efficient computations are considered. In this paper, Reversible\\u000aeight-bit Parallel Binary Adder\\/Subtractor with Design I, Design II and Design\\u000aIII are proposed. In all the three design approaches,

H. G. Rangaraju; U. Venugopal; K. N. Muralidhara; K. B. Raja

2010-01-01

46

Fractal ladder models and power law wave equations

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters.

Kelly, James F.; McGough, Robert J.

2009-01-01

47

Singularity problems of the power law for modeling creep compliance

NASA Technical Reports Server (NTRS)

An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.

Dillard, D. A.; Hiel, C.

1985-01-01

48

Hidden power law patterns in the top European football leagues

NASA Astrophysics Data System (ADS)

Because sports are stylized combat, sports may follow power laws similar to those found for wars, individual clashes, and acts of terrorism. We show this fact for football (soccer) by adjusting power laws that show a close relationship between rank and points won by the clubs participating in the latest seasons of the top fifteen European football leagues. In addition, we use Shannon entropy for gauging league competitive balance. As a result, we are able to rank the leagues according to competitiveness.

Da Silva, Sergio; Matsushita, Raul; Silveira, Eliza

2013-11-01

49

Power-Law Scaling in the Brain Surface Electric Potential

Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form from 80 to 500 Hz. This scaling index, , is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, , increases. We observe a “knee” in the spectra at , implying the existence of a characteristic time scale . Below , we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory “asynchronous,” scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent “synchronous” rhythm-based paradigm.

Miller, Kai J.; Sorensen, Larry B.; Ojemann, Jeffrey G.; den Nijs, Marcel

2009-01-01

50

Power-law friction in closely packed granular materials

NASA Astrophysics Data System (ADS)

In order to understand the nature of friction in dense granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the shear rate, the exponent of which does not depend on the material constants. Using a nondimensional parameter that is known as the inertial number, the power law can be cast in a generalized form so that the friction coefficients at different confining pressures collapse on the same curve. We show that the volume fraction also obeys a power law.

Hatano, Takahiro

2007-06-01

51

Power-law connections: From Zipf to Heaps and beyond

In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf’s law, Pareto’s law, and Heaps’ law—three elemental empirical power-laws that are ubiquitously observed in the sciences. -- Highlights: ? The large-ensemble asymptotic statistics of rank distributions are explored. ? Lorenzian, oligarchic, and Heapsian asymptotic analyses are applied. ? Associated oligarchy sizes and induced innovation rates are analyzed. ? General elemental statistical connections are established. ? The underlying connections between Zipf’s, Pareto’s and Heaps’ laws are unveiled.

Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il [Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel); Cohen, Morrel H., E-mail: mcohen@physics.rutgers.edu [Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019 (United States); Department of Chemistry, Princeton University, Princeton, NJ 08544 (United States)

2013-05-15

52

There is more than a power law in Zipf.

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf's Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto's or Benford's, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf's law for the largest cities. This pathology is reflected in the fact that Zipf's Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call 'coherence' and it corresponds to a 'screening' between various elements of the set. We show how it should be accounted for when fitting Zipf's Law. PMID:23139862

Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano

2012-01-01

53

ERIC Educational Resources Information Center

A case involving the mental health rights of children is currently working its way toward the Supreme Court. That case, Bartley v. Kremens, challenges the power of parents to institutionalize their children in mental hospitals or institutions for the retarded without due process of law. (Author/RK)

Ellis, James W.

1976-01-01

54

Transient ultrasonic fields in power law attenuation media

NASA Astrophysics Data System (ADS)

Ultrasonic waves in biological media experience frequency dependent attenuation. Extensive measurement of the attenuation coefficient in human and mammalian tissue in the ultrasonic range has revealed a power law dependence on frequency, where the power law exponent ranges between 0 and 2. For most tissue, the power law exponent ranges between 1 and 1.7, which cannot be explained by classical theories for ultrasonic absorption, such as thermo-viscosity or molecular relaxation. The purpose of this thesis is threefold: (1) to understand the analytical structure of transient fields in power law media, (2) to provide a possible description of the physical mechanism responsible for power law attenuation in biological media, and (3) to develop analytical models for transient, three-dimensional sound beams in power law media. Insight into general dissipative media is gained by studying the approximations available in viscous media. The Stokes wave equation is considered in the time domain, and an asymptotic, causal Green's function is rigorously derived and verified using the material impulse response function (MIRF) approach. A lossy impulse response for the Stokes wave equation is derived for calculations of transient fields generated by finite aperture radiators. Expressions for the uniform circular aperture (in both the nearfield and the farfield), the uniform rectangular aperture in the nearfield, and the spherical shell in the nearfield are then derived. Power-law media is then studied using fractional partial differential equations (FPDEs), which add loss to the wave equation with a time-fractional or space-fractional derivative. A FPDE is derived that exactly describes power law attenuation, and analytical, time-domain James F. Kelly Green's functions in power law media are derived for exponents between 0 and 2. To construct solutions, stable law probability distributions are utilized, which are widely used in the study of anomalous diffusion and in the study of fractal media. For exponents strictly less than 1, the Green's functions are causal, while for exponents greater than or equal than 1, the Green's functions are noncausal. To address the lack of causality, alternate power law FPDEs based on fractional spatial operators are considered: the Chen-Holm wave equation and a spatially dispersive wave equation. Green's functions are derived for both equations, yielding causal solutions for all applicable power law exponents. The Chen-Holm equation is shown to be non-dispersive, while the spatially dispersive wave equation supports a phase velocity predicted by the Kramers-Kronig relations. To address the physical basis for FPDEs, a fractal ladder network is proposed as a model for the stress-strain relationship in tissue. This constitutive equation is based on a lumped-parameter infinite-ladder topology involving alternating springs and dashpots to capture the viscoelastic and self-similar properties of tissue. This ladder network yields a stress-strain constitutive equation involving a time-fractional derivative. The Caputo-Wismer FPDE is derived from this constitutive equation. Finally, the impulse response derived for viscous media is generalized to power law media. Expressions for finite apertures are then derived in dispersive media, thus forming the basis for ultrasonic image simulation in biological media.

Kelly, James F.

55

Primordial scalar perturbations in tachyonic power-law inflation

NASA Astrophysics Data System (ADS)

In this work we determine the power spectrum of the gravitational potential of the primordial fluctuations for an inflationary model whose inflaton is a noncanonical scalar field of the tachyon-type. The respective background field equations for an inverse-square potential produce a power-law inflation, and it is explicitly shown that for such a potential the power spectrum tends to be scale independent for highly accelerated regimes in the inflationary expansion.

de Souza, Rudinei C.; Kremer, Gilberto M.

2014-01-01

56

Binary optics beam mode transformer and its application in high-power laser processing

Based on the newly developed binary optics, a new kind of optics device used for laser beam mode transforming has been developed. This kind of binary optics device is worked with the principle of optical diffraction. It can be used to transform very efficiently the beam mode of high power laser of long wavelength. Using such a binary optics device

Wenjin Liu; Yanxiang Li; Jie Zhao; Haicheng Zhang; Shusen Deng; Pin Long; Yansong Cheng

1998-01-01

57

Statistical Models of Power-law Distributions in Homogeneous Plasmas

A variety of in-situ measurements in space plasmas point out to an intermittent formation of distribution functions with elongated tails and power-law at high energies. Power-laws form ubiquitous signature of many complex systems, plasma being a good example of a non-Boltzmann behavior for distribution functions of energetic particles. Particles, which either undergo mutual collisions or are scattered in phase space by electromagnetic fluctuations, exhibit statistical properties, which are determined by the transition probability density function of a single interaction, while their non-asymptotic evolution may determine the observed high-energy populations. It is shown that relaxation of the Brownian motion assumptions leads to non-analytical characteristic functions and to generalization of the Fokker-Planck equation with fractional derivatives that result in power law solutions parameterized by the probability density function.

Roth, Ilan [Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States)

2011-01-04

58

Testing power-law cross-correlations: rescaled covariance test

NASA Astrophysics Data System (ADS)

We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range cross-correlated processes. Utilizing a heteroskedasticity and auto-correlation robust estimator of the long-term covariance, we develop a test with desirable statistical properties which is well able to distinguish between short- and long-range cross-correlations. Such test should be used as a starting point in the analysis of long-range cross-correlations prior to an estimation of bivariate long-term memory parameters. As an application, we show that the relationship between volatility and traded volume, and volatility and returns in the financial markets can be labeled as the power-law cross-correlated one.

Kristoufek, Ladislav

2013-10-01

59

A COSMIC COINCIDENCE: THE POWER-LAW GALAXY CORRELATION FUNCTION

We model the evolution of galaxy clustering through cosmic time to investigate the nature of the power-law shape of {xi}(r), the galaxy two-point correlation function. While {xi}(r) at large scales is set by primordial fluctuations, departures from a power law are governed by galaxy pair counts at small scales, subject to nonlinear dynamics. We assume that galaxies reside within dark matter halos and subhalos. Therefore, the shape of the correlation function at small scales depends on the amount of halo substructure. We use a semi-analytic substructure evolution model to study subhalo populations within host halos. We find that tidal mass loss and, to a lesser extent, dynamical friction dramatically deplete the number of subhalos within larger host halos over time, resulting in a {approx}90% reduction by z = 0 compared to the number of distinct mergers that occur during the assembly of a host halo. We show that these nonlinear processes resulting in this depletion are essential for achieving a power law {xi}(r). We investigate how the shape of {xi}(r) depends on subhalo mass (or luminosity) and redshift. We find that {xi}(r) breaks from a power law at high masses, implying that only galaxies of luminosities {approx}< L{sub *} should exhibit power-law clustering. Moreover, we demonstrate that {xi}(r) evolves from being far from a power law at high redshift, toward a near power-law shape at z = 0. We argue that {xi}(r) will once again evolve away from a power law in the future. This is in large part caused by the evolving competition between the accretion and destruction rates of subhalos over time, which happen to strike just the right balance at z {approx} 0. We then investigate the conditions required for {xi}(r) to be a power law in a general context. We use the halo model, along with simple parameterizations of the halo occupation distribution, to probe galaxy occupation at various masses and redshifts. We show that the key ingredients determining the shape of {xi}(r) are the fraction of galaxies that are satellites, the relative difference in mass between the halos of isolated galaxies and halos that contain a single satellite on average, and the rareness of halos that host galaxies. These pieces are intertwined and we find no simple, universal rule for which a power law {xi}(r) will occur. However, we do show that the physics responsible for setting the galaxy content of halos do not care about the conditions needed to achieve a power law {xi}(r) and that these conditions are met only in a narrow mass and redshift range. We conclude that the power-law nature of {xi}(r) for L{sub *} and fainter galaxy samples at low redshift is a cosmic coincidence.

Watson, Douglas F.; Berlind, Andreas A. [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States); Zentner, Andrew R. [Department of Physics and Astronomy, The University of Pittsburgh, Pittsburgh, PA 15260 (United States)

2011-09-01

60

Estimation in a fluctuating medium and power-law distributions

NASA Astrophysics Data System (ADS)

We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power-law probability distributions. Beck, Cohen and others have provided plausible mechanisms explaining how power-law probability distributions naturally emerge in scenarios characterized by either finite dimension or fluctuation effects. This Letter tries to further contribute to such an idea. As an application, a new and multivariate version of the central limit theorem is obtained that provides a convenient alternative to the one recently presented in [S. Umarov, C. Tsallis, S. Steinberg, cond-mat/0603593].

Vignat, C.; Plastino, A.

2007-01-01

61

Power-Law Creep from Discrete Dislocation Dynamics

NASA Astrophysics Data System (ADS)

We report two-dimensional discrete dislocation dynamics simulations of combined dislocation glide and climb leading to “power-law” creep in a model aluminum crystal. The approach fully accounts for matter transport due to vacancy diffusion and its coupling with dislocation motion. The existence of quasiequilibrium or jammed states under the applied creep stresses enables observations of diffusion and climb over time scales relevant to power-law creep. The predictions for the creep rates and stress exponents fall within experimental ranges, indicating that the underlying physics is well captured.

Keralavarma, Shyam M.; Cagin, T.; Arsenlis, A.; Benzerga, A. Amine

2012-12-01

62

Power law relaxation in a complex system: Omori law after a financial market crash

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the

Fabrizio Lillo; Rosario N. Mantegna

2001-01-01

63

Power-law relaxation in a complex system: Omori law after a financial market crash

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the

F. Lilloand; Rosario N. Mantegna

2003-01-01

64

Asymptotic function for multigrowth surfaces using power-law noise.

Numerical simulations are used to investigate the multiaffine exponent alpha(q) and multigrowth exponent beta(q) of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of beta(q) are compared with the asymptotic function beta(q)=1/q that is approximated from the power-law behavior of the distribution of height differences over time. They are in good agreement for large q. The simulated alpha(q) is found in the range 1/q< or =alpha(q)< or =2/(q+1). This implies that large rare events tend to break the Kardar-Parisi-Zhang universality scaling law at higher order q. PMID:12636508

Katsuragi, Hiroaki; Honjo, Haruo

2003-01-01

65

Power-Law Distribution for Solar Energetic Proton Events

NASA Astrophysics Data System (ADS)

Analyses of the time-integrated fluxes of solar energetic particle events during the period 1965 1990 show that the differential distribution of events with flux F is given by a power law, with indices between 1.2 and 1.4 depending on energy. The power law represents a good fit over three to four orders of magnitude in fluence. Similar power-law distributions have been found for peak proton and electron fluxes, X-ray flares and radio and type III bursts. At fluences greater than 109 cm-2, the slope of the distribution steepens and beyond 1010 cm-2 the power-law index is estimated to be 3.5. At energies greater than 10 MeV, the slope of the distribution was found to be essentially independent of solar cycle, when the active years of solar cycles 20, 21, and 22 were analysed. The results presented are the first for a complete period of 27 years, covering nearly 3 complete solar cycles. Other new aspects of the results include the invariance of the exponent with solar cycle and also with integral energy.

Gabriel, S. B.; Feynman, J.

1996-05-01

66

Modeling the densification of powder composites by power law creep

A model describing the densification under isotropic pressure of a powder composite, consisting of viscoplastic particles deforming by power law creep mixed with rigid inclusions of the same size, is presented. A description of the behavior of each type of contacts is first proposed, from which an expression for the densification rate of the mixture is deduced. The evolution of

Bouvard

1993-01-01

67

Unsteady magnetic boundary layer flow of power-law fluids

The Galerkin approximation technique is used to solve the flow problem of an infinite plate immersed in a non-Newtonian power law fluid in the presence of a constant transverse magnetic field. The velocity outside the boundary layer depends exponentially on time.

Djordje S. Djukic

1974-01-01

68

Power scaling laws and dimensional transitions in solid mechanics

Physicists have often observed a scaling behaviour of the main physical quantities during experiments on systems exhibiting a phase transition. The main assumption of a scaling theory is that these characteristic quantities are self-similar functions of the independent variables of the phenomenon and, therefore, such a scaling can be interpreted be means of power-laws. Since a characteristic feature of phase

Alberto Carpinteri; Bernardino Chiaia

1996-01-01

69

Second law analysis of a conventional steam power plant

NASA Technical Reports Server (NTRS)

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.

Liu, Geng; Turner, Robert H.; Cengel, Yunus A.

1993-01-01

70

Second law analysis of a conventional steam power plant

NASA Astrophysics Data System (ADS)

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.

Liu, Geng; Turner, Robert H.; Cengel, Yunus A.

1993-11-01

71

Thermal emission in fatigue described by power laws

NASA Astrophysics Data System (ADS)

In the present work, a theoretical model proposed by the literature and focused on the relationship between microplasticizations thermal behaviour and fatigue scatter is analysed and applied to fatigue test results of standard and notched steel specimens. The same experimental data are subjected to the TCM (Two Curves Method) thermographic elaboration technique, in order to quickly evaluate fatigue limit values. TCM method has been modified, aiming at interpolating thermal data referred to the region of loads upper than fatigue limit with a non linear regression law having the same mathematical structure of the theoretical model equations (power laws).

Curti, G.; Curã, F.; Gallinatti, A. E.; Sesana, R.

2010-06-01

72

Spectral geometry of power-law potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

It is supposed that a single particle moves in openR3 in an attractive central power-law potential V(q)(r)=sgn(q)rq, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues Enl(q) of the Hamiltonian H=-?+V(q) depend on the power parameter q\\? Pure power-law potentials have the elementary property that, for p

Hall, Richard L.

1989-06-01

73

Deviation from Power Law Behavior in Landslide Phenomenon

NASA Astrophysics Data System (ADS)

Power law distribution of magnitude is widely observed in many natural hazards (e.g., earthquake, floods, tornadoes, and forest fires). Landslide is unique as the size distribution of landslide is characterized by a power law decrease with a rollover in the small size end. Yet, the emergence of the rollover, i.e., the deviation from power law behavior for small size landslides, remains a mystery. In this contribution, we grouped the forces applied on landslide bodies into two categories: 1) the forces proportional to the volume of failure mass (gravity and friction), and 2) the forces proportional to the area of failure surface (cohesion). Failure occurs when the forces proportional to volume exceed the forces proportional to surface area. As such, given a certain mechanical configuration, the failure volume to failure surface area ratio must exceed a corresponding threshold to guarantee a failure. Assuming all landslides share a uniform shape, which means the volume to surface area ratio of landslide regularly increase with the landslide volume, a cutoff of landslide volume distribution in the small size end can be defined. However, in realistic landslide phenomena, where heterogeneities of landslide shape and mechanical configuration are existent, a simple cutoff of landslide volume distribution does not exist. The stochasticity of landslide shape introduce a probability distribution of the volume to surface area ratio with regard to landslide volume, with which the probability that the volume to surface ratio exceed the threshold can be estimated regarding values of landslide volume. An experiment based on empirical data showed that this probability can induce the power law distribution of landslide volume roll down in the small size end. We therefore proposed that the constraints on the failure volume to failure surface area ratio together with the heterogeneity of landslide geometry and mechanical configuration attribute for the deviation from power law behavior in landslide phenomenon. Figure shows that a rollover of landslide size distribution in the small size end is produced as the probability for V/S (the failure volume to failure surface ratio of landslide) exceeding the mechanical threshold applied to the power law distribution of landslide volume.

Li, L.; Lan, H.; Wu, Y.

2013-12-01

74

There is More than a Power Law in Zipf

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law.

Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano

2012-01-01

75

Power Law for Rough Favorable Pressure Gradient Turbulent Boundary Layers

NASA Astrophysics Data System (ADS)

Current studies on rough favorable pressure gradient (FPG) boundary layers are very challenging particularly since it is difficult to obtain values of skin friction as a function of roughness, pressure gradient strength and Re?. This study presents a new modified form of the power law from George and Castillo (1997) developed for smooth zero pressure gradient boundary layers. The new form accounts for mild pressure gradients, and aids in the account for rough surface boundary layers. Emphasis will be given to its application to rough FPG flows. The values of the skin friction for smooth FPG boundary layers are obtained within 3%. Moreover, the composite profile for the mean velocity accurately describes both FPG and APG flows. The modified power law solution has the advantage of being a continuous solution for smooth and rough profiles subject to external pressure gradients. In addition, by using the Navier Stokes equation the Reynolds shear stress is accurately calculated from the composite description of the mean velocity.

Newhall, Katherine; Castillo, Luciano

2006-11-01

76

Power law rank-abundance relationships in marine phage populations

NASA Astrophysics Data System (ADS)

Phage are the most abundant biological entities in the biosphere, with an estimated 10^31 particles on the planet. About 25% of oceanic organic carbon is cycled through phage every day. Metagenomic analyses show that the rank-abundance curve for marine phage communities follows a power law distribution. This distribution is consistent with a proposed, modified version of Lotka-Volterra predator-prey dynamics, where blooms of a specific microbial species leads to blooms of their corresponding phage and a subsequent decrease in abundance. The model predicts that the majority of phage types in a population will be rare and it is unlikely that the most abundant phage will be the same at different time points. The model is based on spatial-temporal heterogeneity and a power law phage decay, which are both supported by empirical data.

Salamon, Peter; Hoffmann, Karl Heinz; Rodriguez-Brito, Beltran

2005-03-01

77

An improved penalty method for power-law Stokes problems

NASA Astrophysics Data System (ADS)

For the numerical approximation of fluid flow phenomena, it is often highly desirable to decouple the equations defining conservation of momentum and conservation of mass by using a penalty function method. The current penalty function methods for power-law Stokes fluids converge at a sublinear rate with respect to the penalty parameter. In this article, we show theoretically and numerically that a linear penalty function approximation to a power-law Stokes problem yields a higher-order accuracy over the known nonlinear penalty method. Theoretically, finite element approximation of the linear penalty function method is shown to satisfy an improved order of approximation with respect to the penalty parameter. The numerical experiments presented in the paper support the theoretical results and satisfy a linear order of approximation.

Borggaard, Jeff; Iliescu, Traian; Roop, John Paul

2009-01-01

78

Power-law distribution in Japanese racetrack betting

NASA Astrophysics Data System (ADS)

Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we present an analysis of the distribution of the final odds of the races organized by the Japan Racing Association. The distribution of the final odds Po(x) indicates a clear power-law Po(x)?1/x, where x represents the final odds. This power-law can be explained on the basis of the assumption that every bettor bets his money on the horse that appears to be the strongest in a race.

Ichinomiya, Takashi

2006-08-01

79

Anomalous thermodynamic power laws near topological transitions in nodal superconductors

NASA Astrophysics Data System (ADS)

Unconventional superconductors are most frequently identified by the observation of power-law behavior on low-temperature thermodynamic or transport properties, such as specific heat. Here, we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example, when point or line nodes first appear as a function of some physical parameter. We identify anomalous, noninteger thermodynamic power laws associated with these new nodal types, and give physical examples of superconductors in which they might be observed experimentally, including the noncentrosymmetric superconductor Li2Pd3-xPtxB.

Mazidian, B.; Quintanilla, J.; Hillier, A. D.; Annett, J. F.

2013-12-01

80

Power law distribution of dividends in horse races

NASA Astrophysics Data System (ADS)

We discovered that the distribution of dividends in Korean horse races follows a power law. A simple model of betting is proposed, which reproduces the observed distribution. The model provides a mechanism to arrive at the true underlying winning probabilities, which are initially unknown, in a self-organized collective fashion, through the dynamic process of betting. Numerical simulations yield excellent agreement with the empirical data.

Park, K.; Domany, E.

2001-02-01

81

Power-law correlations in column ozone over Antarctica

Detrended fluctuation analysis is applied on springtime daily column ozone at the edge and into the Antarctic ozone hole, by using observations deduced from ground?based (1972–2003) and satellite?borne instrumentation (1979–2003). First, extreme column ozone fluctuations obey a power?law with exponents, implying that large fluctuations are more likely to occur into the ozone hole than at its edge. Secondly, for time?scales

Costas Varotsos

2005-01-01

82

The power law in particle size analysis for aquacultural facilities

Fine particles tend to accumulate in recirculating aquacultural facilities, which can lead to serious fish health problems. The literature indicated that in many particle systems, the particle size distribution may be accurately represented by a two-parameter, hyperbolic power-law function, dN\\/dl=Al??.The purpose of this paper is to investigate whether this observation holds for aquacultural facilities. Particle size distribution data from four

Richard N. Patterson; K. Christopher Watts; Michael B. Timmons

1999-01-01

83

Power-law Correlations of Landslide Areas in Central Italy

NASA Astrophysics Data System (ADS)

We have studied the frequency-area statistics of landslides in central Italy. We consider two data sets. Data set A contains 16,809 landslide areas in the Umbria--Marche area of central Italy; they represent a reconnaissance inventory of very old, old, and recent (modern) landslides. The noncumulative frequency-area distribution of these landslides correlate well with a power-law relation, exponent 2.5, over the range 0.03 km2 < AL < 3 km2, where AL is the landslide area. Data set B contains 4233 landslides that were triggered by a sudden change in temperature on 1 January 1997, resulting in extensive melting of snow cover. An inventory of these snow-melt triggered landslides was obtained from aerial photographs taken 3 months after the event. These landslides also correlate well with a power-law relation with exponent 2.5, over the range 0.001 km2 < AL < 0.1 km2. We show that the correlation of data set B is essentially identical to the correlation of 11,000 landslides triggered by the 17 January 1994 Northridge, California earthquake. We attribute a rollover for small landslides in data set A to incompleteness of the record due to erosion and other processes, and to limitations in the reconnaissance mapping technique used to complete the inventory. On the other hand, we conclude that rollovers for small landslides in data set B and the California earthquake data are real and are associated with the surface morphology. We conclude that the power-law distribution is valid over a wide range of landslide areas and discuss possible reasons. We find very close statistical distributions of landslide area for inventories resulting from different triggers: earthquake, snow-melt, and rain-fall. We take this as possible evidence that there is a universal probability density function (pdf) for triggered landslide events. This universal pdf has a fat (power-law) tail.

Malamud, B. D.; Turcotte, D. L.; Guzzetti, F.; Reichenbach, P.

2001-12-01

84

NASA Astrophysics Data System (ADS)

The paper presents an analysis of two-dimensional zero pressure gradient (ZPG) turbulent boundary layers (TBL) with regard to the application of power laws. Only TBL with low Reynolds number 300 < Re?2 < 6200 are taken into account. It is found that a certain region of the mean velocity profile can be described with a power law of the formu +=C Pow{*}y +a. This power law region is not a priori identical with the overlap region. An algorithm for the determination of the wall skin friction using the power law is proposed. The method was applied with good result to ZPG TBL and to adverse pressure gradient (APG) TBL. To bridge the gap between the wall and the power law region an approach for the turbulent viscosity is suggested.

Buschmann, Matthias

2000-03-01

85

Development of Jet Noise Power Spectral Laws Using SHJAR Data

NASA Technical Reports Server (NTRS)

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.

Khavaran, Abbas; Bridges, James

2009-01-01

86

Binary optics used in high-power laser shaping

On the basis of the analysis of the existed optimization algorithms, three kinds of hybrid algorithms are developed for phase design of the Binary Optical Element to realize beam shaping, including Global\\/local united search algorithm (GLUSA), the modified GLUSA, and the modified GLUSA with multi-resolution. Four masks have been used to produce a (phi) 50 mm binary phase plate with

Guofan Jin; Qiaofeng Tan; Yingbai Yan; Minxian Wu

1999-01-01

87

SHJAR Jet Noise Data and Power Spectral Laws

NASA Technical Reports Server (NTRS)

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. The measured spectral data are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of 0.0 to 10.0. The measured data are reported as lossless (i.e., atmospheric attenuation is added to measurements), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter (200-in.) arc. Following the work of Viswanathan, velocity power factors are evaluated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit and the confidence margins for the two regression parameters are studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. As an immediate application of the velocity power laws, spectral density in shockcontaining jets are decomposed into components attributed to jet mixing noise and shock noise. From this analysis, jet noise prediction tools can be developed with different spectral components derived from different physics.

Khavaran, Abbas; Bridges, James

2009-01-01

88

Power-law correlations of landslide areas in central Italy

NASA Astrophysics Data System (ADS)

We have studied the frequency-area statistics of landslides in central Italy. We consider two data sets. Data set A contains 16?809 landslide areas in the Umbria-Marche area of central Italy; they represent a reconnaissance inventory of very old, old, and recent (modern) landslides. The noncumulative frequency-area distribution of these landslides correlates well with a power-law relation, exponent -2.5, over the range 0.03 km 2< AL<4 km 2. Data set B contains 4233 landslides that were triggered by a sudden change in temperature on 1 January 1997, resulting in extensive melting of snow cover. An inventory of these snow-melt-triggered landslides was obtained from aerial photographs taken 3 months after the event. These landslides also correlate well with a power-law relation with exponent -2.5, over the range 0.001 km 2< AL<0.1 km 2. We show that the correlation of data set B is essentially identical to the correlation of 11?000 landslides triggered by the 17 January 1994 Northridge, California earthquake. We attribute a rollover for small landslides in data set A to incompleteness of the record due to erosion and other processes, and to limitations in the reconnaissance mapping technique used to complete the inventory. On the other hand, we conclude that rollovers for small landslides in data set B and the California earthquake data are real and are associated with the surface morphology. We conclude that the power-law distribution is valid over a wide range of landslide areas and discuss possible reasons. We also discuss the contribution of the snow-melt- and earthquake-triggered landslide events to the total landslide inventory.

Guzzetti, Fausto; Malamud, Bruce D.; Turcotte, Donald L.; Reichenbach, Paola

2002-02-01

89

Universal power law for front propagation in all fiber resonators.

We consider a bistable system consisting of all fiber cavity driven by an external injected continuous wave. We report on front propagation in a high finesse cavity. We study the asymptotic behavior of the front velocity. We show that the front velocity is affected by the distance from the critical point associated with bistability. We provide a scaling low governing its evolution near the up-switching point of the bistable curve. We show also that the velocity of front propagation obeys a generic power law when the front velocity approaches asymptotically its linear growing value. PMID:24515008

Coulibaly, S; Taki, M; Tlidi, M

2014-01-13

90

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 classes in the city size distributions are snapshots of stable states within urban systems in flux. ?? 2008.

Garmestani, A. S.; Allen, C. R.; Gallagher, C. M.

2008-01-01

91

Adhesion of nanoscale asperities with power-law profiles

NASA Astrophysics Data System (ADS)

The behavior of single-asperity micro- and nanoscale contacts in which adhesion is present is important for the performance of many small-scale mechanical systems and processes, such as atomic force microscopy (AFM). When analyzing such problems, the bodies in contact are often assumed to have paraboloidal shapes, thus allowing the application of the familiar Johnson-Kendall-Roberts (JKR), Derjaguin-Müller-Toporov (DMT), or Maugis-Dugdale (M-D) adhesive contact models. However, in many situations the asperities do not have paraboloidal shapes and, instead, have geometries that may be better described by a power-law function. An M-D-n analytical model has recently been developed to extend the M-D model to asperities with power-law profiles. We use a combination of M-D-n analytical modeling, finite element (FE) analysis, and experimental measurements to investigate the behavior of nanoscale adhesive contacts with non-paraboloidal geometries. Specifically, we examine the relationship between pull-off force, work of adhesion, and range of adhesion for asperities with power-law-shaped geometries. FE analysis is used to validate the M-D-n model and examine the effect of the shape of the adhesive interaction potential on the pull-off force. In the experiments, the extended M-D model is applied to analyze pull-off force measurements made on nanoscale tips that are engineered via gradual wear to have power-law shapes. The experimental and modeling results demonstrate that the range of the adhesive interaction is a crucial parameter when quantifying the adhesion of non-paraboloidal tips, quite different than the familiar paraboloidal case. The application of the M-D-n model to the experimental results yields an unusually large adhesion range of 4-5 nm, a finding we attribute to either the presence of long-range van der Waals forces or deviations from continuum theory due to atomic-scale roughness of the tips. Finally, an adhesion map to aid in analysis of pull-off force measurements of non-paraboloidal tips is presented. The map delineates the cases in which a simplified rigid analysis can be used to analyze experimental data.

Grierson, David S.; Liu, Jingjing; Carpick, Robert W.; Turner, Kevin T.

2013-02-01

92

Long-range power-law correlations in stock returns

NASA Astrophysics Data System (ADS)

This study investigates long-range power-law correlations in US, UK, Japanese, German, French and Spanish stock markets using daily data and applying a recently developed residual analysis termed detrended fluctuation analysis (DFA). We quantify correlations for the returns, absolute value of returns and square of returns. The results show that there is little evidence of long-range correlations in returns but there is strong evidence of long-range correlation in absolute and squared returns. For the absolute returns, a cross-over of approximately 41 days is found.

Grau-Carles, Pilar

2001-10-01

93

Optimized dynamical decoupling for power-law noise spectra

We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal pi pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder.

Pasini, S.; Uhrig, G. S. [Lehrstuhl fuer Theoretische Physik I, TU Dortmund, Otto-Hahn Strasse 4, D-44221 Dortmund (Germany)

2010-01-15

94

Positive feedbacks promote power-law clustering of Kalahari vegetation.

The concept of local-scale interactions driving large-scale pattern formation has been supported by numerical simulations, which have demonstrated that simple rules of interaction are capable of reproducing patterns observed in nature. These models of self-organization suggest that characteristic patterns should exist across a broad range of environmental conditions provided that local interactions do indeed dominate the development of community structure. Readily available observations that could be used to support these theoretical expectations, however, have lacked sufficient spatial extent or the necessary diversity of environmental conditions to confirm the model predictions. We use high-resolution satellite imagery to document the prevalence of self-organized vegetation patterns across a regional rainfall gradient in southern Africa, where percent tree cover ranges from 65% to 4%. Through the application of a cellular automata model, we find that the observed power-law distributions of tree canopy cluster sizes can arise from the interacting effects of global-scale resource constraints (that is, water availability) and local-scale facilitation. Positive local feedbacks result in power-law distributions without entailing threshold behaviour commonly associated with criticality. Our observations provide a framework for integrating a diverse suite of previous studies that have addressed either mean wet season rainfall or landscape-scale soil moisture variability as controls on the structural dynamics of arid and semi-arid ecosystems. PMID:17851523

Scanlon, Todd M; Caylor, Kelly K; Levin, Simon A; Rodriguez-Iturbe, Ignacio

2007-09-13

95

Power Law Distributions of Patents as Indicators of Innovation

The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Here we present evidence that the distribution of patents amongst applicants within many countries is well-described by power laws with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.

