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Sample records for binary power law

  1. Spatial and Temporal Stability of the Estimated Parameters of the Binary Power Law

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The binary power law has become a standard approach for describing and quantifying spatial patterns of disease incidence and summarizing the spatial dynamics of disease over the course of an epidemic. However, the portability and temporal stability of parameter estimates of the binary form of the p...

  2. Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The binary power law (BPL) has been successfully used to characterize heterogeneity (over dispersion 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...

  3. Power-Law Behavior in Geometric Characteristics of Full Binary Trees

    NASA Astrophysics Data System (ADS)

    Paik, Kyungrock; Kumar, Praveen

    2011-02-01

    Natural river networks exhibit regular scaling laws in their topological organization. Here, we investigate whether these scaling laws are unique characteristics of river networks or can be applicable to general binary tree networks. We generate numerous binary trees, ranging from purely ordered trees to completely random trees. For each generated binary tree, we analyze whether the tree exhibits any scaling property found in river networks, i.e., the power-laws in the size distribution, the length distribution, the distance-load relationship, and the power spectrum of width function. We found that partially random trees generated on the basis of two distinct types of deterministic trees, i.e., deterministic critical and supercritical trees, show contrasting characteristics. Partially random trees generated on the basis of deterministic critical trees exhibit all power-law characteristics investigated in this study with their fitted exponents close to the values observed in natural river networks over a wide range of random-degree. On the other hand, partially random trees generated on the basis of deterministic supercritical trees rarely follow scaling laws of river networks.

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

    PubMed

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

    2011-12-01

    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

  5. The Causal Connection Between Disc and Power-Law Variability in Hard State Black Hole X-Ray Binaries

    NASA Technical Reports Server (NTRS)

    Uttley, P.; Wilkinson, T.; Cassatella, P.; Wilms, J.; Pottschimdt, K.; Hanke, M.; Boeck, M.

    2010-01-01

    We use the XMM-Newton EPIC-pn instrument in timing mode to extend spectral time-lag studies of hard state black hole X-ray binaries into the soft X-ray band. \\Ve show that variations of the disc blackbody emission substantially lead variations in the power-law emission, by tenths of a second on variability time-scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time-delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time-scales less than a second the disc lags the power-law variations by a few ms, consistent with the disc variations being dominated by X-ray heating by the power-law, with the short lag corresponding to the light-travel time between the power-law emitting region and the disc. Our results indicate that instabilities in the accretion disc are responsible for continuum variability on time-scales of seconds or longer and probably also on shorter time-scales.

  6. Using Local Radiation MHD Simulations to Attempt to Understand the Very High/Steep Power Law State of Black Hole X-ray Binaries

    NASA Astrophysics Data System (ADS)

    Blaes, Omer

    Stellar mass black holes in certain types of binary systems accrete matter from their companion stars through rotating, turbulent flows known as accretion disks. These disks are observed by space X-ray missions to have a number of distinct spectral/variability states, the most mysterious one being the very high/steep power law state that generally occurs at very high luminosities. This state is particularly interesting as it exhibits unique quasi-periodic oscillations observed in the X-rays that, if understood, might help us directly measure the properties of the black hole spacetime. Radiation pressure is an important physical process at such high luminosities, and modifies the character of the accretion disk in a number of unique ways. One of the ways that it does this is that it enables turbulent speeds in the disk to exceed thermal speeds of electrons, thereby introducing a completely new radiation process - turbulent Comptonization. This radiation process is promising for explaining the unique spectral characteristics of the very high/steep power law state. We will test this hypothesis by making detailed calculations of the emergent radiation spectrum from numerical simulation data of the turbulence in local patches of the disk at high levels of radiation pressure. These will be the first detailed theoretical calculations of turbulent Comptonization, which should be an important process for modeling NASA data from high luminosity black hole accretion. We hope that this will shed light on the nature of the mysterious very high/steep power law state. The research will form the basis of the PhD thesis of a graduate student, in line with NASA's educational and training objectives.

  7. Zipf's law, power laws and maximum entropy

    NASA Astrophysics Data System (ADS)

    Visser, Matt

    2013-04-01

    Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.

  8. Power-law inflation

    NASA Astrophysics Data System (ADS)

    Lucchin, F.; Matarrese, S.

    1985-09-01

    The outstanding cosmological problems (horizon, flatness, . . .) which may be solved by the usual inflationary models may also find a solution in the frame of a ``generalized'' inflationary cosmology which is characterized by a suitable phase of accelerated expansion. The usual exponential growth of the scale factor S is just a particular case of such a general idea. Following this line of thought, we study in some detail a simple inflationary model characterized by a scale factor which grows like S~tp, with p a constant greater than one, which we call power-law inflation (PLI). Some properties of PLI have been analyzed, in different contexts, also by other authors. We consider the constraints on this model coming from the requirement of solving the horizon, flatness, ``good'' reheating, and ``convenient'' perturbation-spectrum problems. In order to obtain the perturbation spectrum when re-entering the horizon during the Friedmann phase, we extend to PLI the gauge-invariant approach developed by Bardeen et al. for the usual inflationary models. We find that the above constraints can be suitably satisfied. Finally, we outline possible connections between PLI and particular inflationary models which have recently been proposed.

  9. Binary-flashing geothermal power plants

    SciTech Connect

    Yuan, Z.; Michaelides, E.E. . Dept. of Mechanical Engineering)

    1993-09-01

    Binary-flashing units utilize new types of geothermal power cycles, which may be used with resources of relatively low temperatures (less than 150 C) where other cycles result in very low efficiencies. The thermodynamic cycles for the binary-flashing units are combinations of the geothermal binary and flashing cycles. They have most of the advantages of these two conventionally used cycles, but avoid the high irreversibilities associated with some of their processes. Any fluid with suitable thermodynamic properties may be used in the secondary Rankine cycle. At the optimum design conditions binary-flashing geothermal power plants may provide up to 25 percent more power than the conventional geothermal units.

  10. First law of mechanics for compact binaries on eccentric orbits

    NASA Astrophysics Data System (ADS)

    Le Tiec, Alexandre

    2015-10-01

    Using the canonical Arnowitt-Deser-Misner Hamiltonian formalism, a "first law of mechanics" is established for binary systems of point masses moving along generic stable bound (eccentric) orbits. This relationship is checked to hold within the post-Newtonian approximation to general relativity, up to third order. Several applications are discussed, including the use of gravitational self-force results to inform post-Newtonian theory and the effective one-body model for eccentric-orbit compact binaries.

  11. Power laws and macroeconomic fluctuations

    NASA Astrophysics Data System (ADS)

    Gaffeo, Edoardo; Gallegati, Mauro; Giulioni, Gianfranco; Palestrini, Antonio

    2003-06-01

    We study the duration distribution of recessions and recoveries occurred in a pool of industrialized countries during the last 120 years. We find that for recessions the duration is distributed according to a power law, and that the power exponent is virtually invariant as we split up the time span into sub-periods. The evidence regarding the duration of recoveries is mixed, however.

  12. Power Law Distribution in Education

    NASA Astrophysics Data System (ADS)

    Gupta, Hari M.; Campanha, José R.; Chavarette, Fábio R.

    We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study-day versus night period (ii) teaching conditions - private versus public school (iii) economical conditions - high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects are due to the nature of the subjects themselves. Further and better study, teaching and economical conditions are more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.

  13. Power Laws in Firm Productivity

    NASA Astrophysics Data System (ADS)

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

    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.

  14. Power colours: simple X-ray binary variability comparison

    NASA Astrophysics Data System (ADS)

    Heil, L. M.; Uttley, P.; Klein-Wolt, M.

    2015-04-01

    We demonstrate a new method of variability classification using observations of black hole X-ray binaries. Using `power colours' - ratios of integrated power in different Fourier frequency bands - we can clearly differentiate different canonical black hole states as the objects evolve during outburst. We analyse (˜2400) Rossi X-ray Timing Explorer observations of 12 transient low-mass black hole X-ray binaries and find that the path taken around the power colour-colour diagram as the sources evolve is highly consistent from object to object. We discuss how the consistency observed in the power colour-colour diagram between different objects allows for easy state classification based on only a few observations, and show how the power-spectral shapes can be simply classified using a single parameter, the power-spectral `hue'. To illustrate the benefits of our simple model-independent approach, we show that the persistent high-mass X-ray binary Cyg X-1 shows very similar power-spectral evolution to the transient black hole sources, with the main difference being caused by a combination of a lack of quasi-periodic oscillations and an excess of low-frequency power-law noise in the Cyg X-1 power spectra during the transitional state. We also compare the transient objects to the neutron star atoll source Aquila X-1, demonstrating that it traces a different path in the power colour-colour plot. Thus, power colours could be an effective method to classify newly discovered X-ray binaries.

  15. Binary power multiplier for electromagnetic energy

    DOEpatents

    Farkas, Zoltan D.

    1988-01-01

    A technique for converting electromagnetic pulses to higher power amplitude and shorter duration, in binary multiples, splits an input pulse into two channels, and subjects the pulses in the two channels to a number of binary pulse compression operations. Each pulse compression operation entails combining the pulses in both input channels and selectively steering the combined power to one output channel during the leading half of the pulses and to the other output channel during the trailing half of the pulses, and then delaying the pulse in the first output channel by an amount equal to half the initial pulse duration. Apparatus for carrying out each of the binary multiplication operation preferably includes a four-port coupler (such as a 3 dB hybrid), which operates on power inputs at a pair of input ports by directing the combined power to either of a pair of output ports, depending on the relative phase of the inputs. Therefore, by appropriately phase coding the pulses prior to any of the pulse compression stages, the entire pulse compression (with associated binary power multiplication) can be carried out solely with passive elements.

  16. First law of mechanics for black hole binaries with spins

    NASA Astrophysics Data System (ADS)

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

    2013-01-01

    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.

  17. Accretion-powered Compact Binaries

    NASA Astrophysics Data System (ADS)

    Mauche, Christopher W.

    2003-12-01

    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.

  18. The power-law galaxies

    NASA Astrophysics Data System (ADS)

    Evans, N. W.

    1994-03-01

    Axisymmetric galaxy models with simple distribution functions (DFs) that are sums of powers of the binding energy E and angular momentum component Lz are presented. They are useful for representing elliptical galaxies, as well as the bulges and haloes of spiral galaxies. The equipotentials are stratified on similar concentric spheroids. The rotation law can be asymptotically rising, flat or declining. The intrinsic and projected velocity dispersions are elementary. In the limit of vanishing core radius, the galaxies are scale-free, and the surface brightness is cusped. Composite models, in which a population of stars with a spheroidal density distribution is embedded within the halo, are easy to construct. For the oblate models, the generic orbits are short-axis tubes, while for the prolate models, they are inner and outer long-axis tubes. The orbital structure of the cored models is simple, with almost all stars moving on tori. When the core radius vanishes, the tube orbits passing close to the centre are replaced by higher order resonant families. This effect is particularly pronounced for prolate models, where the infinitesimally thin inner long-axis tubes undergo a sequence of period-multiplying bifurcations. This causes their complete replacement by resonant families at low Lz. The simplicity of the DFs enables the line profiles (LPs) and the higher Gauss-Hermite moments to be found. Composite models with constant fractions of counter-streaming stars are useful for analysing the LPs of stars in the outer parts of galaxies. When the streaming is greatest, the LPs are skewed towards velocities greater than the mean, in contradiction with the observations. Models with 1/4 of the stars counter-streaming with respect to the rest of the galaxy have LPs with more realistic asymmetries. The LPs of the self-consistent coreless haloes are scale-free and invariant along the rays of constant position angle on the plane of the sky. The effects of flattening of the mass model on the skewness and bimodality of the LP are analysed. power-law DFs that connect the cold, centrifugally supported discs with the hot, pressure-supported discs. All the intrinsic properties of the discs are simple-in particular, the Toomre and Ostriker-Peebles criteria for local and global stability can be exactly calculated. *The spherical scale-free limit also provides a set of star cluster models with sequences of simple power-law DFs.