O'Neale, Dion R. J.; Hendy, Shaun C.

2012-01-01

96

Power Law Distributions of Patents as Indicators of Innovation

NASA Astrophysics Data System (ADS)

The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Such figures however give an overly simplistic measure of innovation within a country. Here we present evidence that the distribution of patents amongst applicants within many countries is well-fitted to a power law distribution with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.

O'Neale, Dion; Hendy, Shaun

2013-03-01

97

A poly(dimethylsiloxane) viscometer for microliter power law fluids

NASA Astrophysics Data System (ADS)

This paper describes a poly(dimethylsiloxane) (PDMS) microfluidic device for measuring the viscosity of power law fluids. The viscometer utilized the high solubility and permeability of air in PDMS to generate vacuum and drive the Poiseuille flow in the degassed PDMS microchannels. Wide ranges of shear rates in PDMS microchannels were generated by controlling the chamber sizes of the PDMS viscometer. By measuring the distance the fluids traveled and the flow velocity in the PDMS microchannel, the flow behavior index n was determined and the viscosity profile of the sample fluid under a range of shear rates was obtained. Only 5 µL or less volume was consumed for the viscosity measurement. Viscosities of poly(ethylene oxide) solutions and blood control standard were successfully measured under shear rates varying from 10 to 500 s-1, and the results were consistent with those from conventional cone-plate rheometers. The PDMS viscometer was applicable to a broad range of power law fluids, such as diluted polymeric solutions and colloidal suspensions.

Han, Zuoyan; Zheng, Bo

2009-11-01

98

Discontinuous Double Power Law Scaling of Magnetic Hysteresis

NASA Astrophysics Data System (ADS)

Frequency(?), applied field(H), and temperature(T) -dependent hysteresis loops of ultrathin Fe films on flat and stepped W(001) surface are measured using the magneto-optic Kerr effect. Power law scaling of the loop area A ~ H^??^? is observed over five decades in ? with exponents similar to those observed for Fe on W(110)^1. In cases where the dynamic coercivity H_c(?) exceeds the applied field, an abrupt collapse of the loop occurs leading to a double-power-law scaling behavior similar to that reported by Luse and Zangwill^2 based on a periodically driven kinetic Ising model. The exponent ?' describing the abrupt loop collapse above the amplitude dependent critical frequency is very large compared to the low frequency range value ?, and ?' is much more sensitive to film thickness than the low frequency regime ?. Supported by DMR-9623494 ^1 Jih-Shin Suen and J. L. Erskine, Bull. Am. Phys. Soc. 41, B22 7 (1996) (and submitted to PRL) ^2 C. N. Luse and A. Zangwill, Phys. Rev. E50, 224 (1994)

Suen, Jih-Shin; Erskine, J. L.

1997-03-01

99

“Slimming” of power-law tails by increasing market returns

NASA Astrophysics Data System (ADS)

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate r?, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r> r? corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power-law exponent and thus the thinner is the tail of the distribution of price returns.

Sornette, D.

2002-06-01

100

An inverse method for rheometry of power-law fluids

NASA Astrophysics Data System (ADS)

This paper is concerned with the determination of the constitutive viscous parameters of dilute solutions of xanthan gum by means of an inverse method used in conjunction with finite element modeling of the governing system of partial differential equations. At low concentrations xanthan gum behaves as a shear-thinning, power-law non-Newtonian fluid. Finite element modeling is used to simulate the pressure-driven flow of xanthan gum solutions in a microchannel T-junction. As the flow is forced to turn the corner of the T-junction a range of shear rates, and hence viscosities, is produced. It is shown that the statistical properties of the velocity field are sensitive to the constitutive parameters of the power-law model. The inverse method is shown to be stable and accurate, with measurement error in the velocity field translating to small errors in the rheological parameter estimation. Due to the particular structure of the inverse map, the error propagation is substantially less than the estimate from the Hadamard criterion.

Hemaka Bandulasena, H. C.; Zimmerman, William B.; Rees, Julia M.

2011-12-01

101

The Photon Power and Stefan-Boltzmann Radiation Law

NASA Astrophysics Data System (ADS)

In [1], according to the world-famous formula of Planck and to the model of the photon, which was suggested in the applications [2, 3], the formula for the practical determination of the power of a light particle was derived: P = const ot f^2 = hf^2 (W). Of course, this theoretical result could be examined by an experiment. However, there is one possibility to test that formula on another way. The use of the relationship q = Q/A = \\varepsilon P/A , the new formula for the photon power together with the estimation of the effective radiation area A leads to the following equation: q = const ot T^4 (W/m^2). This formula represents the well-known Stefan-Boltzmann radiation law, so that fact could be considered as a very proof confirmation of the derived equation of the photon power. The details of the theoretical procedure will be presented and discussed during the meeting. References 1. About the calculation of the photon power. S. Reissig, APS four corners meeting, Arizona, 2003 2. About the dualism of the light. S. Reissig, The 12th General Conference of the European Physical Society "Trends in Physics, Budapest, 2002 3. About the nature of the photon. S. Reissig, www.efbr.de/de/ publikationen/, 2003

Reissig, Sergej

2004-03-01

102

Binary conversion cycles for concentrating solar power technology

It is recognized that the temperature potential of concentrated solar energy is much higher than needed by standard conversion cycles. High temperature solar receivers are in the development stage hopefully leading to the use of solarized gas turbines or of solar combined cycles. These systems are analyzed and taken as a reference standard. Binary alkali-metal steam cycles are shown to

Gianfranco Angelino; Costante Invernizzi

2008-01-01

103

Random sequences with power-law correlations exhibit proteinlike behavior

NASA Astrophysics Data System (ADS)

We use a replica approach to investigate the thermodynamic properties of the random heteropolymers with persistent power-law correlations in monomer sequence. We show that this type of sequences possess proteinlike properties. In particular, we show that they can fold into stable unique three-dimensional structure (the ``native'' structure, in protein terminology) through two different types of pathways. One is a fast folding pathway and leads directly to the native structure. Another one, a more slower pathway, passes through the microphase separated (MPS) state and includes a number of intermediate glassy states. The scale and the magnitude of the MPS are calculated. The frozen state can be reached only by sequences with weak long-range correlations. The critical value for the correlation exponent is found, above which (strong correlations) freezing is impossible.

Mamasakhlisov, Yevgeni Sh.; Hayryan, Shura; Hu, Chin-Kun

2007-04-01

104

Unexpected power-law stress relaxation of entangled ring polymers.

After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers. PMID:18953345

Kapnistos, M; Lang, M; Vlassopoulos, D; Pyckhout-Hintzen, W; Richter, D; Cho, D; Chang, T; Rubinstein, M

2008-12-01

105

Power-law fluid flow in heated vertical ducts

NASA Astrophysics Data System (ADS)

A hydrodynamically and thermally fully developed flow in a vertical duct is investigated. It is assumed that the wall of the duct is maintained at a temperature which varies linearly with respect to the depth of the duct to model a vertical duct in the Earth. Furthermore, in order to investigate flows during the drilling of muds and the cementing process in oil wells, the fluid is assumed to be a power-law fluid and the fluid flow in concentric annuli are investigated. The conditions under which multiple solutions are obtained is studied and the effects of the Rayleigh number n, the relative thickness of the channels, and the enforced pressure gradient are investigated.

Jones, A. T.; Ingham, D. B.

1994-04-01

106

Bootstrap Percolation in Power-Law Random Graphs

NASA Astrophysics Data System (ADS)

A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remains so forever. The parameter is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse this process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent , where , then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function such that with the following property. Assuming that is the number of vertices of the underlying random graph, if , then the process does not evolve at all, with high probability as grows, whereas if , then there is a constant such that, with high probability, the final set of infected vertices has size at least . This behaviour is in sharp contrast with the case where the underlying graph is a random graph with . It follows from an observation of Balogh and Bollobás that in this case if the number of initially infected vertices is sublinear, then there is lack of evolution of the process. It turns out that when the maximum degree is , then depends also on . But when the maximum degree is , then.

Amini, Hamed; Fountoulakis, Nikolaos

2014-04-01

107

Wellhead-sized binary-cycle geothermal power plants. Final report

Conceptual designs and estimates of capital costs as well as operating and maintenance costs were developed for wellhead binary-cycle geothermal power plants. Known geothermal resources were characterized, and three were selected as typical of the geothermal resources most likely to be developed for utility use within the next decade. Two wellhead power plant sizes were evaluated for each resource, resulting

P. A. Linam; W. M. Norman; T. W. Outten; A. L. Tanner

1985-01-01

108

Power-Law Template for IR Point Source Clustering

NASA Technical Reports Server (NTRS)

We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.

Addison, Graeme E.; Dunkley, Joanna; Hajian, Amir; Viero, Marco; Bond, J. Richard; Das, Sudeep; Devlin, Mark; Halpern, Mark; Hincks, Adam; Hlozek, Renee; Marriage, Tobias A.; Moodley, Kavilan; Page, Lyman A.; Reese, Erik D.; Scott, Douglass; Spergel, David N.; Staggs,Suzanne T.; Wollack, Edward

2011-01-01

109

POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING

We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 {approx}< l {approx}< 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 {mu}m; 1000 {approx}< l {approx}< 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C{sup clust}{sub l}{proportional_to}l{sup -n} with n = 1.25 {+-} 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, {nu}{sup {beta}} B({nu}, T{sub eff}), with a single emissivity index {beta} = 2.20 {+-} 0.07 and effective temperature T{sub eff} = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be {alpha}{sub 150-220} = 3.68 {+-} 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.

Addison, Graeme E.; Dunkley, Joanna [Sub-department of Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH (United Kingdom); Hajian, Amir; Das, Sudeep; Hincks, Adam D.; Page, Lyman A.; Staggs, Suzanne T. [Joseph Henry Laboratories of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544 (United States); Viero, Marco [Department of Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Bond, J. Richard [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada); Devlin, Mark J.; Reese, Erik D. [Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104 (United States); Halpern, Mark; Scott, Douglas [Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z4 (Canada); Hlozek, Renee; Marriage, Tobias A.; Spergel, David N. [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544 (United States); Moodley, Kavilan [Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041 (South Africa); Wollack, Edward [NASA/Goddard Space Flight Center, Code 665, Greenbelt, MD 20771 (United States)

2012-06-20

110

Kramers escape rate in overdamped systems with the power-law distribution

NASA Astrophysics Data System (ADS)

Kramers escape rate in the overdamped systems is restudied for the power-law distribution. By using the mean first passage time, we derive the escape rate with the power-law distribution and obtain the Kramers' infinite barrier escape rate in this case. We show that the escape rate with the power-law distribution extends the Kramers' overdamped result to the relatively low barrier. Furthermore, we apply the escape rate with the power-law distribution to the unfolding of titin and show a better agreement with the experimental rate than the traditional escape rate.

Zhou, Yanjun; Du, Jiulin

2014-05-01

111

Universal Fractional Noncubic Power Law for Density of Metallic Glasses

NASA Astrophysics Data System (ADS)

As a fundamental property of a material, density is controlled by the interatomic distances and the packing of microscopic constituents. The most prominent atomistic feature in a metallic glass (MG) that can be measured is its principal diffraction peak position (q1) observable by x-ray, electron, or neutron diffraction, which is closely associated with the average interatomic distance in the first shell. Density (and volume) would naturally be expected to vary under compression in proportion to the cube of the one-dimensional interatomic distance. However, by using high pressure as a clean tuning parameter and high-resolution in situ techniques developed specifically for probing the density of amorphous materials, we surprisingly found that the density of a MG varies with the 5/2 power of q1, instead of the expected cubic relationship. Further studies of MGs of different compositions repeatedly produced the same fractional power law of 5/2 in all three MGs we investigated, suggesting a universal feature in MG.

Zeng, Qiaoshi; Kono, Yoshio; Lin, Yu; Zeng, Zhidan; Wang, Junyue; Sinogeikin, Stanislav V.; Park, Changyong; Meng, Yue; Yang, Wenge; Mao, Ho-Kwang; Mao, Wendy L.

2014-05-01

112

Universal fractional noncubic power law for density of metallic glasses.

As a fundamental property of a material, density is controlled by the interatomic distances and the packing of microscopic constituents. The most prominent atomistic feature in a metallic glass (MG) that can be measured is its principal diffraction peak position (q1) observable by x-ray, electron, or neutron diffraction, which is closely associated with the average interatomic distance in the first shell. Density (and volume) would naturally be expected to vary under compression in proportion to the cube of the one-dimensional interatomic distance. However, by using high pressure as a clean tuning parameter and high-resolution in situ techniques developed specifically for probing the density of amorphous materials, we surprisingly found that the density of a MG varies with the 5/2 power of q1, instead of the expected cubic relationship. Further studies of MGs of different compositions repeatedly produced the same fractional power law of 5/2 in all three MGs we investigated, suggesting a universal feature in MG. PMID:24856706

Zeng, Qiaoshi; Kono, Yoshio; Lin, Yu; Zeng, Zhidan; Wang, Junyue; Sinogeikin, Stanislav V; Park, Changyong; Meng, Yue; Yang, Wenge; Mao, Ho-Kwang; Mao, Wendy L

2014-05-01

113

Directly observed relations in complete galaxy samples (apparent magnitude or diameter vs. redshift) are compared with the predictions of redshift-distance power laws. The predictions are obtained by an objective, nonparametric, statistically uniform, and fully reproducible procedure. In all cases the linear law fits even more poorly than a cubic law, and the optimal law is approximately quadratic. Even a 1.2 power law is conspicuously better-fitting than a linear law. The results of the present study in terms of directly measured quantities are consistent with and confirm earlier studies in terms of theoretical quantities such as absolute magnitudes and diameters. They show that there is no positive evidence for the Hubble law in manifestly fair galaxy samples and that the law can be reconciled with the data in complete samples only, if at all, by the adjunction of a tissue of ancillary hypotheses, none of which is capable of direct observational substantiation.

Segal, I. E.

1986-01-01

114

Transport coefficients in Lorentz plasmas with the power-law kappa-distribution

Transport coefficients in Lorentz plasma with the power-law ?-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient, and thermal conductivity for the power-law ?-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the ?-parameter, and in the limit of the parameter ??? they are reduced to the standard forms for a Maxwellian distribution.

Jiulin, Du [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China)] [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China)

2013-09-15

115

Power-law dependence of pressure broadening of spectral lines on temperature

It is known that the temperature variations of the widths of pressure broadened spectral lines are represented by a power-law relation when the applied potentials V(R) for the upper and lower level of the emitting atom are approximated by a simple inverse law. This power-law relation is obtained theoretically in a simple analytical form and examined in a wide temperature

M. S. Helmi; G. D. Roston

2001-01-01

116

Power-law dependence of pressure broadening of spectral lines on temperature

It is known that the temperature variations of the widths of pressure broadened spectral lines are represented by a power—law relation when the applied potentials V(R) for the upper and lower level of the emitting atom are approximated by a simple inverse law. This power—law relation is obtained theoretically in a simple analytical form and examined in a wide temperature

M. S. Helmi; G. D. Roston

2001-01-01

117

Consistency relation in power law G-inflation

NASA Astrophysics Data System (ADS)

In the standard inflationary scenario based on a minimally coupled scalar field, canonical or non-canonical, the subluminal propagation of speed of scalar perturbations ensures the following consistency relation: r <= ?8nT, where r is the tensor-to-scalar-ratio and nT is the spectral index for tensor perturbations. However, recently, it has been demonstrated that this consistency relation could be violated in Galilean inflation models even in the absence of superluminal propagation of scalar perturbations. It is therefore interesting to investigate whether the subluminal propagation of scalar field perturbations impose any bound on the ratio r/|nT| in G-inflation models. In this paper, we derive the consistency relation for a class of G-inflation models that lead to power law inflation. Within these class of models, it turns out that one can have r > ?8nT or r <= ?8nT depending on the model parameters. However, the subluminal propagation of speed of scalar field perturbations, as required by causality, restricts r <= ?(32/3) nT.

Unnikrishnan, Sanil; Shankaranarayanan, S.

2014-07-01

118

160 micron Photometry of A star Power Laws

NASA Astrophysics Data System (ADS)

We propose 160 um imaging for a sample of 4 planetary debris disks around main-sequence A stars, with MIPS 24 and 70 um excess, and for which the 5-35 um IRS data are best fit by power-laws of slopes ranging from 1.1 to 2.4. By extending our observations out to 160 um, we may find evidence for substantial reservoirs of colder material that considerably outweighs the warmer material seen shortward of 70 um. Other debris disks do not show evidence for such SEDs, nor for such large amounts of cold material. It is not clear whether this difference is due to the greater luminosity of the A stars, their higher mass and light/mass ratio, or their naturally younger ages, but we may be able to explore this interesting question. The result of these measurements will be an SED that extends over a factor of 10 in wavelength and as much as a factor of 100 in radial distance from the star. This broad range of spectral coverage can be used to test models of the structure and evolution of debris disks and their underlying planetary systems.

Rieke, George; Morales, Farisa; Bryden, Geoffrey; Stapelfeldt, Karl; Su, Kate; Werner, Michael

2008-03-01

119

Heat transfer enhancement in laminar slurry pipe flows with power law thermal conductivities

Generalized theoretical results for heat transfer in laminar pipe flow with power law varying thermal conductivities are presented. The study is motivated by experimental observations that above a threshold shear rate the effective thermal conductivity for disperse two-phase mixtures increases with shear rate. Using a relatively general three parameter power law model for conductivity as a function of shear rate,

C. W. Sohn; M. M. Chen

1984-01-01

120

Power-law tail probabilities of drainage areas in river basins

The significance of power-law tail probabilities of drainage areas in river basins was discussed. The convergence to a power law was not observed for all underlying distributions, but for a large class of statistical distributions with specific limiting properties. The article also discussed about the scaling properties of topologic and geometric network properties in river basins.

Veitzer, S. A.; Troutman, B. M.; Gupta, V. K.

2003-01-01

121

A study of optimum load capacity of slider bearings lubricated with power law fluids

A general theoretical study of an infinitely wide lubricated slider bearing is presented, considering the lubricant to be an incompressible, isothermal, power law fluid. A set of algebraic equations is developed to obtain the pressure gradient for any value of the power law index. To illustrate the mathematical development, the set of equations is used to calculate the pressure gradient

N. C. Das

1999-01-01

122

Power-laws from critical gravitiational collapse: The mass distribution of subsolar objects

At large mass, the initial mass function [IMF], which describes the size distribution of stellar objects, is characterized by a power-law with the Salpeter exponent. At small [substellar] mass, theory indicates that there must be some change in this power law. Indeed, direct observation indicates that the IMF is certainly modified below approximately one-tenth of a solar mass. We demonstrate

Nicolas Yunes

2004-01-01

123

A New Yield Power Law Analysis Tool Improves Insulating Annular Fluid Design

Engineering analysis can help avoid significant problems in deep offshore completions. Because yield- power-law fluids offer better convective heat-loss control, new algorithms have been developed that allow the modeling of convective heat transfer through such fluids. Special cases - Newtonian, Bingham Plastic, and power law - were also included in this model. This new software permits appropriate annular fluid design

Robert L. Horton; Thor S. Froitland; William E. Foxenberg; Dave Knox

2005-01-01

124

NASA Astrophysics Data System (ADS)

In this paper we determine the tidal distortion parameter km of the secondary partner (mass loser) of the semi-detached eclipsing binary system V621 Cen by comparing the phenomenologically determined orbital period P=3.683549(11) d to the Keplerian one P computed with the values of the relevant system's parameters determined independently of the third Kepler law itself. Our result is km=-1.5±0.6. Using the periastron precession, as traditionally done with other eclipsing binaries in eccentric orbits, would have not been possible because of the circularity of the V621 Cen path.

Iorio, Lorenzo

2008-10-01

125

Power law distribution in high frequency financial data? An econometric analysis

NASA Astrophysics Data System (ADS)

Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov-Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.

Todorova, Lora; Vogt, Bodo

2011-11-01

126

Exergy analysis of a dual-level binary geothermal power plant

Exergy analysis of a 12.4 MW existing binary geothermal power plant is performed using actual plant data to assess the plant performance and pinpoint sites of primary exergy destruction. Exergy destruction throughout the plant is quantified and illustrated using an exergy flow diagram, and compared to the energy flow diagram. The causes of exergy destruction in the plant include the

Mehmet Kanoglu

2002-01-01

127

Energy dependence of power-spectral noise in X-ray binaries

NASA Astrophysics Data System (ADS)

Black hole and neutron star X-ray binaries show variability on time-scales ranging from milliseconds to years. In the last two decades a detailed phenomenological picture of short-term variability in low-mass X-ray binaries has emerged mainly based on RXTE observations that cover energies above 3 keV. This picture comprises periodic or quasi-periodic variability, seen as spikes or humps in power density spectra, that are superposed on broad noise components. The overall shape of the noise components as well as the occurrence of quasi-periodic oscillations is known to vary with the state of the X-ray binary. We are accomplishing a comprehensive study of archival XMM-Newton observations in timing or burst mode of more than ten black hole and more than thirty neutron star low-mass X-ray binaries to investigate the variability properties of these sources at softer energies where the thermal disk component starts to emerge.Here we present some results of the energy dependence of the noise component in power density spectra: a discussion of the energy dependence of the power spectral state that we found in the “plateau” state of GRS 1915+105 and the intermediate state of 4U 1630-47; the dependence of the break-frequency of the band-limited noise component as well as the quasi-periodic oscillations on the studied energy band in several X-ray binaries like GX 339-4 or Swift J1753.5-0127. We will discuss the implications of these findings for the picture of the accretion geometry in black hole X-ray binaries.

Stiele, Holger; Yu, Wenfei

2014-08-01

128

Multiplicative processes and power laws in human reaction times derived from hyperbolic functions

NASA Astrophysics Data System (ADS)

In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéron's law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipf's law are analyzed.

Medina, José M.

2012-04-01

129

NASA Astrophysics Data System (ADS)

Layered and nanotubular systems that are metallic or graphitic are known to exhibit unusual dispersive van der Waals (vdW) power laws under some circumstances. In this Brief Report we investigate the vdW power laws of bulk and finite layered systems and their interactions with other layered systems and atoms in the electromagnetically nonretarded case. The investigation reveals substantial difference between “cleavage” and “exfoliation” of graphite and metals where cleavage obeys a C2D-2 vdW power law while exfoliation obeys a C3log(D/D0)D-3 law for graphitics and a C5/2D-5/2 law for layered metals. This leads to questions of relevance in the interpretation of experimental results for these systems which have previously assumed more trivial differences. Furthermore we gather further insight into the effect of scale on the vdW power laws of systems that simultaneously exhibit macroscopic and nanoscopic dimensions. We show that, for metallic and graphitic layered systems, the known “unusual” power laws can be reduced to standard or near standard power laws when the effective scale of one or more dimension is changed. This allows better identification of the systems for which the commonly employed “sum of C6D-6 ” type vdW methods might be valid such as layered bulk to layered bulk and layered bulk to atom.

Gould, Tim; Gray, Evan; Dobson, John F.

2009-03-01

130

Raft River binary-cycle geothermal pilot power plant final report

The design and performance of a 5-MW(e) binary-cycle pilot power plant that used a moderate-temperature hydrothermal resource, with isobutane as a working fluid, are examined. Operating problems experienced and solutions found are discussed and recommendations are made for improvements to future power plant designs. The plant and individual systems are analyzed for design specification versus actual performance figures.

Bliem, C.J.; Walrath, L.F.

1983-04-01

131

Swings between rotation and accretion power in a binary millisecond pulsar.

It is thought that neutron stars in low-mass binary systems can accrete matter and angular momentum from the companion star and be spun-up to millisecond rotational periods. During the accretion stage, the system is called a low-mass X-ray binary, and bright X-ray emission is observed. When the rate of mass transfer decreases in the later evolutionary stages, these binaries host a radio millisecond pulsar whose emission is powered by the neutron star's rotating magnetic field. This evolutionary model is supported by the detection of millisecond X-ray pulsations from several accreting neutron stars and also by the evidence for a past accretion disc in a rotation-powered millisecond pulsar. It has been proposed that a rotation-powered pulsar may temporarily switch on during periods of low mass inflow in some such systems. Only indirect evidence for this transition has hitherto been observed. Here we report observations of accretion-powered, millisecond X-ray pulsations from a neutron star previously seen as a rotation-powered radio pulsar. Within a few days after a month-long X-ray outburst, radio pulses were again detected. This not only shows the evolutionary link between accretion and rotation-powered millisecond pulsars, but also that some systems can swing between the two states on very short timescales. PMID:24067710

Papitto, A; Ferrigno, C; Bozzo, E; Rea, N; Pavan, L; Burderi, L; Burgay, M; Campana, S; Di Salvo, T; Falanga, M; Filipovi?, M D; Freire, P C C; Hessels, J W T; Possenti, A; Ransom, S M; Riggio, A; Romano, P; Sarkissian, J M; Stairs, I H; Stella, L; Torres, D F; Wieringa, M H; Wong, G F

2013-09-26

132

Can power-law scaling and neuronal avalanches arise from stochastic dynamics?

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain activity and show that event size distributions defined as negative LFP peaks can be close to power-law distributions. However, this result is not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov-Smirnov test. Similar power-law scaling is observed for surrogate signals, suggesting that power-law scaling may be a generic property of thresholded stochastic processes. We next investigate this problem analytically, and show that, indeed, stochastic processes can produce spurious power-law scaling without the presence of underlying self-organized criticality. However, this power-law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov-Smirnov test. The same analysis was also performed on an artificial network known to display self-organized criticality. In this case, both the graphical representations and the rigorous statistical analysis reveal with no ambiguity that the avalanche size is distributed as a power-law. We conclude that logarithmic representations can lead to spurious power-law scaling induced by the stochastic nature of the phenomenon. This apparent power-law scaling does not constitute a proof of self-organized criticality, which should be demonstrated by more stringent statistical tests. PMID:20161798

Touboul, Jonathan; Destexhe, Alain

2010-01-01

133

Summary of Investigations of the Use of Modified Turbine Inlet Conditions in a Binary Power Plant

Investigators at the Idaho National Engineering and Environmental Laboratory (INEEL) are developing technologies that will enhance the feasibility of generating electrical power from a hydrothermal resource. One of the concepts investigated is the use of modified inlet conditions in geothermal binary power plant turbines to increase the power generation. An inlet condition of interest allows the expanding vapor to enter the two-phase region, a mode of operation typically avoided because of concern that condensate would form and damage the turbine, degrading performance. INEEL investigators postulated that initially a supersaturated vapor would be supported, and that no turbine damage would occur. This paper summarizes the investigation of these expansions that began with testing of their condensation behavior, and culminated with the incorporation of these expansions into the operation of several commercial binary plant turbines.

Mines, Gregory Lee

2000-09-01

134

Summary of investigations of the use of modified turbine inlet conditions in a binary power plant

Investigators at the Idaho National Engineering and Environmental Laboratory (INEEL) are developing technologies that will enhance the feasibility of generating electrical power from a hydrothermal resource. One of the concepts investigated is the use of modified inlet conditions in geothermal binary power plant turbines to increase the power generation. An inlet condition of interest allows the expanding vapor to enter the two-phase region, a mode of operation typically avoided because of concern that condensate would form and damage the turbine, degrading performance. INEEL investigators postulated that initially a supersaturated vapor would be supported, and that no turbine damage would occur. This paper summarizes the investigation of these expansions that began with testing of their condensation behavior, and culminated with the incorporation of these expansions into the operation of several commercial binary plant turbines.

G. L. Mines

2000-09-24

135

Escape rate for the power-law distribution in low-to-intermediate damping

NASA Astrophysics Data System (ADS)

Escape rate in the low-to-intermediate damping connecting the low damping with the intermediate damping is established for the power-law distribution on the basis of flux over population theory. We extend the escape rate in the low damping to the low-to-intermediate damping, and get an expression for the power-law distribution. Then we apply the escape rate for the power-law distribution to the experimental study of the excited-state isomerization, and show a good agreement with the experimental value. The extra current and the improvement of the absorbing boundary condition are discussed.

Zhou, Yanjun; Du, Jiulin

2014-06-01

136

Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?

NASA Astrophysics Data System (ADS)

We examine whether the principle of detailed balance holds for the power-law distributions that are generated from the well-known two-variable Langevin equation and the associated Fokker-Planck equations. With the detailed balance and the generalized fluctuation-dissipation relation, we derive analytically the stationary power-law distribution from the Ito’s, Stratonovich’s and Zwanzig’s Fokker-Planck equations, and conclude that the power-law distributions can either be a stationary nonequilibrium distribution or an equilibrium distribution, which depend on information about the form of the diffusion coefficient function and the existence and uniqueness of an equilibrium state.

Guo, Ran; Du, Jiulin

2014-07-01

137

Blinking in quantum dots: The origin of the grey state and power law statistics

NASA Astrophysics Data System (ADS)

Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.

Ye, Mao; Searson, Peter C.

2011-09-01

138

AEGIS: A MULTIWAVELENGTH STUDY OF SPITZER POWER-LAW GALAXIES

This paper analyzes a sample of 489 Spitzer/Infrared Array Camera (IRAC) sources in the Extended Groth Strip (EGS), whose spectral energy distributions fit a red power law (PL) from 3.6 to 8.0 {mu}m. The median redshift for sources with known redshifts is (z) = 1.6. Though all or nearly all of the sample galaxies are likely to be active galactic nuclei (AGNs), only 33% were detected in the EGS X-ray survey (AEGIS-X) using 200 ks Chandra observations. The detected sources are X-ray luminous with L {sub X}>10{sup 43} erg s{sup -1} and moderately to heavily obscured with N {sub H}>10{sup 22} cm{sup -2}. Stacking the X-ray-undetected sample members yields a statistically significant X-ray signal, suggesting that they are on average more distant or more obscured than sources with X-ray detections. The ratio of X-ray to mid-infrared fluxes suggests that a substantial fraction of the sources undetected in X-rays are obscured at the Compton-thick level, in contrast to the X-ray-detected sources, all of which appear to be Compton thin. For the X-ray-detected PL sources with redshifts, an X-ray luminosity L {sub X} {approx} 10{sup 44} erg s{sup -1} marks a transition between low-luminosity, blue sources dominated by the host galaxy to high-luminosity, red PL sources dominated by nuclear activity. X-ray-to-optical ratios, infrared variability, and 24 {mu}m properties of the sample are consistent with the identification of infrared PL sources as active nuclei, but a rough estimate is that only 22% of AGNs are selected by the PL criteria. Comparison of the PL selection technique and various IRAC color criteria for identifying AGNs confirms that high-redshift samples selected via simple IRAC colors may be heavily contaminated by starlight-dominated objects.

Park, S. Q.; Barmby, P.; Willner, S. P.; Ashby, M. L. N.; Fazio, G. G. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Georgakakis, A. [National Observatory of Athens, I. Metaxa and V. Paulou, Athens 15236 (Greece); Ivison, R. J. [UK Astronomy Technology Centre, Science and Technology Facilities Council, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ (United Kingdom); Konidaris, N. P.; Rosario, D. J. [UCO/Lick Observatory, University of California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 (United States); Miyazaki, S. [National Astronomical Observatory of Japan, Osawa Mitaka, Tokyo 181-8588 (Japan); Nandra, K., E-mail: spark@cfa.harvard.ed [Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ (United Kingdom)

2010-07-10

139

The duration of recessions follows an exponential not a power law

NASA Astrophysics Data System (ADS)

Ormerod and Mounfield (Physica A 293 (2001) 573) analyse GDP data of 17 leading capitalist economies from 1870 to 1994 and conclude that the frequency of the duration of recessions is consistent with a power law. But in fact the data is consistent with an exponential (Boltzmann-Gibbs) law.

Wright, Ian

2005-01-01

140

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities

Wayne S. Kendal; Bent Jørgensen

2011-01-01

141

New statistic for financial return distributions: Power-law or exponential?

NASA Astrophysics Data System (ADS)

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power-laws or for exponentials correspondingly, regardless of the value of the exponent or of the form parameter. This is particularly useful for testing the structure of a distribution (power-law or not, exponential or not) independently of the possibility of quantifying the values of the parameters. We apply these statistics to the distribution of returns of one century of daily data for the Dow Jones Industrial Average and over 1 year of 5-min data of the Nasdaq Composite index. Our analysis confirms previous works showing the tendency for the tails to resemble more and more a power-law for the highest quantiles but we can detect clear deviations that suggest that the structure of the tails of the distributions of returns is more complex than usually assumed; it is clearly more complex that just a power-law. Our new TP- and TE-statistic should also be useful for other applications in the natural sciences as a powerful non-parametric test for power-laws and exponentials.

Pisarenko, V.; Sornette, D.

2006-07-01

142

Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales

NASA Technical Reports Server (NTRS)

The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.

Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.

2006-01-01

143

Ultra-relativistic nonthermal power-law ensembles: Cosmic-ray electrons and positron fraction

NASA Astrophysics Data System (ADS)

Thermodynamically stable ultra-relativistic power-law distributions are employed to model the recently measured cosmic-ray electron flux and the positron fraction. The probability density of power-law ensembles in phase space is derived, as well as an extensive entropy functional. The phase-space measure is transformed into a spectral number density, parameterized with the Lorentz factor of the charges and quantized in Fermi statistics. Relativistic power-law ensembles admit positive heat capacities and compressibilities ensuring mechanical stability as well as positive root mean squares quantifying thermodynamic fluctuations. The wideband spectral fitting of dilute nonthermal electron-positron plasmas with ultra-relativistic power-law densities is explained.