  19. Power Law Decay in High Intensity Turbulence

    NASA Astrophysics Data System (ADS)

    Koster, Timothy; Puga, Alejandro; Nguyen, Baolong; Larue, John

    2015-11-01

    In the study reported herein, the region where the power decay law is applicable for active grid generated turbulence is found by an iterative approach which determines the largest range where the ratio of the dissipation from the power law and the dissipation from the temporal velocity derivative are unity. The square of the Taylor microscale, as noted by Batchelor (1953), is linearly related to downstream distance relative to the virtual origin and can be used in a straightforward manner to find the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for various mean velocities to show the decay exponent as a function of the Taylor Reynolds number.

  20. Improving geothermal power plants with a binary cycle

    NASA Astrophysics Data System (ADS)

    Tomarov, G. V.; Shipkov, A. A.; Sorokina, E. V.

    2015-12-01

    The recent development of binary geothermal technology is analyzed. General trends in the introduction of low-temperature geothermal sources are summarized. The use of single-phase low-temperature geothermal fluids in binary power plants proves possible and expedient. The benefits of power plants with a binary cycle in comparison with traditional systems are shown. The selection of the working fluid is considered, and the influence of the fluid's physicochemical properties on the design of the binary power plant is discussed. The design of binary power plants is based on the chemical composition and energy potential of the geothermal fluids and on the landscape and climatic conditions at the intended location. Experience in developing a prototype 2.5 MW Russian binary power unit at Pauzhetka geothermal power plant (Kamchatka) is outlined. Most binary systems are designed individually for a specific location. Means of improving the technology and equipment at binary geothermal power plants are identified. One option is the development of modular systems based on several binary systems that employ the heat from the working fluid at different temperatures.

  1. Power law inflation with electromagnetism

    SciTech Connect

    Luo, Xianghui; Isenberg, James

    2013-07-15

    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}, ϕ{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},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,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}, ϕ{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.

  2. Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---

    NASA Astrophysics Data System (ADS)

    Kaizoji, T.

    In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, P (S > x) ˜ x^{-α}, with an exponent that moves in the range of 1.09 < α < 1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.

  3. Hierarchical networks, power laws, and neuronal avalanches.

    PubMed

    Friedman, Eric J; Landsberg, Adam S

    2013-03-01

    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. PMID:23556972

  4. Hierarchical networks, power laws, and neuronal avalanches

    NASA Astrophysics Data System (ADS)

    Friedman, Eric J.; Landsberg, Adam S.

    2013-03-01

    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.

  5. Power Law and Forest Fires in China

    NASA Astrophysics Data System (ADS)

    Salvador, P.; Sanz, J.; Rodriguez, J.; Casanova, J.-L.; Qin, Xianlin; Li, Zengyuan; Zu, Xiaofeng; Deng, Guang

    2014-11-01

    Recent research indicates that satellite FRP retrievals over individual burned areas and fires have power law distributions. In order to get the FRP power law probability distribution function parameters we have analyzed more than 650,000 forest fires detected, from 2000 to 2012, by MODIS-Terra and MODIS-Aqua sensors in China. In such way, the fire radiative energy FRE has been estimated as a product of the fire duration and the expected FRP value derived from the FRP power law probability distribution function. Taking into account that the sparse satellite sampling is unable to provide enough data for complete coverage during the fire life, this methodology allow us to determine the FRE by means of the temporal integral of fire radiative power, FRP.

  6. The resolving power of LISA: comparing techniques for binary analysis

    NASA Astrophysics Data System (ADS)

    Larson, Shane L.; Finn, Lee Samuel

    2006-11-01

    Millions of short period binaries in the Milky Way will radiate gravitational waves in the low-frequency band with enough power to be detectable by LISA, making the foreground of galactic binaries the most prolific source in the band. Characterizing the resolving power of LISA is important for understanding what science will be possible with LISA observations of these binaries (e.g., mass transfer rates in accreting binaries, the structure of the galaxy, etc.) and understanding how well other sources can be resolved amidst the myriad of resolvable LISA sources. This paper reports on a work in-progress to understand how well different analysis methods can resolve pairs of binary star systems on the sky and in frequency. Preliminary quantitative results described here focus on two methods - gCLEAN and MaxEnt - and their ability to resolve sources of identical frequency as a function of angular separation.

  7. Power-law distributions in protoneutron stars

    NASA Astrophysics Data System (ADS)

    Gervino, G.; Lavagno, A.; Pigato, D.

    2016-01-01

    We investigate the physical properties of the protoneutron stars in the framework of a relativistic mean-field theory based on nonextensive statistical mechanics, characterized by power-law distributions. We study the finite-temperature equation of state in, β-stable matter at fixed entropy per baryon, in the absence and in the presence of hyperons and trapped neutrinos. We show that nonextensive power-law effects could play a crucial role in the structure and in the evolution of the protoneutron stars also for small deviations from the standard Boltzmann-Gibbs statistics.

  8. Power law analysis of the human microbiome.

    PubMed

    Ma, Zhanshan Sam

    2015-11-01

    Taylor's (1961, Nature, 189:732) power law, a power function (V = am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs. PMID:26407082

  9. Relativity, nonextensivity, and extended power law distributions.

    PubMed

    Silva, R; Lima, J A S

    2005-11-01

    A proof of the relativistic theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the parameter lies on the interval [0,2]. It is also proven that the collisional equilibrium states (null entropy source term) are described by the relativistic power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory. PMID:16383791

  10. Robust model comparison disfavors power law cosmology

    NASA Astrophysics Data System (ADS)

    Shafer, Daniel L.

    2015-05-01

    Late-time power law expansion has been proposed as an alternative to the standard cosmological model and shown to be consistent with some low-redshift data. We test power law expansion against the standard flat ? CDM cosmology using goodness-of-fit and model comparison criteria. We consider type Ia supernova (SN Ia) data from two current compilations (JLA and Union2.1) along with a current set of baryon acoustic oscillation (BAO) measurements that includes the high-redshift Lyman-? forest measurements from BOSS quasars. We find that neither power law expansion nor ? CDM is strongly preferred over the other when the SN Ia and BAO data are analyzed separately but that power law expansion is strongly disfavored by the combination. We treat the Rh=c t cosmology (a constant rate of expansion) separately and find that it is conclusively disfavored by all combinations of data that include SN Ia observations and a poor overall fit when systematic errors in the SN Ia measurements are ignored, despite a recent claim to the contrary. We discuss this claim and some concerns regarding hidden model dependence in the SN Ia data.

  11. Power laws governing epidemics in isolated populations

    NASA Astrophysics Data System (ADS)

    Rhodes, C. J.; Anderson, R. M.

    1996-06-01

    TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1-11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12-14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16-19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.

  12. Classical orbits in power-law potentials

    NASA Astrophysics Data System (ADS)

    Grant, Aaron K.; Rosner, Jonathan L.

    1994-04-01

    The motion of bodies in power-law potentials of the form V(r)=?r? has been of interest ever since the time of Newton and Hooke. Aspects of the relation between powers ? and ?, where (?+2)(?+2)=4, are derived for classical motion and the relation to the quantum-mechanical problem is given. An improvement on a previous expression for the WKB quantization condition for nonzero orbital angular momenta is obtained. Relations with previous treatments, such as those of Newton, Bertrand, Bohlin, Faur, and Arnold, are noted, and a brief survey of the literature on the problem over more than three centuries is given.

  13. Poissonian renormalizations, exponentials, and power laws.

    PubMed

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises. PMID:23767505

  14. Spectra that behave like power-laws are not necessarily power-laws

    NASA Astrophysics Data System (ADS)

    Podesta, John J.

    2016-02-01

    It is shown that measured power spectral densities (spectra) that closely resemble power-law spectra may, in fact, have mathematical forms that are not power laws in the mathematical sense. If power spectral estimates show a good fit to a straight line on a log-log plot over a finite frequency range, that is not sufficient evidence to conclude that the mathematical form of the spectrum is, in fact, a power-law over that range. It is also pointed out that to accurately fit a power-law function to experimental data using linear least squares techniques in log-log space, as is often done in practice, it is essential that the data is uniformly distributed along the abscissa in log-space (in the stochastic sense) or, otherwise, the data must be linearly interpolated onto a uniform grid to ensure that the data employed in the fitting procedure is equally weighted along the abscissa. These two important points are not widely appreciated by researchers in the field and the pitfalls associated with commonly used fitting techniques are often overlooked in the analysis of solar wind data.

  15. Existence Theory for Stochastic Power Law Fluids

    NASA Astrophysics Data System (ADS)

    Breit, Dominic

    2015-06-01

    We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.

  16. A Universal Power Law Governing Pedestrian Interactions

    NASA Astrophysics Data System (ADS)

    Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.

    2015-03-01

    Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena. Work at Argonne National Laboratory is supported by the U.S. Department of Energy, under Contract No. DE-AC02-06CH11357. Work at the University of Minnesota is supported by MnDRIVE Initiative on Robotics, Sensors, and Advanced Manufacturing.

  17. Power laws and fragility in flow networks?

    PubMed Central

    Shore, Jesse; Chu, Catherine J.; Bianchi, Matt T.

    2015-01-01

    What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence. PMID:26082568

  18. 29 CFR 417.6 - Powers of Administrative Law Judge.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 29 Labor 2 2010-07-01 2010-07-01 false Powers of Administrative Law Judge. 417.6 Section 417.6... Administrative Law Judge. The designated Administrative Law Judge shall have authority: (a) To give notice... other actions authorized by the regulations in this part. The Administrative Law Judge's authority...

  19. Power-law parametrized quintessence model

    SciTech Connect

    Rahvar, Sohrab; Movahed, M. Sadegh

    2007-01-15

    We propose a simple power-law parametrized quintessence model with time-varying equation of state and obtain corresponding quintessence potential of this model. This model is compared with Supernova Type Ia (SNIa) Gold sample data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and structure formation from the 2dFGRS survey and put constrain on the parameters of model. The parameters from the best fit indicates that the equation of state of this model at the present time is w{sub 0}=-1.40{sub -0.65}{sup +0.40} at 1{sigma} confidence level. Finally we calculate the age of universe in this model and compare it with the age of old cosmological objects.

  20. A (varying power)-law modified gravity

    NASA Astrophysics Data System (ADS)

    Hammad, Fayçal

    2014-02-01

    In the present paper, we analyze a toy model for f(ϕ ,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 Rϕ 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.

  1. Fractional power-law spatial dispersion in electrodynamics

    SciTech Connect

    Tarasov, Vasily E.; Trujillo, Juan J.

    2013-07-15

    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.

  2. Power Law Mapping in Human Area Perception

    NASA Astrophysics Data System (ADS)

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

    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 r2α 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 α is smallest for the circle (α∘ ≈ 1.33) and largest for triangle (α△ ≈ 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.

  3. Power-law spatial dispersion from fractional Liouville equation

    SciTech Connect

    Tarasov, Vasily E.

    2013-10-15

    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.

  4. Advanced binary geothermal power plants: Limits of performance

    NASA Astrophysics Data System (ADS)

    Bliem, C. J.; Mines, G. L.

    1991-01-01

    The Heat Cycle Research Program is investigating potential improvements to power cycles utilizing moderate temperature geothermal resources to produce electrical power. Investigations have specifically examined Rankine cycle binary power systems. Binary Rankine cycles are more efficient than the flash steam cycles at moderate resource temperature, achieving a higher net brine effectiveness. At resource conditions similar to those at the Heber binary plant, it has been shown that mixtures of saturated hydrocarbons (alkanes) or halogenated hydrocarbons operating in a supercritical Rankine cycle gave improved performance over Rankine cycles with the pure working fluids executing single or dual boiling cycles or supercritical cycles. Recently, other types of cycles have been proposed for binary geothermal service. The feasible limits on efficiency of a plant given practical limits on equipment performance is explored and the methods used in these advanced concept plants to achieve the maximum possible efficiency are discussed. (Here feasible is intended to mean reasonably achievable and not cost effective.) No direct economic analysis was made because of the sensitivity of economic results to site specific input. The limit of performance of three advanced plants were considered. The performance predictions were taken from the developers of each concept. The advanced plants considered appear to be approaching the feasible limit of performance. Ultimately, the plant designer must weigh the advantages and disadvantages of the the different cycles to find the best plant for a given service. In addition, a standard is presented of comparison of the work which has been done in the Heat Cycle Research Program and in the industrial sector by Exergy, Inc. and Polythermal Technologies.

  5. Small power systems for law enforcement applications

    NASA Astrophysics Data System (ADS)

    Sims, Paul E.; Mauk, Michael G.; Sulima, Oleg V.

    2002-08-01

    Recent events have increased interest in the use of sensors by law enforcement and homeland defense related organizations. Autonomous sensors such as those under development for the Unattended Ground Sensor (UGS) program are suitable for some of these applications. The operational lifetime of a UGS depends on the power consumption of the package and the space allocated for batteries. We survey and assess options for powering these devices ina long-term scenario. These alternatives are in various stages of development, and range from conventional batteries and solar cells that are ready for deployment and are now commercially available; to technologies developed for other applications (e.g., power for deep-space probes, man portable power for soldiers, or for sensors in oil drilling bore holes) that would need to be adapted to UGS's; to new and often speculative concepts that are in the laboratory or are still on the drawing board. Ideally, unattended ground sensors do not require servicing, re- energizing or refueling; and are capable of autonomous operation for weeks or even years. Further, UGS's may need to be used covertly, which restricts schemes that would provide a detectable signature. Reliability, ruggedness, cost, weight, size, camouflaging, use of toxic materials and other safety or disposal aspects, restrictions on their deployment (e.g., whether UGS's can be dropped form the air or whether they need to be uprighted or favorably oriented), storage and inventorying considerations, temperature ranges of operation, and complexity of associated electronics are also important issues. In this paper, we will limit the discussion to systems where operating power does not exceed 5 watts since larger systems are commercially available. Some subjectivity in comparisons is perhaps inevitable, but despite the disparate physics upon which these devices are based, a few common criteria can be invoked for discussing their suitability for energy storage and powering UGS's. Metrics can be developed to assess and compare options, but since most of the options are in very different stages of development, one is sometimes forced to use performance specifications that are predicted, rather than demonstrated. Thus, in some cases the comparisons are tentative or speculative.

  6. Arrhenius' law in turbulent media and an equivalent tunnel effect. [in binary exchange chemical reactions

    NASA Technical Reports Server (NTRS)

    Tsuge, S.; Sagara, K.

    1978-01-01

    The indeterminacy inherent to the formal extension of Arrhenius' law to reactions in turbulent flows is shown to be surmountable in the case of a binary exchange reaction with a sufficiently high activation energy. A preliminary calculation predicts that the turbulent reaction rate is invariant in the Arrhenius form except for an equivalently lowered activation energy. This is a reflection of turbulence-augmented molecular vigor, and causes an appreciable increase in the reaction rate. A similarity to the tunnel effect in quantum mechanics is indicated. The anomaly associated with the mild ignition of oxy-hydrogen mixtures is discussed in this light.

  7. Power law exponents characterizing human DNA

    NASA Astrophysics Data System (ADS)

    Provata, A.; Oikonomou, Th.

    2007-05-01

    The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc(S) of size S present long tails Pnc(S)˜S-1-μnc , with exponents μnc ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments Pc(S) in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.

  8. Power law models of stock indices

    NASA Astrophysics Data System (ADS)

    Tse, Man Kit

    Viewing the stock market as a self-organized system, Sornette and Johansen introduced physics-based models to study the dynamics of stock market crashes from the perspective of complex systems. This involved modeling stock market Indices using a mathematical power law exhibiting log-periodicity as the system approaches a market crash, which acts like a critical point in a thermodynamic system. In this dissertation, I aim to investigate stock indices to determine whether or not they exhibit log-periodic oscillations, according to the models proposed by Sornette, as they approach a crash. In addition to analyzing stock market crashes in the frequency domain using the discrete Fourier transform and the Lomb-Scargle periodogram, I perform a detailed analysis of the stock market crash models through parameter estimation and model testing. I find that the probability landscapes have a complex topography and that there is very little evidence that these phase transition-based models accurately describe stock market crashes.

  9. A law of mixtures for transport properties in binary particulate composites

    SciTech Connect

    Duncan, K.L.; Lodenquai, J.F.; Wagh, A.S.; Goretta, K.C.

    1998-09-01

    A connected-grain model was developed earlier to explain mechanical and thermal properties of porous ceramics and sedimentary rocks. We have now generalized this model for binary particulate composites, based on simulation of a connected-grain structure of individual components of the composites by randomly selecting individual grains and shrinking them. Repetition of this procedure results in a structure of a binary particulate composite that contains channels of individual components, through which transport occurs. We developed a generalized law of mixtures in which transport properties are expressed as scaling relationships that depend on the shrinking parameter expressed as an exponent. This parameter provides the skewness of the distribution of the grains. The model is compared with various transport properties of binary composites reported in the literature. In addition, the model is tested on YBa{sub 2}Cu{sub 3}O{sub x} superconductors and Ag composites that were fabricated in our laboratory and tested for electrical conductivity and elastic modulus. This test demonstrates how the model predicts two entirely different transport properties through their common microstructure and grain-size distribution. {copyright} {ital 1998 American Institute of Physics.}

  10. Development of Jet Noise Power Spectral Laws

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas; Bridges, James

    2011-01-01

    High-quality jet noise spectral data measured at the Aero-Acoustic Propulsion Laboratory (AAPL) at NASA Glenn is used to develop jet noise scaling laws. A FORTRAN algorithm was written that provides detailed spectral prediction of component jet noise at user-specified conditions. The model generates quick estimates of the jet mixing noise and the broadband shock-associated noise (BBSN) in single-stream, axis-symmetric jets within a wide range of nozzle operating conditions. Shock noise is emitted when supersonic jets exit a nozzle at imperfectly expanded conditions. A successful scaling of the BBSN allows for this noise component to be predicted in both convergent and convergent-divergent nozzles. Configurations considered in this study consisted of convergent and convergent- divergent nozzles. Velocity exponents for the jet mixing noise were evaluated as a function of observer angle and jet temperature. Similar intensity laws were developed for the broadband shock-associated noise in supersonic jets. A computer program called sJet was developed that provides a quick estimate of component noise in single-stream jets at a wide range of operating conditions. A number of features have been incorporated into the data bank and subsequent scaling in order to improve jet noise predictions. Measurements have been converted to a lossless format. Set points have been carefully selected to minimize the instability-related noise at small aft angles. Regression parameters have been scrutinized for error bounds at each angle. Screech-related amplification noise has been kept to a minimum to ensure that the velocity exponents for the jet mixing noise remain free of amplifications. A shock-noise-intensity scaling has been developed independent of the nozzle design point. The computer program provides detailed narrow-band spectral predictions for component noise (mixing noise and shock associated noise), as well as the total noise. Although the methodology is confined to single streams, efforts are underway to generate a data bank and algorithm applicable to dual-stream jets. Shock-associated noise in high-powered jets such as military aircraft can benefit from these predictions.

  11. Rate-Controlling Mechanisms in Five-Power-Law Creep

    SciTech Connect

    Michael E. Kassner

    2004-04-20

    OAK-B135 Rate-Controlling Mechanisms in Five-Power-Law Creep. The initial grant emphasized the rate-controlling processes for five power-law creep. The effort has six aspects: (1) Theory of Taylor hardening from the Frank dislocation network in five power law substructures. (2) The dual dynamical and hardening nature of dislocations in five power law substructures. (3) Determination of the existence of long-range internal stress in five-power law creep dislocation substructures. (4) Dynamic recovery mechanisms associated with dislocation heterogeneities during five power law creep. (5) Versatility of five power law creep concept to other (hcp) crystal structures. (6) Writing of a book on ''Fundamental of Creep in Metals and Alloys'' by M.E. Kassner and Maria-Teresa Perez-Frado (postdoctoral scholar, funded by this project) Elsevier Press, 2004, in press. These areas are consistent with the original goals of this project as delineated in the original proposal to Basic Energy Sciences. The progress in each of these areas will be discussed separately and there will be an attempt to tie each aspect together so as to allow a summary regarding the conclusions with respect to the rate-controlling mechanisms of five power-law creep.

  12. Power-law confusion: You say incremental, I say differential

    NASA Technical Reports Server (NTRS)

    Colwell, Joshua E.

    1993-01-01

    Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.

  13. Resurrecting power law inflation in the light of Planck results

    SciTech Connect

    Unnikrishnan, Sanil; Sahni, Varun E-mail: varun@iucaa.ernet.in

    2013-10-01

    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 f{sub N{sub L}{sup equil}} 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.

  14. Resurrecting power law inflation in the light of Planck results

    NASA Astrophysics Data System (ADS)

    Unnikrishnan, Sanil; Sahni, Varun

    2013-10-01

    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.

  15. Evolution of power law distributions in science and society

    NASA Astrophysics Data System (ADS)

    Jeon, Young-Pyo; McCoy, Benjamin J.

    2005-09-01

    Power law distributions have been observed in numerous physical and social systems; for example, the size distributions of particles, aerosols, corporations, and cities are often power laws. Each system is an ensemble of clusters, comprising units that combine with or dissociate from the cluster. Constructing models and investigating their properties are needed to understand how such clusters evolve. To describe the growth of clusters, we hypothesize that a distribution obeys a governing population dynamics equation based on a reversible association-dissociation process. The rate coefficients are considered to depend on the cluster size as power expressions, thus providing an explanation for the asymptotic evolution of power law distributions.

  16. Thresholded Power law Size Distributions of Instabilities in Astrophysics

    NASA Astrophysics Data System (ADS)

    Aschwanden, Markus J.