Tomaschitz, Roman

2014-01-01

144

Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown. PMID:15169127

Sato, Aki-Hiro

2004-04-01

145

NASA Astrophysics Data System (ADS)

Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.

Sato, Aki-Hiro

2004-04-01

146

Research on power-law acoustic transient signal detection based on wavelet transform

NASA Astrophysics Data System (ADS)

Aiming at the characteristics of acoustic transient signal emitted from antisubmarine weapon which is being dropped into water (torpedo, aerial sonobuoy and rocket assisted depth charge etc.), such as short duration, low SNR, abruptness and instability, based on traditional power-law detector, a new method to detect acoustic transient signal is proposed. Firstly wavelet transform is used to de-noise signal, removes random spectrum components and improves SNR. Then Power- Law detector is adopted to detect transient signal. The simulation results show the method can effectively extract envelop characteristic of transient signal on the condition of low SNR. The performance of WT-Power-Law markedly outgoes that of traditional Power-Law detection method.

Han, Jian-hui; Yang, Ri-jie; Wang, Wei

2007-11-01

147

Exploring the effect of power law social popularity on language evolution.

Abstract We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the ? value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors. PMID:24730762

Gong, Tao; Shuai, Lan

2014-01-01

148

Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

NASA Astrophysics Data System (ADS)

In a one-dimensional (1D) superconductor, zero-temperature quantum fluctuations destroy phase coherence. Here we put forward a mechanism which can restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard model with power-law hopping using Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, noninteger spatial dimensionality deff. For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppresses fluctuations and restores superconducting long-range order for any deff>1, at zero temperature. A detailed DMRG analysis fully supports these findings. These results are also of direct relevance to quantum magnetism as our model can be mapped onto an S=1/2 XXZ spin chain with power-law decaying couplings, which can be studied experimentally with cold-ion-trap techniques.

Lobos, Alejandro M.; Tezuka, Masaki; García-García, Antonio M.

2013-10-01

149

New model for single spherical particle settling velocity in power law (visco-inelastic) fluids

Particle settling in a non-Newtonian power law fluid is of interest to many industrial applications, including chemical, food, pharmaceutical, and petroleum industry. Conventionally, the Newtonian model for the drag coefficient prediction is extended to non-Newtonian fluids. The approach of merely replacing a viscosity term in Newtonian correlation with a power law apparent viscosity is reported to be inadequate.In this investigation,

Subhash N. Shah; Youness El Fadili; R. P. Chhabra

2007-01-01

150

Steady flow of a power-law fluid past a cylinder

Summary Considered in this paper is the two-dimensional steady flow of a power-law fluid past a stationary circular cylinder. The governing nonlinear equations, expressed in terms of a stream function and vorticity, were solved by finite differences for Reynolds numbers (based on the radius of the cylinder)R=5,20, 40 for various power-law indices,n. Parameters such as the drag coefficient, separation angle,

S. J. D. D'Alessio; J. P. Pascal

1996-01-01

151

Two Power-Law States of the Ultraluminous X-Ray Source IC 342 X-1

NASA Astrophysics Data System (ADS)

In order to elucidate the emission properties of ultraluminous X-ray sources (ULXs) during their power-law (PL) state, we examined long-term X-ray spectral data of IC 342 X-1 during its PL state by using our own Suzaku data and archival data by XMM-Newton, Chandra, and Swift observations. The PL state of this source seems to be classified into two sub-states in terms of the X-ray luminosities in the 0.5-10 keV band: the low-luminosity PL state with (4-6) × 1039 erg s-1 and the high-luminosity one with (1.1-1.4) × 1040 erg s-1 . During Suzaku observations, which were made in 2010 August and 2011 March, X-1 stayed in the low-luminosity PL state. The observed X-ray luminosity (4.9-5.6 × 1039 erg s-1) and the spectral shape (photon index = 1.67-1.83) slightly changed between the two observations. Using the Suzaku PIN detector, we for the first time confirmed a PL tail extending up to at least 20 keV with no signatures of a high-energy turnover in both of the Suzaku observations. In contrast, a turnover at about 6 keV was observed during the high-luminosity PL state in 2004 and 2005 with XMM-Newton. Importantly, the photon indices are similar between the two PL states, and so are the Compton y-parameters of y ˜ 1, which indicates a similar energy balance (between the corona and the accretion disk) holding in the two PL states despite different electron temperatures. From spectral similarities with recent studies about other ULXs, and the Galactic black-hole binary GRS 1915+ 105, IC 342 X-1 is also likely to be in a state with a supercritical accretion rate, although more sensitive higher energy observations would be necessary to make any conclusion.

Yoshida, Tessei; Isobe, Naoki; Mineshige, Shin; Kubota, Aya; Mizuno, Tsunefumi; Saitou, Kei

2013-04-01

152

On the origin of power-law rheology during the evolution of damage

NASA Astrophysics Data System (ADS)

Many composite materials, including rocks undergoing semi-brittle failure by stress-enhanced corrosion reactions, exhibit power law scaling between bulk stress and strain rate. Chemical reaction rate theory on a uniform material predicts instead an exponential dependence, so mean field models to account for power law behaviour usually require a specific (often power-law) underlying distribution of local material properties to account for this, ideally conditioned on experimental and theoretical studies of microstructures. This mean field approach however breaks down at higher crack density, where bulk properties also depend on the collective dynamics or interaction of a population of microstructures. To examine the relative contribution of material heterogeneity and crack-crack interactions, we develop a 2-dimensional spring-dashpot network with breaking bonds, and investigate the influence of the distribution of microscopic relaxation times generate a macroscopic rheology of power-law form. Specifically, we examine the possibility of non-power-law microscopic heterogeneity, e.g. a Gaussian distribution of relaxation times, leading to macroscopic power-law rheology.

Kawada, Yusuke; Naylor, Mark; Touati, Sarah; Main, Ian

2010-05-01

153

Frequency dependence of solar flare occurrence rates—inferred from power-law distribution

NASA Astrophysics Data System (ADS)

Based on the frequency dependence of the power-law distribution of the peak fluxes in 486 radio bursts in 1-35 GHz observed by Nobeyama Radio Polarimeters (see Song et al. in Astrophys. J. 750:160, 2012), we have first suggested in this paper that the events with power-law behaviors may be emitted from the optically-thin regions, which can be considered as a good measure for the flare energy release. This result is supported by that both the power-law and optical-thin events gradually increase with radio frequencies, which are well fitted by a power-law function with similar indices of 0.48 and 0.80, respectively. Moreover, a flare occurrence rate is newly defined by the power-law event number in per unit frequency. Its values in lower frequencies are evidently larger than those in higher frequencies, which just imply that most flares are trigged in higher corona. Hence, the frequency variation of power-law event number may indicate different energy dissipation rates on different coronal heights.

Song, Qiwu; Huang, Guangli; Huang, Yu

2013-09-01

154

The statistical overlap theory of chromatography using power law (fractal) statistics.

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small ?) is shown to generate more uniform chromatograms. Large scale range chromatograms (large ?) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics. PMID:22088670

Schure, Mark R; Davis, Joe M

2011-12-30

155

ANN based optimization of supercritical ORC-Binary geothermal power plant: Simav case study

Artificial neural network is a new tool, which works rapidly for decision making and modeling of the processes within the expertise. Therefore, ANN can be a solution for the design and optimization of complex power cycles, such as ORC-Binary. In the present study, the back-propagation learning algorithm with three different variants, namely Levenberg–Marguardt (LM), Pola-Ribiere Conjugate Gradient (CGP), and Scaled

Oguz Arslan; Ozge Yetik

2011-01-01

156

Second law analysis of a combined power plant.

National Technical Information Service (NTIS)

This thesis is an examination of a combined power plant, based on an exergy analysis. The analysis contains both measured values and theoretical ones for the power plant. It also contains theoretical calculations for the origin of the exergy losses. Calcu...

U. Mathiasson T. Olsson

1991-01-01

157

Power law scaling in synchronization of brain signals depends on cognitive load

As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors.

Tinker, Jesse; Velazquez, Jose Luis Perez

2014-01-01

158

Second law analysis of solar powered absorption cooling cycles and systems

The Second Law of Thermodynamics is used to analyze solar powered absorption cooling cycles and systems. Irreversibility is used as a figure of merit for components and cycles. The irreversibility of individual components is determined for several solar-powered absorption cycles and systems. The understanding of the causes of these irreversibilities identifies the areas of possible cycle and system improvements.

D. K. Anand; W. J. Kennish; K. W. Lindler; S. Schweitzer

1984-01-01

159

Statistical evidence for power law temporal correlations in exploratory behaviour of rats.

Dynamics of exploratory behaviour of rats and home base establishment is investigated. Time series of instantaneous speed of rats was computed from their position during exploration. The probability distribution function (PDF) of the speed obeys a power law distribution with exponents ranging from 2.1 to 2.32. The PDF of the recurrence time of large speed also exhibits a power law, P(?) ~ ?(??) with ? from 1.56 to 2.30. The power spectrum of the speed is in general agreement with the 1/f spectrum reported earlier. These observations indicate that the acquisition of spatial information during exploration is self-organized with power law temporal correlations. This provides a possible explanation for the home base behaviour of rats during exploration. The exploratory behaviour of rats resembles other systems exhibiting self-organized criticality, e.g., earthquakes, solar flares etc. PMID:20688133

Yadav, Chetan K; Verma, Mahendra K; Ghosh, Subhendu

2010-01-01

160

The fractal nature of nature: power laws, ecological complexity and biodiversity.

Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science.

Brown, James H; Gupta, Vijay K; Li, Bai-Lian; Milne, Bruce T; Restrepo, Carla; West, Geoffrey B

2002-01-01

161

Second Law Analysis of a Conventional Steam Power Plant.

National Technical Information Service (NTIS)

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature ...

G. Liu R. H. Turner Y. A. Cengel

1993-01-01

162

NASA Technical Reports Server (NTRS)

Magnetospheric radio frequency emission power has been shown to vary as a function of both solar wind and planetary values such as magnetic field by Kaiser and Desch (1984). Planetary magnetic fields have been shown to scale with planetary variables such as density and angular momentum by numerous researchers. This paper combines two magnetic scaling laws with the radiometric law to yield 'Bode's'-type laws governing planetary radio emissions. Further analysis allows the reduction of variables to planetary mass and orbital distance. These generalized laws are then used to predict the power otuput of Neptune to be about 1.6 x 10 to the 7th W; with the intensity peaking at about 3 MHz.

Million, M. A.; Goertz, C. K.

1988-01-01

163

Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

NASA Astrophysics Data System (ADS)

Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy ($E_c$). The growth rate of LWs increases with the steepness index ($\\delta$) and decreases with the power-law index ($\\alpha$). The wave number of the fastest growing LWs ($k\\lambda_D$), decreases with the characteristic velocity of the power-law electrons ($v_{c}=\\sqrt{2E_{c}/m_{e}}$) and increases with the thermal velocity of ambient electrons ($v_T$). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.

Tang, Jianfei; Wu, Dejin; Zhao, Guoqing; Chen, Ling; Tan, Chengming

2014-06-01

164

Predicting the long tail of book sales: Unearthing the power-law exponent

NASA Astrophysics Data System (ADS)

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.

Fenner, Trevor; Levene, Mark; Loizou, George

2010-06-01

165

Alpha-power law MOSFET model and its applications to CMOS inverter delay and other formulas

An ?-power-law MOS model that includes the carrier velocity saturation effect, which becomes prominent in short-channel MOSFETs, is introduced. The model is an extension of Shockley's square-law MOS model in the saturation region. Since the model is simple, it can be used to handle MOSFET circuits analytically and can predict the circuit behavior in the submicrometer region. Using the model,

T. Sakurai; A. R. Newton

1990-01-01

166

Power-Law Template for IR Point Source Clustering

We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545 and 857 GHz, over angular scales 100 < l < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 um; 1000 < l < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148

Graeme E. Addison; Joanna Dunkley; Amir Hajian; Marco Viero; J. Richard Bond; Sudeep Das; Mark Devlin; Mark Halpern; Adam Hincks; Renée Hlozek; Tobias A. Marriage; Kavilan Moodley; Lyman A. Page; Erik D. Reese; Douglas Scott; David N. Spergel; Suzanne T. Staggs; Edward Wollack

2011-01-01

167

Power law scaling of topographic depressions and their hydrologic connectivity

NASA Astrophysics Data System (ADS)

Topographic depressions, areas of no lateral surface flow, are ubiquitous characteristics of the land surface that control many ecosystem and biogeochemical processes. High density of depressions increases the surface storage capacity, whereas lower depression density increases runoff, thus influencing soil moisture states, hydrologic connectivity, and the climate-soil-vegetation interactions. With the widespread availability of high-resolution lidar-based digital elevation model (lDEM) data, it is now possible to identify and characterize the structure of the spatial distribution of topographic depressions for incorporation in ecohydrologic and biogeochemical studies. Here we use lDEM data to document the prevalence and patterns of topographic depressions across five different landscapes in the United States and quantitatively characterize the probability distribution of attributes, such as surface area, storage volume, and the distance to the nearest neighbor. Through the use of a depression identification algorithm, we show that these probability distributions of attributes follow scaling laws indicative of a structure in which a large fraction of land surface areas can consist of high number of topographic depressions of all sizes and can account for 4 to 21 mm of depression storage. This implies that the impacts of small-scale topographic depressions in the landscapes on the redistribution of material fluxes, evaporation, and hydrologic connectivity are quite significant.

Le, Phong V. V.; Kumar, Praveen

2014-03-01

168

Effective velocity power laws for electron-neutral collision frequencies. [in ionosphere

NASA Technical Reports Server (NTRS)

Calculations of electron transport coefficients in the ionosphere are simplified if the electron-neutral collision frequency can be expressed as a power law in velocity. A new method for determining the effective power law representation for electron-neutral collision frequencies of arbitrary velocity dependence is presented. This method is applied to ionospheric gases in a model calculation. Comparison with similar results of Schunk and Walker and with exact calculations of transport coefficient correction factors demonstrates this technique to be more accurate than the other. Effective power law indexes are computed for both Banks' and Itikawa's collision frequencies. Relative differences between these indexes are found to be considerably larger than the differences between the collision frequencies themselves; however, the effects on transport calculations are shown to be smaller.

Comfort, R. H.

1975-01-01

169

NASA Astrophysics Data System (ADS)

Power law distributions of macroscopic observables are ubiquitous in both the natural and social sciences. They are indicative of correlated, cooperative phenomena between groups of interacting agents at the microscopic level. In this paper, we argue that when one is considering aggregate macroeconomic data (annual growth rates in real per capita GDP in the seventeen leading capitalist economies from 1870 through to 1994) the magnitude and duration of recessions over the business cycle do indeed follow power law like behaviour for a significant proportion of the data (demonstrating the existence of cooperative phenomena amongst economic agents). Crucially, however, there are systematic deviations from this behaviour when one considers the frequency of occurrence of large recessions. Under these circumstances the power law scaling breaks down. It is argued that it is the adaptive behaviour of the agents (their ability to recognise the changing economic environment) which modifies their cooperative behaviour.

Ormerod, Paul; Mounfield, Craig

2001-04-01

170

Power-law distributions in random multiplicative processes with non-Gaussian colored multipliers

NASA Astrophysics Data System (ADS)

One class of universal mechanisms that generate power-law probability distributions is that of random multiplicative processes. In this paper, we consider a multiplicative Langevin equation driven by non-Gaussian colored multipliers. We analytically derive a formula that relates the power-law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two-valued Markov process. We also investigate the relationship between our treatment and the large deviation analysis of time series, and demonstrate the appearance of log-periodic fluctuations superimposed on the power-law distribution due to the non-Gaussian nature of the multipliers.

Kitada, Shuya

2006-10-01

171

Power-law X-ray and gamma-ray emission from relativistic thermal plasmas

NASA Technical Reports Server (NTRS)

A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.

Zdziarski, A. A.

1985-01-01

172

Power-law decay of the spatial correlation function in exciton-polariton condensates

We create a large exciton-polariton condensate and employ a Michelson interferometer setup to characterize the short- and long-distance behavior of the first order spatial correlation function. Our experimental results show distinct features of both the two-dimensional and nonequilibrium characters of the condensate. We find that the gaussian short-distance decay is followed by a power-law decay at longer distances, as expected for a two-dimensional condensate. The exponent of the power law is measured in the range 0.9–1.2, larger than is possible in equilibrium. We compare the experimental results to a theoretical model to understand the features required to observe a power law and to clarify the influence of external noise on spatial coherence in nonequilibrium phase transitions. Our results indicate that Berezinskii–Kosterlitz–Thouless-like phase order survives in open-dissipative systems.

Roumpos, Georgios; Lohse, Michael; Nitsche, Wolfgang H.; Keeling, Jonathan; Szymanska, Marzena Hanna; Littlewood, Peter B.; Loffler, Andreas; Hofling, Sven; Worschech, Lukas; Forchel, Alfred; Yamamoto, Yoshihisa

2012-01-01

173

Tanner's simple model of crystallization for power-law fluids extended

NASA Astrophysics Data System (ADS)

Tanner et al. (Rheol. Acta, 48, 2009, 499-507) presented a simple model for power-law fluids in which it was possible to derive semi-analytical solutions based on some key simplifying assumptions. These include shear flows in tubes and channels, a 'step function' or 'amorphous-frozen' model of the viscosity changes due to crystallization, and a power-law index of 1/3 valid for a crystallizing poly(butene-1) polymer for which experiments were available. Their work compared favorably with experimental data for the onset of crystallization times. In the present work, we have repeated and verified the Tanner model and extended it to power-law indices from 1 (Newtonian behavior) down to 0 (extreme shear thinning) in order to study the effect of the different problem parameters and place a set of results that will act as reference for future and more detailed computational calculations through the Finite Element Method.

Mitsoulis, E.; Zisis, Th.

2014-05-01

174

The rate coefficients of unimolecular reactions in the systems with power-law distributions

NASA Astrophysics Data System (ADS)

The rate coefficient formulae of unimolecular reactions are generalized to the systems with the power-law distributions based on nonextensive statistics, and the power-law rate coefficients are derived in the high and low pressure limits, respectively. The numerical analyses are made of the rate coefficients as functions of the ?-parameter, the threshold energy, the temperature and the number of degrees of freedom. We show that the new rate coefficients depend strongly on the ?-parameter different from one (thus from a Boltzmann-Gibbs distribution). Two unimolecular reactions, CH3CO?CH3+CO and CH3NC?CH3CN, are taken as application examples to calculate their power-law rate coefficients, which obtained with the ?-parameters slightly different from one can be exactly in agreement with all the experimental studies on these two reactions in the given temperature ranges.

Yin, Cangtao; Guo, Ran; Du, Jiulin

2014-08-01

175

NASA Astrophysics Data System (ADS)

In this paper, we propose a comprehensive analysis of ultrathin oxide reliability that includes the validation of the power law model (TBD˜ V-n), area scaling (TBD˜ A-1/?), and process optimization. We show that the power law exponent n (=38) of a pFET is less than that of a nFET (n=48). Then a proper area range for ? determination and process optimization for n improvement are pointed out, especially for pFETs. A novel explanation is discussed of ultrathin oxide pFET degradation behavior with lower decoupled plasma nitridation (DPN) pressure or higher substrate bias stress (Vbs>0 V) that lowers the exponent in power-law fitting. This phenomenon shortens the lifetime predicted for ultrathin oxide pFETs. From the view of reliability projections, a new failure criterion is suggested with and further extended to 65 nm technology and to higher operating voltage applications.

Shieh, Jerry; Lin, Cheng-Li; Kang, Ting-Kuo; Lo, Oswin; Chen, Ju-Ping; Su, K. C.

2006-01-01

176

Fertility heterogeneity as a mechanism for power law distributions of recurrence times

NASA Astrophysics Data System (ADS)

We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future events. Specifically, we analyze the impact of the power law distribution of fertilities with exponent ?, where the fertility of an event is the number of triggered events of first generation, on the probability distribution function (PDF) f(?) of the recurrence times ? between successive events. The other input of the model is an exponential law quantifying the PDF of waiting times between an event and its first generation triggered events, whose characteristic time scale is taken as our time unit. At short-time scales, we discover two intermediate power law asymptotics, f(?)˜?-(2-?) for ???c and f(?)˜?-? for ?c???1, where ?c is associated with the self-excited cascades of triggered events. For 1???1/?, we find a constant plateau f(?)?const, while at long times, 1/???, f(?)?e-?? has an exponential tail controlled by the arrival rate ? of exogenous events. These results demonstrate a novel mechanism for the generation of power laws in the distribution of recurrence times, which results from a power law distribution of fertilities in the presence of self-excitation and cascades of triggering.

Saichev, A.; Sornette, D.

2013-02-01

177

Unbounded Binary Search for a Fast and Accurate Maximum Power Point Tracking

NASA Astrophysics Data System (ADS)

This paper presents a technique for maximum power point tracking (MPPT) of a concentrating photovoltaic system using cell level power optimization. Perturb and observe (P&O) has been a standard for an MPPT, but it introduces a tradeoff between the tacking speed and the accuracy of the maximum power delivered. The P&O algorithm is not suitable for a rapid environmental condition change by partial shading and self-shading due to its tracking time being linear to the length of the voltage range. Some of researches have been worked on fast tracking but they come with internal ad hoc parameters. In this paper, by using the proposed unbounded binary search algorithm for the MPPT, tracking time becomes a logarithmic function of the voltage search range without ad hoc parameters.

Kim, Yong Sin; Winston, Roland

2011-12-01

178

Shape of gas flow paths causes power law tailing

In soil and\\/or groundwater remediation, we often see prolonged tailings: continuous outflow of low concentration pollutants for very long time, and in many cases power low behavior of late-time time-concentration curves. We considered that this kind of tailing can be caused by the shape of the gaseous flow introduced in saturated\\/unsaturated porous media. When gas is introduced to porous media,

T. Kawanishi; A. Sakami; Y. Hayashi

2004-01-01

179

Tweedie convergence: a mathematical basis for Taylor's power law, 1/f noise, and multifractality.

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality. PMID:22304168

Kendal, Wayne S; Jørgensen, Bent

2011-12-01

180

Tweedie convergence: A mathematical basis for Taylor's power law, 1/f noise, and multifractality

NASA Astrophysics Data System (ADS)

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/f noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/f noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/f noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/f noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/f noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality.

Kendal, Wayne S.; Jørgensen, Bent

2011-12-01

181

Non-Gaussian Fluctuations Resulting from Power-Law Trapping in a Lipid Bilayer

NASA Astrophysics Data System (ADS)

Anomalous diffusion in lipid bilayers is usually attributed to viscoelastic behavior. We compute the scaling exponent of relative fluctuations of the time-averaged mean square displacement in a lipid bilayer, by using a molecular dynamics simulation. According to the continuous time random walk theory, this exponent indicates non-Gaussian behavior caused by a power-law trapping time. Our results provide the first evidence that a lipid bilayer has not only viscoelastic properties but also trapping times distributed according to a power law.

Akimoto, Takuma; Yamamoto, Eiji; Yasuoka, Kenji; Hirano, Yoshinori; Yasui, Masato

2011-10-01

182

Non-Gaussian fluctuations resulting from power-law trapping in a lipid bilayer.

Anomalous diffusion in lipid bilayers is usually attributed to viscoelastic behavior. We compute the scaling exponent of relative fluctuations of the time-averaged mean square displacement in a lipid bilayer, by using a molecular dynamics simulation. According to the continuous time random walk theory, this exponent indicates non-Gaussian behavior caused by a power-law trapping time. Our results provide the first evidence that a lipid bilayer has not only viscoelastic properties but also trapping times distributed according to a power law. PMID:22107588

Akimoto, Takuma; Yamamoto, Eiji; Yasuoka, Kenji; Hirano, Yoshinori; Yasui, Masato

2011-10-21

183

Frequency Dependence of the Power-law Index of Solar Radio Bursts

NASA Astrophysics Data System (ADS)

We process solar flare observations of Nobeyama Radio Polarimeters with an improved maximum likelihood method developed recently by Clauset et al. The method accurately extracts power-law behaviors of the peak fluxes in 486 radio bursts at six frequencies (1-35 GHz) and shows an excellent performance in this study. The power-law indices on 1-35 GHz given by this study vary around 1.74-1.87, which is consistent with earlier statistics in different solar cycles and very close to the simulations of the avalanche model by Lu.

Song, Qiwu; Huang, Guangli; Tan, Baolin

2012-05-01

184

Power Law Inflation and the Cosmic No Hair Theorem in Brane World

We study the cosmic no hair theorem for anisotropic Bianchi models that admit power law inflation with a scalar field in the framework of Brane world. The power law inflationary solution obtained here is driven by the curvature term in the modified field equation in Brane. It is found that all Bianchi models except Bianchi type IX, transit to an inflationary regime with vanishing anisotropy. We note that in the Brane world anisotropic universe isotropizes much faster than that in the general theory of relativity.

Paul, B. C. [Physics Department, North Bengal University, Siliguri, Pin: 734 013 (India); Beesham, A. [Department of Mathematical Sciences, Zululand University, Kwadlangezwa (South Africa)

2006-11-03

185

NASA Astrophysics Data System (ADS)

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the updating of their states. We show with numerical simulation that these aptitudes can contribute to group formation or speciation in social fields. Moreover, they can lead to power-law topological correlations of complex networks. By coupling updating states of nodes with variation of connections in a network, structural properties with power-laws and functions like multifractality, spontaneous ranking and evolutionary branching of node states can emerge simultaneously from the present self-organized model of coevolutionary processes.

Zhu, Chen-Ping; Zhou, Tao; Yang, Hui-Jie; Xiong, Shi-Jie; Gu, Zhi-Ming; Shi, Da-Ning; He, Da-Ren; Wang, Bing-Hong

2008-02-01

186

Origin of power-law composition dependence in ionic transport glasses

NASA Astrophysics Data System (ADS)

The origin of a power-law correlation between ionic conductivity and cation-contents, found commonly in oxide and chalcogenide glasses, is discussed using the concept of configuration entropy. It is suggested that power-law dependence is primarily attributed to an increase in configuration entropy with mixing cation components into glasses. This effect reduces the potential barrier height to be surmounted by mobile ions, which results in a higher diffusion coefficient (and hence conductivity). The origin of anomalous pre-exponential factors of diffusion coefficient and conductivity can be interpreted in terms of the present context.

Shimakawa, K.; Wagner, T.

2013-04-01

187

Universal power-law index of energy spectrum in downstream region of quasi-parallel shocks

NASA Astrophysics Data System (ADS)

We have performed collisionless shock simulations using one-dimensional Hybrid particle-in-cell method to investigate the energy spectra around the quasi-parallel shocks. The system size is large enough (200,000 inertia length) to eliminate the unphysical effect caused by the upstream boundary. The obtained spectrum have the shape of power-law with exponentially falling off in higher energy as predicted previous simulations, however, the power-law indices and e-holding energy do not depend on the shock parameters of Mach number and shock angle. This independent profiles are obtained because the pitch angle distribution in the upstream region shows similar profile in each run.

Sugiyama, T.

2010-12-01

188

Steady flow of power-law fluids across an unconfined elliptical cylinder

The momentum transfer characteristics of the power-law fluid flow past an unconfined elliptic cylinder is investigated numerically by solving continuity and momentum equations using FLUENT (version 6.2) in the two-dimensional steady cross-flow regime. The influence of the power-law index (0.2?n?1.8), Reynolds number (0.01?Re?40) and the aspect ratio of the elliptic cylinder (0.2?E?5) on the local and global flow characteristics has

P. Sivakumar; Ram Prakash Bharti; R. P. Chhabra

2007-01-01

189

Alternative least-squares finite element models of Navier-Stokes equations for power-law fluids

Purpose – Most studies of power-law fluids are carried out using stress-based system of Navier-Stokes equations; and least-squares finite element models for vorticity-based equations of power-law fluids have not been explored yet. Also, there has been no study of the weak-form Galerkin formulation using the reduced integration penalty method (RIP) for power-law fluids. Based on these observations, the purpose of

V. P. Vallala; J. N. Reddy; K. S. Surana

2011-01-01

190

ERIC Educational Resources Information Center

Proposes a simple procedure based on an expansion of the exponential terms of Raoult's law by applying it to the case of the benzene-toluene mixture. The results with experimental values are presented as a table. (YP)

Cardinali, Mario Emilio; Giomini, Claudio

1989-01-01

191

Powerful Exact Unconditional Tests for Agreement between Two Raters with Binary Endpoints

Asymptotic and exact conditional approaches have often been used for testing agreement between two raters with binary outcomes. The exact conditional approach is guaranteed to respect the test size as compared to the traditionally used asymptotic approach based on the standardized Cohen's kappa coefficient. An alternative to the conditional approach is an unconditional strategy which relaxes the restriction of fixed marginal totals as in the conditional approach. Three exact unconditional hypothesis testing procedures are considered in this article: an approach based on maximization, an approach based on the conditional p-value and maximization, and an approach based on estimation and maximization. We compared these testing procedures based on the commonly used Cohen's kappa with regards to test size and power. We recommend the following two exact approaches for use in practice due to power advantages: the approach based on conditional p-value and maximization and the approach based on estimation and maximization.

Shan, Guogen; Wilding, Gregory E.

2014-01-01

192

A Brief History of Generative Models for Power Law and Lognormal Distributions

Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in

Michael Mitzenmacher

2003-01-01

193

Mittag-Leffler Waiting Time, Power Laws,Rarefaction, Continuous Time Random Walk, Diffusion Limit

We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a generic power law waiting time to the Mittag-Leffler waiting time distribution via rescaling and respeeding the clock of time. By a second respeeding (by rescaling the

Rudolf Gorenflo

2010-01-01

194

Melt-clast interaction and power-law size distribution of clasts in pseudotachylytes

NASA Astrophysics Data System (ADS)

Before the onset of melting along frictional interfaces, the wall rocks of seismic faults are crushed to generate a power-law grain-size distribution pattern. Theoretical analysis with the help of numerical models shows that, under conditions of uniform rim melting of the grains, the pre-melting power-law pattern survives in a modified form in the relicts, which occur as clasts in the quenched product, i.e. pseudotachylyte. The size distribution of clasts in experimentally produced as well as natural pseudotachylytes, including those from the Sarwar-Junia fault zone in western India, shows a pattern similar to that predicted by theoretical analysis. A micron-scale mantle of glass±microlites around a large number of clasts, and minute beads of glass set within glassy matrix, are the observed evidence of rim melting. Post-melting clast size distribution in the numerical models follows the relationship N?(1+ z/ z') - D, where N is number of clasts of size ? z. Size z may be represented by mean diameter r, or sectional area a, or volume v, and D(= D r, D a or D v) is the modified power-law exponent. z' (= r', a' or v') is a constant that depends on thickness ( ?) of uniform rim melting, and r'= ?, a' =?2, and v' =?3. The analysis suggests that the modified power-law clast-size distribution pattern is a characteristic feature of all fault-related pseudotachylytes.

Ray, Sumit Kumar

2004-10-01

195

Power law for the duration of recession and prosperity in Latin American countries

NASA Astrophysics Data System (ADS)

Ormerod and Mounfield [P. Ormerod, C. Mounfield, Power law distribution of duration and magnitude of recessions in capitalist economies: Breakdown of scaling, Physica A 293 (2001) 573] and Ausloos et al. [M. Ausloos, J. Mikiewicz, M. Sanglier, The durations of recession and prosperity: Does their distribution follow a power or an exponential law? Physica A 339 (2004) 548] have independently analyzed the duration of recessions for developed countries through the evolution of the GDP in different time windows. It was found that there is a power law governing the duration distribution. We have analyzed data collected from 19 Latin American countries in order to observe whether such results are valid or not for developing countries. The case of prosperity years is also discussed. We observe that the power law of recession time intervals, see Ref. [1], is valid for Latin American countries as well. Thus an interesting point is discovered: the same scaling time is found in the case of recessions for the three data sets (ca. 1 year), and this could represent a universal feature. Other time scale parameters differ significantly from each other.

Redelico, Francisco O.; Proto, Araceli N.; Ausloos, Marcel

2008-11-01

196

Power-law accelerating growth complex networks with mixed attachment mechanisms

NASA Astrophysics Data System (ADS)

In this paper, motivated by the thoughts and methods of the mixture of preferential and uniform attachments, we extend the Barabási-Albert (BA) model, and establish a network model with the power-law accelerating growth and the mixture of the two attachment mechanisms. In our model, the number of edges generated by each newly-introduced node is proportional to the power of ? (0??<1) of time t, i.e., mt?. By virtue of the continuum approach, we have deduced the degree distribution P(k,t) of our model with the extended power-law form P(k,t)=A(t)[. When the number of edges k generated by each new node is much greater than the value of B(t), the degree distribution P(k,t) will converge to the power-law form P(k,t)=A(t)k. When k is much less than the value of B(t), the degree distribution P(k,t) will converge to the exponential-law form P(k,t)={A(t)}/{[}e. By virtue of numerical simulations, we also discuss the dependence of the degree distribution P(k,t) on the model’s parameters (where t is considered as a constant in the simulations). Finally, we investigate the possible application of our model in the spreading and evolution of epidemics in some real-world systems.

Chen, Tao; Shao, Zhi-Gang

2012-04-01

197

A weighted penalty finite element method for the analysis of power-law fluid flow problems

In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid\\/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.

Chen Da-peng; Zhao Zhong

1990-01-01

198

Exponential and power-law contact distributions represent different atmospheric conditions.

It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions. PMID:21770775

Reynolds, A M

2011-12-01

199

Dampened Power Law: Reconciling the Tail Behavior of Financial Asset Returns

ABSTRACT This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is ba sed on a pure jump L´ evy process, wherein the jump arrival rate obeys a power law dampened,by an exponential function. The model allows for different degrees of dampening for positive and negative jumps, and also

L. Wu

2005-01-01

200

Model-based discrete relaxation process representation of band-limited power-law attenuation.

Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal derivatives. It has also been shown that certain continuous distributions may give causal wave equations with fractional-order temporal derivatives. This paper demonstrates analytically that if the wave-frequency ? satisfies ?L??????H, a continuous relaxation distribution populating only ??[?L,?H] gives the same effective wave equation as for a fully populated distribution. This insight sparks the main contribution: the elaboration of a method to determine discrete relaxation parameters intended for mimicking a desired attenuation behavior for band-limited waves. In particular, power-law attenuation is discussed as motivated by its prevalence in complex media, e.g., biological tissue. A Mittag-Leffler function related distribution of relaxation mechanisms has previously been shown to be related to the fractional Zener wave equation of three power-law attenuation regimes. Because these regimes correspond to power-law regimes in the relaxation distribution, the idea is to sample the distribution's compressibility contributions evenly in logarithmic frequency while appropriately taking the stepsize into account. This work thence claims to provide a model-based approach to determination of discrete relaxation parameters intended to adequately model attenuation power-laws. PMID:23464043

Näsholm, Sven Peter

2013-03-01

201

CALIBRATING A MARKET FRACTION MODEL TO THE POWER-LAW BEHAVIOUR IN THE DAX 30

Bounded rationality and heterogeneity have been incorporated in re- cent asset pricing literature to explain complicated market behaviour, such as market booms and crashes, and various stylized facts in high frequency data, such as volatility clustering, fat tails, and other power-law behaviour of returns, which are difficult to be explained by the standard asset pricing theory based on rational expectations

YOUWEI LI; XUE-ZHONG HE

202

An empirical analysis on the law of purchasing power parity and international economic deepening

This article empirically investigates the effect of international trade on the deviation of Purchasing Power Parity (PPP) law and on the international economic deepening in four developed countries (Japan, USA, UK and France), and three Asian developing ones (South Korea, Singapore and Malaysia), using International Financial Statistics (IFS) data issued by International Monetary Fund (IMF). Our results show that in

Takaaki Aoki

2013-01-01

203

Graph Structure in Three National Academic Webs: Power Laws with Anomalies.

ERIC Educational Resources Information Center

Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)

Thelwall, Mike; Wilkinson, David

2003-01-01

204

Universal correlations and power-law tails in financial covariance matrices

We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial

Gernot Akemann; Jonit Fischmann; Pierpaolo Vivo

2010-01-01

205

Fitting the Log Periodic Power Law to financial crashes: a critical analysis

A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condition. This paper examines these claims and the robustness of

David S. Bree; Nathan Lael Joseph

2010-01-01

206

A theory of power-law distributions in financial market fluctuations

Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financial system, huge databases now exist that facilitate the analysis of large fluctuations and the characterization of their statistical behaviour. Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations in stock price, trading volume and the number of

Xavier Gabaix; Parameswaran Gopikrishnan; Vasiliki Plerou; H. Eugene Stanley

2003-01-01

207

A new look at the laminar flow of power law fluids through granular beds

Summary The paper deals with laminar flow of power law fluids through granular beds. A critical review of the assumptions concerning the capillary model of the bed, applied by various authors, led us to the conclusion that the derivation of the correlation eq. [13] given byChristopher andMiddleman was based on a too simplified model of the granular bed. Taking advantage

Z. Kemblowski; M. Michniewicz

1979-01-01

208

Power-law cosmic expansion in f(R) gravity models

We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R{sup n} gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.

Goheer, Naureen; Larena, Julien [Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, Cape Town (South Africa); Dunsby, Peter K. S. [Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, Cape Town (South Africa); South African Astronomical Observatory, Observatory 7925, Cape Town (South Africa)

2009-09-15

209

NASA Astrophysics Data System (ADS)

In a recent publication [Phys. Rev. E 63, 047201 (2001)], Ausloos and Ivanova report power-law probability distributions, fractal properties, and antipersistent long-range correlations in the southern oscillation index. As a comparison with artificial short-range correlated data shows, most of these findings are possibly due to misleading interpretation of the analysis techniques used.

Metzler, Richard

2003-01-01

210

Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method

NASA Astrophysics Data System (ADS)

In this study, unsteady one-dimensional mass transfer during osmotic dehydration of apple was modeled using an approximate mathematical model. The mathematical model has been developed based on a power law profile approximation for moisture and solute concentrations in the spatial direction. The proposed model was validated by the experimental water loss and solute gain data, obtained from osmotic dehydration of infinite slab and cylindrical shape samples of apple in sucrose solutions (30, 40 and 50 % w/w), at different temperatures (30, 40 and 50 °C). The proposed model's predictions were also compared with the exact analytical and also a parabolic approximation model's predictions. The values of mean relative errors respect to the experimental data were estimated between 4.5 and 8.1 %, 6.5 and 10.2 %, and 15.0 and 19.1 %, for exact analytical, power law and parabolic approximation methods, respectively. Although the parabolic approximation leads to simpler relations, the power law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time. Considering both simplicity and precision of the mathematical models, the power law model for short dehydration times and the simplified exact analytical model for long dehydration times could be used for explanation of the variations of the average water loss and solute gain in the whole domain of dimensionless times.

Abbasi Souraki, B.; Tondro, H.; Ghavami, M.

2014-04-01

211

Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?

ERIC Educational Resources Information Center

Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less…

Bauer, Ben

2009-01-01

212

Evidence of power-law flow in the Mojave desert mantle.

Studies of the Earth's response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress-strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine--the most abundant mineral in the upper mantle--and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust. PMID:15282602

Freed, Andrew M; Bürgmann, Roland

2004-07-29

213

Laminar heat transfer for power-law fluids in thermal entrance region of annular sector ducts

NASA Astrophysics Data System (ADS)

Laminar heat transfer of a power law fluid in the thermal entrance region of an annular sector duct is analyzed. The effect of geometric shape, power law index, axial conduction and viscous dissipation are investigated. Both boundary conditions of uniform temperature and uniform heat flux peripherally are considered. The annular sector duct flow configuration is one of the common arrangements in industry, for example, compact heat exchangers, nuclear reactors and injection molds. The power law fluid is one of the frequently used non-Newtonian heat transferring media. It is important to understand the details of heat transfer and fluid flow for this type of application. The solution algorithm is based on a finite difference methodology. Numerical experiments are performed and comparisons are made between the results obtained and the existing limiting solutions to ensure the accuracy of the present numerical scheme. In the thermal entrance region, there exists a large difference in Nusselt number for different Peclet numbers. The viscous dissipation effect is stronger in the developing region than in the developed region. It is found that due to the reduction in friction and the increase in heat transfer rates, power law fluids with n less than 1 are better working fluids in heat exchange equipments.

Hsia, Rong Ping

214

Power law catchment-scale recessions arising from heterogeneous linear small-scale dynamics

Power law recession behavior has typically been attributed to the hydraulics of subsurface flows in the landscape (e.g., the Boussinesq equation). Many catchments exhibit enormous heterogeneity in their characteristics, such as the permeability of soils, hillslope length and gradient, and soil mantle thickness. In the paper we demonstrate using a simple linear flow model that the between-hillslope heterogeneity alone can

C. J. Harman; M. Sivapalan; P. Kumar

2009-01-01

215

Propagation\\/Inversion in viscoelastic power law media: application to ultrasonic laboratory data

Realistic propagation\\/inversion of seismic wave need a model which is mathematically rigorous, physically acceptable and flexible enough. Such a model need to include ab-sorption and dispersion effects and also to satisfy causality principle. Power laws are the simplest models of causal and attenuating media including absorption and dispersion effects. In this work we present an adaptation of viscoelastic inversion originally

A. Ribodetti; A. Hanyga

2003-01-01

216

Saturation and power law dependence of nonlinear waves guided by a single interface

The formalism recently developed by Langbein et al. (1985) is applied to study the effects of saturation and nonquadratic field dependences on waves guided by the interface between a self-focusing and normal dielectric medium. The power dependences of the propagation constant and field disributions are calculated for both power-law and saturable field-dependent dielectric constants. The general features are found to

G. I. Stegeman; C. T. Seaton; J. Ariyasu; T. P. Shen; J. V. Moloney

1986-01-01

217

Frequency variations of solar radio zebras and their power-law spectra

NASA Astrophysics Data System (ADS)

Context. During solar flares several types of radio bursts are observed. The fine striped structures of the type IV solar radio bursts are called zebras. Analyzing them provides important information about the plasma parameters of their radio sources. We present a new analysis of zebras. Aims: Power spectra of the frequency variations of zebras are computed to estimate the spectra of the plasma density variations in radio zebra sources. Methods: Frequency variations of zebra lines and the high-frequency boundary of the whole radio burst were determined with and without the frequency fitting. The computed time dependencies of these variations were analyzed with the Fourier method. Results: First, we computed the variation spectrum of the high-frequency boundary of the whole radio burst, which is composed of several zebra patterns. This power spectrum has a power-law form with a power-law index -1.65. Then, we selected three well-defined zebra-lines in three different zebra patterns and computed the spectra of their frequency variations. The power-law indices in these cases are found to be in the interval between -1.61 and -1.75. Finally, assuming that the zebra-line frequency is generated on the upper-hybrid frequency and that the plasma frequency ?pe is much higher than the electron-cyclotron frequency ?ce, the Fourier power spectra are interpreted to be those of the electron plasma density in zebra radio sources.

Karlický, M.

2014-01-01

218

In the framework of Fractional Action Cosmology (FAC), we study the generalized second law of thermodynamics for the Friedmann Universe enclosed by a boundary. We use the four well-known cosmic horizons as boundaries namely, apparent horizon, future event horizon, Hubble horizon and particle horizon. We construct the generalized second law (GSL) using and without using the first law of thermodynamics.

Ujjal Debnath; Mubasher Jamil; Surajit Chattopadhyay

2011-01-01

219

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence

NASA Astrophysics Data System (ADS)

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.

Kendal, Wayne S.; Jørgensen, Bent

2011-06-01

220

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence.

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism. PMID:21797449

Kendal, Wayne S; Jørgensen, Bent

2011-06-01

221

Forming limits of anisotropic sheets with non-power-law hardening

NASA Astrophysics Data System (ADS)

For aluminum alloys and some advanced high-strength steels, the tensile flow curve exhibits a tendency to saturate. The suitability of constitutive equations was analyzed for aluminum 6111-T4 and a general non-power-law hardening model was adopted in the derivation of forming limits incorporated material anisotropy with varying R-values. A bifurcation analysis was conducted for the left-hand-side FLD under the assumption of proportional loading and zero-extension necking orientation. Analytical results showed good correlation with Nakajima forming limit test data for aluminum sheets following Voce hardening law.

Chen, Jieshi; Chen, Jun; Xia, Cedric

2013-12-01

222

The steady flow of generalized Newtonian fluid around a stationary cylinder placed between two parallel plates was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of the Reynolds number Re and the Power law index n values.

Ignacijo Bilus; Primoz Ternik; Zoran Žuni?

2011-01-01

223

Strain-rate Dependence of Power-law Creep and Folding of Rocks

NASA Astrophysics Data System (ADS)

Kocks (1987) proposed how the kinetics of deformation associated with different stress levels results in different shear stress-shear strain rate behaviours, with a cross-over or threshold from thermally activated dislocation motion at low stresses to viscous glide at some critical shear stress. Cordier (pers. comm.; Carrez et al., 2010) clarified this transition at least for MgO through atomistic, single dislocation and Dislocation Dynamics calculations. These studies indicate that the power-law relations observed experimentally for deforming rocks may be different for geological strain-rates, in that rate laws may become relatively strain-rate insensitive at low strain-rates. This transition from power law behaviour with relatively small values of the stress exponent, N, (N = 1 to 5) to large values of N (N = 5 to 20) has important implications for the development of localised behaviour during deformation as has been demonstrated at the other end of the spectrum for high stresses by Schmalholz and Fletcher (2011). Since localisation of fold systems arises from softening of the tangential viscosity, large values of N mean that little softening occurs with changes in strain rate, and sinusoidal folds are expected. There is therefore a critical range of N-values where localised, natural looking, folds develop. We explore the implications for folding of linear viscous single layers embedded in power-law viscous materials with N that varies with the stress level. The strain-rate dependence of the power law parameters results in strongly localised, aperiodic folding as opposed to the fold styles that arise from the linear Biot theory of folding. Also developed are axial plane shear fabrics. These structures resemble natural ones more than those that arise from simple Newtonian viscous or power-law behaviour with constant N. The results show that new studies of folded rocks and associated axial plane structures in the field may give important information on the transition from thermally activated dislocation motion to viscous glide. References. Amodeo, J., Carrez, Ph., Devincre, B., & Cordier, P. 2011. Multiscale modelling of MgO plasticity. Acta Materialia, 59, 2291-2301. Kocks, U. F. 1987. Constitutive behavior based on crystal plasticity. In: Unified Constitutive Equations for Creep and Plasticity. Ed. by A. K. Miller, Elsevier, pp. 1-88. Schmalholz, S. M., & Fletcher, R. C. 2011. The exponential flow law applied to necking and folding of a ductile layer. Geophys. J. Int., 184, 83-89.

Ord, A.; Hobbs, B. E.

2011-12-01

224

As geothermal resources that are more expensive to develop are utilized for power generation, there will be increased incentive to use more efficient power plants. This is expected to be the case with Enhanced Geothermal System (EGS) resources. These resources will likely require wells drilled to depths greater than encountered with hydrothermal resources, and will have the added costs for stimulation to create the subsurface reservoir. It is postulated that plants generating power from these resources will likely utilize the binary cycle technology where heat is rejected sensibly to the ambient. The consumptive use of a portion of the produced geothermal fluid for evaporative heat rejection in the conventional flash-steam conversion cycle is likely to preclude its use with EGS resources. This will be especially true in those areas where there is a high demand for finite supplies of water. Though they have no consumptive use of water, using air-cooling systems for heat rejection has disadvantages. These systems have higher capital costs, reduced power output (heat is rejected at the higher dry-bulb temperature), increased parasitics (fan power), and greater variability in power generation on both a diurnal and annual basis (larger variation in the dry-bulb temperature). This is an interim report for the task ‘Air-Cooled Condensers in Next- Generation Conversion Systems’. The work performed was specifically aimed at a plant that uses commercially available binary cycle technologies with an EGS resource. Concepts were evaluated that have the potential to increase performance, lower cost, or mitigate the adverse effects of off-design operation. The impact on both cost and performance were determined for the concepts considered, and the scenarios identified where a particular concept is best suited. Most, but not all, of the concepts evaluated are associated with the rejection of heat. This report specifically addresses three of the concepts evaluated: the use of recuperation, the use of turbine reheat, and the non-consumptive use of EGS make-up water to supplement heat rejection

Daniel S. Wendt; Greg L. Mines

2010-09-01

225

National Technical Information Service (NTIS)

A 10 MW-class binary cycle power generation plant has been developed using a down hole pump (DHP) which exchanges the hydrothermal energy with secondary medium in the heat exchanger. For constructing the plant at Kuju-machi, Oita Prefecture, site preparat...

1996-01-01

226

Some power law and scaling behaviors of forest and urban fire disasters

NASA Astrophysics Data System (ADS)

Power-law distribution have been found in many actual systems, such as the earthquake, rainfall and forest fires etc, and considered as one of the characteristics of SOC(Self-Organized Critical) systems (introduced by P. Bak in 1987). It is found that there are three types of power-law relations in forest fire system, i.e. frequency-size distribution, frequency-interval distribution, and the relation between population density and fire probability. Some of these characteristics are attributed to the SOC. The frequency-interval distribution of forest fires showes periodic change, different to that of frequency-size distribution. On the base of the traditional forest fire model proposed by Drossel and Schwabl in 1992 (DS model), the effects of influencing factors to the forest fire are studied. A Weather-Driven forest fire model (WD model) was built, in which the igniting probability is calculated with the weather parameter, i.e. relative humility, instead of a constant. The results demonstrate that the temporal distribution agrees well with that of actual forest fire data. Furthermore, it is found that the change of weather data also exhibits a power-law relation with periodic fluctuations, implying that the external driving from weather parameters is the essential reason for the power-law behavior of fire intervals. In order to explore the temporal scaling behavior of forest and urban fires, Allan factor (AF), Fano factor (FF) and Detrended Fluctuation Analysis (DFA) are used to investigate the fire data in different countries or regions. It is found that both the forest and urban fires exhibit time-scaling behavior, and the scaling exponents of urban fires are larger than forest fires, signifying a more intense clustering. Similar power-law characterizes the relative humidity, and its AF and FF plot validate the existence of a strong link between weather and fires. By studying the forest fire area series, it is found that both the forest fire and the weather parameters, including temperature, relative humidity and rainfall, all have similar "crossover" points and behave persistent long-range power-law correlations in large timescales. The long-range correlation of urban fires seems weaker than that of forest fire, and the human behavior or uneven population density may effect the relation in some way. Similar results are obtained analyzing Chinese urban fires. The suty may be useful to understand the scaling behaviors and their origins.

Song, Weiguo; Zheng, Hongyang

2010-05-01

227

NASA Astrophysics Data System (ADS)

Energetic particle transport in the interplanetary space is strongly influenced by turbulence and by the properties of magnetic field fluctuations. For istance, normalized magnetic field variances play a crucial role in the determination of the pitch angle scattering times and then of the transport regime. We have analyzed the time behavior of the normalized variances of the magnetic field fluctuations, measured by the Ulysses spacecraft upstream of some corotating interaction region (CIR) shocks. Recently, analyzing the accelerated particle time profiles upstream of CIRs, we found that energetic electrons exhibit superdiffusive transport, since their profiles decay as a power law in time (in the case of normal diffusion an exponential decay is expected). Superdiffusion can be described in terms of a Levy random walk, which is a statistical process implying a power law distribution of free path lengths and free path durations. The latter can be estimated from the pitch angle scattering time, which can be obtained from the normalized magnetic variance at the gyroresonant scale. The analysis presented shows that the normalized magnetic field variances are quasi steady-state in time from about 10 hours to 100 hours from the shock front. This rules out the presence of a spatially varying diffusion coefficient, which might produce a power law time profile for energetic particles upstream of a shock even in the case of normal transport, and confirms the possibility of superdiffusion for energetic electrons. A statistical analysis of the scattering times obtained from the magnetic fluctuations upstream of the CIRs events has also been performed. These power law distributions imply long free paths, long range correlations and weak pitch angle scattering. The power law slopes are often between 2 and 3, in good agreement with superdiffusive processes described by a Levy random walk. This shows that the power law distribution of pitch angle scattering times can be the physical origin of superdiffusion in the solar wind. We have also extended the theory of diffusive shock acceleration to the superdiffusive case: the main results will be presented, including a new expression for the energy spectral index of accelerated particles, which depends on the exponent of the mean square displacement growth, i.e.,

Zimbardo, G.; Perri, S.

2012-12-01

228

A spatial network explanation for a hierarchy of urban power laws

NASA Astrophysics Data System (ADS)

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.

Andersson, Claes; Hellervik, Alexander; Lindgren, Kristian

2005-01-01

229

A generalized power-law detection algorithm for humpback whale vocalizations.

Conventional detection of humpback vocalizations is often based on frequency summation of band-limited spectrograms under the assumption that energy (square of the Fourier amplitude) is the appropriate metric. Power-law detectors allow for a higher power of the Fourier amplitude, appropriate when the signal occupies a limited but unknown subset of these frequencies. Shipping noise is non-stationary and colored and problematic for many marine mammal detection algorithms. Modifications to the standard power-law form are introduced to minimize the effects of this noise. These same modifications also allow for a fixed detection threshold, applicable to broadly varying ocean acoustic environments. The detection algorithm is general enough to detect all types of humpback vocalizations. Tests presented in this paper show this algorithm matches human detection performance with an acceptably small probability of false alarms (P(FA) < 6%) for even the noisiest environments. The detector outperforms energy detection techniques, providing a probability of detection P(D) = 95% for P(FA) < 5% for three acoustic deployments, compared to P(FA) > 40% for two energy-based techniques. The generalized power-law detector also can be used for basic parameter estimation and can be adapted for other types of transient sounds. PMID:22501048

Helble, Tyler A; Ierley, Glenn R; D'Spain, Gerald L; Roch, Marie A; Hildebrand, John A

2012-04-01

230

Elementary scaling laws for the design of low and high power hall effect thrusters

NASA Astrophysics Data System (ADS)

An advanced set of scaling laws for Hall effect thrusters running with Xenon as propellant is established on the basis of the existence of an optimum atom number density that warrants a high efficiency thruster operation. A set of general relationships between macroscopic quantities, like thrust and input power, dimensions, including the channel length, the channel width and the channel mean diameter, and magnetic field strength are inferred from the main physical processes at work in a Hall thruster discharge. The "atom density constraint" of which the nature is here critically interpreted allows simplifying those relationships as it leads to a linear dependency between the channel length and mean diameter. Scaling laws which represent an essential tool for sizing up and down Hall thrusters are eventually obtained after proportionnality coefficients are determined. This last step is realized by means of a vast database that presently encompasses 33 single-stage Hall thrusters. In order to illustrate the usefulness of this new set of scaling laws, two practical applications are given and discussed. The scaling laws are first employed to calculate the dimensions and the operating parameters for a 20-kilowatt Hall thruster capable of producing 1 N of thrust. Such an electrical engine would permit orbit transfer of large communication satellites. Finally, the geometry of a Hall thruster is determined for tolerating 100 kW, an interesting power level for interplanetary trips.

Dannenmayer, K.; Mazouffre, S.

2011-10-01

231

Wellhead-sized binary-cycle geothermal power plants. Final report

Conceptual designs and estimates of capital costs as well as operating and maintenance costs were developed for wellhead binary-cycle geothermal power plants. Known geothermal resources were characterized, and three were selected as typical of the geothermal resources most likely to be developed for utility use within the next decade. Two wellhead power plant sizes were evaluated for each resource, resulting in six cases. Ten wellhead power plants were considered for the full development of a geothermal resource field. Prefabrication of modules containing portions of the facility was evaluated and included in the design where appropriate. The design development and cost estimates were based on mature technology indicative of the 5th to 10th plant installation to eliminate first-of-a-kind engineering and development costs. Estimates of the cost of elecricity were developed for each case. The sensitivity of the cost of electricity was examined for a number of variables. At brine costs of about $1 per million Btu, one of the plants was judged to be competitive. 50 figs., 76 tabs.

Linam, P.A.; Norman, W.M.; Outten, T.W.; Tanner, A.L.

1985-08-01

232

The use of ammonia-water mixtures as working fluids in binary geothermal power generation systems is investigated. The available thermodynamic data is discussed and the methods of extrapolating this data to give the quantities needed to perform analyses of the system is given. It is indicated that for a system without a recuperator and with a working fluid which is 50%

C. J. Bliem

1983-01-01

233

A metallic binary grating with two grooves per period is applied to side-pump high-power fiber lasers for the first time. By combining a gradient algorithm and micro-genetic algorithm, the grating is optimized and the maximum coupling efficiencies of 94.77% and 77.27% for TM and TE polarization waves respectively are demonstrated.

Fan Zhang; Chuncan Wang; Zhi Tong; Geng Rui; Ning Tigang

2007-01-01

234

Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow

NASA Astrophysics Data System (ADS)

Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.

Matsubara, Yoshitsugu; Hieida, Yasuhiro; Tadaki, Shin-ichi

2013-09-01

235

Speed-invariant encoding of looming object distance requires power law spike rate adaptation

Neural representations of a moving object’s distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent’s response to “looming” object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent’s response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent’s firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.

Clarke, Stephen E.; Naud, Richard; Longtin, Andre; Maler, Leonard

2013-01-01

236

Self-similar solution in the Leith model of turbulence: anomalous power law and asymptotic analysis

NASA Astrophysics Data System (ADS)

We consider a Leith model of turbulence (Leith C 1967 Phys. Fluids 10 1409) in which the energy spectrum obeys a nonlinear diffusion equation. We analytically prove the existence of a self-similar solution with a power-law asymptotic on the low-wavenumber end and a sharp boundary on the high-wavenumber end, which propagates to infinite wavenumbers in a finite-time t*. We prove that this solution has a power-law asymptotic with an anomalous exponent x*, which is less than the Kolmogorov value, x* > 5/3. This is a result that was previously discovered by numerical simulations in Connaughton and Nazarenko (2004 Phys. Rev. Lett. 92 044501). We also prove the convergence to this self-similar solution of the spectrum evolving from an arbitrary finitely supported initial data as t ? t*.

Grebenev, V. N.; Nazarenko, S. V.; Medvedev, S. B.; Schwab, I. V.; Chirkunov, Yu A.

2014-01-01

237

Fractionally integrated process with power-law correlations in variables and magnitudes

NASA Astrophysics Data System (ADS)

Motivated by the fact that many empirical time series—including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values—exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two parameters, where one controls the correlations in the variables and the other controls the correlations in their magnitudes. We apply the process to time series of heartbeat interval changes and air temperature changes and find that the statistical properties of the modeled time series are in agreement with those observed in the data.

Podobnik, Boris; Ivanov, Plamen Ch.; Biljakovic, Katica; Horvatic, Davor; Stanley, H. Eugene; Grosse, Ivo

2005-08-01

238

The relationship between randomness and power-law distributed move lengths in random walk algorithms

NASA Astrophysics Data System (ADS)

Recently, we proposed a new random walk algorithm, termed the REV algorithm, in which the agent alters the directional rule that governs it using the most recent four random numbers. Here, we examined how a non-bounded number, i.e., "randomness" regarding move direction, was important for optimal searching and power-law distributed step lengths in rule change. We proposed two algorithms: the REV and REV-bounded algorithms. In the REV algorithm, one of the four random numbers used to change the rule is non-bounded. In contrast, all four random numbers in the REV-bounded algorithm are bounded. We showed that the REV algorithm exhibited more consistent power-law distributed step lengths and flexible searching behavior.

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2014-05-01

239

Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources

NASA Technical Reports Server (NTRS)

Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.

Fiorito, Ralph; Titarchuk, Lev

2004-01-01

240

Segmentation of genomic DNA through entropic divergence: Power laws and scaling

NASA Astrophysics Data System (ADS)

Genomic DNA is fragmented into segments using the Jensen-Shannon divergence. Use of this criterion results in the fragments being entropically homogeneous to within a predefined level of statistical significance. Application of this procedure is made to complete genomes of organisms from archaebacteria, eubacteria, and eukaryotes. The distribution of fragment lengths in bacterial and primitive eukaryotic DNAs shows two distinct regimes of power-law scaling. The characteristic length separating these two regimes appears to be an intrinsic property of the sequence rather than a finite-size artifact, and is independent of the significance level used in segmenting a given genome. Fragment length distributions obtained in the segmentation of the genomes of more highly evolved eukaryotes do not have such distinct regimes of power-law behavior.

Azad, Rajeev K.; Bernaola-Galván, Pedro; Ramaswamy, Ramakrishna; Rao, J. Subba

2002-05-01

241

Mixed convection heat transfer to power law fluids in arbitrary cross-sectional ducts

NASA Astrophysics Data System (ADS)

An analytical investigation of three-dimensional mixed conveciton flow and heat transfer to power-law fluids in horizontal arbitrary cross-sectional ducts is undertaken. The continuity equation and parabolic forms of the energy and momentum equations in rectangular coordinates are transformed into new orthogonal coordinates with the boundaries of the duct coinciding with the coordinate surfaces. The transformed equations are solved by the finite difference technique. The fluid enters the duct with constant velocity and temperature profiles with the wall of the duct subjected to constant temperature. Local heat transfer coefficients and pressure drop for several values of Gr/Re and power-law index n are computed for the triangular, square, trapezoidal, pentagonal, and circular ducts. The buoyancy force is found to increase both the Nusselt number and the pressure drop.

Lawal, A.

1989-05-01

242

Mixed convection heat transfer to power law fluids in arbitrary cross-sectional ducts

An analytical investigation of three-dimensional mixed convection flow and heat transfer to power-law fluids in horizontal abritrary cross-sectional ducts is undertaken. The continuity equation and parabolic forms of the energy and momentum equations in rectangular coordinates are transformed into new orthogonal coordinates with the boundaries of the duct coinciding with the coordinate surfaces. The transformed equations are solved by the finite difference technique. The fluid enters the duct with constant velocity and temperature profiles with the wall of the duct subjected to constant temerature. Local heat transfer coefficients and pressure drop for several values of Gr/Re and power-law index n are computed for the triangular, square, trapezoidal, pentagonal, and circular ducts. The buoyancy force is found to increase both the Nusselt number and the pressure drop.

Lawal, A. (Univ. of Port Harcourt (Nigeria))

1989-05-01

243

Power-law autocorrelated stochastic processes with long-range cross-correlations

NASA Astrophysics Data System (ADS)

We develop a stochastic process with two coupled variables where the absolute values of each variable exhibit long-range power-law autocorrelations and are also long-range cross-correlated. We investigate how the scaling exponents characterizing power-law autocorrelation and long-range cross-correlation behavior in the absolute values of the generated variables depend on the two parameters in our model. In particular, if the autocorrelation is stronger, the cross-correlation is also stronger. We test the utility of our approach by comparing the autocorrelation and cross-correlation properties of the time series generated by our model with data on daily returns over ten years for two major financial indices, the Dow Jones and the S&P500, and on daily returns of two well-known company stocks, IBM and Microsoft, over five years.

Podobnik, B.; Fu, D. F.; Stanley, H. E.; Ivanov, P. Ch.

2007-03-01

244

Speed-invariant encoding of looming object distance requires power law spike rate adaptation.

Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli. PMID:23898185

Clarke, Stephen E; Naud, Richard; Longtin, André; Maler, Leonard

2013-08-13

245

Power-law solutions and accelerated expansion in scalar-tensor theories

We find exact power-law solutions for scalar-tensor theories and clarify the conditions under which they can account for an accelerated expansion of the Universe. These solutions have the property that the signs of both the Hubble rate and the deceleration parameter in the Jordan frame may be different from the signs of their Einstein-frame counterparts. For special parameter combinations we identify these solutions with asymptotic attractors that have been obtained in the literature through dynamical-system analysis. We establish an effective general-relativistic description for which the geometrical equivalent of dark energy is associated with a time dependent equation of state. The present value of the latter is consistent with the observed cosmological 'constant'. We demonstrate that this type of power-law solution for accelerated expansion cannot be realized in f(R) theories.

Batista, C. E. M.; Zimdahl, W. [Universidade Federal do Espirito Santo, Departamento de Fisica, Av. Fernando Ferrari, 514, Campus de Goiabeiras, CEP 29075-910, Vitoria, Espirito Santo (Brazil)

2010-07-15

246

Power-law behavior in the quantum-resonant evolution of the ? -kicked accelerator

NASA Astrophysics Data System (ADS)

We consider the atom-optical ? -kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power-law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by 1. To demonstrate the power-law behavior explicitly we consider the evolutions of the second- and fourth-order momentum moments, and cumulants, for an initially Gaussian momentum distribution corresponding to the Maxwell-Boltzmann distribution of an ideal gas at thermal equilibrium.

Halkyard, P. L.; Saunders, M.; Gardiner, S. A.; Challis, K. J.

2008-12-01

247

Power laws reveal phase transitions in landscape controls of fire regimes.

Understanding the environmental controls on historical wildfires, and how they changed across spatial scales, is difficult because there are no surviving explicit records of either weather or vegetation (fuels). Here we show how power laws associated with fire-event time series arise in limited domains of parameters that represent critical transitions in the controls on landscape fire. Comparison to a self-organized criticality model shows that the latter mimics historical fire only in a limited domain of criticality, and is not an adequate mechanism to explain landscape fire dynamics, which are shaped by both endogenous and exogenous controls. Our results identify a continuous phase transition in landscape controls, marked by power laws, and provide an ecological analogue to critical behaviour in physical and chemical systems. This explicitly cross-scale analysis provides a paradigm for identifying critical thresholds in landscape dynamics that may be crossed in a rapidly changing climate. PMID:22395617

McKenzie, Donald; Kennedy, Maureen C

2012-01-01

248

NASA Technical Reports Server (NTRS)

Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.

Raj, S. V.; Pharr, G. M.

1989-01-01

249

Power-law exponents for a spreading front and growing interface in an irreversible wetting

NASA Astrophysics Data System (ADS)

Using computer simulations, the power-law behavior of the interface growth of a spreading fluid is studied in a two-dimensional lattice model. The interface width exponent ? and the dynamical exponent k for the evolution of the front are consistent with their dynamical scaling relation. The magnitude of these exponents seems to depend upon the nature of the substrate and the concentration of the carriers of the wetting fluid.

Willett, Evan; Pandey, Ras

1990-12-01

250

Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length–volume scaling power law ( where Lc and Vc are crown length and volume) were found for both the high-fat and control groups (R2 = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, KLV, decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow–length scaling power law, however, was nearly unaffected by the positive remodelling. The length–volume and flow–length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. KLV < 18 in the length–volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans.