    2015-11-01

    Power-law-like size distributions are ubiquitous in astrophysical instabilities. There are at least four natural effects that cause deviations from ideal power law size distributions, which we model here in a generalized way: (1) a physical threshold of an instability; (2) incomplete sampling of the smallest events below a threshold x0; (3) contamination by an event-unrelated background xb; and (4) truncation effects at the largest events due to a finite system size. These effects can be modeled in the simplest terms with a “thresholded power law” distribution function (also called generalized Pareto [type II] or Lomax distribution), N(x){dx}\\propto {(x+{x}0)}-a{dx}, where x0 > 0 is positive for a threshold effect, while x0 < 0 is negative for background contamination. We analytically derive the functional shape of this thresholded power law distribution function from an exponential growth evolution model, which produces avalanches only when a disturbance exceeds a critical threshold x0. We apply the thresholded power law distribution function to terrestrial, solar (HXRBS, BATSE, RHESSI), and stellar flare (Kepler) data sets. We find that the thresholded power law model provides an adequate fit to most of the observed data. Major advantages of this model are the automated choice of the power law fitting range, diagnostics of background contamination, physical instability thresholds, instrumental detection thresholds, and finite system size limits. When testing self-organized criticality models that predict ideal power laws, we suggest including these natural truncation effects.

  17. Power-law distribution of family names in Japanese societies

    NASA Astrophysics Data System (ADS)

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

    2000-04-01

    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.

  18. Fractal ladder models and power law wave equations

    PubMed Central

    Kelly, James F.; McGough, Robert J.

    2009-01-01

    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. PMID:19813816

  19. Punctuated equilibrium and power law in economic dynamics

    NASA Astrophysics Data System (ADS)

    Gupta, Abhijit Kar

    2012-02-01

    This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called 'feedback' was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of 'fitness' and 'selection' in the present model of economic evolution.

  20. The power laws of nanoscale forces in ambient conditions

    NASA Astrophysics Data System (ADS)

    Chiesa, Matteo; Santos, Sergio; Lai, Chia-Yun

    Power laws are ubiquitous in the physical sciences and indispensable to qualitatively and quantitatively describe physical phenomena. A nanoscale force law that accurately describes the phenomena observed in ambient conditions at several nm or fractions of a nm above a surface however is still lacking. Here we report a power law derived from experimental data and describing the interaction between an atomic force microscope AFM tip modelled as a sphere and a surface in ambient conditions. By employing a graphite surface as a model system the resulting effective power is found to be a function of the tip radius and the distance. The data suggest a nano to mesoscale transition in the power law that results in relative agreement with the distance-dependencies predicted by the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only

  1. General 2.5 power law of metallic glasses.

    PubMed

    Zeng, Qiaoshi; Lin, Yu; Liu, Yijin; Zeng, Zhidan; Shi, Crystal Y; Zhang, Bo; Lou, Hongbo; Sinogeikin, Stanislav V; Kono, Yoshio; Kenney-Benson, Curtis; Park, Changyong; Yang, Wenge; Wang, Weihua; Sheng, Hongwei; Mao, Ho-Kwang; Mao, Wendy L

    2016-02-16

    Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its "disordered" structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous "composition" change of 4f-localized "big Ce" to 4f-itinerant "small Ce," indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs. PMID:26831105

  2. Hidden power law patterns in the top European football leagues

    NASA Astrophysics Data System (ADS)

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

    2013-11-01

    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.

  3. Electric field in media with power-law spatial dispersion

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2016-04-01

    In this paper, we consider electric fields in media with power-law spatial dispersion (PLSD). Spatial dispersion means that the absolute permittivity of the media depends on the wave vector. Power-law type of this dispersion is described by derivatives and integrals of non-integer orders. We consider electric fields of point charge and dipole in media with PLSD, infinite charged wire, uniformly charged disk, capacitance of spherical capacitor and multipole expansion for PLSD-media.

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

    PubMed

    Lillo, F; Mantegna, R N

    2003-07-01

    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 Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power-law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models. PMID:12935212

  5. The distance-decay function of geographical gravity model: Power law or exponential law?

    NASA Astrophysics Data System (ADS)

    Chen, Yanguang

    2015-08-01

    The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be explained with the ideas from Euclidean geometry. This results in what is called dimension dilemma. In particular, the gravity model based on power law could not be derived from general principles by traditional ways. Consequently, a negative exponential function substituted for the inverse power function to serve for a distance-decay function for the gravity model. However, the exponential-based gravity model goes against the first law of geography. This paper is devoted to solve these kinds of problems by mathematical reasoning and empirical analysis. First, it can be proved that the distance exponent of the gravity model is essentially a fractal dimension. Thus the dimensional dilemma of the power-based gravity model can be resolved using the concepts from fractal geometry. Second, the exponential function indicates locality and localization, which violates the basic principle of spatial interaction. The power function implies action at a distance, which is the necessary condition of geographical gravitation. Third, the gravity model based on power law decay can be derived from the entropy- maximizing principle by introducing a proper postulate. The observational data of China's cities and regions are employed to verify the theoretical inferences, and the results support power-law distance decay. A conclusion can be reached that the preferred form of geographical gravity model is its original form, which is based on an inverse power law rather than a negative exponential law.

  6. Relaxation Dynamics of Non-Power-Law Fluids

    NASA Astrophysics Data System (ADS)

    Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong

    2013-12-01

    The relaxation of non-Newtonian liquids with non-power-law rheology on partially wetted surfaces is rarely investigated. This study assesses the relaxation behavior of 14 partial wetting systems with non-power-law fluids by sessile drop method. These systems are two carboxymethylcellulose sodium solutions on two kinds of slides, cover glass, and silicon wafer surfaces; three polyethylene glycol (PEG400) + silica nanoparticle suspensions on polymethyl methacrylate and polystyrene surfaces. The dynamic contact angle and moving velocity of contact line relationship data for relaxation drops of the 14 tested systems demonstrate a power-law fluid-like behavior, and the equivalent power exponent for a certain fluid on different solid substrates are uniform. By analyzing the relationship between the equivalent power exponent and shear rate, it is proposed that a fluid regime with shear rates of a few tens of s controls relaxation dynamics.

  7. Distortion of power law blinking with binning and thresholding

    SciTech Connect

    Amecke, Nicole; Heber, André; Cichos, Frank

    2014-03-21

    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 α{sub on/off} ≳ 1.6, especially if α{sub on} ≠ α{sub 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.

  8. A COSMIC COINCIDENCE: THE POWER-LAW GALAXY CORRELATION FUNCTION

    SciTech Connect

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

    2011-09-01

    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.

  9. MHD micropumping of power-law fluids: A numerical solution

    NASA Astrophysics Data System (ADS)

    Moghaddam, Saied

    2013-02-01

    The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.

  10. Power-law hereditariness of hierarchical fractal bones.

    PubMed

    Deseri, Luca; Di Paola, Mario; Zingales, Massimiliano; Pollaci, Pietro

    2013-12-01

    In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law. PMID:23836622

  11. Scaling and power-laws in ecological systems.

    PubMed

    Marquet, Pablo A; Quiñones, Renato A; Abades, Sebastian; Labra, Fabio; Tognelli, Marcelo; Arim, Matias; Rivadeneira, Marcelo

    2005-05-01

    Scaling relationships (where body size features as the independent variable) and power-law distributions are commonly reported in ecological systems. In this review we analyze scaling relationships related to energy acquisition and transformation and power-laws related to fluctuations in numbers. Our aim is to show how individual level attributes can help to explain and predict patterns at the level of populations that can propagate at upper levels of organization. We review similar relationships also appearing in the analysis of aquatic ecosystems (i.e. the biomass spectra) in the context of ecological invariant relationships (i.e. independent of size) such as the 'energetic equivalence rule' and the 'linear biomass hypothesis'. We also discuss some power-law distributions emerging in the analysis of numbers and fluctuations in ecological attributes as they point to regularities that are yet to be integrated with traditional scaling relationships and which we foresee as an exciting area of future research. PMID:15855405

  12. Statistical Models of Power-law Distributions in Homogeneous Plasmas

    SciTech Connect

    Roth, Ilan

    2011-01-04

    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.

  13. The power law relationship for landslide fatality data

    NASA Astrophysics Data System (ADS)

    Petley, D. N.

    2011-12-01

    In recent years there has been considerable interest in the nature of the power law relationship in landslide area and volume datsets. In other hazards, similar fat-tailed power law distributions have been observed for loss data. For example, both earthquake fatality datasets for large events (Knopoff and Sornette 1995) and for flood losses (Pisarenko 1998) have been shown to display power law distributions. Data from very large rockslope failures also suggests that fat tailed power law distributions may describe the occurrence of fatalities associated with these events (Evans et al. 2006). However, there has been a lack of rigorous analysis of the statistical distributions for fatality datasets for all landslide events, which is unfortunate given the potential use of this data to examine potential losses from forecast events. This paper examines nine years of rainfall induced landslide data from the Durham Fatal Landslide database, which provides records losses of life from landslides on a global basis. It is demonstrated that the landslide fatality data exhibits a clear fat tailed power law distribution. A roll-over is noted for events with small numbers of fatalities (i.e. one or two deaths per event), suggesting under-sampling in that part of the distribution. Examination of this roll-over for the data for individual years suggests that its magnitude is becoming smaller, which in turn implies that the quality of the dataset may be improving with time. An examination is made of the power law distribution for different geographical areas; it is suggested that differences in the scaling of the dataset may be related to a combination of the physical conditions associated with the landslides themselves (e.g. topography, climate, geology and land cover) and the social setting (e.g. population density, household size and wealth).

  14. Turbulent pipe flow of power-law fluids

    SciTech Connect

    Malin, M.R.

    1997-11-01

    Flows of non-Newtonian fluids through pipes are relevant in many engineering applications, especially within the manufacturing, process and wastewater industries. This paper reports on the numerical computation of the turbulent flow of power-law fluids in smooth circular tubes. The turbulence is represented by means of a modified version of an existing two-equation turbulence model. Numerical results are presented for the fully-developed friction factor and velocity profile, and compared with experimental data. The model is shown to produce fairly good agreement with experiment over a wide range of values for the power-law index and generalized Reynolds number.

  15. The power law distribution for lower tail cities in India

    NASA Astrophysics Data System (ADS)

    Devadoss, Stephen; Luckstead, Jeff; Danforth, Diana; Akhundjanov, Sherzod

    2016-01-01

    The city size distribution for lower tail cities has received scant attention because a small portion of the population lives in rural villages, particularly in developed countries, and data are not readily available for small cities. However, in developing countries much of the population inhabits rural areas. The purpose of this study is to test whether power law holds for small cities in India by using the most recent and comprehensive Indian census data for the year 2011. Our results show that lower tail cities for India do exhibit a power law.

  16. Power-law creep from discrete dislocation dynamics.

    PubMed

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

    2012-12-28

    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. PMID:23368581

  17. Power-law cosmologies in minimal and maximal gauged supergravity

    NASA Astrophysics Data System (ADS)

    Blåbäck, J.; Borghese, A.; Haque, S. S.

    2013-06-01

    In this paper we search for accelerating power-law solutions and ekpyrotic solutions within minimal and maximal four dimensional supergravity theories. We focus on the STU model for {N} = 1 and on the new CSO( p, q, r) theories, which were recently obtained exploiting electromagnetic duality, for {N} = 8. In the minimal case we find some new ekpyrotic solutions, while in the maximal case we find some new generic power-law solutions. We do not find any new accelerating solutions for these models.

  18. Universal power law behaviors in genomic sequences and evolutionary models

    NASA Astrophysics Data System (ADS)

    Martignetti, Loredana; Caselle, Michele

    2007-08-01

    We study the length distribution of a particular class of DNA sequences known as the 5' untranslated regions exons. These exons belong to the messenger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that in both mice and humans these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model, which may explain this finding. We conjecture that this power law behavior could indeed be a general feature of higher eukaryotes.