Huo, Yunlong; Choy, Jenny Susana; Wischgoll, Thomas; Luo, Tong; Teague, Shawn D.; Bhatt, Deepak L.; Kassab, Ghassan S.

2013-01-01

251

The Forbes 400, the Pareto power-law and efficient markets

NASA Astrophysics Data System (ADS)

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.

Klass, O. S.; Biham, O.; Levy, M.; Malcai, O.; Solomon, S.

2007-01-01

252

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

Mirels, Harold

1959-01-01

253

Power-law persistence and trends in the atmosphere: A detailed study of long temperature records

We use several variants of the detrended fluctuation analysis to study the appearance of long-term persistence in temperature records, obtained at 95 stations all over the globe. Our results basically confirm earlier studies. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, decays for large s as a power law, C(s)˜s-gamma. For

J. F. Eichner; Eva Koscielny-Bunde; Armin Bunde; Shlomo Havlin; H.-J. Schellnhuber

2003-01-01

254

Friction factors of power-law fluids in chevron-type plate heat exchangers

In the present work laminar flows of Newtonian and power-law fluids through cross-corrugated chevron-type plate heat exchangers (PHEs) are numerically studied in terms of the geometry of the channels. The plates area enlargement factor was a typical one (1.17), the corrugation angle, ?, varied between 30° and 60° and the flow index behaviour, n, between 0.25 and 1. Single friction

Carla S. Fernandes; Ricardo P. Dias; João M. Nóbrega; João M. Maia

2008-01-01

255

Mixed convection heat transfer to power law fluids in arbitrary cross-sectional ducts

An analytical investigation of three-dimensional mixed conveciton flow and heat transfer to power-law fluids in horizontal arbitrary cross-sectional ducts is undertaken. The continuity equation and parabolic forms of the energy and momentum equations in rectangular coordinates are transformed into new orthogonal coordinates with the boundaries of the duct coinciding with the coordinate surfaces. The transformed equations are solved by the

A. Lawal

1989-01-01

256

Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields

We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.

Steffen, J. H.; Baumbaugh, A.; Chou, A. S.; Mazur, P. O.; Tomlin, R.; Wester, W. [Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 (United States); Upadhye, A. [Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637 (United States); Weltman, A. [Astrophysics, Cosmology and Gravity Centre, University of Cape Town, Rondebosch, Private Bag, 7700 (South Africa)

2010-12-31

257

Improved power-law estimates from multiple samples provided by millennium climate simulations

NASA Astrophysics Data System (ADS)

Using the long annual mean temperature time series provided by millennium Earth System Model simulations and a method of discrete Fourier transform with varying starting point and length of time window together with averaging, we get good fits to power laws between two characteristic oscillatory timescales of the model climate: multidecadal (50-80 years) and El Nino (3-6 years) timescales. For global mean temperature, we fit ? ˜ 0.35 in a relation S(f) ˜ f -? in a simulation without external climate forcing and ? over 0.7 in a simulation with external forcing included. The power law is found both with and without external forcing despite the forcings, e.g. the volcanic forcing, not showing similar behaviour, indicating a nonlinear temperature response to time-varying forcing. We also fit a power law with ? ˜ 8 to the narrow frequency range between El Nino frequencies (up to 1/(3.2 years)) and the Nyquist frequency (1/(2 years)). Also, monthly mean temperature time series are considered and a decent power-law fit for frequencies above 1/year is obtained. Regional variability in best-fit ? is explored, and the impact of choosing the frequency range on the result is illustrated. When all resolved frequencies are used, land areas seem to have lower ?s than ocean areas on average, but when fits are restricted to frequencies below 1/(6 years), this difference disappears, while regional differences still remain. Results compare well with measurements both for global mean temperature and for the central England temperature record.

Henriksson, S. V.; Räisänen, P.; Silen, J.; Järvinen, H.; Laaksonen, A.

2014-03-01

258

Laboratory constraints on chameleon dark energy and power-law fields.

We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter. PMID:21231645

Steffen, J H; Upadhye, A; Baumbaugh, A; Chou, A S; Mazur, P O; Tomlin, R; Weltman, A; Wester, W

2010-12-31

259

Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length-volume scaling power law ( where L(c) and V(c) are crown length and volume) were found for both the high-fat and control groups (R(2) = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, K(LV), decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow-length scaling power law, however, was nearly unaffected by the positive remodelling. The length-volume and flow-length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. K(LV) < 18 in the length-volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans. PMID:23365197

Huo, Yunlong; Choy, Jenny Susana; Wischgoll, Thomas; Luo, Tong; Teague, Shawn D; Bhatt, Deepak L; Kassab, Ghassan S

2013-04-01

260

Negative effective-mass transition and anomalous transport in power-law hopping bands

The stability of spinless Fermions with power-law hopping Hij?|i-j|-alpha is investigated. It is shown that at precisely alphac=2 , the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective-mass regime, malpha*<0 characterized by retarded transport in the presence of an electric field. Moreover, bands with alpha<=2 must be accompanied by counter

Shimul Akhanjee

2009-01-01

261

Power-law dependence of the pressure broadening of spectral lines on temperature

Temperature variations of the widths of pressure-broadened spectral lines in a wide temperature range are examined on the basis of a power-law relation in the framework of the adiabatic phase shift theory. It is shown that the temperature-dependence index can be related to the details of interatomic potential curves. Model calculations performed for a Lennard-Jones potential indicate that some caution

A. Bielski; R. Bobkowski; J. Szudy

1989-01-01

262

Comment on "Time needed to board an airplane: a power law and the structure behind it".

Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the "back-to-front" strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups. PMID:23005813

Bernstein, Noam

2012-08-01

263

Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

NASA Astrophysics Data System (ADS)

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.

Fouxon, Itzhak; Posch, Harald A.

2012-01-01

264

Power-law behavior in complex organizational communication networks during crisis

NASA Astrophysics Data System (ADS)

Communication networks can be described as patterns of contacts which are created due to the flow of messages and information shared among participating actors. Contemporary organizations are now commonly viewed as dynamic systems of adaptation and evolution containing several parts, which interact with one another both in internal and in external environment. Although there is limited consensus among researchers on the precise definition of organizational crisis, there is evidence of shared meaning: crisis produces individual crisis, crisis can be associated with positive or negative conditions, crises can be situations having been precipitated quickly or suddenly or situations that have developed over time and are predictable etc. In this research, we study the power-law behavior of an organizational email communication network during crisis from complexity perspective. Power law simply describes that, the probability that a randomly selected node has k links (i.e. degree k) follows P(k)?k, where ? is the degree exponent. We used social network analysis tools and techniques to analyze the email communication dataset. We tested two propositions: (1) as organization goes through crisis, a few actors, who are prominent or more active, will become central, and (2) the daily communication network as well as the actors in the communication network exhibit power-law behavior. Our preliminary results support these two propositions. The outcome of this study may provide significant advancement in exploring organizational communication network behavior during crisis.

Uddin, Shahadat; Murshed, Shahriar Tanvir Hasan; Hossain, Liaquat

2011-08-01

265

Effects of diversity and procrastination in priority queuing theory: The different power law regimes

NASA Astrophysics Data System (ADS)

Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law ˜1/t? with 0power law tail ˜1/t1/2 , resulting from a first-passage solution of an equivalent Wiener process. Taking into account a diversity of time deficit parameters in a population of individuals, the power law tail is changed into 1/t? , with ??(0.5,?) , including the well-known case 1/t . We also study the effect of “procrastination,” defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks. This regime provides an explanation for even slower apparent decay and longer persistence.

Saichev, A.; Sornette, D.

2010-01-01

266

NASA Astrophysics Data System (ADS)

We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.

Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.

2014-09-01

267

Comment on ``Time needed to board an airplane: A power law and the structure behind it''

NASA Astrophysics Data System (ADS)

Frette and Hemmer [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.011130 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the “back-to-front” strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.

Bernstein, Noam

2012-08-01

268

On the transition from power law creep to Harper-Dorn creep

At intermediate to high temperature single and polycrystalline metals, alloys, ceramics and minerals often deform by the diffusion-controlled dislocation mechanism of power law creep at high stresses, but by a mechanism of Harper-Dorn (H-D) creep at low stresses. H-D creep is characterized by a stress exponent n of unity and an activation energy equal to that for power law creep and a strain rate independent of grain size. Several dislocation mechanisms have been proposed for H-D creep. Langdon and Yavari explain H-D creep from the climb of edge dislocations under conditions of vacancy saturation. According to Weertman and Blacic, H-D creep may be produced by a low-amplitude thermal cycling effect which causes a cyclic change in equilibrium point defect concentration. Raj postulated a mechanism with the generation of dislocations from surface sources controlling the strain rate. Ardell and Lee considered H-D creep as the result of a dislocation network coarsening. Based on the assumption of the presence of internal stress, Wu and Sherby and Ruano et al. treated Harper-Dorn creep as an extension of power law creep into the low stress region. It is the intent of this communication to show that H-D creep starts to operate at stresses equal to the Peierls stress.

Wang, J.N. (Monash Univ., Clayton (Australia). Dept. of Earth Science)

1993-09-01

269

Powering the second 2012 outburst of SN 2009ip by repeating binary interaction

NASA Astrophysics Data System (ADS)

We propose that the major 2012 outburst of the supernova impostor SN 2009ip was powered by an extended and repeated interaction between the luminous blue variable (LBV) and a more compact companion. Motivated by the recent analysis of Margutti et al. (2013) of ejected clumps and shells, we consider two scenarios. In both scenarios, the major 2012b outburst with total (radiated + kinetic) energy of ˜5 × 1049 erg was powered by accretion of ˜2-5 M? on to the companion during a periastron passage (the first passage) of the binary system approximately 20 d before the observed maximum of the light curve. In the first scenario, the surviving companion scenario, the companion was not destructed and still exists in the system after the outburst. It ejected partial shells (or collimated outflows or clumps) for two consecutive periastron passages after the major one. The orbital period was reduced from ˜38 to ˜25 d as a result of the mass transfer process that took place during the first periastron passage. In the second scenario, the merger scenario, some partial shells/clumps were also ejected in a second periastron passage that took place ˜20 d after the first one. After this second periastron passage, the companion dived too deep into the LBV envelope to launch more outflows and merged with the LBV.

Kashi, Amit; Soker, Noam; Moskovitz, Nitsan

2013-12-01

270

NASA Astrophysics Data System (ADS)

Understanding runoff generation is important for management of freshwater systems. Determining transit time distributions of streamwaters and how they change with discharge gives information on the flowpaths and recharge sources of streams - vital information for determining the responses of streams to stressors such as pollution, landuse change, or climate change. This work takes a first look at unique information on how transit time distributions change with discharge in some New Zealand catchments. Transit time distributions of streamwaters have been determined from tritium measurements on single samples in this work. This allows changes with stream discharge to be observed, in contrast to previous isotope studies which have given averaged transit time distributions based on series of samples. In addition, tritium reveals the wide spectrum of ages present in streams whereas oxygen-18 or chloride variations only show the younger ages (Stewart et al., 2010). It was found that the mean transit time (MTT) data could be reasonably represented by straight lines in log-log plots, indicating power law relationships between MTT and discharge. Similar power law behaviour has been observed for the rock forming elements such as silica in streamwaters (Godsey et al., 2009). Case studies are presented for two New Zealand catchments, both with volcanic ash substrates. Toenepi is a dairy catchment near Hamilton, which shows well-constrained power law relationships between MTT and discharge, and between silica concentration and discharge (Morgenstern et al., 2010). Baseflow MTTs vary from 2.5 to 157 years. Tutaeuaua is a pastoral farming catchment near Taupo. Results for nested catchments along the stream also show power law relationships for both MTT and silica with discharge. Streamwater MTTs vary from 1 to 11 years. The results indicate that (1) relatively old waters dominate many streams, (2) streamwater ages vary with discharge, and (3) age, like silica, varies according to power law relationships with stream discharge. References: Godsey, S.E., Kirchner, J.W., Clow, D.W. Hydrological Processes 23, 1844-1864, 2009. Morgenstern, U., Stewart M. K., Stenger, R. Hydrology and Earth System Sciences 14, 2289-2301, 2010. Stewart, M.K., Morgenstern, U., McDonnell, J.J. Hydrological Processes 24(12), 1646-1659, 2010.

Stewart, Michael; Morgenstern, Uwe

2013-04-01

271

Double Power-law Distribution of Magnetic Energy in the Solar Corona over an Active Region

NASA Astrophysics Data System (ADS)

In this paper, we study the magnetic energy (ME) structure contained in the solar corona over the active region NOAA 11158. The time period is chosen as from 0:00 to 06:00 UT on 2011 February 15, during which an X-class flare occurred. The nonlinear force-free field (NLFFF) and the potential field extrapolation are carried out to model the coronal magnetic field over this active region, using high-quality photospheric vector magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory as boundary conditions. We find that the volume distribution for the density of the ME (B 2/8?) and the ohmic dissipation power (ODP, j 2/?), in which j is the electric current density (c/4?? × B) and ? is the conductivity in the corona, can be readily fitted by a broken-down double-power law. The turn-over density for the spectrum of the ME and ODP is found to be fixed at ~1.0 × 104 erg cm-3 and ~2.0 × 10-15 W cm-3 (assuming ? = 105 ?-1 m-1), respectively. Compared with their first power-law spectra (fitted below the corresponding turn-over value) which remain unchanged, the second power-law spectra (fitted above the corresponding turn-over value) for the NLFFF's ME and ODP show flare-associated changes. The potential field remains steady. These results indicate that a magnetic field with energy density larger than the turn-over energy density plays a dominant role in powering the flare.

Shen, Jinhua; Ji, Haisheng; Wiegelmann, Thomas; Inhester, Bernd

2013-02-01

272

DOUBLE POWER-LAW DISTRIBUTION OF MAGNETIC ENERGY IN THE SOLAR CORONA OVER AN ACTIVE REGION

In this paper, we study the magnetic energy (ME) structure contained in the solar corona over the active region NOAA 11158. The time period is chosen as from 0:00 to 06:00 UT on 2011 February 15, during which an X-class flare occurred. The nonlinear force-free field (NLFFF) and the potential field extrapolation are carried out to model the coronal magnetic field over this active region, using high-quality photospheric vector magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory as boundary conditions. We find that the volume distribution for the density of the ME (B {sup 2}/8{pi}) and the ohmic dissipation power (ODP, j {sup 2}/{sigma}), in which j is the electric current density (c/4{pi}{nabla} Multiplication-Sign B) and {sigma} is the conductivity in the corona, can be readily fitted by a broken-down double-power law. The turn-over density for the spectrum of the ME and ODP is found to be fixed at {approx}1.0 Multiplication-Sign 10{sup 4} erg cm{sup -3} and {approx}2.0 Multiplication-Sign 10{sup -15} W cm{sup -3} (assuming {sigma} = 10{sup 5} {Omega}{sup -1} m{sup -1}), respectively. Compared with their first power-law spectra (fitted below the corresponding turn-over value) which remain unchanged, the second power-law spectra (fitted above the corresponding turn-over value) for the NLFFF's ME and ODP show flare-associated changes. The potential field remains steady. These results indicate that a magnetic field with energy density larger than the turn-over energy density plays a dominant role in powering the flare.

Shen, Jinhua; Ji, Haisheng [Purple Mountain Observatory, 2 West Beijing Road, Nanjing 210008 (China)] [Purple Mountain Observatory, 2 West Beijing Road, Nanjing 210008 (China); Wiegelmann, Thomas; Inhester, Bernd [Max-Planck-Institut fuer sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau (Germany)] [Max-Planck-Institut fuer sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau (Germany)

2013-02-10

273

Bose-Einstein condensation with a finite number of particles in a power-law trap

Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number N of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation temperature T{sub c} in terms of a power series in x{sub 0}={epsilon}{sub 0}/k{sub B}T{sub c}, where {epsilon}{sub 0} denotes the zero-point energy of the trapping potential. This expression, which applies in Cartesian, cylindrical, and spherical power-law traps, is given analytically at infinite order. It is also given numerically for specific potential shapes as an expansion in powers of x{sub 0} up to the second order. We show that, for a harmonic trap, the well-known first-order shift of the critical temperature {Delta}T{sub c}/T{sub c{proportional_to}}N{sup -1/3} is inaccurate when N{<=}10{sup 5}, the next order (proportional to N{sup -1/2}) being significant. We also show that finite-size effects on the condensation temperature cancel out in a cubic trapping potential, e.g., V(r){proportional_to}r{sup 3}. Finally, we show that in a generic power-law potential of higher order, e.g., V(r){proportional_to}r{sup {alpha}} with {alpha}>3, the shift of the critical temperature becomes positive. This effect provides a large increase of T{sub c} for relatively small atom numbers. For instance, an increase of about +40% is expected with 10{sup 4} atoms in a V(r){proportional_to}r{sup 12} trapping potential.

Jaouadi, A. [Universite Paris-Sud, Institut des Sciences Moleculaires d'Orsay (ISMO), F-91405 Orsay cedex (France); CNRS, F-91405 Orsay cedex (France); LSAMA, Department of Physics, Faculty of Science of Tunis, University of Tunis El Manar, TN-2092 Tunis (Tunisia); Telmini, M. [LSAMA, Department of Physics, Faculty of Science of Tunis, University of Tunis El Manar, TN-2092 Tunis (Tunisia); National Centre for Nuclear Science and Technology, Sidi Thabet Technopark, TN-2020 Ariana (Tunisia); Charron, E. [Universite Paris-Sud, Institut des Sciences Moleculaires d'Orsay (ISMO), F-91405 Orsay cedex (France); CNRS, F-91405 Orsay cedex (France)

2011-02-15

274

Single photon detection methods are used to acquire fluorescence trajectories from single CdSe/ZnS colloidal quantum dots (QDs) and analyze their blinking behavior. Although the "off-time" distributions follow ideal power law behavior at all wavelengths and intensities, significant deviations from power law behavior are observed for the "on-times". Specifically, with improved time resolution, trajectory durations, and photon statistics, we report a near-exponential falloff of on-time probability distributions at long times. Investigation of this falloff behavior as a function of laser wavelength and power demonstrate that these deviations originate from multiexciton dynamics, whose formation probabilities can be very low on a "per laser pulse" basis, but become nearly unity on the time scales of the longest on-times. The near quadratic, power-dependent results indicate the predominant role of biexcitons in the long time on-to-off blinking dynamics, which can be interpreted in terms of an Auger ionization event. In conjunction with Poisson modeling of the photon statistics, the data is consistent with QD ionization efficiencies of order approximately 10(-5) and highlight a novel role for biexcitons and Auger ionization in QD blinking. PMID:19072721

Peterson, Jeffrey J; Nesbitt, David J

2009-01-01

275

Extended power-law scaling of heavy-tailed random fields or processes

NASA Astrophysics Data System (ADS)

We analyze the scaling behaviors of two log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along two horizontal transects on a 21 m long outcrop of lower-shoreface bioturbated sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ? (q) of separation scale or lag, s, over limited ranges of s. A procedure known as Extended Self-Similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ? (q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm, stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm functions.

Guadagnini, A.; Riva, M.; Neuman, S. P.

2012-06-01

276

Effect of acoustic coupling on power-law flame acceleration in spherical confinement

NASA Astrophysics Data System (ADS)

A model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach number flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into an existing theory of self-similar flame acceleration in free space [V. Akkerman, C. K. Law, and V. Bychkov, ``Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering,'' Phys. Rev. E 83, 026305 (2011)]. Being reflected from the chamber wall, flame-generated acoustics interact with the flamefront and the attendant hydrodynamic flamefront cellular instability. This in turn affects the subsequent flame morphology and propagation speed. It is shown that the acoustics modify the power-law flame acceleration, concomitantly facilitating or inhibiting the transition to detonation in confinement, which allows reconciliation of a discrepancy in experimental measurements of different groups.

Akkerman, V'yacheslav; Law, Chung K.

2013-01-01

277

NASA Technical Reports Server (NTRS)

A multi-input, multi-output control law design methodology, named "CRAFT", is presented. CRAFT stands for the design objectives addressed, namely, Control power, Robustness, Agility, and Flying Qualities Tradeoffs. The methodology makes use of control law design metrics from each of the four design objective areas. It combines eigenspace assignment, which allows for direct specification of eigenvalues and eigenvectors, with a graphical approach for representing the metrics that captures numerous design goals in one composite illustration. Sensitivity of the metrics to eigenspace choice is clearly displayed, enabling the designer to assess the cost of design tradeoffs. This approach enhances the designer's ability to make informed design tradeoffs and to reach effective final designs. An example of the CRAFT methodology applied to an advanced experimental fighter and discussion of associated design issues are provided.

Murphy, Patrick C.; Davidson, John B.

1998-01-01

278

Extent of power-law scaling for natural fractures in rock

The scaling of natural fractures in rock has broad implications for a wide variety of problems in tectonics, seismic hazard assessment, hydrocarbon reservoirs, aquifers, waste repositories, and hydrothermal mineralization. New data sets from natural faults and extension fractures exhibit simple power-law scaling across 3.4--4.9 orders of magnitude, regardless of rock type or movement mode. The data show no evidence of natural gaps or scaling changes. Each data set consists of independent measurements made at different observational scales; a powder-law regression to the subset of smaller fractures in each case provides an extrapolation that accurately predicts associated larger fractures. Consequently, data representing a limited range of fracture sizes may be used to characterize a much broader spectrum of fracture sizes.

Marrett, R.; Ortega, O.J.; Kelsey, C.M. [Univ. of Texas, Austin, TX (United States). Dept. of Geological Sciences] [Univ. of Texas, Austin, TX (United States). Dept. of Geological Sciences

1999-09-01

279

In potable water treatment, the use of the power law to describe particle size distributions (PSDs) in particle counting practice is common. The power law is popular because it allows the reduction of numerous data bits to two meaningful parameters that completely describe the size distribution characteristics of a particle suspension. The model is however flawed. This paper presents the further development of an improved model (the variable-beta model) first proposed by Lawler (1997). Both the power law model and variable-beta model are used to describe the PSDs of a large number of potable water treatment samples taken from full-scale plants and the resulting correlations are compared. The findings from the comparison of data reduction methodologies support the argument that the variable-beta model is fundamentally more correct than the power law model and consequently describes the PSDs better. PMID:15644239

Ceronio, A D; Haarhoff, J

2005-01-01

280

Mathematical modeling of genome evolution: Where do the power laws come from

NASA Astrophysics Data System (ADS)

Power law distributions appear in numerous biological, physical, social and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interaction partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium were derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models were found and their appearance depending on model parameters was investigated. It was proved that the power law asymptotics appears if, and only if, the model is balanced, i.e., domain duplication (birth) and deletion (death) rates are asymptotically equal up to the second order. It was further proved that any power asymptotic with the degree not equal to -1 can appear only if the assumption of independence of the birth/death rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, were explored in detail and the distributions of the equilibrium frequencies of domain families of different size were determined for each case. The BDIM formalism was applied to the analysis of the domain family size distributions in prokaryotic and eukaryotic proteomes and an excellent fit was observed between these empirical data and a particular form of the model, the second-order balanced linear BDIM. Calculation of the parameters of these models suggests surprisingly high innovation rates, comparable to the total domain birth (duplication) and death (elimination) rates, particularly for prokaryotic genomes. Thus, a straightforward model of genome evolution, which does not explicitly include selection, seems to be sufficient to explain the observed distributions of domain family sizes, in which power laws appear as asymptotic. However, for the model to be compatible with the data, there has to be a precise balance between domain birth, death and innovation rates, and this is likely to be maintained by selection. The developed approach is oriented at a mathematical description of evolution of domain composition of proteomes, but a simple reformulation could be applied to models of other evolving networks with preferential attachment.

Koonin, Eugene

2003-03-01

281

Exploring parameter constraints on quintessential dark energy: The inverse power law model

We report on the results of a Markov chain Monte Carlo analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data sets as a representation of future dark energy experiments. We generate simulated data sets for a {lambda}CDM background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model, and present our results in the form of likelihood contours generated by these two background cosmologies. We find that the relative constraining power of the various DETF data sets on the IPL model parameters is broadly equivalent to the DETF results for the w{sub 0}-w{sub a} parametrization of dark energy. Finally, we gauge the power of DETF 'stage 4' data by demonstrating a specific IPL model which, if realized in the universe, would allow stage 4 data to exclude a cosmological constant at better than the 3{sigma} level.

Yashar, Mark; Bozek, Brandon; Abrahamse, Augusta; Albrecht, Andreas; Barnard, Michael [Department of Physics, University of California at Davis, One Shields Avenue, Davis, California 95616 (United States)

2009-05-15

282

Power Law and Scaling in the Energy of Tropical Cyclones (Invited)

NASA Astrophysics Data System (ADS)

The influence of climate variability and global warming on the occurrence of tropical cyclones is a controversial issue. Existing historical databases on the subject are not fully reliable, but a more fundamental hindrance is the lack of basic understanding regarding the intrinsic nature of tropical-cyclone genesis and evolution. It is known that tropical cyclones involve more than a passive response to changing external forcing, but it is not clear which dynamic behavior best describes them. We present an approach based on the application of the power dissipation index, which constitutes an estimation of released energy, to individual tropical cyclones. A robust law emerges for the statistics of power dissipation index, valid in four different ocean basins and over long time periods. In addition to suggesting a description of the physics of tropical cyclones in terms of critical phenomena, the scaling law enables us to quantify their response to changing climatic conditions, with an increase in the largest power dissipation index values with sea surface temperature or the presence of El Niño phenomena, depending on the basin under consideration. In this way, we demonstrate that the recent upswing in North Atlantic hurricane activity does not involve tropical cyclones that are quantitatively different from those in other sustained high-activity periods before 1970. A. Corral, A. Osso, and J.E. Llebot, Nature Phys. 2010.

Corral, A.; Osso, A.; Llebot, J.

2010-12-01

283

Stochastic modeling of aphid population growth with nonlinear, power-law dynamics.

This paper develops a deterministic and a stochastic population size model based on power-law kinetics for the black-margined pecan aphid. The deterministic model in current use incorporates cumulative-size dependency, but its solution is symmetric. The analogous stochastic model incorporates the prolific reproductive capacity of the aphid. These models are generalized in this paper to include a delayed feedback mechanism for aphid death. Whereas the per capita aphid death rate in the current model is proportional to cumulative size, delayed feedback is implemented by assuming that the per capita rate is proportional to some power of cumulative size, leading to so-called power-law dynamics. The solution to the resulting differential equations model is a left-skewed abundance curve. Such skewness is characteristic of observed aphid data, and the generalized model fits data well. The assumed stochastic model is solved using Kolmogrov equations, and differential equations are given for low order cumulants. Moment closure approximations, which are simple to apply, are shown to give accurate predictions of the two endpoints of practical interest, namely (1) a point estimate of peak aphid count and (2) an interval estimate of final cumulative aphid count. The new models should be widely applicable to other aphid species, as they are based on three fundamental properties of aphid population biology. PMID:17306309

Matis, James H; Kiffe, Thomas R; Matis, Timothy I; Stevenson, Douglass E

2007-08-01

284

Full investigation on the dynamics of power-law kinetic quintessence

NASA Astrophysics Data System (ADS)

We give a full investigation on the dynamics of power-law kinetic quintessence L(X ,?)=V(?)(-X+X2) by considering the potential related parameter ?(=VV/''V'2) as a function of another potential parameter ?(=V/'?V3/2), which correspondingly extends the analysis of the dynamical system of our Universe from two dimensional to three dimensional. In addition to the critical points found in previous papers, we find a new de Sitter- like dominant attractor (cp6) and give its stable condition using the center manifold theorem. For the dark energy dominant solution (cp6 and cp7), it could be distinguished from canonical quintessence and tachyon models since the sound speed cs2=0 or cs2?1. For the scaling solution (cp8), it is very interesting that the sound speed cs2=1/5, while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on the cold dark matter power spectrum and the cosmic microwave background both at early time, when this scalar field is an early dark energy with ?? being non-negligible at high redshift, and at late time, when it drives the accelerating expansion. We still do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future.

Fang, Wei; Tu, Hong; Li, Ying; Huang, Jiasheng; Shu, Chenggang

2014-06-01

285

Universal inverse power-law distribution for temperature and rainfall in the UK region

NASA Astrophysics Data System (ADS)

Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.

Selvam, A. M.

2014-06-01

286

Power-law spin correlations in the pyrochlore antiferromagnet Tb(2)Ti(2)O(7).

We investigate the low-temperature state of the rare-earth pyrochlore Tb(2)Ti(2)O(7) using polarized neutron scattering. Tb(2)Ti(2)O(7) is often described as an antiferromagnetic spin liquid with spin correlations extending over lengths comparable to individual tetrahedra of the pyrochlore lattice. We confirm this picture at 20 K but find that at 0.05 K the data contain evidence of pinch-point scattering, suggesting that the low temperature state of Tb(2)Ti(2)O(7) has power-law spin correlations. PMID:23031127

Fennell, T; Kenzelmann, M; Roessli, B; Haas, M K; Cava, R J

2012-07-01

287

Laboratory constraints on chameleon dark energy and power-law fields

We report results from the GammeV Chameleon Afterglow Search - a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.

Steffen, Jason H.; /Fermilab; Upadhye, Amol; /KICP, Chicago; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; /Fermilab; Weltman, Amanda; /Cape Town U.; Wester, William; /Fermilab

2010-10-01

288

Precision of quantization of the hall conductivity in a finite-size sample: Power law

A microscopic calculation of the conductivity in the integer quantum Hall effect (IQHE) mode is carried out. The precision of quantization is analyzed for finite-size samples. The precision of quantization shows a power-law dependence on the sample size. A new scaling parameter describing this dependence is introduced. It is also demonstrated that the precision of quantization linearly depends on the ratio between the amplitude of the disorder potential and the cyclotron energy. The data obtained are compared with the results of magnetotransport measurements in mesoscopic samples.

Greshnov, A. A.; Kolesnikova, E. N.; Zegrya, G. G. [Russian Academy of Sciences, Ioffe Physicotechnical Institute (Russian Federation)], E-mail: zegrya@mail.ioffe.ru

2006-01-15

289

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.

2002-01-01

290

Underdamped strain dynamics of a martensitic model with power-law interactions

NASA Astrophysics Data System (ADS)

Focusing on conversion-time delays in athermal martensites, we present our results on underdamped strain dynamics of triple-well Landau free-energies with power-law anisotropic interactions for square-rectangle ferroelastic transition. After a temperature quench of 2% initial martensite seeds, the deterministic underdamped strain dynamics shows, interestingly, both fast conversions below a temperature and incubation delays above it, as in experiment and Monte Carlo simulations. On increasing damping constant, the fast conversions transform to incubation delays. Surprisingly, conversion-time delays have Vogel-Fulcher divergences as in Monte Carlo simulations. Microstructural evolutions are in good agreement with earlier studies.

Shankaraiah, N.; Puri, Sanjay; Shenoy, S. R.

2014-04-01

291

Sensitivity of Exponents of Three-Power Laws to Hybrid Ratio in Weighted HUHPM

NASA Astrophysics Data System (ADS)

The sensitivity of exponents of three-power laws for node degree, node strength and edged weight to hybrid ratio are studied analytically and numerically in the weighted harmonious unifying hybrid preferential model (HUHPM), which is extended from un-weighted hybrid preferential attachment model we proposed previously [Chin. Phys. Lett. 22 (2005) 719]. Our weighted HUHPMs plus the Barrat-Barthelemy-Vespignani model and the traffic-driven evolution model, respectively, are taken as two typical examples for demonstration and application of the HUHPM.

Fang, Jin-Qing; Bi, Qiao; Li, Yong; Lu, Xin-Biao; Liu, Qiang

2007-01-01

292

Observation of a power-law memory kernel for fluctuations within a single protein molecule.

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t(-0.51 +/- 0.07) in a broad range of time scales (10(-3)-10 s). Such a long-time memory effect could have implications for protein functions. PMID:16090221

Min, Wei; Luo, Guobin; Cherayil, Binny J; Kou, S C; Xie, X Sunney

2005-05-20

293

The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schroedinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schroedinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.

Ding Zhonghai [Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154-4020 (United States); Department of Mathematics and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, Taiwan (China); Chen, Goong [Department of Mathematics and Institute for Quantum Science and Engineering, Texas A and M University, College Station, Texas 77843 (United States); Department of Mathematics and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, Taiwan (China); Lin, Chang-Shou [Department of Mathematics and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, Taiwan (China)

2010-12-15

294

Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids

The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.

Maloney, C. E. [Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Robbins, M. O. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States)

2009-06-05

295

Extended power-law scaling of air permeabilities measured on a block of tuff

NASA Astrophysics Data System (ADS)

We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ?(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ?(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ?(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

Siena, M.; Guadagnini, A.; Riva, M.; Neuman, S. P.

2012-01-01

296

A theoretical design was performed for the condenser\\/boiler of a space-based solar dynamic power system. The base system is a binary Rankine cycle with mercury and toluene as the working fluids. System output is 75 KWe with a combined efficiency of 41.1%. Design goals were to develop the most reliable, mass efficient unit possible for delivery to a space station.