  19. Emphasize the difference: On the energy dependance of power spectral states in Black Hole X-ray Binaries

    NASA Astrophysics Data System (ADS)

    Stiele, Holger; Yu, W.

    2014-01-01

    Transient black hole X-ray binaries usually evolve through different energy spectral states that show characteristic spectral and variability properties. These characteristics mainly resulted from the energy spectra and the power density spectra obtained by the RXTE in the energy band above 3 keV. This picture has been challenged through our recent study on MAXI J1659-152, in which we found a clear energy dependence of the power spectral state; the thermal disk spectral component in the hard and the intermediate state is of a power-law noise with a possible cut-off at a frequency below the characteristic frequencies of the band-limited noise and QPOs seen simultaneously in the Comptonized component, which is similar to the power spectrum of the soft state. Here, we present the results of our comprehensive study of archival XMM-Newton observations of black hole X-ray binaries, which comprises GRS 1915+105, GX 339-4, H1743-322 and other sources. For the observations of GRS 1915+105 in the "plateau" state we will discuss the overall shape of the power density spectra related to the noise component and the presence or absence of quasi-periodic oscillations in different energy bands. Furthermore, we will present a summary of the power density spectra and related time lags in the observations of GX 339-4. The presence of quasi-periodic oscillations and band-limited noise in the power density spectra above ~2 keV and the simultaneous domination by a power-law noise in the power density spectra at lower energies imply that the quasi-periodic oscillations and the band-limited noise are in the Comptonized component and the optically thick disk contributes to a power-law noise which is independent of the energy spectral state. We will discuss the implications of this finding for the picture of the accretion geometry in black hole X-ray binaries.

  20. Power-law phenomena in adhesive de-bonding

    NASA Astrophysics Data System (ADS)

    Kendall, Gay

    Acoustic emission (AE) was recorded during the peeling of pressure-sensitive adhesive (PSA) tapes from their surfaces. The viscous and non-linear behavior of PSA tapes produces significant energy dissipation in the form of adhesive fibril formation, elongation and final failure within the peel zone. AE generated during the peeling process corresponds to the final de-bonding event, in which elastic energy is rapidly released to the substrate. The recording and analyzing of AE generated during peeling is used here in a novel application for characterizing microscopic de-bonding events. Present results indicate that the distribution of AE event magnitudes have the form of power-laws and the power spectral densities have the form of flicker noise. Both power-law dependencies and flicker noise are recognized as consequences of SOC in homogeneous systems. A significant feature of power-law dependencies is the absence of any characteristic length or time scales. The present results, however, indicate that the interface is not homogeneous and that pre-existing surface conditions cause non-uniform adhesive bonding. This is heavily supported by the literature regarding the nature of engineering surfaces. Consequentially, Mandelbrot's fractal concepts were applied to characterize the heterogeneous adhesive interface, and to investigate the relation of interfacial structure with the power-law features of the PSA de-bonding process. It is concluded that fractally distributed variations in adhesive bond strengths at the PSA-glass interface produce the observed hyperbolic distributions in AE events. All the formalism of SOC: applies under this alternative explanation of PSA de-bonding phenomena because of the observed hyperbolic distributions of the AE data. It may be that the explanation based on an underlying fractal structure may be a more general explanation to power law and flicker noise phenomena than the SOC model for heterogeneous systems.

  1. Power law relationships for rain attenuation and reflectivity

    NASA Technical Reports Server (NTRS)

    Devasirvatham, D. M. J.; Hodge, D. B.

    1978-01-01

    The equivalent reflectivity, specific attenuation and volumetric backscatter cross section of rain are calculated and tabulated at a number of frequencies from 1 to 500 GHz using classical Mie theory. The first two parameters are shown to be closely approximated as functions of rain rate by the power law aR to the b power. The a's and b's are also tabulated and plotted for convenient reference.

  2. Medical practices display power law behaviors similar to spoken languages

    PubMed Central

    2013-01-01

    Background Medical care commonly involves the apprehension of complex patterns of patient derangements to which the practitioner responds with patterns of interventions, as opposed to single therapeutic maneuvers. This complexity renders the objective assessment of practice patterns using conventional statistical approaches difficult. Methods Combinatorial approaches drawn from symbolic dynamics are used to encode the observed patterns of patient derangement and associated practitioner response patterns as sequences of symbols. Concatenating each patient derangement symbol with the contemporaneous practitioner response symbol creates “words” encoding the simultaneous patient derangement and provider response patterns and yields an observed vocabulary with quantifiable statistical characteristics. Results A fundamental observation in many natural languages is the existence of a power law relationship between the rank order of word usage and the absolute frequency with which particular words are uttered. We show that population level patterns of patient derangement: practitioner intervention word usage in two entirely unrelated domains of medical care display power law relationships similar to those of natural languages, and that–in one of these domains–power law behavior at the population level reflects power law behavior at the level of individual practitioners. Conclusions Our results suggest that patterns of medical care can be approached using quantitative linguistic techniques, a finding that has implications for the assessment of expertise, machine learning identification of optimal practices, and construction of bedside decision support tools. PMID:24007376

  3. The power laws of nanoscale forces under ambient conditions.

    PubMed

    Lai, Chia-Yun; Olukan, Tuza; Santos, Sergio; Al Ghaferi, Amal; Chiesa, Matteo

    2015-12-25

    We report a power law derived from experimental atomic force microscopy (AFM) data suggesting a nano to mesoscale transition in force-distance dependencies. Our results are in relative agreement with the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only. PMID:26486193

  4. Electrokinetically modulated peristaltic transport of power-law fluids.

    PubMed

    Goswami, Prakash; Chakraborty, Jeevanjyoti; Bandopadhyay, Aditya; Chakraborty, Suman

    2016-01-01

    The electrokinetically modulated peristaltic transport of power-law fluids through a narrow confinement in the form of a deformable tube is investigated. The fluid is considered to be divided into two regions - a non-Newtonian core region (described by the power-law behavior) which is surrounded by a thin wall-adhering layer of Newtonian fluid. This division mimics the occurrence of a wall-adjacent cell-free skimming layer in blood samples typically handled in microfluidic transport. The pumping characteristics and the trapping of the fluid bolus are studied by considering the effect of fluid viscosities, power-law index and electroosmosis. It is found that the zero-flow pressure rise is strongly dependent on the relative viscosity ratio of the near-wall depleted fluid and the core fluid as well as on the power-law index. The effect of electroosmosis on the pressure rise is strongly manifested at lower occlusion values, thereby indicating its importance in transport modulation for weakly peristaltic flow. It is also established that the phenomenon of trapping may be controlled on-the-fly by tuning the magnitude of the electric field: the trapping vanishes as the magnitude of the electric field is increased. Similarly, the phenomenon of reflux is shown to disappear due to the action of the applied electric field. These findings may be applied for the modulation of pumping in bio-physical environments by means of external electric fields. PMID:26524260

  5. Vacuum flash geothermal power plants: Second Law analysis and optimization

    SciTech Connect

    DiPippo, R.

    1997-12-31

    Hibara et al (1990) describe the concept of a vacuum-flash geothermal steam plant. The idea involves the use of near-boiling-point water available at numerous hot spring areas. The authors show that a steam plant using a vacuum pump to create the flash process for steam generation can compete thermodynamically and economically with binary plants of small capacity. However, the thermal efficiency they quote is very low (1.4%) and might discourage the use of such a scheme. This paper examines vacuum-flash plants using Second Law analysis, a thermodynamically appropriate method to assess the performance of the system (Moran, 1982; DiPippo and Marcille, 1984), and the results are both more revealing and more encouraging.

  6. Second law analysis of a conventional steam power plant

    NASA Astrophysics Data System (ADS)

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

    1993-11-01

    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.

  7. Second law analysis of a conventional steam power plant

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

    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.

  8. Spectrum of power laws for curved hand movements.

    PubMed

    Huh, Dongsung; Sejnowski, Terrence J

    2015-07-21

    In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead. PMID:26150514

  9. Scaling range of power laws that originate from fluctuation analysis

    NASA Astrophysics Data System (ADS)

    Grech, Dariusz; Mazur, Zygmunt

    2013-05-01

    We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.

  10. Scaling range of power laws that originate from fluctuation analysis.

    PubMed

    Grech, Dariusz; Mazur, Zygmunt

    2013-05-01

    We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R^{2} of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible. PMID:23767586

  11. Decay Power Law in, High Intensity, Isotropic Turbulent Flow

    NASA Astrophysics Data System (ADS)

    Koster, Timothy; Puga, Alejandro; Larue, John

    2014-11-01

    In the study reported here, isotropy is determined using the measure proposed by George (1992), where isotropy corresponds to those downstream positions where the product of the Taylor Reynolds number and the skewness of the velocity derivative is a constant. Straight forward approach can be used which is based on the observation of Batchelor (1953), that the square of the Talor micorscale is linearly related to downstream distance relative to the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for mean velocities of 6 and 8 m/s for the downstream decay of the parameters listed in the preceding. The corresponding values of the Taylor Reynolds number at the start of the isotropic region are 290 and 400, and the variance decay exponent and virtual origin are found to be respectively -1.707 and -1.298 and -27.95 and -5.757. The exponents in the decay law for the other parameters are found to be within +/- 3% of the expected values. University of California Irvine Research Funds.

  12. Non-power law behavior in fragmentation cascades

    NASA Astrophysics Data System (ADS)

    Belyaev, Mikhail A.; Rafikov, Roman R.

    2011-07-01

    Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper Belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for the particle mass distribution is a power law in the mass. However, previous studies have typically assumed that the mass of the largest fragment produced in a collision with just enough energy to shatter the target and disperse half its mass to infinity is directly proportional to the target mass. We show that if this assumption is not satisfied, then the power law solution for the steady-state particle mass distribution is modified by a multiplicative factor, which is a slowly varying function of the mass. We derive analytic solutions for this correction factor and confirm our results numerically. We find that this correction factor proves important when extrapolating over many orders of magnitude in mass, such as when inferring the number of large objects in a system based on infrared observations. In the course of our work, we have also discovered an unrelated type of non-power law behavior: waves can persist in the mass distribution of objects even in the absence of upper or lower cutoffs to the mass distribution or breaks in the strength law.

  13. On the power law of passive scalars in turbulence

    NASA Astrophysics Data System (ADS)

    Gotoh, Toshiyuki; Watanabe, Takeshi

    2015-11-01

    It has long been considered that the moments of the scalar increment with separation distance r obey power law with scaling exponents in the inertial convective range and the exponents are insensitive to variation of pumping of scalar fluctuations at large scales, thus the scaling exponents are universal. We examine the scaling behavior of the moments of increments of passive scalars 1 and 2 by using DNS up to the grid points of 40963. They are simultaneously convected by the same isotropic steady turbulence atRλ = 805 , but excited by two different methods. Scalar 1 is excited by the random scalar injection which is isotropic, Gaussian and white in time at law wavenumber band, while Scalar 2 is excited by the uniform mean scalar gradient. It is found that the local scaling exponents of the scalar 1 has a logarithmic correction, meaning that the moments of the scalar 1 do not obey simple power law. On the other hand, the moments of the scalar 2 is found to obey the well developed power law with exponents consistent with those in the literature. Physical reasons for the difference are explored. Grants-in-Aid for Scientific Research 15H02218 and 26420106, NIFS14KNSS050, HPCI project hp150088 and hp140024, JHPCN project jh150012.

  14. Deviation from Power Law Behavior in Landslide Phenomenon

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

    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.

  15. COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS

    SciTech Connect

    Mota, David F.; Winther, Hans A.

    2011-05-20

    In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to {Lambda}CDM, but can in some special cases enhance the growth of the linear perturbations at low redshifts. For the models we consider, it is found that this region of the parameter space is ruled out by local gravity constraints. Imposing a coupling to dark matter only, the local constraints are avoided, and it is possible to have observable signatures on the linear matter perturbations.

  16. Power laws and elastic nonlinearity in materials with complex microstructure

    NASA Astrophysics Data System (ADS)

    Scalerandi, M.

    2016-01-01

    Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities.

  17. On estimating the exponent of power-law frequency distributions.

    PubMed

    White, Ethan P; Enquist, Brian J; Green, Jessica L

    2008-04-01

    Power-law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning-based methods traditionally used in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation outperforms other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited. PMID:18481513

  18. Power-Law Singularities in Gravity-Capillary Waves

    NASA Astrophysics Data System (ADS)

    Lathrop, Daniel P.; Shi, William T.; Errett Hogrefe, J.

    1997-11-01

    Strongly driven waves will break and produce local singularities. Parametrically forced standing waves (Faraday waves) may break in a way that shows a local power-law divergence on the free surface. We experimentally explore this state for its local structure, time dynamics and creation threshold. A local analytical model for the surface height compares favorably with image sequences taken of individual events. This local model is based on liquid collapsing into a cylindrical void, and leads to a flow field with an upward jet. Surface tension and inertial forces are in balance in this special solution, thus selecting one power law form for the free surface. Inertial forces may overwhelm surface tension in other solution types possibly leading to a family of different singularities.

  19. Lévy flights with power-law absorption

    NASA Astrophysics Data System (ADS)

    Cattivelli, Luca; Agliari, Elena; Sartori, Fabio; Cassi, Davide

    2015-10-01

    We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ +1 . Assuming that the walker moves in the presence of a distribution a (x ) of targets (traps) depending on the spatial coordinate x , we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a (x ) ˜x-α and we find that, as long as μ <α , there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.

  20. The origin of power-law rheology in foams

    NASA Astrophysics Data System (ADS)

    Hwang, Hyun Joo; Riggleman, Robert; Crocker, John

    Soft glassy matter (SGM) such as foams, emulsions, and colloids, exhibit interesting rheological properties that have long defied explanation. In particular, the shear modulus of these materials displays weak power law frequency dependence. To understand the origin of this property in more depth, we have built a three-dimensional, modified Bubble Dynamics model. The bubbles interact with a purely repulsive harmonic potential and ripen according to diffusion-based governing equations. Notably, the bubble motion has a Levy flight character, in addition to being spatially correlated in the form of avalanches. Microrheology studies reveal that the power-law shear modulus is the result of constraint release driven by the bubbles' super-diffusive motion combined with simple yield of the resulting stress. The super-diffusive motion of the bubbles, in turn, is the result of the system taking a fractal path in configuration space. We shall discuss the origins of this fractal scaling.

  1. Power-law distribution in Japanese racetrack betting

    NASA Astrophysics Data System (ADS)

    Ichinomiya, Takashi

    2006-08-01

    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.

  2. Linear growth in power law f (T ) gravity

    NASA Astrophysics Data System (ADS)

    Basilakos, Spyros

    2016-04-01

    We provide for the first time the growth index of linear matter fluctuations of the power law f (T )∝(-T )b gravity model. We find that the asymptotic form of this particular f (T ) model is γ ≈6/11 -6 b , which obviously extends that of the Λ CDM model, γΛ≈6 /11 . Finally, we generalize the growth index analysis of f (T ) gravity in the case where γ is allowed to vary with redshift.

  3. Power law distribution of dividends in horse races

    NASA Astrophysics Data System (ADS)

    Park, K.; Domany, E.

    2001-02-01

    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.

  4. Power-law cosmology, SN Ia, and BAO

    SciTech Connect

    Dolgov, Aleksander; Halenka, Vitali; Tkachev, Igor E-mail: vithal@umich.edu

    2014-10-01

    We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime a(t) ∼ t{sup β} with β close to 3/2 in a spatially flat universe is a good fit to these data.

  5. Power-law behavior of power spectra in low Prandtl number Rayleigh-Bénard convection.

    PubMed

    Paul, M R; Cross, M C; Fischer, P F; Greenside, H S

    2001-10-01

    The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics. PMID:11580703

  6. Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

    SciTech Connect

    Paul, M. R.; Cross, M. C.; Fischer, P. F.; Greenside, H. S.

    2001-10-08

    The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.

  7. Analysis of Indentation-Derived Power-Law Creep Response

    NASA Astrophysics Data System (ADS)

    Martinez, Nicholas J.; Shen, Yu-Lin

    2016-02-01

    The use of instrumented indentation to characterize power-law creep is studied by computational modeling. Systematic finite element analyses were conducted to examine how indentation creep tests can be employed to retrieve the steady-state creep parameters pertaining to regular uniaxial loading. The constant indentation load hold and constant indentation-strain-rate methods were considered, first using tin (Sn)-based materials as a model system. The simulated indentation-strain rate-creep stress relations were compared against the uniaxial counterparts serving as model input. It was found that the constant indentation-strain-rate method can help establish steady-state creep, and leads to a more uniform behavior than the constant-load hold method. An expanded parametric analysis was then performed using the constant indentation-strain-rate method, taking into account a wide range of possible power-law creep parameters. The indentation technique was found to give rise to accurate stress exponents, and a certain trend for the ratio between indentation strain rate and uniaxial strain rate was identified. A contour-map representation of the findings serves as practical guidance for determining the uniaxial power-law creep response based on the indentation technique.

  8. Coalescence of Drops of a Power-law Fluid

    NASA Astrophysics Data System (ADS)

    Kamat, Pritish; Thete, Sumeet; Basaran, Osman

    2014-11-01

    Drop coalescence is crucial in a host of industrial, household, and natural processes that involve dispersions. Coalescence is a rate-controlling process in breaking emulsions and strongly influences drop-size-distributions in sprays. In a continuum approach, coalescence begins by the formation of a microscopic, non-slender bridge connecting the two drops. Indefinitely large axial curvature at the neck results in local lowering of pressure that drives fluid from the bulk of the drops toward the neck, thereby causing the bridge radius r (t) and height z (t) to increase in time t. The coalescence of Newtonian drops in air has heretofore been thoroughly studied. Here, we extend these earlier studies by analyzing the coalescence of drops of power-law fluids because many fluids encountered in real applications, including cosmetic creams, shampoos, grease, and paint, exhibit power-law (deformation-rate thinning) rheology. On account of the non-slender geometry of the liquid bridge connecting the two drops (z << r) , we analyze the resulting free surface flow problem by numerical simulation. Among other results, we present and discuss the nature of flows and scaling behaviors for r and z as functions of the initial viscosity and power-law index (0 < n <= 1) .

  9. Estimation of shear modulus in media with power law characteristics.

    PubMed

    Zhang, Wei; Holm, Sverre

    2016-01-01

    Shear wave propagation in tissue generated by the radiation force is usually modeled by either a lossless or a classical viscoelastic equation. However, experimental data shows power law behavior which is not consistent with those approaches. It is well known that fractional derivatives results in power laws, therefore a time fractional wave equation, the Caputo equation, which can be derived from the fractional Kelvin-Voigt stress and strain relation is tested. This equation is solved using the finite difference method with experimental parameters obtained from the existing literature. The equation is characterized by a fractional order which is also the power law exponent of the frequency dependent shear modulus. It is shown that for fractional order between 0 and 1, the equation gives smaller shear modulus than the classical model. The opposite situation applies for fractional order greater than 1. The numerical simulation also shows that the shear wave velocity method is only reliable for small losses. In our case, this is only for a small fractional order. Based on the published values of fractional order from other studies, there is therefore a chance for biased estimation of the shear modulus. PMID:26385841

  10. Analysis of Indentation-Derived Power-Law Creep Response

    NASA Astrophysics Data System (ADS)

    Martinez, Nicholas J.; Shen, Yu-Lin

    2016-03-01

    The use of instrumented indentation to characterize power-law creep is studied by computational modeling. Systematic finite element analyses were conducted to examine how indentation creep tests can be employed to retrieve the steady-state creep parameters pertaining to regular uniaxial loading. The constant indentation load hold and constant indentation-strain-rate methods were considered, first using tin (Sn)-based materials as a model system. The simulated indentation-strain rate-creep stress relations were compared against the uniaxial counterparts serving as model input. It was found that the constant indentation-strain-rate method can help establish steady-state creep, and leads to a more uniform behavior than the constant-load hold method. An expanded parametric analysis was then performed using the constant indentation-strain-rate method, taking into account a wide range of possible power-law creep parameters. The indentation technique was found to give rise to accurate stress exponents, and a certain trend for the ratio between indentation strain rate and uniaxial strain rate was identified. A contour-map representation of the findings serves as practical guidance for determining the uniaxial power-law creep response based on the indentation technique.

  11. Development of Jet Noise Power Spectral Laws Using SHJAR Data

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas; Bridges, James

    2009-01-01

    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.

  12. 29 CFR 102.35 - Duties and powers of administrative law judges; stipulations of cases to administrative law...

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 29 Labor 2 2010-07-01 2010-07-01 false Duties and powers of administrative law judges; stipulations of cases to administrative law judges or to the Board; assignment and powers of settlement judges. 102.35 Section 102.35 Labor Regulations Relating to Labor NATIONAL LABOR RELATIONS BOARD RULES AND REGULATIONS, SERIES 8 Procedure Under Section 10...

  13. 29 CFR 102.35 - Duties and powers of administrative law judges; stipulations of cases to administrative law...

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 29 Labor 2 2012-07-01 2012-07-01 false Duties and powers of administrative law judges; stipulations of cases to administrative law judges or to the Board; assignment and powers of settlement judges. 102.35 Section 102.35 Labor Regulations Relating to Labor NATIONAL LABOR RELATIONS BOARD RULES AND REGULATIONS, SERIES 8 Procedure Under Section 10...

  14. Power-law connections: From Zipf to Heaps and beyond

    SciTech Connect

    Eliazar, Iddo I.; Cohen, Morrel H.

    2013-05-15

    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.

  15. Interfacial pattern formation in confined power-law fluids.

    PubMed

    Brandão, Rodolfo; Fontana, João V; Miranda, José A

    2014-07-01

    The interfacial pattern formation problem in an injection-driven radial Hele-Shaw flow is studied for the situation in which a Newtonian fluid of negligible viscosity displaces a viscous non-Newtonian power-law fluid. By utilizing a Darcy-law-like formulation, we tackle the fluid-fluid interface evolution problem perturbatively, and we derive second-order mode-coupling equations that describe the time evolution of the perturbation amplitudes. This allows us to investigate analytically how the non-Newtonian nature of the dislocated fluid determines the morphology of the emerging interfacial patterns. If the pushed fluid is shear-thinning, our results indicate the development of side-branching structures. On the other hand, if the displaced fluid is shear-thickening, one detects the formation of petal-like shapes, markedly characterized by strong tip-splitting events. Finally, a time-dependent injection protocol is presented that is able to restrain finger proliferation via side-branching and tip-splitting. This permits the emergence of symmetric n-fold interfacial shapes for which the number of fingers remains fixed as time progresses. This procedure generalizes existing controlling strategies for purely Newtonian flow circumstances to the case of a non-Newtonian, displaced power-law fluid. PMID:25122375

  16. Interfacial pattern formation in confined power-law fluids

    NASA Astrophysics Data System (ADS)

    Brandão, Rodolfo; Fontana, João V.; Miranda, José A.