Randy M. Cotton

1987-01-01

297

ENERGY-DEPENDENT POWER SPECTRAL STATES AND ORIGIN OF APERIODIC VARIABILITY IN BLACK HOLE BINARIES

We found that the black hole candidate MAXI J1659-152 showed distinct power spectra, i.e., power-law noise (PLN) versus band-limited noise (BLN) plus quasi-periodic oscillations (QPOs) below and above about 2 keV, respectively, in observations with Swift and the Rossi X-ray Timing Explorer during the 2010 outburst, indicating a high energy cutoff of the PLN and a low energy cutoff of the BLN and QPOs around 2 keV. The emergence of the PLN and the fading of the BLN and QPOs initially took place below 2 keV when the source entered the hard intermediate state and settled in the soft state three weeks later. The evolution was accompanied by the emergence of the disk spectral component and decreases in the amplitudes of variability in the soft and hard X-ray bands. Our results indicate that the PLN is associated with an optically thick disk in both hard and intermediate states, and the power spectral state is independent of the X-ray energy spectral state in a broadband view. We suggest that in the hard or intermediate state, the BLN and QPOs emerge from the innermost hot flow subjected to Comptonization, while the PLN originates from the optically thick disk farther out. The energy cutoffs of the PLN and the BLN or QPOs then follow the temperature of the seed photons from the inner edge of the optically thick disk, while the high frequency cutoff of the PLN follows the orbital frequency of the inner edge of the optically thick disk as well.

Yu Wenfei; Zhang Wenda, E-mail: wenfei@shao.ac.cn [Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030 (China)

2013-06-20

298

Background: Sample size calculations are an important tool for planning epidemiological studies. Large sample sizes are often required in Mendelian randomization investigations. Methods and results: Resources are provided for investigators to perform sample size and power calculations for Mendelian randomization with a binary outcome. We initially provide formulae for the continuous outcome case, and then analogous formulae for the binary outcome case. The formulae are valid for a single instrumental variable, which may be a single genetic variant or an allele score comprising multiple variants. Graphs are provided to give the required sample size for 80% power for given values of the causal effect of the risk factor on the outcome and of the squared correlation between the risk factor and instrumental variable. R code and an online calculator tool are made available for calculating the sample size needed for a chosen power level given these parameters, as well as the power given the chosen sample size and these parameters. Conclusions: The sample size required for a given power of Mendelian randomization investigation depends greatly on the proportion of variance in the risk factor explained by the instrumental variable. The inclusion of multiple variants into an allele score to explain more of the variance in the risk factor will improve power, however care must be taken not to introduce bias by the inclusion of invalid variants.

Burgess, Stephen

2014-01-01

299

The time-domain behavior of power-law noises. [of many geophysical phenomena

NASA Technical Reports Server (NTRS)

The power spectra of many geophysical phenomena are well approximated by a power-law dependence on frequency or wavenumber. A simple expression for the root-mean-square variability of a process with such a spectrum over an interval of time or space is derived. The resulting expression yields the powerlaw time dependence characteristic of fractal processes, but can be generalized to give the temporal variability for more general spectral behaviors. The method is applied to spectra of crustal strain (to show what size of strain events can be detected over periods of months to seconds) and of sea level (to show the difficulty of extracting long-term rates from short records).

Agnew, Duncan C.

1992-01-01

300

Semiclassical trace formula for the two-dimensional radial power-law potentials

NASA Astrophysics Data System (ADS)

The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate up to a constant shift the radial dependence of the Woods-Saxon potential and its quantum spectra in a bound region, was derived by the improved stationary phase method. The specific analytical results are obtained for the powers ?=4 and 6. The enhancement of periodic-orbit contribution to the level density near the bifurcations are found to be significant for the description of the fine shell structure. The semiclassical trace formulas for the shell corrections to the level density and the energy of many-fermion systems reproduce the quantum results with good accuracy through all the bifurcation (symmetry breaking) catastrophe points, where the standard stationary-phase method breaks down. Various limits (including the harmonic oscillator and the spherical billiard) are obtained from the same analytical trace formula.

Magner, A. G.; Vlasenko, A. A.; Arita, K.

2013-06-01

301

Validation of a power-law noise model for simulating small-scale breast tissue

NASA Astrophysics Data System (ADS)

We have validated a small-scale breast tissue model based on power-law noise. A set of 110 patient images served as truth. The statistical model parameters were determined by matching the radially averaged power-spectrum of the projected simulated tissue with that of the central tomosynthesis patient breast projections. Observer performance in a signal-known exactly detection task in simulated and actual breast backgrounds was compared. Observers included human readers, a pre-whitening observer model and a channelized Hotelling observer model. For all observers, good agreement between performance in the simulated and actual backgrounds was found, both in the tomosynthesis central projections and the reconstructed images. This tissue model can be used for breast x-ray imaging system optimization. The complete statistical description of the model is provided.

Reiser, I.; Edwards, A.; Nishikawa, R. M.

2013-09-01

302

Power law approximations of movement network data for modeling infectious disease spread.

Globalization and increased mobility of individuals enable person-to-person transmitted infectious diseases to spread faster to distant places around the world, making good models for the spread increasingly important. We study the spatiotemporal pattern of spread in the remotely located and sparsely populated region of North Norway in various models with fixed, seasonal, and random effects. The models are applied to influenza A counts using data from positive microbiology laboratory tests as proxy for the underlying disease incidence. Human travel patterns with local air, road, and sea traffic data are incorporated as well as power law approximations thereof, both with quasi-Poisson regression and based on the adjacency structure of the relevant municipalities. We investigate model extensions using information about the proportion of positive laboratory tests, data on immigration from outside North Norway and by connecting population to the movement network. Furthermore, we perform two separate analyses for nonadults and adults as children are an important driver for influenza A. Comparisons of one-step-ahead predictions generally yield better or comparable results using power law approximations. PMID:24843881

Geilhufe, Marc; Held, Leonhard; Skrøvseth, Stein Olav; Simonsen, Gunnar S; Godtliebsen, Fred

2014-05-01

303

The US business cycle: power law scaling for interacting units with complex internal structure

NASA Astrophysics Data System (ADS)

In the social sciences, there is increasing evidence of the existence of power law distributions. The distribution of recessions in capitalist economies has recently been shown to follow such a distribution. The preferred explanation for this is self-organised criticality. Gene Stanley and colleagues propose an alternative, namely that power law scaling can arise from the interplay between random multiplicative growth and the complex structure of the units composing the system. This paper offers a parsimonious model of the US business cycle based on similar principles. The business cycle, along with long-term growth, is one of the two features which distinguishes capitalism from all previously existing societies. Yet, economics lacks a satisfactory theory of the cycle. The source of cycles is posited in economic theory to be a series of random shocks which are external to the system. In this model, the cycle is an internal feature of the system, arising from the level of industrial concentration of the agents and the interactions between them. The model-in contrast to existing economic theories of the cycle-accounts for the key features of output growth in the US business cycle in the 20th century.

Ormerod, Paul

2002-11-01

304

Nonexponential ``blinking'' kinetics of single CdSe quantum dots: A universal power law behavior

NASA Astrophysics Data System (ADS)

Single molecule confocal microscopy is used to study fluorescence intermittency of individual ZnS overcoated CdSe quantum dots (QDs) excited at 488 nm. The confocal apparatus permits the distribution of ``on'' and ``off'' times (i.e., periods of sustained fluorescence emission and darkness) to be measured over an unprecedentedly large dynamic range (109) of probability densities, with nonexponential behavior in ?off over a 105 range in time scales. In dramatic contrast, these same ?off distributions in all QDs are described with remarkable simplicity over this 109-fold dynamic range by a simple inverse power law, i.e., P(?off)~1/?off1+?. Such inverse power law behavior is a clear signature of distributed kinetics, such as predicted for (i) an exponential distribution of trap depths or (ii) a distribution of tunneling distances between QD core/interface states. This has important statistical implications for all previous studies of fluorescence intermittency in semiconductor QDs and may have broader implications for other systems such as single polymer molecules.

Kuno, M.; Fromm, D. P.; Hamann, H. F.; Gallagher, A.; Nesbitt, D. J.

2000-02-01

305

Robust statistical tests of Dragon-Kings beyond power law distributions

NASA Astrophysics Data System (ADS)

We ask the question whether it is possible to diagnose the existence of "Dragon-Kings" (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis, which can use an exponential or power law distribution. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in Germany.

Pisarenko, V. F.; Sornette, D.

2012-05-01

306

NASA Astrophysics Data System (ADS)

In predictive engineering for polymer processes, the proper prediction of material microstructure from known processing conditions and constituent material properties is a critical step forward properly predicting bulk properties in the finished composite. Operating within the context of long-fiber thermoplastics (LFT, length > 15mm) this investigation concentrates on the influence of the power law index on the final fiber length distribution within the injection molded part. To realize this, the Autodesk Simulation Moldflow Insight Scandium 2013 software has been used. In this software, a fiber breakage algorithm is available from this release on. Using virtual material data with realistic viscosity levels allows to separate the influence of the power law index on the fiber breakage from the other material and process parameters. Applying standard settings for the fiber breakage parameters results in an obvious influence on the fiber length distribution through the thickness of the part and also as function of position in the part. Finally, the influence of the shear rate constant within the fiber breakage model has been investigated illustrating the possibility to fit the virtual fiber length distribution to the possible experimentally available data.

Desplentere, Frederik; Six, Wim; Bonte, Hilde; Debrabandere, Eric

2013-04-01

307

Continuum percolation of overlapping disks with a distribution of radii having a power-law tail

NASA Astrophysics Data System (ADS)

We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between R and R+dR is proportional to R-(a+1), where a>2. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range interaction, we argue that in our problem, the critical exponents take their short-range values for a>3-?sr whereas they depend on a for a<3-?sr where ?sr is the anomalous dimension for the usual percolation problem. The mean-field regime obtained in the fluid problem corresponds to the fully covered regime, a?2, in the percolation problem. We propose an approximate renormalization scheme to determine the correlation length exponent ? and the percolation threshold. We carry out Monte Carlo simulations and determine the exponent ? as a function of a. The determined values of ? show that it is independent of the parameter a for a>3-?sr and is equal to that for the lattice percolation problem, whereas ? varies with a for 2

Sasidevan, V.

2013-08-01

308

Power-law scaling during shadowing growth of nanocolumns by oblique angle deposition

The authors have investigated the power-law behaviors of various morphological parameters during the shadowing growth of ruthenium (Ru) nanocolumns by an oblique angle sputter deposition technique with substrate rotation. Particularly, wavelength and column number density were measured at different column heights (h). The exponents associated with the wavelength (p{sub {lambda}}) and column number density (p{sub n}), correlated by the geometrical relationship p{sub {lambda}}{approx_equal}-(1/2)p{sub n}, were measured by atomic force microscopy to be {approx}0.5 and {approx}-1.0, respectively. Using a one-dimensional facet growth model based upon the principle of evolutionary selection under oblique angle deposition, they showed that the exponents associated with the column number density and wavelength can be predicted. The authors also illustrated that the exponent value associated with column number density originates from the competitive growth among columns that have different vertical growth rates. The simulated exponent values are independent of the shape of the facet, which indicates the universality of these power-law exponents.

Tang, F.; Karabacak, T.; Li, L.; Pelliccione, M.; Wang, G.-C.; Lu, T.-M. [Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States); Department of Applied Science, University of Arkansas at Little Rock, Little Rock, Arkansas 72204 (United States); Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States)

2007-01-15

309

Beyond power laws: A new approach for analyzing single molecule photoluminescence intermittency

NASA Astrophysics Data System (ADS)

The photoluminescence intermittency (PI) exhibited by single emitters has been studied for over a decade. To date, the vast majority of PI analyses involve parsing the data into emissive and non-emissive events, constructing histograms of event durations, and fitting these histograms to either exponential or power law probability distributions functions (PDFs). Here, a new method for analyzing PI data is presented where the data are used directly to construct a cumulative distribution function (CDF), and maximum-likelihood estimation techniques are used to determine the best fit of a model PDF to the CDF. Statistical tests are then employed to quantitatively evaluate the hypothesis that the CDF (data) is represented by the model PDF. The analysis method is outlined and applied to PI exhibited by single CdSe/CdS core-shell nanocrystals and the organic chromophore violamine R isolated in single crystals of potassium-acid phthalate. Contrary to previous studies, the analysis presented here demonstrates that the PI exhibited by these systems is not described by a power law. The analysis developed here is also used to quantify heterogeneity within PI data obtained from a collection of CdSe/CdS nanocrytals, and for the determination of statistically significant changes in PI accompanying perturbation of the emitter. In summary, the analysis methodology presented here provides a more statistically robust approach for analyzing PI data.

Riley, E. A.; Hess, C. M.; Whitham, P. J.; Reid, P. J.

2012-05-01

310

So You Think the Crab is Described by a Power-Law Spectrum

NASA Technical Reports Server (NTRS)

X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.

Weisskopf, Martin C.

2008-01-01

311

On the sensitivity of tidal network characterization to power law estimation

NASA Astrophysics Data System (ADS)

Long-term simulations (3000 yr) of an idealized basin using different tidal ranges (1, 2 and 3 m) and grain sizes (120, 480 and 960 ?m) have been performed in order to cover a range of hydrodynamic and sedimentary conditions. Two different cell sizes (50 and 100 m) have been used to study the impact of cell size on tidal network development. The probability distributions of the drainage area and the drainage volume have been computed for every simulation (during an ebb and a flood phase). Power law distributions are observed in drainage area and drainage volume distribution. As an objective estimation of the exponent of a power law is an open issue, different approaches (linear binning, normalized logarithmic binning, cumulative distribution function and maximum likelihood) proposed by White et al. (2008) to estimate the exponent have been used to carry out a sensitivity analysis. Our findings indicate that although all methods results in high and significant correlation coefficients, more work is needed to develop a universal, objective estimation of the exponent.

Jiménez, M.; Castanedo, S.; Zhou, Z.; Coco, G.; Medina, R.; Rodriguez-Iturbe, I.

2014-04-01

312

A power-law approximation for fluvial incision by tools and bed coverage processes

NASA Astrophysics Data System (ADS)

The stream-power model is widely used to represent fluvial incision in bedrock channels. The model does not account for the amount of sediment in the channel, which can abrade the channel at low concentrations or armor the channel at high concentrations. Here we use a natural example (Clearwater River, Washington State, USA) and numerical experiments to explore how sediment flux influences bedrock incision at a drainage-wide scale. We have generated numerical landscapes with different uplift patterns using the CHILD numerical model and incision rules that include a tools-and-coverage formulation. We then use regression analysis to fit a power-law function I=K*Am*Sn*, where I is incision rate, S slope, and A drainage area, and K*, m*, and n* are fit parameters. We find that this formulation works very well for the Clearwater and all of our numerical experiments. The function has the same form as the stream-power model, but the parameters are empirically defined (as indicated by the asterisks) and can take on values quite different than those inferred from process-based arguments. The best-fit parameters appear to be constant at the scale of a single drainage, but they vary between drainages depending on the pattern of uplift, and whether or not the landscape has reached steady-state. In all cases, slope-area steepness analysis works well for estimating relative incision rates. Our analysis indicates that, in some cases, m* can be quite low, apparently due to the fact that bed coverage increases with increasing area. We conclude that the power-law formulation provides a good functional representation of fluvial incision, but that there are no universal values for m* and n*. These conclusions have important implications for the size of mountain belts and feedbacks between tectonic uplift and surface processes.

Brandon, M. T.; Gasparini, N. M.

2005-12-01

313

On the power spectra of the wind-fed X-ray binary pulsar GX 301 - 2

NASA Technical Reports Server (NTRS)

A phenomenological model of accretion which is applied to the wind-fed X-ray binary pulsar GX 301 - 2 is developed, assuming that the accretion onto the neutron star does not occur from a continuous flux of plasma, but from blobs of matter which are threaded by the magnetic field lines onto the magnetic polar caps of the neutron star. These 'lumps' are produced at the magnetospheric limit by magnetohydrodynamical instability, introducing a 'noise' in the accretion process, due to the discontinuity in the flux of matter onto the neutron star. This model is able to describe the change of slope observed in the continuum component of the power spectra of the X-ray binary pulsar GX 301 - 2, in the frequency range 0.01 - 0.1 Hz. The physical properties of the infalling blobs derived in the model are in agreement with the constraints imposed by observations.

Orlandini, Mauro; Morfill, G. E.

1992-01-01

314

Network-state modulation of power-law frequency-scaling in visual cortical neurons.

Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m) activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m) reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the "effective" connectivity responsible for the dynamical signature of the population signals measured at different integration levels, from Vm to LFP, EEG and fMRI. PMID:19779556

El Boustani, Sami; Marre, Olivier; Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves

2009-09-01

315

A full compensating system for distribution networks, able to eliminate harmonics, correct unbalanced loads, and generate or absorb reactive power, is presented. The system is based on a combination of a thyristor binary compensator (TBC), and a pulsewidth-modulation insulated gate bipolar transistor active power filter (APF) connected in cascade. The TBC compensates the fundamental reactive power and balances the load

Juan Dixon; Yamille del Valle; Marcos Orchard; Micah Ortúzar; Luis Morán; Carlos Maffrand

2003-01-01

316

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

NASA Astrophysics Data System (ADS)

Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.

Deluca, Anna; Corral, Álvaro

2013-12-01

317

The unipolar induction DC circuit model, originally developed by Goldreich and Lynden-Bell for the Jupiter-Io system, has been applied to different types of binary systems in recent years. We show that there exists an upper limit to the magnetic interaction torque and energy dissipation rate in such a model. This arises because when the resistance of the circuit is too small, the large current flow severely twists the magnetic flux tube connecting the two binary components, leading to the breakdown of the circuit. Applying this limit, we find that in coalescing neutron star binaries, magnetic interactions produce negligible correction to the phase evolution of the gravitational waveform, even for magnetar-like field strengths. However, energy dissipation in the binary magnetosphere may still give rise to electromagnetic radiation prior to the final merger. For ultracompact white dwarf binaries, we find that unipolar induction does not provide adequate energy dissipation to explain the observed X-ray luminosities of several sources. For exoplanetary systems containing close-in Jupiters or super-Earths, the magnetic torque and energy dissipation induced by the orbital motion are negligible, except possibly during the early T Tauri phase, when the stellar magnetic field is stronger than 10{sup 3} G.

Lai Dong [Department of Astronomy, Cornell University, Ithaca, NY 14850 (United States)

2012-09-20

318

Listing triangles in expected linear time on a class of power law graphs.

Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysis for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is in the range that is relevant for the degree distribution of the World-Wide Web.

Nordman, Daniel J. (Iowa State University, Ames, Iowa); Wilson, Alyson G. (Iowa State University, Ames, Iowa); Phillips, Cynthia Ann; Berry, Jonathan W.

2010-07-01

319

Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT

Purpose: To determine the x-ray photon energy dependence of the anatomic power spectrum of the breast when imaged with dedicated breast computed tomography (CT). Methods: A theoretical framework for scaling the empirically determined anatomic power spectrum at one x-ray photon energy to that at any given x-ray photon energy when imaged with dedicated breast CT was developed. Theory predicted that when the anatomic power spectrum is fitted with a power curve of the form k?f??, where k and ? are fit coefficients and f is spatial frequency, the exponent ? would be independent of x-ray photon energy (E), and the amplitude k scales with the square of the difference in energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues. Twenty mastectomy specimens based numerical phantoms that were previously imaged with a benchtop flat-panel cone-beam CT system were converted to 3D distribution of glandular weight fraction (fg) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of fg and after converting to linear attenuation coefficients at monoenergetic x-ray photon energies of 20–80 keV in 5 keV intervals. The 1D power spectra along the axes were extracted and fitted with a power curve of the form k?f??. The energy dependence of k and ? were analyzed. Results: For the 20 mastectomy specimen based numerical phantoms used in the study, the exponent ? was found to be in the range of 2.34–2.42, depending on the axis of measurement. Numerical simulations agreed with the theoretical predictions that for a power-law anatomic spectrum of the form k?f??, ? was independent of E and k(E) = k1[?g(E) ? ?a(E)]2, where k1 is a constant, and ?g(E) and ?a(E) represent the energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues, respectively. Conclusions: Numerical simulations confirmed the theoretical predictions that in dedicated breast CT, the spatial frequency dependence of the anatomic power spectrum will be independent of x-ray photon energy, and the amplitude of the anatomic power spectrum scales by the square of difference in linear attenuation coefficients of fibroglandular and adipose tissues.

Vedantham, Srinivasan; Shi, Linxi; Glick, Stephen J.; Karellas, Andrew

2013-01-01

320

Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT

Purpose: To determine the x-ray photon energy dependence of the anatomic power spectrum of the breast when imaged with dedicated breast computed tomography (CT). Methods: A theoretical framework for scaling the empirically determined anatomic power spectrum at one x-ray photon energy to that at any given x-ray photon energy when imaged with dedicated breast CT was developed. Theory predicted that when the anatomic power spectrum is fitted with a power curve of the form k f{sup -{beta}}, where k and {beta} are fit coefficients and f is spatial frequency, the exponent {beta} would be independent of x-ray photon energy (E), and the amplitude k scales with the square of the difference in energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues. Twenty mastectomy specimens based numerical phantoms that were previously imaged with a benchtop flat-panel cone-beam CT system were converted to 3D distribution of glandular weight fraction (f{sub g}) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of f{sub g} and after converting to linear attenuation coefficients at monoenergetic x-ray photon energies of 20-80 keV in 5 keV intervals. The 1D power spectra along the axes were extracted and fitted with a power curve of the form k f{sup -{beta}}. The energy dependence of k and {beta} were analyzed. Results: For the 20 mastectomy specimen based numerical phantoms used in the study, the exponent {beta} was found to be in the range of 2.34-2.42, depending on the axis of measurement. Numerical simulations agreed with the theoretical predictions that for a power-law anatomic spectrum of the form k f{sup -{beta}}, {beta} was independent of E and k(E) =k{sub 1}[{mu}{sub g}(E) -{mu}{sub a}(E)]{sup 2}, where k{sub 1} is a constant, and {mu}{sub g}(E) and {mu}{sub a}(E) represent the energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues, respectively. Conclusions: Numerical simulations confirmed the theoretical predictions that in dedicated breast CT, the spatial frequency dependence of the anatomic power spectrum will be independent of x-ray photon energy, and the amplitude of the anatomic power spectrum scales by the square of difference in linear attenuation coefficients of fibroglandular and adipose tissues.

Vedantham, Srinivasan; Shi, Linxi; Glick, Stephen J.; Karellas, Andrew [Department of Radiology, University of Massachusetts Medical School, Worcester, Massachusetts 01655 (United States)

2013-01-15

321

Taylor's law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin–Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA.

Cohen, Joel E.; Xu, Meng; Schuster, William S. F.

2013-01-01

322

Power law signature of media exposure in human response waiting time distributions.

We study the humanitarian response to the destruction brought by the tsunami generated by the Sumatra earthquake of December 26, 2004, as measured by donations, and find that it decays in time as a power law ?1/t? with ?=2.5 ± 0.1 . This behavior is suggested to be the rare outcome of a priority queuing process in which individuals execute tasks at a rate slightly faster than the rate at which new tasks arise. We believe this to be an empirical evidence documenting the recently predicted [G. Grinstein and R. Linsker, Phys. Rev. E 77, 012101 (2008)] regime, and provide additional independent evidence that suggests that this "highly attentive regime" arises as a result of the intense focus placed on this donation "task" by the media. PMID:20866291

Crane, Riley; Schweitzer, Frank; Sornette, Didier

2010-05-01

323

Power-Law Distributions for the Free Path Length in Lorentz Gases

NASA Astrophysics Data System (ADS)

It is well known that, in the Boltzmann-Grad limit, the distribution of the free path length in the Lorentz gas with disordered scatterer configuration has an exponential density. If, on the other hand, the scatterers are located at the vertices of a Euclidean lattice, the density has a power-law tail proportional to . In the present paper we construct scatterer configurations whose free path lengths have a distribution with tail for any positive integer . We also discuss the properties of the random flight process that describes the Lorentz gas in the Boltzmann-Grad limit. The convergence of the distribution of the free path length follows from equidistribution of large spheres in products of certain homogeneous spaces, which in turn is a consequence of Ratner's measure classification theorem.

Marklof, Jens; Strömbergsson, Andreas

2014-06-01

324

Power-Law Distributions for the Free Path Length in Lorentz Gases

NASA Astrophysics Data System (ADS)

It is well known that, in the Boltzmann-Grad limit, the distribution of the free path length in the Lorentz gas with disordered scatterer configuration has an exponential density. If, on the other hand, the scatterers are located at the vertices of a Euclidean lattice, the density has a power-law tail proportional to ? ^{-3} . In the present paper we construct scatterer configurations whose free path lengths have a distribution with tail ? ^{-N-2} for any positive integer N . We also discuss the properties of the random flight process that describes the Lorentz gas in the Boltzmann-Grad limit. The convergence of the distribution of the free path length follows from equidistribution of large spheres in products of certain homogeneous spaces, which in turn is a consequence of Ratner's measure classification theorem.

Marklof, Jens; Strömbergsson, Andreas

2014-02-01

325

Evidence for power-law tail of the wealth distribution in India

NASA Astrophysics Data System (ADS)

The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-2004. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year under analysis). This provides a comparison with previous studies of wealth distribution, which have all been confined to Western advanced capitalist economies. We conclude with a discussion on the appropriateness of multiplicative stochastic process as a model for asset accumulation, the relation between the wealth and income distributions (we estimate the Pareto exponent for the latter to be around 1.5 for India), as well as possible sources of error in measuring the Pareto exponent for wealth.

Sinha, Sitabhra

2006-01-01

326

Power law signature of media exposure in human response waiting time distributions

NASA Astrophysics Data System (ADS)

We study the humanitarian response to the destruction brought by the tsunami generated by the Sumatra earthquake of December 26, 2004, as measured by donations, and find that it decays in time as a power law ˜1/t? with ?=2.5±0.1 . This behavior is suggested to be the rare outcome of a priority queuing process in which individuals execute tasks at a rate slightly faster than the rate at which new tasks arise. We believe this to be an empirical evidence documenting the recently predicted [G. Grinstein and R. Linsker, Phys. Rev. E 77, 012101 (2008)] regime, and provide additional independent evidence that suggests that this “highly attentive regime” arises as a result of the intense focus placed on this donation “task” by the media.

Crane, Riley; Schweitzer, Frank; Sornette, Didier

2010-05-01

327

Theoretical Foundations and Mathematical Formalism of the Power-Law Tailed Statistical Distributions

NASA Astrophysics Data System (ADS)

We present the main features of the mathematical theory generated by the \\kappa-deformed exponential function exp_{\\kappa}(x)=(\\sqrt{1+\\kappa^2 x^2}+\\kappa x)^{1/\\kappa}, with 0<\\kappa<1, developed in the last twelve years, which turns out to be a continuous one parameter deformation of the ordinary mathematics generated by the Euler exponential function. The \\kappa-mathematics has its roots in special relativity and furnishes the theoretical foundations of the \\kappa-statistical mechanics predicting power law tailed statistical distributions which have been observed experimentally in many physical, natural and artificial systems. After introducing the \\kappa-algebra we present the associated \\kappa-differential and \\kappa-integral calculus. Then we obtain the corresponding \\kappa-exponential and \\kappa-logarithm functions and give the \\kappa-version of the main functions of the ordinary mathematics.

Kaniadakis, Giorgio

2013-09-01

328

Mechanics of adhesive contact on a power-law graded elastic half-space

NASA Astrophysics Data System (ADS)

We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E= E0( z/ c0) k (0< k<1) while Poisson's ratio ? remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of P cr=-( k+3) ?R? ?/2 where ? ? is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k=0, the Gibson solid when k?1 and ?=0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off.

Chen, Shaohua; Yan, Cong; Zhang, Peng; Gao, Huajian

2009-09-01

329

A study of dynamic contact angles of shear-thickening power-law fluids

NASA Astrophysics Data System (ADS)

We study the dynamic wetting of shear-thickening power-law fluids in a liquid-solid-gas contact system. In the previous model based on hydrodynamic analysis, microscopic effects near the contact line are neglected. In this work, we adopt two different physical models, slip boundary model and molecular force model, to incorporate microscopic effects and relieve the stress singularity at the moving contact line in hydrodynamics analysis. The two models, which are mathematically equivalent for Newtonian fluids, lead to different results on the dependence of the liquid's dynamic contact angle on its moving speed in both complete wetting and partial wetting cases. By comparing with experiments, we find that the slip boundary model matches the experiments better than the previous model and the molecular force model.

Wang, Yu; Zhu, Ke-Qin

2014-05-01

330

Efficiency and its bounds for thermal engines at maximum power using Newton's law of cooling

NASA Astrophysics Data System (ADS)

We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case, this model can simulate Otto, Joule-Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as that from Esposito [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.150603 105, 150603 (2010)] are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines.

Yan, H.; Guo, Hao

2012-01-01

331

The nature of the hard X-ray power-law tail in M 87

NASA Astrophysics Data System (ADS)

Spatially-resolved spectroscopy of the elliptical galaxy M 87 with the MECS instrument on board BeppoSAX demonstrates that the hard X-ray power-law tail, originally discovered by ASCA (Matsumoto et al. 1996; Allen et al. 1999), originates in the innermost 2arcmin . Our results are consistent with it being produced in an Accretion Dominated Flow, although a substantial jet contribution cannot be ruled out. An origin from a Seyfert-like nucleus is disfavored by our data. As a by-product of this result, we present an analysis of the thermal emission coming from the center of the Virgo cluster, which exhibits a strong positive radial temperature gradient, along with a radial decrease of the iron abundance.

Guainazzi, Matteo; Molendi, Silvano

1999-11-01

332

Power-law solution of new agegraphic modified f(R) Horava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

We study the reconstruction scenario of modified gravity with a dynamical dark-energy model filling the universe. In this context, we consider the Modified f(R) Horava-Lifshitz Gravity with a new agegraphic dark-energy model using the power-law form of the scale factor. We construct a modified f(R) Horava-Lifshitz model and check its behavior along its argument. To discuss the accelerated expansion of the universe, some cosmological parameters are discussed as well. The equation-of-state parameter represents the phantom behavior of the universe as well as the statefinder diagnostic pair gives the phantom and quintessence regions. Also, the stability analysis is carried out through squared speed of sound which points out the stable modified f(R) Horava-Lifshitz model except in a small time interval.

Jawad, Abdul; Chattopadhyay, Surajit; Pasqua, Antonio

2014-03-01

333

Modelling of semi-solid processing using a modified temperature-dependent power-law model

NASA Astrophysics Data System (ADS)

A fairly simple one-phase rheological model has been implemented into a commercial fluid flow finite element software to simulate mould filling during the semi-solid processing (thixoforming) of aluminium alloys. This model is of purely viscous nature. Its temperature-dependent viscosity is a power-law function of the shear rate with a shear rate cut-off. The constitutive parameters of this model were determined for a rheocast A356 alloy. For that purpose, simulation results were compared with instrumented thixoforming experiments performed on a production-scale injection machine. The selected configuration was that of a transient flow near a bifurcation, i.e. obstruction of an established Poiseuille-type flow by a shaft placed at the centre of a tube. Using these parameters, the model was then further validated by comparing the simulation of an axisymmetric reservoir mould filling with the shape of solidified shells obtained after interrupted injection experiments.

Orgéas, L.; Gabathuler, J.-P.; Imwinkelried, Th.; Paradies, Ch.; Rappaz, M.

2003-07-01

334

Leptonic decays of vector mesons in a power-law potential model of independent quarks

NASA Astrophysics Data System (ADS)

A relativistic power-law potential model of independent quarks is used to study the leptonic decays of neutral vector mesons. Here, the transition probability amplitude for leptonic decay of meson is determined from the momentum distribution function which is found from the assumption of a strong correlation existing between the momenta of quark and antiquark inside the meson. The model parameters are first determined from the application of the model to study the ground state spectra of ?, ?, ?, ? and ? mesons together with the radiative decay widths of mesons. The same model with no adjustable parameters is then used to evaluate the leptonic decay widths and the electromagnetic decay constants for the vector mesons ?, ?, ?, ? and ?. The calculated results are in remarkable agreement with the corresponding experimental values.

Jena, S. N.; Nanda, P. K.; Sahoo, S.; Panda, P.

2014-04-01

335

NASA Technical Reports Server (NTRS)

The analytic solutions for radiatively driven winds are given for the case in which the winds are driven by absorption of line and continuum radiation. The wind solutions are analytically estimated for different parameters of the central source and for different power law spectra. For flat spectra, three sonic points can exist; it is shown, however, that only one of these sonic points is physically realistic. Parameters of the central source are given which generate winds of further interest for explaining the narrow and broad absorption lines in quasars. For the quasar model presented here, winds which could give rise to the narrow absorption lines are generated by central sources with parameters which are not realistic for quasars.

Beltrametti, M.

1980-01-01

336

Low prevalence, quasi-stationarity and power-law behavior in a model of contagion spreading

NASA Astrophysics Data System (ADS)

While contagion (information, infection, etc.) spreading has been extensively studied recently, the role of active local agents has not been fully considered. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local probabilistic dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. We study such spreading dynamics on Erdös-Rényi as well as scale free networks. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. These properties, while absent in standard theoretical models, are observed in recent empirical observations.

Montakhab, Afshin; Manshour, Pouya

2012-09-01

337

Origins of power-law degree distribution in the heterogeneity of human activity in social networks

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a “maximum entropy attachment” model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.

Muchnik, Lev; Pei, Sen; Parra, Lucas C.; Reis, Saulo D. S.; Andrade Jr, Jose S.; Havlin, Shlomo; Makse, Hernan A.