    2014-07-01

    The interfacial pattern formation problem in an injection-driven radial Hele-Shaw flow is studied for the situation in which a Newtonian fluid of negligible viscosity displaces a viscous non-Newtonian power-law fluid. By utilizing a Darcy-law-like formulation, we tackle the fluid-fluid interface evolution problem perturbatively, and we derive second-order mode-coupling equations that describe the time evolution of the perturbation amplitudes. This allows us to investigate analytically how the non-Newtonian nature of the dislocated fluid determines the morphology of the emerging interfacial patterns. If the pushed fluid is shear-thinning, our results indicate the development of side-branching structures. On the other hand, if the displaced fluid is shear-thickening, one detects the formation of petal-like shapes, markedly characterized by strong tip-splitting events. Finally, a time-dependent injection protocol is presented that is able to restrain finger proliferation via side-branching and tip-splitting. This permits the emergence of symmetric n-fold interfacial shapes for which the number of fingers remains fixed as time progresses. This procedure generalizes existing controlling strategies for purely Newtonian flow circumstances to the case of a non-Newtonian, displaced power-law fluid.

  17. Power laws, flicker noise, and the Barkhausen effect

    NASA Astrophysics Data System (ADS)

    Meisel, L. V.; Cote, P. J.

    1992-11-01

    The Barkhausen effect was studied in three ferromagnetic metals: an amorphous alloy, iron, and alumel. The data exhibit all the characteristics of self-organized critical behavior enumerated by Bak, Tang, and Wiesenfeld: The distributions of pulse durations, areas, and energies have the form of power laws, which have been modified to account for finite-size effects as suggested by Kadanoff, Nagel, Wu, and Zhou, and the power spectral densities have the form of flicker noise. Furthermore, the parameters describing the Barkhausen noise pulse distributions are consistent with those characterizing the power spectral density in the light of the results of Jensen, Christensen, and Fogedby. The data are also consistent with a model based on an inherent static fractal structure, independent of a self-organizing principle.

  18. Influence of DBT reconstruction algorithm on power law spectrum coefficient

    NASA Astrophysics Data System (ADS)

    Vancamberg, Laurence; Carton, Ann-Katherine; Abderrahmane, Ilyes H.; Palma, Giovanni; Milioni de Carvalho, Pablo; Iordache, R?zvan; Muller, Serge

    2015-03-01

    In breast X-ray images, texture has been characterized by a noise power spectrum (NPS) that has an inverse power-law shape described by its slope ? in the log-log domain. It has been suggested that the magnitude of the power-law spectrum coefficient ? is related to mass lesion detection performance. We assessed ? in reconstructed digital breast tomosynthesis (DBT) images to evaluate its sensitivity to different typical reconstruction algorithms including simple back projection (SBP), filtered back projection (FBP) and a simultaneous iterative reconstruction algorithm (SIRT 30 iterations). Results were further compared to the ? coefficient estimated from 2D central DBT projections. The calculations were performed on 31 unilateral clinical DBT data sets and simulated DBT images from 31 anthropomorphic software breast phantoms. Our results show that ? highly depends on the reconstruction algorithm; the highest ? values were found for SBP, followed by reconstruction with FBP, while the lowest ? values were found for SIRT. In contrast to previous studies, we found that ? is not always lower in reconstructed DBT slices, compared to 2D projections and this depends on the reconstruction algorithm. All ? values estimated in DBT slices reconstructed with SBP were larger than ? values from 2D central projections. Our study also shows that the reconstruction algorithm affects the symmetry of the breast texture NPS; the NPS of clinical cases reconstructed with SBP exhibit the highest symmetry, while the NPS of cases reconstructed with SIRT exhibit the highest asymmetry.

  19. SHJAR Jet Noise Data and Power Spectral Laws

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas; Bridges, James

    2009-01-01

    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.

  20. Adhesion of nanoscale asperities with power-law profiles

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

    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.

  1. Elastohydrodynamic analysis using a power law pressure-viscosity relation

    NASA Technical Reports Server (NTRS)

    Loewenthal, S. H.; Zaretsky, E. V.

    1973-01-01

    An isothermal elastohydrodynamic (EHD) inlet analysis of the Grubin type which considers a power law pressure-viscosity relation and a finite pressure at the inlet edge of the Hertzian contact zone was performed. Comparisons made with published X-ray EHD film thickness data for a synthetic paraffinic oil and when conventional EHD theory showed that the present theory exhibits a slightly stronger film thickness load dependence than do previous isothermal EHD theories but far less than that exhibited by the measured data.

  2. Inflation in the generalized inverse power law scenario

    SciTech Connect

    Lu, Zhun

    2013-11-01

    We propose a single field inflationary model by generalizing the inverse power law potential from the intermediate model. We study the implication of our model on the primordial anisotropy of cosmological microwave background radiation. Specifically, we apply the slow-roll approximation to calculate the scalar spectral tilt n{sub s} and the tensor-to-scalar ratio r. The results are compared with the recent data measured by the Planck satellite. We find that by choosing proper values for the parameters, our model can well describe the Planck data.

  3. Power-law photoluminescence decay in quantum dots

    SciTech Connect

    Král, Karel; Menšík, Miroslav

    2014-05-15

    Some quantum dot samples show a long-time (power-law) behavior of their luminescence intensity decay. This effect has been recently explained as being due to a cooperation of many tunneling channels transferring electrons from small quantum dots with triplet exciton to quantum dots at which the electrons can recombine with the holes in the valence band states. In this work we show that the long-time character of the sample luminescence decay can also be caused by an intrinsic property of a single dot, namely, by a non-adiabatic effect of the electron occupation up-conversion caused by the electron-phonon multiple scattering mechanism.

  4. Power laws, discontinuities and regional city size distributions

    USGS Publications Warehouse

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

    2008-01-01

    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.

  5. On string tunneling in power law inflationary universes

    NASA Astrophysics Data System (ADS)

    Larsen, A. L.; Axenides, Minos

    1993-11-01

    We consider the evolution of circular string loops in power law expanding universes represented by a spatially flat Friedman-Robertson-Walker metric with scale factor a(t) ~ tp, where t is the cosmic time and p >= 0. Our main result is the existence of a ``magic'' power pm = 3 + 2sqrt(2). In spacetimes with p < pm a circular string expands either forever or to a maximal radius and then contracts until it collapses into a point (black hole). For p >= pm, however, we find additional types of solutions. They include configurations which contract from a positive initial radius to a minimal one and then expand forever. Their existence we interpret as an indication for the presence of a finite potential barrier. Equivalently the new solutions signal string nucleation and tunneling, phenomena recently shown to occur in de Sitter space.

  6. Optimized dynamical decoupling for power-law noise spectra

    SciTech Connect

    Pasini, S.; Uhrig, G. S.

    2010-01-15

    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.

  7. Raft River 5MW power plant: A small binary power plant

    NASA Astrophysics Data System (ADS)

    Whitbeck, J. F.; Dibello, E. G.; Walrath, L. F.

    1982-06-01

    The Raft River 5MW power plant is a binary cycle pilot plant. The system uses isobutane in a dual boiling cycle. This cycle was selected because the well field and temperatures were not well known at the time of cycle selection, and therefore, a boiling cycle was desirable. The dual boiling features provides about 15 to 20% more power and makes the output less sensitive to changes in geothermal temperature changes than a single boiler system. The plant design was based upon a 290F geothermal fluid temperature at the inlet to the plant and has a gross nominal generator rating of 5MW; however, actual output will vary according to ambient wet bulb temperatures over a range from 4.4MW to 6.2MW with the actual plant inlet temperature of 278F being obtained. The plant is supplied by three production wells. Geothermal fluid boost pumps within the plant inlet provide the pressure necessary to overcome plant pressure drop and return the fluid to the two injection sites.

  8. An inverse method for rheometry of power-law fluids

    NASA Astrophysics Data System (ADS)

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

    2011-12-01

    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.

  9. Power Laws in Real Estate Prices during Bubble Periods

    NASA Astrophysics Data System (ADS)

    Ohnishi, Takaaki; Mizuno, Takayuki; Shimizu, Chihiro; Watanabe, Tsutomu

    How can we detect real estate bubbles? In this paper, we propose making use of information on the cross-sectional dispersion of real estate prices. During bubble periods, prices tend to go up considerably for some properties, but less so for others, so that price inequality across properties increases. In other words, a key characteristic of real estate bubbles is not the rapid price hike itself but a rise in price dispersion. Given this, the purpose of this paper is to examine whether developments in the dispersion in real estate prices can be used to detect bubbles in property markets as they arise, using data from Japan and the U.S. First, we show that the land price distribution in Tokyo had a power-law tail during the bubble period in the late 1980s, while it was very close to a lognormal before and after the bubble period. Second, in the U.S. data we find that the tail of the house price distribution tends to be heavier in those states which experienced a housing bubble. We also provide evidence suggesting that the power-law tail observed during bubble periods arises due to the lack of price arbitrage across regions.

  10. Beyond the power law: Uncovering stylized facts in interbank networks

    NASA Astrophysics Data System (ADS)

    Vandermarliere, Benjamin; Karas, Alexei; Ryckebusch, Jan; Schoors, Koen

    2015-06-01

    We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over August 1998-October 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio) and edge weights (loan size and counterparty exposure). We search for the theoretical distribution that fits the data best and report the "best" fit parameters. We observe that all studied distributions are heavy tailed. The fat tail typically contains 20% of the data and can be mostly described well by a truncated power law. Also the power law, stretched exponential and log-normal provide reasonably good fits to the tails of the data. In most cases, however, separating the bulk and tail parts of the data is hard, so we proceed to study the full range of the events. We find that the stretched exponential and the log-normal distributions fit the full range of the data best. These conclusions are robust to (1) whether we aggregate the data over a week, month, quarter or year; (2) whether we look at the "growth" versus "maturity" phases of interbank market development; and (3) with minor exceptions, whether we look at the "normal" versus "crisis" operation periods. In line with prior research, we find that the network topology changes greatly as the interbank market moves from a "normal" to a "crisis" operation period.

  11. Power Law Distributions of Patents as Indicators of Innovation

    PubMed Central

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

    2012-01-01

    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. PMID:23227144

  12. Power law statistics of force and acoustic emission from a slowly penetrated granular bed

    NASA Astrophysics Data System (ADS)

    Matsuyama, K.; Katsuragi, H.

    2014-01-01

    Penetration-resistant force and acoustic emission (AE) from a plunged granular bed are experimentally investigated through their power law distribution forms. An AE sensor is buried in a glass bead bed. Then, the bed is slowly penetrated by a solid sphere. During the penetration, the resistant force exerted on the sphere and the AE signal are measured. The resistant force shows power law relation to the penetration depth. The power law exponent is independent of the penetration speed, while it seems to depend on the container's size. For the AE signal, we find that the size distribution of AE events obeys power laws. The power law exponent depends on grain size. Using the energy scaling, the experimentally observed power law exponents are discussed and compared to the Gutenberg-Richter (GR) law.