2013-01-01

338

On syntheses of the X-ray background with power-law sources

NASA Technical Reports Server (NTRS)

The conditions under which the combined emission from power-law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low-luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit steeper spectra at higher energies.

De Zotti, G.; Boldt, E. A.; Marshall, F. E.; Swank, J. H.; Szymkowiak, A. E.; Cavaliere, A.; Danese, L.; Franceschini, A.

1982-01-01

339

Constraints on transient and power-law rheologies from rapid uplift in the Antarctic Peninsula

NASA Astrophysics Data System (ADS)

Commencement of large glacial unloading in the Antarctic Peninsula since 1995, and especially 2002, is now well observed in terms of the unloading and the solid Earth response. The observed uplift requires a viscoelastic response to the unloading, and modelling based on a linear Maxwell rheology closely reproduces the observations. However, wider geophysical and laboratory studies suggest that a more complex rheological model may be required to correctly interpret the observed deformation. This well observed event offers a rare opportunity to constrain the rheology of the upper mantle using post-glacial rebound data and without large ambiguity in the ice history. Here, we report on two separate modelling efforts, respectively adopting a linear viscoelastic Burgers and power-law rheology, and discuss the constraints placed on such models by this dataset.

King, M. A.; Barletta, V. R.; Bordoni, A.; Nield, G. A.; Spada, G.; Memin, A.

2013-12-01

340

We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on both the secondary emitted electron flux and the dust charging currents, and this effect depends strongly on the ratio of the electrostatic potential energy of the primary electrons at the dust grain's surface to the thermodynamic energy, implying that a competition in the dusty plasma between these two energies plays a crucial role in this novel effect.

Gong Jingyu; Du Jiulin [Department of Physics, School of Science, Tianjin University, Tianjin 300072 (China)

2012-06-15

341

Musical rhythm spectra from Bach to Joplin obey a 1/f power law.

Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/f(?) power law across 16 subgenres and 40 composers, with ? ranging from ?0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities. PMID:22355125

Levitin, Daniel J; Chordia, Parag; Menon, Vinod

2012-03-01

342

Musical rhythm spectra from Bach to Joplin obey a 1/f power law

Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/f? power law across 16 subgenres and 40 composers, with ? ranging from ?0.5–1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.

Levitin, Daniel J.; Chordia, Parag; Menon, Vinod

2012-01-01

343

Dipole-dipole interactions in optical lattices do not follow an inverse cube power law

NASA Astrophysics Data System (ADS)

We study the effective dipole-dipole interactions in ultracold quantum gases on optical lattices as a function of asymmetry in confinement along the principal axes of the lattice. In particular, we study the matrix elements of the dipole-dipole interaction in the basis of lowest band Wannier functions which serve as a set of low-energy states for many-body physics on the lattice. We demonstrate that, for shallow lattices in quasi-reduced dimensional scenarios, the effective interaction between dipoles in an optical lattice is non-algebraic in the inter-particle separation at short to medium distance on the lattice scale and has a long-range power-law tail, in contrast to the pure power-law behavior of the dipole-dipole interaction in free space. The modifications to the free-space interaction can be sizable; we identify differences of up to 36% from the free-space interaction at the nearest-neighbor distance in quasi-one-dimensional arrangements. The interaction difference depends essentially on asymmetry in confinement, due to the d-wave anisotropy of the dipole-dipole interaction. Our results do not depend on statistics, applying to both dipolar Bose-Einstein condensates and degenerate Fermi gases. Using matrix product state simulations, we demonstrate that use of the correct lattice dipolar interaction leads to significant deviations from many-body predictions using the free-space interaction. Our results are relevant to up and coming experiments with ultracold heteronuclear molecules, Rydberg atoms and strongly magnetic atoms in optical lattices.

Wall, M. L.; Carr, L. D.

2013-12-01

344

This paper describes a novel pattern recognition based myoelectric control system that uses parallel binary classification and class specific thresholds. The system was designed with an intuitive configuration interface, similar to existing conventional myoelectric control systems. The system was assessed quantitatively with a classification error metric and functionally with a clothespin test implemented in a virtual environment. For each case,

Levi J. Hargrove; Kevin B. Englehart; Bernard S. Hudgins

2010-01-01

345

NASA Astrophysics Data System (ADS)

Often materials exhibit nonlinearity and hysteresis in their response to an elastic excitation and the dependence of the nonlinear indicator on the excitation energy is a power law function. From the theoretical point of view, such behavior could be described using multistate elastic models based on a generalized Preisach-Mayergoyz (PM) approach. In these models a statistical distribution of transition parameters is usually introduced. We show in this paper the existence of a link between the power law exponent predicted by the model and the properties of the chosen distribution. Numerical results are discussed, based on an implementation in the PM formalism of an adhesion model.

Scalerandi, M.; Gliozzi, A. S.; Idjimarene, S.

2014-10-01

346

Estimation of Power-Law Scaling in Time-Uncertain Series of Data With Application to GISP2

NASA Astrophysics Data System (ADS)

Errors in the timing assigned to observations degrade estimates of the power spectrum in a complicated and non-local fashion. It is clear that errors in timing will smear concentrations of spectral energy across a wide band of frequencies, leading to uncertainties in the analysis of the distribution of energy around these spectral peaks. Less understood is the influence of timing errors upon the background continuum. Surprisingly, we find that for power-law distributions of energy the expected value of the background continuum is insensitive to a broad class of errors in timing, at least at frequencies substantially lower than the Nyquist frequency associated with the largest gaps in the record. This can be understood as a consequence of the self-similarity of power-law signals, and is unexpected given the complex response of narrowband processes to time-uncertainty. Less surprisingly, age errors do tend to increase the uncertainty associated with estimates of power-law scaling exponents, which are a useful diagnostic of the long-term memory of the climate system. These insights are applied in the context of evaluating the power-law behavior of the GISP2 delta-18O record. Nonstationarity leads to a greater sensitivity of the record to timing errors in the vicinity of the last glacial maximum.

Rhines, A.; Huybers, P.

2009-12-01

347

NASA Astrophysics Data System (ADS)

Analytical expressions for the time-domain Green's function that exactly solve the wave equation for power-law media with an attenuation term that is proportional to frequency to the power were recently derived. These analytical expressions are causal for power-law exponents less than one and noncausal for power-law exponents greater than or equal to one. A causal expression for the lossy impulse response for a circular piston is obtained for power-law exponent when the impulse response of the time-domain Rayleigh-Sommerfeld integral is evaluated by superposing the causal Green's function in space and in time. The lossy impulse response is also computed in the frequency-domain for the same piston. Numerical results are computed in the time and frequency-domains for a circular piston with a radius of 15mm. Problems with aliasing are identified in the frequency-domain impulse response calculation, whereas these problems are avoided in the time-domain calculation.

Johnson, Christopher T.; McGough, Robert J.

2011-03-01

348

We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett. 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of (1-(A/A{sub cr})), A is the number of condensate atoms and A{sub cr} is the critical number near collapse. We observe that the power-law exponent becomes (1/6) in our calculation for the pure harmonic trap and it becomes (1/7), for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.

Debnath, P. K. [Santoshpur Sri Gouranga Vidyapith (H.S.), P.O. Kulitapara, Howrah 711312 (India); Chakrabarti, Barnali [Department of Physics, Lady Brabourne College, P1/ 2 Surawardi Avenue, Kolkata 700017 (India)

2010-10-15

349

NASA Astrophysics Data System (ADS)

In several high-energy astrophysical sites, shocks are assumed to produce a power-law distribution of accelerated charged particles (e.g., electrons, protons) and to generate mild to strong magnetic fields, which favours synchrotron emission. For such environments and conditions, we have performed and present here four practical formulas, with different levels of accuracy, for fitting the synchrotron spectral power radiated by a pure power-law particle distribution, with isotropic pitch angle distribution. The first three ones can be useful compared to the fourth one, because of their simplicity, in the case of particle distribution with no high-energy cutoff. However, the fourth formula, the more accurate one, can be of great interest for astrophysical applications (even though it is more complicated) for the more general case of a power-law distribution with high-energy sharp cutoff. The latter is derived for index p within the range, 1 < p < 6, with maximum relative error of less than 0.5 per cent in the case of infinite energy range and of less than 8.2 per cent in the more general case of particle energy with sharp cutoff. The latter is expressed in terms of parameters as functions of index p. These parameters have been fitted with adopting the Levenberg-Marquardt algorithm in log-log scale. According to these formulas, initially derived for the total spectral power, we have then derived (1) the degree of polarization, (2) cooling spectra for a broken power-law distribution and (3) synchrotron self-absorption spectra for both the broken and non-broken power-law distributions. The proposed expressions are relevant for non-thermal astrophysical sources in the sense that by using them one avoids usually complicated and long CPU time calculations, without performing any integration.

Fouka, M.; Ouichaoui, S.

2014-08-01

350

Highly optimized tolerance and power laws in dense and sparse resource regimes

NASA Astrophysics Data System (ADS)

Power law cumulative frequency (P) versus event size (l) distributions P(?l)˜l-? are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete highly optimized tolerance (HOT) model, referred to as the probability, loss, resource (PLR) model, gives the exponent ?=1/d as a function of the dimension d of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts ?=1+1/d . In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.

Manning, M.; Carlson, J. M.; Doyle, J.

2005-07-01

351

Cascade model of gamma-ray bursts: Power-law and annihilation-line components

NASA Technical Reports Server (NTRS)

If, in a neutron star magnetosphere, an electron is accelerated to an energy of 10 to the 11th or 12th power eV by an electric field parallel to the magnetic field, motion of the electron along the curved field line leads to a cascade of gamma rays and electron-positron pairs. This process is believed to occur in radio pulsars and gamma ray burst sources. Results are presented from numerical simulations of the radiation and photon annihilation pair production processes, using a computer code previously developed for the study of radio pulsars. A range of values of initial energy of a primary electron was considered along with initial injection position, and magnetic dipole moment of the neutron star. The resulting spectra was found to exhibit complex forms that are typically power law over a substantial range of photon energy, and typically include a dip in the spectrum near the electron gyro-frequency at the injection point. The results of a number of models are compared with data for the 5 Mar., 1979 gamma ray burst. A good fit was found to the gamma ray part of the spectrum, including the equivalent width of the annihilation line.

Harding, A. K.; Sturrock, P. A.; Daugherty, J. K.

1988-01-01

352

The phase-integral approximation devised by Froeman and Froeman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform-approximation methods.

Rojas, Clara; Villalba, Victor M. [Centro de Fisica IVIC Apdo 21827, Caracas 1020A (Venezuela)

2007-03-15

353

We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF slope recovery in this paper are lower limits, as we do not explicitly consider all possible sources of uncertainty, including dynamical effects (e.g., mass segregation), unresolved binaries, and non-coeval populations. We briefly discuss how each of these effects can be incorporated into extensions of the present framework. Finally, we emphasize that the technique and lessons learned are applicable to more general problems involving power-law fitting.

Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.; Clifton Johnson, L.; Beerman, Lori C.; Williams, Benjamin F. [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States)] [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States); Hogg, David W.; Foreman-Mackey, Daniel T. [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States)] [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Rix, Hans-Walter; Gouliermis, Dimitrios [Max Planck Institute for Astronomy, Koenigstuhl 17, D-69117 Heidelberg (Germany)] [Max Planck Institute for Astronomy, Koenigstuhl 17, D-69117 Heidelberg (Germany); Dolphin, Andrew E. [Raytheon Company, 1151 East Hermans Road, Tucson, AZ 85756 (United States)] [Raytheon Company, 1151 East Hermans Road, Tucson, AZ 85756 (United States); Lang, Dustin [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States)] [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Bell, Eric F. [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States)] [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States); Gordon, Karl D.; Kalirai, Jason S. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)] [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Skillman, Evan D., E-mail: dweisz@astro.washington.edu [Minnesota Institute for Astrophysics, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States)

2013-01-10

354

NASA Technical Reports Server (NTRS)

Recent observations indicate that the eclipsing pulsar binary PSR B1957+20 undergoes alternating epochs of orbital period increase and decrease. We apply a model developed to explain orbital period changes of alternating sign in other binaries to the PSR B1957+20 system and find that it fits the pulsars observations well. The novel feature of the PSR B1957+20 system is that the energy flow in the companion needed to power the orbital period change mechanism can be supplied by tidal dissipation, making the companion the first identified tidally powered star. The flow of energy in the companion drives magnetic activity, which underlies the observed orbital period variations. The magnetic activity and the wind driven by the pulsar irradiation results in a torque on the spin of the companion. This torque holds the companion out of synchronous rotation, causing tidal dissipation of energy. We propose that the progenitor had a approximately 2 hr orbital period and a companion mass of 0.1-0.2 solar mass, and the system is evolving to longer orbital periods by mass and angular momentum loss on a timescale of 10(exp 8) yr.

Applegate, James H.; Shaham, Jacob

1994-01-01

355

Statistical Tests Black swans or dragon-kings? A simple test for deviations from the power law?

NASA Astrophysics Data System (ADS)

We develop a simple test for deviations from power law tails. Actually, from the tails of any distribution. We use this test - which is based on the asymptotic properties of the empirical distribution function - to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon-kings or `only' as black swans.

Janczura, J.; Weron, R.

2012-05-01

356

EVIDENCE FOR DEPARTURE FROM A POWER-LAW FLARE SIZE DISTRIBUTION FOR A SMALL SOLAR ACTIVE REGION

Active region 11029 was a small, highly flare-productive solar active region observed at a time of extremely low solar activity. The region produced only small flares: the largest of the >70 Geostationary Observational Environmental Satellite (GOES) events for the region has a peak 1-8 A flux of 2.2 x 10{sup -6} W m{sup -2} (GOES C2.2). The background-subtracted GOES peak-flux distribution suggests departure from power-law behavior above 10{sup -6} W m{sup -2}, and a Bayesian model comparison strongly favors a power-law plus rollover model for the distribution over a simple power-law model. The departure from the power law is attributed to this small active region having a finite amount of energy. The rate of flaring in the region varies with time, becoming very high for 2 days coinciding with the onset of an increase in complexity of the photospheric magnetic field. The observed waiting-time distribution for events is consistent with a piecewise-constant Poisson model. These results present challenges for models of flare statistics and of energy balance in solar active regions.

Wheatland, M. S., E-mail: m.wheatland@physics.usyd.edu.a [Sydney Institute for Astronomy, School of Physics, University of Sydney, NSW 2006 (Australia)

2010-02-20

357

Bradford's law in relation to the evolution of a field. A case study of solar power research

Based on the data of growth of literature in the field of solar power, the present paper investigates the stage of evolution at which the scattering of articles over journals is similar to Bradford's curve, i.e. the stage at which Bradford's law is valid. Traces the related changes that take place in the size and elements of the core during

K. C. Garg; Praveen Sharma; Lalita Sharma

1993-01-01

358

A procedure has been developed to obtain microscope images of regions of contact between roughened surfaces of transparent materials, while the surfaces are subjected to static loads or undergoing frictional slip. Static loading experiments with quartz, calcite, soda-lime glass and acrylic plastic at normal stresses to 30 MPa yield power law distributions of contact areas from the smallest contacts that

James H. Dieterich; Brian D. Kilgore

1996-01-01

359

Data power law scaling behavior is observed in many fields. Velocity of fully developed turbulent flow, telecommunication traffic in networks, financial time series are some examples among many others. The goal of the present contribution is to show the scaling behavior of physiological time series in marathon races using wavelet leaders and the Detrended Fluctuation Analysis. Marathon race is an

Eva Wesfreid; Véronique Billat

2009-01-01

360

The results of an investigation are presented for non-Newtonian fluid heat transfer studies in noncircular ducts. Laminar fully developed flow of a purely viscous fluid is analyzed with two power law fluid models in isosceles triangular ducts. Three major components are covered: (1) The temperature distributions and heat transfer coefficients for a hydrodynamically and thermally fully developed newtonian fluid for

J. A. J. Cheng

1984-01-01

361

The steady laminar flow and heat transfer of an incompressible, electrically conducting, power law non-Newtonian fluids in a rectangular duct are studied in the presence of an external uniform magnetic field. The momentum and energy equations are solved iteratively using a finite difference method. Two cases of the thermal boundary conditions are considered; (1) T thermal boundary condition “constant temperature

Mohamed Eissa Sayed Ahmed

2006-01-01

362

NASA Astrophysics Data System (ADS)

The nonlinear Schrödinger equation with dual-power law nonlinearity for describing the propagation of pulses through an optical fiber in an optical communication system is studied. The first integral method, which is based on the division theorem, is used for obtaining the exact 1-soliton solution of this equation. The exact 1-soliton solution is constructed through the established first integral.

Eslami, Mostafa; Mirzazadeh, Mohammad

2013-11-01

363

The variation of the wind profile power-law exponent with respect to changes in surface roughness and atmospheric stability is depicted using the formulation of Nickerson and Smiley for specifying the vertical variations of the horizontal wind. The theoretical estimates of the po...

364

NASA Astrophysics Data System (ADS)

A model in which the nondimensional eddy viscosity and velocity distributions in circular pipe flow are applicable to noncircular passage flows was applied to the prediction of fully developed turbulent pressure drops in triangular ducts for Newtonian and power law fluids. The numerical calculations for the predicted turbulent velocity profiles and friction factors in triangular ducts were carried out by utilizing a modified integral transformation after Krajewski and the laminar velocity solutions for power law fluids. Friction factors for Newtonian and power law fluid flows were experimentally investigated over a Reynolds number range of 500 to 40000 in isosceles triangular ducts having apex angles of 10 and 60 degrees. Comparisons were made between the theoretical and experimental results. For the 60 degree duct, the model was successful in predicting friction factor-Reynolds number relations for power law fluids in the range 0.857 n 1. For the 10 degree duct, the model was unable to account for the laminarization of the flow in the apex region and the presence of secondary flows.

Chang, T. D.

365

Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges

Summary The classical solution of the steady-state creep problem for a pressurized thick-walled cylinder is based on the power law\\u000a constitutive equation. Several heat resistant steels show, however, the linear dependence of the creep rate on the applied\\u000a stress within a certain stress range. In this paper we apply an extended constitutive equation which includes both the linear\\u000a and the power

Holm Altenbach; Y. Gorash; K. Naumenko

2008-01-01

366

The XMM deep survey in the CDF-S. VI. Obscured AGN selected as infrared power-law galaxies

NASA Astrophysics Data System (ADS)

Context. Accretion onto supermassive black holes is believed to occur mostly in obscured active galactic nuclei (AGN). Such objects are proving rather elusive in surveys of distant galaxies, including those at X-ray energies. Aims: Our main goal is to determine whether the revised IRAC criteria of Donley et al. (2012, ApJ, 748, 142; objects with an infrared (IR) power-law spectral shape), are effective at selecting X-ray type-2 AGN (i.e., absorbed NH > 1022 cm-2). Methods: We present the results from the X-ray spectral analysis of 147 AGN selected by cross-correlating the highest spectral quality ultra-deep XMM-Newton and the Spitzer/IRAC catalogues in the Chandra Deep Field South. Consequently it is biased towards sources with high S/N X-ray spectra. In order to measure the amount of intrinsic absorption in these sources, we adopt a simple X-ray spectral model that includes a power-law modified by intrinsic absorption at the redshift of each source and a possible soft X-ray component. Results: We find 21/147 sources to be heavily absorbed but the uncertainties in their obscuring column densities do not allow us to confirm their Compton-Thick nature without resorting to additional criteria. Although IR power-law galaxies are less numerous in our sample than IR non-power-law galaxies (60 versus 87 respectively), we find that the fraction of absorbed (NHintr > 1022 cm-2) AGN is significantly higher (at about 3 sigma level) for IR-power-law sources (~2/3) than for those sources that do not meet this IR selection criteria (~1/2). This behaviour is particularly notable at low luminosities, but it appears to be present, although with a marginal significance, at all luminosities. Conclusions: We therefore conclude that the IR power-law method is efficient in finding X-ray-absorbed sources. We would then expect that the long-sought dominant population of absorbed AGN is abundant among IR power-law spectral shape sources not detected in X-rays.

Castelló-Mor, N.; Carrera, F. J.; Alonso-Herrero, A.; Mateos, S.; Barcons, X.; Ranalli, P.; Pérez-González, P. G.; Comastri, A.; Vignali, C.; Georgantopoulos, I.

2013-08-01

367

Scalable Solvers for Optimal Control of a Power-Law Fluid

NASA Astrophysics Data System (ADS)

Inverse problems such as determining internal fields or basal boundary conditions quickly become very large when applied to large glaciers or ice sheets. Millions of degrees of freedom are required to resolve critical flow features in a three dimensional ice sheet model. Traditional inverse methods involve forming and factoring a linearized inverse operator which is a dense matrix. The memory needed to store a single 106 × 106 matrix is 8 terabytes and the CPU cost to factor such a matrix is impractical. Instead, we pose the inverse problem as PDE-constrained optimization and apply fully iterative methods. For our problems, the design and state spaces are mesh-dependent, so we seek a method which scales linearly with respect to both spaces. The recently developed Lagrange-Newton-Krylov-Schur (LNKS) method applies the well-established Newton-Krylov machinery directly to the first-order optimality condition. Unlike reduced space quasi-Newton methods, the Newton iteration displays mesh-independent quadratic convergence and the Krylov iteration will also exhibit mesh-independent convergence if an optimal preconditioner is available. Obtaining an optimal preconditioner is difficult since the Jacobian matrix has saddle point structure and is very poorly conditioned, but Schur complement preconditioning is effective and frequently optimal. Since the incompressible flow constraint also has saddle point structure, we require two levels of Schur complement preconditioning, providing a vast array of choices. For a power-law fluid, globalization by continuation in the exponent is natural but reduced space alternatives are available when the preconditioning matrix is expensive to form. We present a computational study of LNKS and reduced space methods in the context of a novel p-version finite element method which applies the full-order Jacobian matrix-free and assembles a much sparser preconditioning matrix using low-order finite elements. We devote special attention to the design of Schur complement preconditioners which are robust with respect to strength of the power-law nonlinearity since these are critical for efficient forward modeling as well.

Brown, J.

2008-12-01

368

NASA Astrophysics Data System (ADS)

A theoretical design was performed for the condenser/boiler of a space-based solar dynamic power system. The base system is a binary Rankine cycle with mercury and toluene as the working fluids. System output is 75 KWe with a combined efficiency of 41.1%. Design goals were to develop the most reliable, mass efficient unit possible for delivery to a space station. The design sized the unit based on toluene properties and used a computer generated heat balance to thermodynamically match the two fluids. Molybdenum was chosen as the material due to mass effectiveness in heat transfer, strength, and resistance to mercury corrosion. The unit transferred 137.46 kilowatts of thermal power and can operate at varying mass flow rates. Effectiveness in heat transfer is 0.96 and mass performance is 0.016 kg/KWth transferred. The design depends on using only existing technologies and the results call for no new developments.

Cotton, Randy M.

1987-05-01

369

This report describes both the theoretical development and the experimental evaluation of a novel, robust methodology for the time-optimal adjustment of a reactor's neutronic power under conditions of closed-loop digital control. Central to the approach are the MIT-SNL Period-Generated Minimum Time Control Laws' which determine the rate at which reactivity should be changed in order to cause a reactor's neutronic power to conform to a specified trajectory. Using these laws, reactor power can be safely raised by five to seven orders of magnitude in a few seconds. The MIT-SNL laws were developed to facilitate rapid increases of neutronic power on spacecraft reactors operating in an SDI environment. However, these laws are generic and have other applications including the rapid recovery of research and test reactors subsequent to an unanticipated shutdown, power increases following the achievement of criticality on commercial reactors, power adjustments on commercial reactors so as to minimize thermal stress, and automated startups. The work reported here was performed by the Massachusetts Institute of Technology under contract to the Sandia National Laboratories. Support was also provided by the US Department of Energy's Division of University and Industry Programs. The work described in this report is significant in that a novel solution to the problem of time-optimal control of neutronic power was identified, in that a rigorous description of a reactor's dynamics was derived in that the rate of change of reactivity was recognized as the proper control signal, and in that extensive experimental trials were conducted of these newly developed concepts on actual nuclear reactors. 43 refs., 118 figs., 11 tabs.

Bernard, J.A. (Massachusetts Inst. of Tech., Cambridge, MA (USA). Nuclear Reactor Lab.)

1989-09-01

370

NASA Astrophysics Data System (ADS)

We perform an explicit one-loop calculation for the gravitational contributions to the two-, three- and four-point gauge Green's functions with paying attention to the quadratic divergences. It is shown for the first time in the diagrammatic calculation that the Slavnov-Taylor identities are preserved even if the quantum graviton effects are included at one-loop level, such a conclusion is independent of the choice of regularization schemes. We also present a regularization scheme independent calculation based on the gauge condition independent background field framework of Vilkovisky-DeWitt's effective action with focusing on both the quadratic divergence and quartic divergence that is not discussed before. With the harmonic gauge condition, the results computed by using the traditional background field method can consistently be recovered from the Vilkovisky-DeWitt's effective action approach by simply taking a limiting case, and are found to be the same as the ones yielded by the diagrammatic calculation. As a consequence, in all the calculations, the symmetry-preserving and divergent-behavior-preserving loop regularization method can consistently lead to a nontrivial gravitational contribution to the gauge coupling constant with an asymptotic free power-law running at one loop near the Planck scale.

Tang, Yong; Wu, Yue-Liang

2011-11-01

371

A unified econophysics explanation for the power-law exponents of stock market activity

NASA Astrophysics Data System (ADS)

We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.

Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, Eugene

2007-08-01

372

Pressure effects on electroosmotic flow of power-law fluids in rectangular microchannels

NASA Astrophysics Data System (ADS)

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids.

Vakili, Mohammad Ali; Sadeghi, Arman; Saidi, Mohammad Hassan

2014-05-01

373

Power-law and logarithmic relaxations of hydrated proteins: A molecular dynamics simulations study

NASA Astrophysics Data System (ADS)

We use molecular dynamics simulations to study anomalous internal protein dynamics observed for the backbone atoms of hydrated elastin and hydrated myoglobin in the picoseconds and nanoseconds regimes. The anomalous dynamics manifests itself in a sublinear increase of the atomic mean square displacements and in a power-law or logarithmic-like decay of correlation functions. We find that several, but not all, observations can be described in the frameworks of rugged potential-energy landscape and fractional Fokker-Planck approaches, in particular, a fractional Ornstein-Uhlenbeck process. Furthermore, mode-coupling theory allows us to rationalize findings at ambient temperatures, but there are deviations between theoretical predictions and simulation results related to the anomalous dynamics at cryogenic temperatures. We argue that the observations are consistent with a scenario where a broad ?-relaxation peak shifts through the picoseconds and nanoseconds regimes when cooling from 300 to 200 K, say. Inspection of trajectories of consecutive nitrogen atoms along the protein backbone reveals that correlated forward-backward jumps, which exhibit a substantial degree of cooperativity, are a key feature of the anomalous dynamics.

Kämpf, K.; Klameth, F.; Vogel, M.

2012-11-01

374

Power-Law Rheology of Isolated Nuclei with Deformation Mapping of Nuclear Substructures

Force-induced changes in genome expression as well as remodeling of nuclear architecture in development and disease motivate a deeper understanding of nuclear mechanics. Chromatin and green fluorescent protein-lamin B dynamics were visualized in a micropipette aspiration of isolated nuclei, and both were shown to contribute to viscoelastic properties of the somatic cell nucleus. Reversible swelling by almost 200% in volume, with changes in salt, demonstrates the resilience and large dilational capacity of the nuclear envelope, nucleoli, and chromatin. Swelling also proves an effective way to separate the mechanical contributions of nuclear elements. In unswollen nuclei, chromatin is a primary force-bearing element, whereas swollen nuclei are an order of magnitude softer, with the lamina sustaining much of the load. In both cases, nuclear deformability increases with time, scaling as a power law—thus lacking any characteristic timescale—when nuclei are either aspirated or indented by atomic force microscopy. The nucleus is stiff and resists distortion at short times, but it softens and deforms more readily at longer times. Such results indicate an essentially infinite spectrum of timescales for structural reorganization, with implications for regulating genome expression kinetics.

Dahl, Kris Noel; Engler, Adam J.; Pajerowski, J. David; Discher, Dennis E.

2005-01-01

375

Contracting bubbles in Hele-Shaw cells with a power-law fluid

NASA Astrophysics Data System (ADS)

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalize the ellipses that characterize the Newtonian case being constructed by the Wiener-Hopf calculation.

McCue, Scott W.; King, John R.

2011-02-01

376

Can log-periodic power law structures arise from random fluctuations?

NASA Astrophysics Data System (ADS)

Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable LPPL structures. To this end, we first estimate the stochastic process underlying the DAX log-returns during the period from mid-1997 until end-2003. The employed data set contains about 3.93?106 intraday DAX quotes at a sampling rate of 15 s. Our results indicate that the DAX log-returns can be described as a Markov process. As a consequence, a Langevin equation is derived. Based on this model equation, we run extensive simulations in order to generate 100 synthetic DAX trajectories each covering 3000 trading days. We find LPPL behavior in ten artificial time series. Moreover, we can establish a link between LPPL patterns and ensuing bubble bursts in seven synthetic 600-week windows. However, the LPPL components in most synthetic trajectories differ fundamentally from those LPPL structures that have previously been detected in real financial time series. Summarized, this paper demonstrates that LPPL structures are not necessarily the signature of imitative behavior among investors but can also stem from noise, even though the likelihood of this is extremely low. Thus, our findings confirm with high statistical confidence that the LPPL structures in the DAX development are rooted deeper than only in the random fluctuations of the German stock market.

Wosnitza, Jan Henrik; Leker, Jens

2014-05-01

377

Success of a simulation approach for magnetic nanosystems: Power of physical laws

NASA Astrophysics Data System (ADS)

The new quantum simulation model and the self-consistent algorithm (SCA) for magnetic nanosystems, that we proposed 2 years ago, were extended to study the magnetic properties of a nanowire consisting of 3d ions which are coupled ferromagnetically. To test the applicability of the algorithm, our simulations in the present work were started from a magnetic structure in which all spins in the whole nanosample were randomly oriented (defined as the random magnetic configuration for later use) as other authors have been doing with Monte Carlo or micromagnetism method, and such calculated results were all reasonable. Especially, the free energies evaluated at the chosen temperatures were found to attenuate spontaneously and quickly, as the program ran, towards the minima according to the principle of lowest free energy as expected. This suggests that the computational algorithm is able to lead the code to converge rapidly to the equilibrium state automatically without the need to minimize the total (free) energy of the system elaborately that must be done if the Monte Carlo or micromagnetism method is used, demonstrating the great power of natural laws.

Liu, Z.-S.; Sechovský, V.; Diviš, M.

2014-05-01

378

Exact, E = 0, classical and quantum solutions for general power-law oscillators

NASA Technical Reports Server (NTRS)

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

Nieto, Michael Martin; Daboul, Jamil

1995-01-01

379

A power-law rheology-based finite element model for single cell deformation.

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury. PMID:22307682

Zhou, E H; Xu, F; Quek, S T; Lim, C T

2012-09-01

380

A stable and robust calibration scheme of the log-periodic power law model

NASA Astrophysics Data System (ADS)

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time tc, defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.

Filimonov, V.; Sornette, D.

2013-09-01

381

Precursors and power-law statistics of acoustic emission and shape memory effect in martensites

NASA Astrophysics Data System (ADS)

We report a detailed numerical investigation of a recently introduced two-dimensional model for square-to-rectangle martensitic transformation that explains several unusual features of the martensitic transformation. This model includes inertial effects, dissipation, long-range interaction between the transformed domains and an inhomogeneous stress field to describe the effect of lattice defects which serves as nucleation centers. Both single-site nucleation and multi-site nucleation has been studied for single quench situation and thermal cycling. The final stage morphologies of single-site nucleation and multi-site nucleation bear considerable similarity suggesting that the initial distribution of the defects is not important. Thermal cycling using continuous cooling and heating simulations show the existence of hysteresis in the transformation. More importantly, the rate of energy dissipated occurs in the forms of bursts with power law statistics for their amplitudes and durations which explains the results of acoustic emission signals observed in experiments. When the system is cycled repeatedly in a restricted domain of temperatures, the dissipated bursts of energy are repetitive, a feature observed in experiments. The associated morphology shows a complete reversal of the martensite domains thus throwing light on the mechanism underlying the shape memory effect. The model also exhibits tweed-like patterns.

Sreekala, S.; Ahluwalia, Rajeev; Ananthakrishna, G.

2004-12-01

382

Black hole in the expanding universe with arbitrary power-law expansion

We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordstroem (RN) black hole and the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the D-dimensional Einstein-Maxwell-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a (D-1)-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential n{sub T}, the U(1) charge Q, and the nonextremality {tau}. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.

Maeda, Kei-ichi [Department of Physics, Waseda University, Okubo 3-4-1, Shinjuku, Tokyo 169-8555 (Japan); Waseda Research Institute for Science and Engineering, Okubo 3-4-1, Shinjuku, Tokyo 169-8555 (Japan); Nozawa, Masato [Department of Physics, Waseda University, Okubo 3-4-1, Shinjuku, Tokyo 169-8555 (Japan)

2010-06-15

383

Power-law scaling and fractal nature of medium-range order in metallic glasses.

The atomic structure of metallic glasses has been a long-standing scientific problem. Unlike crystalline metals, where long-range ordering is established by periodic stacking of fundamental building blocks known as unit cells, a metallic glass has no long-range translational or orientational order, although some degrees of short- and medium-range order do exist. Previous studies have identified solute- (minority atom)-centred clusters as the fundamental building blocks or short-range order in metallic glasses. Idealized cluster packing schemes, such as efficient cluster packing on a cubic lattice and icosahedral packing as in a quasicrystal, have been proposed and provided first insights on the medium-range order in metallic glasses. However, these packing schemes break down beyond a length scale of a few clusters. Here, on the basis of neutron and X-ray diffraction experiments, we propose a new packing scheme-self-similar packing of atomic clusters. We show that the medium-range order has the characteristics of a fractal network with a dimension of 2.31, and is described by a power-law correlation function over the medium-range length scale. Our finding provides a new perspective of order in disordered materials and has broad implications for understanding their structure-property relationship, particularly those involving a change in length scales. PMID:19060888

Ma, D; Stoica, A D; Wang, X-L

2009-01-01

384

Designing a simple rheometer: Unsteady dam-break flows of power-law fluids

NASA Astrophysics Data System (ADS)

Many geophysical flows, such as mud slides, debris flows and avalanches, are non-Newtonian, and consequently exhibit complex flow behaviour. This is often due to an underlying microstructure within the flow -- for example, a suspension of particles within an interstitial fluid. We develop a method for determining the rheological parameters of a power-law fluid through the utilization of both numerical results and data from simple laboratory experiments. The model employed describes an unsteady dam-break flow of a viscous material within a rectangular channel, capturing the shape of the free surface and the streamwise velocity; a novel feature of this work is that it accounts for the effect of the containing side walls of a channel of any specified dimensions. Much of the previous work in this area has neglected this aspect of the physics, but here it can be shown that the side walls have an appreciable influence on the flow. The method relies on the numerical calculation of the flux through a cross-section of the channel, which has been done using both a finite element solver and a pseudo-spectral method, coupled to an evolution equation along the axis of the channel. Results from laboratory experiments will be shown in order to demonstrate the application, and effectiveness, of the method.

Childs, Laura; Hogg, Andrew J.

2011-11-01

385

Ionization of H Rydberg atoms: Fractals and power-law decay

NASA Astrophysics Data System (ADS)

Concepts from the theory of transient chaos are applied to study the classical ionization process of a one-dimensional model of kicked hydrogen Rydberg atoms. It is proved analytically that for a range of field parameters the associated classical phase space is devoid of regular islands. In this case, the fraction of atoms PB(t) not ionized after time t decays asymptotically according to PB(t)~t-? with ?~=1.65. The origin of the algebraic decay can be traced back to the fractal structure of the invariant set of never-ionizing phase-space points, and is explained by the symbolic dynamics of this system, which consists of a countably infinite number of symbols. The algebraic decay is reproduced by an analytically solvable diffusion model that predicts ?=3/2. Replacing zero-width ? kicks with smooth finite-width pulses, a subset of phase space is regular. For this case we observe that PB(t) shows a transition between two power-law regimes with ?~=1.65 for short times and ?~=2.1 for long times, where the effect of Cantori and regular islands is felt.

Hillermeier, C. F.; Blümel, R.; Smilansky, U.

1992-03-01

386

Cosmological evolution of Einstein-Aether models with power-law-like potential

NASA Astrophysics Data System (ADS)

The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the present work, we study the cosmological evolution of Einstein-Aether models with power-law-like potential, by using the method of dynamical system. In the case without matter, there are two attractors which correspond to an inflationary universe in the early epoch, or a de Sitter universe in the late time. In the case with matter but there is no interaction between dark energy and matter, there are only two de Sitter attractors, and no scaling attractor exists. So, it is difficult to alleviate the cosmological coincidence problem. Therefore, we then allow the interaction between dark energy and matter. In this case, several scaling attractors can exist under some complicated conditions, and hence the cosmological coincidence problem could be alleviated.

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-05-01

387

Periodic orbits in the generalized photogravitational Chermnykh-like problem with power-law profile

NASA Astrophysics Data System (ADS)

The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more realistic model in which a disk, with power-law density profile, is rotating around the common center of mass of the system. Then, we analyze the periodic motion in the neighborhood of Lagrangian equilibrium points for the value of mass parameter 0

Kishor, Ram; Kushvah, Badam Singh

2013-04-01

388

Interim Report on the Power Law Index of Interplanetary Suprathermal Ion Spectra

There is a continuing debate about the applicability of the theory presented by Fisk and Gloeckler (FG) regarding the formation of suprathermal ion tails in phase space density vs. velocity spectra; in the solar wind frame the FG theory predicts a power law index of-5 (which is equivalent to a differential intensity vs. energy index of-1.5). There has also been uncertainty and perhaps misunderstanding regarding the extent to which such spectra are actually observed; i.e., is there really a significant preference for the -5 index? Here we report the results of an interim technique we use to analyze {approx}1-100 keV/nucleon interplanetary suprathermal H{sup +}, He{sup +}, and He{sup ++}, spectra measured at the Cassini spacecraft by the Charge Energy Mass Spectrometer (CHEMS) instrument of the Magnetospheric Imaging Instrument (MIMI) suite during the cruise to Saturn. We analyzed 18 active periods and report a mean index in the solar wind frame of 4.9{+-}0.4 for protons, 5.2{+-}0.5 for He{sup +}, and 4.7{+-}0.2 for alpha particles. MIMI/CHEMS offers much needed independent observations of heliospheric ions in the suprathermal energy range.

Hill, M. E. [Johns Hopkins Applied Physics Laboratory, Laurel, Maryland 20723 (United States); Hamilton, D. C. [University of Maryland College Park, Maryland 20742 (United States)

2010-12-30

389

NASA Astrophysics Data System (ADS)

We employ the log-periodic power law (LPPL) to analyze the late-2000 financial crisis from the perspective of critical phenomena. The main purpose of this study is to examine whether LPPL structures in the development of credit default swap (CDS) spreads can be used for default classification. Based on the different triggers of Bear Stearns’ near bankruptcy during the late-2000 financial crisis and Ford’s insolvency in 2009, this study provides a quantitative description of the mechanism behind bank runs. We apply the Johansen-Ledoit-Sornette (JLS) positive feedback model to explain the rise of financial institutions’ CDS spreads during the global financial crisis 2007-2009. This investigation is based on CDS spreads of 40 major banks over the period from June 2007 to April 2009 which includes a significant CDS spread increase. The qualitative data analysis indicates that the CDS spread variations have followed LPPL patterns during the global financial crisis. Furthermore, the univariate classification performances of seven LPPL parameters as default indicators are measured by Mann-Whitney U tests. The present study supports the hypothesis that discrete scale-invariance governs the dynamics of financial markets and suggests the application of new and fast updateable default indicators to capture the buildup of long-range correlations between creditors.

Wosnitza, Jan Henrik; Denz, Cornelia

2013-09-01

390

Cosmology with nonminimal kinetic coupling and a power-law potential

NASA Astrophysics Data System (ADS)

We consider cosmological dynamics in the theory of gravity with the scalar field possessing a nonminimal kinetic coupling to gravity, ?G??????, and the power-law potential V(?)=V0?N. Using the dynamical system method, we analyze all possible asymptotical regimes of the model under investigation and show that for sloping potentials with 0

Skugoreva, Maria A.; Sushkov, Sergey V.; Toporensky, Alexei V.

2013-10-01

391

Binary Neutron Star Mergers Naturally form Jets that can Power Short Gamma-Ray Bursts

NASA Astrophysics Data System (ADS)

Short Gamma-Ray Bursts (SGRB) are among the most energetic explosions in the universe, releasing in less than a second the energy emitted by the whole Galaxy over one year. Despite decades of observations, the nature of their “central engine”, where the physical conditions are the most extreme, remains largely obscure. Here we show that, starting from generic initial conditions consisting of a binary system of magnetized neutron stars in full general relativity, the final fate of the system is a rapidly spinning black hole (BH) surrounded by a hot and highly magnetized torus feeding a jet with half opening-angle of ˜30 deg. In particular, performing simulations on timescales four times longer than previous ones, we show that magnetohydrodynamical instabilities developing after BH formation amplify an initial turbulent magnetic field of ˜1012 G, to produce an ordered jet along the BH spin axis with strengths ˜1015 G. The formation of this configuration from abinitio calculations provides strong evidence that the merger of neutron-star (NS) binaries is potentially behind the central engine of a SGRB. We anticipate that our study will set the basis for the realistic description of the physics behind one the most extreme phenomena in the universe.

Rezzolla, L.

2012-07-01

392

The Stellar Angular Correlation: Clues to Wide Binary Star Properties

NASA Astrophysics Data System (ADS)

The angular distribution of stars brighter than visual magnitude 14 is analyzed for evidence of gravitationally bound systems with widely separated components. Binary stars with separations on the order of 0.1 parsec are interesting as probes of Galactic dynamics, disk dark matter, the Oort comet cloud, and the postulated solar companion star, Nemesis. Catalogs of stars, complete to a resolution limit of four arcseconds, were constructed from digitized Schmidt telescope plates covering over 600 square degrees of the sky in four directions. I analyze the clustering properties of stars and star pairs using two-point and three-point angular correlation functions. Significant correlation (assumed to be due to binary stars) is detected only for angular separations less than 40 arcseconds. No significant numbers of ternary systems are detected. Employing a modified Wasserman-Weinberg technique, I directly compare the angular correlation functions with a simple model of wide binary star properties. The wide binary semimajor axis distribution at low Galactic latitudes is best described as a single power law of index -1.3. Near the North Galactic Pole (NGP), the power law is less steep and the distribution is consistent with a cutoff near 0.1~parsec. The derived wide binary density is unrealistically large, suggesting that the basic model inadequately characterizes wide binary properties. I also study a sample of stars from the Space Telescope Guide Star Catalog (GSC). The region analyzed lies within thirty degrees of the NGP and covers 2500 square degrees of sky. This large, low-resolution sample complements the smaller, more uniform plate catalogs. I identify many systematic errors in the GSC and attempt to account for image misclassifications and poorly defined resolution limits. The corrected stellar correlation function from the GSC is found to be consistent with a wide binary separation cutoff near 0.1parsec. The dissolution of a poor Galactic cluster at the NGP may explain the observed wide binary distribution in that direction. Evidence for weak clustering on scales of one degree is seen in the pair-pair correlation function. The unphysically large wide binary density derived from magnitude-limited samples is explained well by a luminosity correlation between the binary components. An alternative solution requires all F to K dwarfs to be members of wide binaries. Based on the observed properties of wide binary stars, the probability that the Sun has a stellar companion capable of inducing periodic mass extinctions on Earth is only 0.05 percent. In an analogy with Oort cloud dynamics, I suggest a mechanism that can substantially reduce the number of wide binaries with separations greater than 0.1 parsec. (SECTION: Dissertation Abstracts)

Garnavich, Peter M.

1993-03-01

393

The stellar angular correlation: Clues to wide binary star properties

NASA Astrophysics Data System (ADS)

The angular distribution of stars brighter than visual magnitude 14 is analyzed for evidence of gravitationally bound systems with widely separated components. Binary stars with separations on the order of 0.1 parsec are interesting as probes of Galactic dynamics, disk dark matter, the Oort comet cloud and the postulated Solar compannion star, Nemesis. Catalogs of stars, complete to a resolution limit of four arcseconds, were constructed from digitized Schmidt telescope plates covering over 600 square degrees of the sky in four directions. I analyze the clustering properties of stars and star pairs using two-point and three-point angular correlation functions. Significant correlation (assumed to be due to binary stars) is detected only for angular separations less than 40 arcseconds. No significant numbers of ternary systems are detected. Employing a modified Wasserman-Weinberg technique, I directly compare the angular correlation functions with a simple model of wide binary star properties. The wide binary semimajor axis distribution at low Galactic latitudes is best described as a single power law of index -1.3. Near the north Galactic pole (NGP), the power law is less steep and the distribution is consistent with a cutoff near 0.1 parsec. The derived wide binary density is unrealistically large, suggesting that the basic model inadequately characterizes wide binary properties. I also study a sample of stars from the Space Telescope Guide Star Catalog (GSC). The region analyzed lies within thirty degrees of the NGP and covers 2500 square degrees of sky. This large, low resolution sample complements the smaller, more uniform plate catalogs. I identify many systematic errors in the GSC and attempt to account for image misclassifications and poorly defined resolution limits. The corrected stellar correlation function from the GSC is found to be consistent with a wide binary separation cutoff 0.1 parsec. The dissolution of a poor Galactic cluster at the NGP may explain the observed wide binary distribution in that direction. Evidence for weak clustering on scales of one degree is seen in the pair-pair correlation function. The unphysically large wide binary density derived from magnitude-limited samples is explained well by luminosity correlation between the binary components.

Garnavich, Peter Marcus

394

Non-power law scaling for access to the H-mode in tokamaks via symbolic regression

NASA Astrophysics Data System (ADS)

The power threshold (PThresh) to access the H-mode in tokamaks remains a subject of active research, because up to now no theoretical relation has proved to be general enough to reliably interpret the L-H transition. Over the last few decades, much effort has therefore been devoted to deriving empirical scalings, assuming ‘a priori’ a power-law model structure. In this paper, an empirical scaling of PThresh without any a priori assumption about the model structure, i.e. about the functional form, is derived. Symbolic regression via genetic programming is applied to the latest version multi-machine International Tokamak Physics Activity International Global Power Threshold Data Base of validated ITER-like discharges. The derived model structure of the scaling for the global database is not in a power law form and includes a term that indicates saturation of PThresh with the strength of the toroidal field, plasma density and elongation. Furthermore, the single machine analysis of the database for the most representative machines of the international fusion scientific program demonstrates that the model structures are similar but the model parameters are different. The better extrapolation capability of the identified model structures with the proposed methodology is verified with a specific analysis of JET data at two different current regimes. The PThresh values extrapolated to ITER using the derived empirical model structures are a factor of two lower than those of traditional scaling laws and are predicted with a significantly better confidence.

Murari, A.; Lupelli, I.; Gelfusa, M.; Gaudio, P.

2013-04-01

395

NASA Astrophysics Data System (ADS)

In the past few decades, many studies have been dedicated to our understanding of the interactions between tectonic and erosion and, in many instances, using numerical models of landscape evolution. Among the numerous parameterizations that have been developed to predict river channel evolution, the Stream Power Law, which links erosion rate to drainage area and slope, remains the most widely used. Despite its simple formulation, its power lies in its capacity to reproduce many of the characteristic features of natural systems (the concavity of river profile, the propagation of knickpoints, etc.). However, the three main coefficients that are needed to relate erosion rate to slope and drainage area in the Stream Power Law remain poorly constrained. In this study, we present a novel approach to constrain the Stream Power Law coefficients under the detachment limited mode by combining a highly efficient Landscape Evolution Model, FastScape, which solves the Stream Power Law under arbitrary geometries and boundary conditions and an inversion algorithm, the Neighborhood Algorithm. A misfit function is built by comparing topographic data of a reference landscape supposedly at steady state and the same landscape subject to both uplift and erosion over one time step. By applying the method to a synthetic landscape, we show that different landscape characteristics can be retrieved, such as the concavity of river profiles and the steepness index. When applied on a real catchment (in the Whataroa region of the South Island in New Zealand), this approach provide well resolved constraints on the concavity of river profiles and the distribution of uplift as a function of distance to the Alpine Fault, the main active structure in the area.

Croissant, T.; Braun, J.

2013-11-01

396

PLNoise: a package for exact numerical simulation of power-law noises

NASA Astrophysics Data System (ADS)

Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1

Milotti, Edoardo

2006-08-01

397

New version of PLNoise: a package for exact numerical simulation of power-law noises

NASA Astrophysics Data System (ADS)

In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0power-law spectrum for any arbitrary sequence of sampling intervals, i.e. the sampling times may be unevenly spaced. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v2_0.html Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2?10, the RAM taken by the list is 200 Kbytes External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press., Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. No. of lines in distributed program, including test data, etc.:2975 No. of bytes in distributed program, including test data, etc.:194 588 Distribution format:tar.gz Catalogue identifier of previous version: ADXV_v1_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212 Does the new version supersede the previous version?: Yes Nature of problem: Exact generation of different types of colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701], possibly followed by an integration step to produce noise with spectral index >2. Reasons for the new version: Extension to 1/f noises with spectral index 2

Milotti, Edoardo

2007-08-01

398

Pseudo-random binary sequency phase modulation in high power Yb-doped fiber amplifiers

NASA Astrophysics Data System (ADS)

We present experimental and theoretical studies on the stimulated Brillouin scattering (SBS) threshold in fiber amplifiers seeded with a spectrally broadened single-frequency laser source. An electro-optic phase modulator is driven with various pseudo-random binary sequence (PRBS) patterns to highlight the unique characteristics of this linewidth broadening technique and its facility in SBS mitigation. Theoretical predictions show a variation in SBS suppression based on PRBS pattern and modulation frequency. These predictions are experimentally investigated in a kilowatt level monolithic fiber amplifier operating with near diffraction-limited beam quality. We also show Rayleigh scattering and other sources of back reflected light in phase modulated signals can seed the SBS process and significantly reduce the nonlinear threshold.

Robin, Craig; Dajani, Iyad; Zernigue, Clint; Flores, Angel; Pulford, Ben; Lanari, Ann; Naderi, Shadi

2013-03-01

399

Generalized power-law stiffness model for nonlinear dynamics of in-plane cable networks

NASA Astrophysics Data System (ADS)

Cross-ties are used for mitigating stay-cable vibration, induced by wind and wind-rain on cable-stayed bridges. In-plane cable networks are obtained by connecting the stays by transverse cross-ties. While taut-cable theory has been traditionally employed for simulating the dynamics of cable networks, the use of a nonlinear restoring-force discrete element in each cross-tie has been recently proposed to more realistically replicate the network vibration when snapping or slackening of the restrainer may be anticipated. The solution to the free-vibration dynamics can be determined by "equivalent linearization method". In an exploratory study by the authors a cubic-stiffness spring element, in parallel with a linear one, was used to analyze the restoring-force effect in a cross-tie on the nonlinear dynamics of two simplified systems. This preliminary investigation is generalized in this paper by considering a power-law stiffness model with a generic integer exponent and applied to a prototype network installed on an existing bridge. The study is restricted to the fundamental mode and some of the higher ones. A time-domain lumped-mass algorithm is used for validating the equivalent linearization method. For the prototype network with quadratic-stiffness spring and a positive stiffness coefficient, a stiffening effect is observed, with a ten percent increment in the equivalent frequency for the fundamental mode. Results also show dependency on vibration amplitude. For higher modes the equivalent nonlinear effects can be responsible for an alteration of the linear mode shapes and a transition from a "localized mode" to a "global mode".

Giaccu, Gian Felice; Caracoglia, Luca

2013-04-01

400

Hubble Space Telescope Morphologies of z ~ 2 Dust Obscured Galaxies. I. Power-Law Sources

NASA Astrophysics Data System (ADS)

We present high-spatial resolution optical and near-infrared imaging obtained using the ACS, WFPC2, and NICMOS cameras aboard the Hubble Space Telescope of 31 24 ?m bright z ? 2 Dust Obscured Galaxies (DOGs) identified in the Boötes Field of the NOAO Deep Wide-Field Survey. Although this subset of DOGs have mid-IR spectral energy distributions dominated by a power-law component suggestive of an AGN, all but one of the galaxies are spatially extended and not dominated by an unresolved component at rest-frame UV or optical wavelengths. The observed V - H and I-H colors of the extended components are 0.2-3 magnitudes redder than normal star-forming galaxies. All but one have axial ratios >0.3, making it unlikely that DOGs are composed of an edge-on star-forming disk. We model the spatially extended component of the surface brightness distributions of the DOGs with a Sérsic profile and find effective radii of 1-6 kpc. This sample of DOGs is smaller than most submillimeter galaxies (SMGs), but larger than quiescent high-redshift galaxies. Nonparametric measures (Gini and M20) of DOG morphologies suggest that these galaxies are more dynamically relaxed than local ULIRGs. We estimate lower limits to the stellar masses of DOGs based on the rest-frame optical photometry and find that these range from ~109-1011 M sun. If major mergers are the progenitors of DOGs, then these observations suggest that DOGs may represent a postmerger evolutionary stage.

Bussmann, R. S.; Dey, Arjun; Lotz, J.; Armus, L.; Brand, K.; Brown, M. J. I.; Desai, V.; Eisenhardt, P.; Higdon, J.; Higdon, S.; Jannuzi, B. T.; Le Floc'h, E.; Melbourne, J.; Soifer, B. T.; Weedman, D.

2009-03-01

401

Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.

A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3

Ruppeiner, George

2005-07-01

402

The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

NASA Astrophysics Data System (ADS)

The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres, and between a flat-ended axisymmetric punch and an elastic half-space respectively. However, the shapes of contacting solids may be more general than spherical or flat ones. In addition, the derivation of the main formulae of these models is based on the assumption that the material points within the contact region can move along the punch surface without any friction. However, it is more natural to assume that a material point that came to contact with the punch sticks to its surface, i.e. to assume that the non-slipping boundary conditions are valid. It is shown that the frictionless JKR model may be generalized to arbitrary convex, blunt axisymmetric body, in particular to the case of the punch shape being described by monomial (power-law) punches of an arbitrary degree d?1. The JKR and Boussinesq-Kendall models are particular cases of the problems for monomial punches, when the degree of the punch d is equal to two or it goes to infinity respectively. The generalized problems for monomial punches are studied under both frictionless and non-slipping (or no-slip) boundary conditions. It is shown that regardless of the boundary conditions, the solution to the problems is reduced to the same dimensionless relations among the actual force, displacements and contact radius. The explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. Connections of the results obtained for problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape and the shape function can be approximated by a monomial function of radius, are discussed.

Borodich, Feodor M.; Galanov, Boris A.; Suarez-Alvarez, Maria M.

2014-08-01

403

NASA Astrophysics Data System (ADS)

Mixed traffic without signal control is complicated. This paper proposes a pedestrian-vehicle cellular automata (CA) model to study the characteristics of the mixed traffic. The model includes two sub models. One is the pedestrian model, in which the heterogeneity is taken into consideration. The other is the vehicle model, in which a safely running mode and a normally running mode are introduced. Simulation results show that (1) the traffic flow experiences four phases, that is, free flow, pedestrians-free flow, vehicles-free flow and jams, (2) pedestrians cross the crosswalk in groups and the sizes of the groups obey power law distribution, and (3) the heterogeneity of pedestrians acts an important role in the system. If the pedestrians are simultaneously homogeneous, the mixed traffic flow shows a “polarization” and these power-laws disappear under high arrival rates of vehicles and pedestrians.

Xin, Xiuying; Jia, Ning; Zheng, Liang; Ma, Shoufeng

2014-07-01

404

Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses

NASA Astrophysics Data System (ADS)

We test the existence of a spin-glass state in an externally-applied (random) magnetic field via Monte Carlo simulations of a power-law diluted one-dimensional Ising spin glass. The model has the advantage over conventional short-range models in that by tuning the exponent of the power-law interactions we are able to scan the full range of possible behaviors from the infinite-range to the non-mean-field regime. Furthermore, due to the average fixed connectivity very large linear system sizes can be studied. An analysis of the two-point correlation length shows that the system in the non-mean-field universality class does not order in a field. This suggests that there is no de Almeida-Thouless line for short-range Ising spin glasses below the upper critical dimension.

Katzgraber, Helmut G.; Larson, Derek A.; Young, A. P.

2009-03-01

405

We calculate the probability density functions P of burst energy e, duration T, and interburst interval tau for a known turbulent system in nature. Bursts in the Earth-Sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organized criticality (SOC). We find also a power-law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence. PMID:11138184

Freeman; Watkins; Riley

2000-12-01

406

A simple goodness-of-fit test for the power-law process, based on the Duane plot

The PLP (power-law process) or the Duane model is a simple model that can be used for both reliability growth and reliability deterioration. GOF (goodness-of-fit) tests for the PLP have attracted much attention. However, the practical use of the PLP model is its graphical analysis or the Duane plot, which is a log-log plot of the cumulative number of failures

Olivier Gaudoin; Bo Yang; Min Xie

2003-01-01

407

NASA Astrophysics Data System (ADS)

We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we derive Fourier expansions in certain rotationally-invariant coordinate systems and Gegenbauer polynomial expansions in Vilenkin's polyspherical coordinates. We compare both of these expansions to generate addition theorems for the azimuthal Fourier coefficients.

Cohl, Howard S.

2013-06-01

408

NASA Astrophysics Data System (ADS)

Shell structures in single-particle energy spectra are investigated against regular tetrahedral type deformation using a radial power-law potential model. Employing a natural way of shape parametrization which interpolates sphere and regular tetrahedron, we find prominent shell effects for rather large tetrahedral deformations, which bring about shell energies much larger than the cases of spherical and quadrupole type shapes. We discuss the semiclassical origin of these anomalous shell structures using periodic orbit theory.

Arita, Ken-ichiro; Mukumoto, Yasunori

2014-05-01

409

Summary This paper is devoted to the theoretical analysis of steady and unsteady boundary layer problems for non-Newtonian power-law fluid flow using a new variational principle ofHamilton's type. The standard method of variational calculus in the form of partial integration is a basic tool for obtaining approximative solutions. The main characteristic of the variational principle developed here is that all

Djordje S. Djukic; Bozidar D. Vujanovic

1975-01-01

410

NASA Astrophysics Data System (ADS)

This paper addresses the Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation with power law nonlinearity. First the soliton solution is obtained by the aid of traveling wave hypothesis and along with it the constraint conditions fall out naturally, in order for the soliton solution to exist. Subsequently, the bifurcation analysis of this equation is carried out and the fixed points are obtained. The phase portraits are also analyzed for the existence of other solutions.

Biswas, Anjan; Song, Ming

2013-07-01

411

Study of the de Almeida-Thouless Line Using Power-Law Diluted One-Dimensional Ising Spin Glasses

NASA Astrophysics Data System (ADS)

We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that a de Almeida-Thouless line occurs only in the mean-field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.

Katzgraber, Helmut G.; Larson, Derek; Young, A. P.

2009-05-01

412

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to

Anthony Papadopoulos

2009-01-01

413

Methodology for thermal design of novel combined refrigeration\\/power binary fluid systems

Refrigeration cogeneration systems which generate power alongside with cooling improve energy utilization significantly, because such systems offer a more reasonable arrangement of energy and exergy “flows” within the system, which results in lower fuel consumption as compared to the separate generation of power and cooling or heating. This paper proposes several novel systems of that type, based on ammonia–water working

Na Zhang; Noam Lior

2007-01-01

414

Conserved, ultraconserved and other classes of constrained elements (collectively referred as CNEs here), identified by comparative genomics in a wide variety of genomes, are non-randomly distributed across chromosomes. These elements are defined using various degrees of conservation between organisms and several thresholds of minimal length. We here investigate the chromosomal distribution of CNEs by studying the statistical properties of distances between consecutive CNEs. We find widespread power-law-like distributions, i.e. linearity in double logarithmic scale, in the inter-CNE distances, a feature which is connected with fractality and self-similarity. Given that CNEs are often found to be spatially associated with genes, especially with those that regulate developmental processes, we verify by appropriate gene masking that a power-law-like pattern emerges irrespectively of whether elements found close or inside genes are excluded or not. An evolutionary model is put forward for the understanding of these findings that includes segmental or whole genome duplication events and eliminations (loss) of most of the duplicated CNEs. Simulations reproduce the main features of the observed size distributions. Power-law-like patterns in the genomic distributions of CNEs are in accordance with current knowledge about their evolutionary history in several genomes. PMID:24787386

Polychronopoulos, Dimitris; Sellis, Diamantis; Almirantis, Yannis

2014-01-01

415

NASA Astrophysics Data System (ADS)

Morphodynamic models of coastal evolution require relatively simple parameterizations of sediment transport for application over larger scales. Calantoni and Thaxton (2008) [6] presented a transport parameterization for bimodal distributions of coarse quartz grains derived from detailed boundary layer simulations for sheet flow and near sheet flow conditions. The simulation results, valid over a range of wave forcing conditions and large- to small-grain diameter ratios, were successfully parameterized with a simple power law that allows for the prediction of the transport rates of each size fraction. Here, we have applied the simple power law to a two-dimensional cellular automaton to simulate sheet flow transport. Model results are validated with experiments performed in the small oscillating flow tunnel (S-OFT) at the Naval Research Laboratory at Stennis Space Center, MS, in which sheet flow transport was generated with a bed composed of a bimodal distribution of non-cohesive grains. The work presented suggests that, under the conditions specified, algorithms that incorporate the power law may correctly reproduce laboratory bed surface measurements of bimodal sheet flow transport while inherently incorporating vertical mixing by size.

Holway, Kevin; Thaxton, Christopher S.; Calantoni, Joseph

2012-11-01

416

NASA Astrophysics Data System (ADS)

A Weibull distribution with power-law tails is confirmed as a good candidate to describe the first passage time process of foreign currency exchange rates. The Lorentz curve and the corresponding Gini coefficient for a Weibull distribution are derived analytically. We show that the coefficient is in good agreement with the same quantity calculated from the empirical data. We also calculate the average waiting time which is an important measure to estimate the time for customers to wait until the next price change after they login to their computer systems. By assuming that the first passage time distribution might change its shape from the Weibull to the power-law at some critical time, we evaluate the averaged waiting time by means of the renewal-reward theorem. We find that our correction of tails of the distribution makes the averaged waiting time much closer to the value obtained from empirical data analysis. We also discuss the deviation from the estimated average waiting time by deriving the waiting time distribution directly. These results make us conclude that the first passage process of the foreign currency exchange rates is well described by a Weibull distribution with power-law tails.

Sazuka, Naoya; Inoue, Jun-Ichi

2007-03-01

417

Conserved, ultraconserved and other classes of constrained elements (collectively referred as CNEs here), identified by comparative genomics in a wide variety of genomes, are non-randomly distributed across chromosomes. These elements are defined using various degrees of conservation between organisms and several thresholds of minimal length. We here investigate the chromosomal distribution of CNEs by studying the statistical properties of distances between consecutive CNEs. We find widespread power-law-like distributions, i.e. linearity in double logarithmic scale, in the inter-CNE distances, a feature which is connected with fractality and self-similarity. Given that CNEs are often found to be spatially associated with genes, especially with those that regulate developmental processes, we verify by appropriate gene masking that a power-law-like pattern emerges irrespectively of whether elements found close or inside genes are excluded or not. An evolutionary model is put forward for the understanding of these findings that includes segmental or whole genome duplication events and eliminations (loss) of most of the duplicated CNEs. Simulations reproduce the main features of the observed size distributions. Power-law-like patterns in the genomic distributions of CNEs are in accordance with current knowledge about their evolutionary history in several genomes.

Polychronopoulos, Dimitris; Sellis, Diamantis; Almirantis, Yannis

2014-01-01

418

NASA Astrophysics Data System (ADS)

Electromagnetic methods of geophysical exploration are a reflection of the spatio-temporal variability in ground conductivity, a macroscopic physical property that is a function of lithology, pore-scale surface chemistry, fracture networks, and the presence and distribution of fluids and partial melts. As such, the bulk electrical properties of some representative elementary volume within the subsurface derive from the macroscopic effect of charge buildup and current pathways across a range of length scales within. Quantifying this relationship between multiscale electrical properties and the observed geophysical data is a critical step toward meaningful geologic interpretation. Previously we presented evidence of near-surface electromagnetic data whose small scale fluctuations are both repeatable and fractally distributed -- an observation that supports the notion of a spatially hierarchical Earth. Bounded by the end member cases from homogenized isotropic and anisotropic media, we present numerical modeling results from textured and spatially-correlated, stochastic geologic media, demonstrating that the electromagnetic response is a power law distribution similar to that seen in the earlier observational data, rather than a smooth response polluted with Gaussian noise as is commonly assumed. Furthermore, we show that such power law behavior is dependent on correlation length within the medium and that the power law distribution of Earth conductivity can be estimated from that of the observed electromagnetic data.

Beskardes, G. D.; Weiss, C. J.; Everett, M. E.

2013-12-01

419

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe. PMID:22712907

Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T

2012-06-01

420

NASA Astrophysics Data System (ADS)

For the simulation of therapeutic ultrasound applications, a method including frequency-dependent attenuation effects directly in the time domain is highly desirable. This paper describes an efficient numerical time-domain implementation of the power-law attenuation model presented by Szabo [Szabo, J. Acoust. Soc. Am. 96, 491-500 (1994)]. Simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time-domain (FDTD) algorithm for nonlinear ultrasound propagation [Ginter et al., J. Acoust. Soc. Am. 111, 2049-2059 (2002)]. Szabo implemented the empirical frequency power-law attenuation using a causal convolutional operator directly in the time-domain equation. Though a variety of time-domain models has been published in recent years, no efficient numerical implementation has been presented so far for frequency power-law attenuation models. Solving a convolutional integral with standard time-domain techniques requires enormous computational effort and therefore often limits the application of such models to 1D problems. In contrast, the presented method is based on a recursive algorithm and requires only three time levels and a few auxiliary data to approximate the convolutional integral with high accuracy. The simulation results are validated by comparison with analytical solutions and measurements. .

Liebler, Marko; Ginter, Siegfried; Dreyer, Thomas; Riedlinger, Rainer E.

2004-11-01