  13. Implication of the power law cutoff evolution in XTE J1550-564

    NASA Astrophysics Data System (ADS)

    Titarchuk, Lev; Shaposhnikov, Nikolai

    We present spectral analysis of data collected using RXTE during two periods of X-ray activity in 1998 and 2000 from the Galactic X-ray black hole binary XTE J1550-564. We particularly concentrate on the behavior of the high energy cutoff of the power law part of the spectrum. The 1998 event was very powerful, showing a quick initial transition from low-hard state to very high state. The power law cutoff energy decreases from low-hard to intermediate states and increased again during transition to very high and high-soft states. For the 2000 outburst we also observe the decrease of the cutoff energy during the start of the state transition, similar to that in 1998 outburst, however the increase of the high energy cutoff (folding energy) is not apparent in this track because the source does not reach the real high-soft state in this event. We attribute this difference in the cutoff energy behavior to the different partial contributions of the thermal and non-thermal (bulk motion) Comptonization in photon upscattering. Namely, during the 1998 event higher accretion rate presumably provided more cooling to Comptonizing media and thus reducing the effectiveness of the thermal upscattering process. Under these conditions the bulk motion should take a leading role in boosting the input soft photons. This observational behavior of the cutoff energy presents an additional evidence of the existence of the converging bulk motion region near the central objects and provides further support for the previously reported index saturations effect as a black hole signature.

  14. Theoretical derivation of solute-solvent interaction parameter in binary solution: case of the deviation from Raoult's law.

    PubMed

    Liron, Z; Srebrenik, S; Martin, A; Cohen, S

    1986-05-01

    In a binary mixture, partial vapor pressure may show either a positive or negative deviation from the predicted value of an ideal solution. In this report we derive the deviation from Raoult's law from the heat of mixing, delta H mix, and the molal volume, V, of each of the components of a binary solution. This derivation is then tested for seven sets of combinations of two different solvents, taken at random from the literature. Each set consists of several different ratios of solute-solvent. The correlation between the reported experimental values of the partial vapor pressure of a given component, P1, and the theoretically derived values is excellent. The same derivation is further applied to calculate the solute-solvent interaction parameter, beta 12, independently from the geometric mean assumption of regular solution theory. In a number of cases, especially in hydrocarbon-alcohol mixtures, beta 12 proves to be significantly different from the calculated geometric mean square root beta 11 beta 22 or from the Walker interaction parameter term, K. PMID:3735084

  15. Raft River binary-cycle geothermal pilot power plant final report

    SciTech Connect

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

    1983-04-01

    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.

  16. Passive mechanical behavior of human neutrophils: power-law fluid.

    PubMed Central

    Tsai, M A; Frank, R S; Waugh, R E

    1993-01-01

    The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid. Images FIGURE 1 FIGURE 4 PMID:8298037

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

    PubMed

    Papitto, A; Ferrigno, C; Bozzo, E; Rea, N; Pavan, L; Burderi, L; Burgay, M; Campana, S; Di Salvo, T; Falanga, M; Filipović, 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

    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

  18. Binary Cycle Geothermal Demonstration Power Plant New Developments

    SciTech Connect

    Lacy, Robert G.; Jacobson, William O.

    1980-12-01

    San Diego Gas and Electric Company (SDG and E) has been associated with geothermal exploration and development in the Imperial Valley since 1971. SDG and E currently has interests in the four geothermal reservoirs shown. Major SDG and E activities have included drilling and flow testing geothermal exploration wells, feasibility and process flow studies, small-scale field testing of power processes and equipment, and pilot plant scale test facility design, construction and operation. Supporting activities have included geothermal leasing, acquisition of land and water rights, pursual of a major new transmission line to carry Imperial Valley geothermal and other sources of power to San Diego, and support of Magma Electric's 10 MW East Mesa Geothermal Power Plant.

  19. Molecular clouds have power-law probability distribution functions

    NASA Astrophysics Data System (ADS)

    Lombardi, Marco; Alves, João; Lada, Charles J.

    2015-04-01

    In this Letter we investigate the shape of the probability distribution of column densities (PDF) in molecular clouds. Through the use of low-noise, extinction-calibrated Herschel/Planck emission data for eight molecular clouds, we demonstrate that, contrary to common belief, the PDFs of molecular clouds are not described well by log-normal functions, but are instead power laws with exponents close to two and with breaks between AK ≃ 0.1 and 0.2 mag, so close to the CO self-shielding limit and not far from the transition between molecular and atomic gas. Additionally, we argue that the intrinsic functional form of the PDF cannot be securely determined below AK ≃ 0.1 mag, limiting our ability to investigate more complex models for the shape of the cloud PDF.

  20. Economic demography in fuzzy spatial dilemmas and power laws

    NASA Astrophysics Data System (ADS)

    Fort, H.; Pérez, N.

    2005-03-01

    Adaptive agents, playing the iterated Prisoner's Dilemma (IPD) in a two-dimensional spatial setting and governed by Pavlovian strategies ("higher success-higher chance to stay"), are used to approach the problem of cooperation between self-interested individuals from a novel angle: We investigate the effect of different possible measures of success (MS) used by players to asses their performance in the game. These MS involve quantities such as: the player's utilities U, his cumulative score (or "capital") W, his neighborhood "welfare", etc. To handle an imprecise concept like "success" the agents use fuzzy logic. The degree of cooperation, the "economic demography" and the "efficiency" attained by the system depend dramatically on the MS. Specifically, patterns of "segregation" or "exploitation" are observed for some MS. On the other hand, power laws, that may be interpreted as signatures of critical self-organization (SOC), constitute a common feature for all the MS.

  1. Power-law creep and residual stresses in carbopol microgels

    NASA Astrophysics Data System (ADS)

    Lidon, Pierre; Manneville, Sebastien

    We report on the interplay between creep and residual stresses in carbopol microgels. When a constant shear stress σ is applied below the yield stress σc, the strain is shown to increase as a power law of time, γ (t) =γ0 +(t / τ) α , with and exponent α ~= 0 . 38 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some characteristic value of about σc / 10 , the microgels experience a more complex creep behavior that we link to the existence of residual stresses and to weak aging of the system after preshear. The influence of the preshear protocol, of boundary conditions and of microgel concentration on residual stresses is investigated. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.

  2. Power-law weighted networks from local attachments

    NASA Astrophysics Data System (ADS)

    Moriano, P.; Finke, J.

    2012-07-01

    This letter introduces a mechanism for constructing, through a process of distributed decision-making, substrates for the study of collective dynamics on extended power-law weighted networks with both a desired scaling exponent and a fixed clustering coefficient. The analytical results show that the connectivity distribution converges to the scaling behavior often found in social and engineering systems. To illustrate the approach of the proposed framework we generate network substrates that resemble steady state properties of the empirical citation distributions of i) publications indexed by the Institute for Scientific Information from 1981 to 1997; ii) patents granted by the U.S. Patent and Trademark Office from 1975 to 1999; and iii) opinions written by the Supreme Court and the cases they cite from 1754 to 2002.

  3. Bubble coalescence in a power-law fluid

    NASA Astrophysics Data System (ADS)

    Kamat, Pritish; Thete, Sumeet; Basaran, Osman

    2015-11-01

    As two spherical gas bubbles in a liquid are slowly brought together, the liquid film or sheet between them drains and ultimately ruptures, forming a circular hole that connects them. The high curvature near the edge of the liquid sheet drives flow radially outward, causing the film to retract and the radius of the hole to increase with time. Recent experimental and theoretical work in this area has uncovered self-similarity and universal scaling regimes when two bubbles coalesce in a Newtonian fluid. Motivated by applications such as polymer and composites processing, food and drug manufacture, and aeration/deaeration systems where the liquids often exhibit deformation-rate thinning rheology, we extend the recent Newtonian studies to bubble coalescence in power-law fluids. In our work, we use a combination of thin-film theory and full 3D, axisymmetric computations to probe the dynamics in the aftermath of the singularity.

  4. Radiative corrections in the (varying power)-law modified gravity

    NASA Astrophysics Data System (ADS)

    Hammad, Fayçal

    2015-06-01

    Although the (varying power)-law modified gravity toy model has the attractive feature of unifying the early- and late-time expansions of the Universe, thanks to the peculiar dependence of the scalar field's potential on the scalar curvature, the model still suffers from the fine-tuning problem when used to explain the actually observed Hubble parameter. Indeed, a more correct estimate of the mass of the scalar field needed to comply with actual observations gives an unnaturally small value. On the other hand, for a massless scalar field the potential would have no minimum and hence the field would always remain massless. What solves these issues are the radiative corrections that modify the field's effective potential. These corrections raise the field's effective mass, rendering the model free from fine-tuning, immune against positive fifth-force tests, and better suited to tackle the dark matter sector.

  5. Solitary and shock waves in discrete double power law materials

    NASA Astrophysics Data System (ADS)

    Herbold, Eric; Nesterenko, Vitali

    2007-06-01

    A novel strongly nonlinear metamaterial is composed using a periodic arrangement of toroidal rings between plates. The toroids are considered massless strongly nonlinear springs where the force versus displacement relationship is described by two additive power-law relationships. In these systems the nonlinearity is due to the dramatic change of the contact plane, which starts as an arbitrarily thin circle then increases in thickness with increasing compression. Solitary and shock waves are examined numerically and experimentally using three different types of polymer or rubber o-rings allowing mitigation of higher amplitude shock impulses in comparison with granular systems. In these systems a train of pulses can consist of two separate groups related to two strongly nonlinear regimes with different values of exponents, depending on the amplitude. In experiments two types of shock waves (monotonic or oscillatory) were observed depending on the type of o-rings.

  6. Unexpected power-law stress relaxation of entangled ring polymers

    PubMed Central

    KAPNISTOS, M.; LANG, M.; PYCKHOUT-HINTZEN, W.; RICHTER, D.; CHO, D.; CHANG, T.

    2016-01-01

    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

  7. Power laws and extreme values in antibody repertoires

    NASA Astrophysics Data System (ADS)

    Boyer, Sebastien; Biswas, Dipanwita; Scaramozzino, Natale; Kumar, Ananda Soshee; Nizak, Clément; Rivoire, Olivier

    2015-03-01

    Evolution by natural selection involves the succession of three steps: mutations, selection and proliferation. We are interested in describing and characterizing the result of selection over a population of many variants. After selection, this population will be dominated by the few best variants, with highest propensity to be selected, or highest ``selectivity.'' We ask the following question: how is the selectivity of the best variants distributed in the population? Extreme value theory, which characterizes the extreme tail of probability distributions in terms of a few universality class, has been proposed to describe it. To test this proposition and identify the relevant universality class, we performed quantitative in vitro experimental selections of libraries of >105 antibodies using the technique of phage display. Data obtained by high-throughput sequencing allows us to fit the selectivity distribution over more than two decades. In most experiments, the results show a striking power law for the selectivity distribution of the top antibodies, consistent with extreme value theory.

  8. Deviations from uniform power law scaling in nonstationary time series

    NASA Technical Reports Server (NTRS)

    Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.

    1997-01-01

    A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.

  9. Power-Law Spectra of Incipient Gas-Curtain Turbulence

    SciTech Connect

    Vorobieff, P.; Vorobieff, P.; Rightley, P.M.; Benjamin, R.F.

    1998-09-01

    We investigate the evolution of a thin curtain of heavy gas (SF{sub 6} ) embedded in a lighter gas (air) and accelerated with a Machthinspthinsp1.2 planar shock wave. The Richtmyer-Meshkov instability leads to growth of the initial perturbations of the curtain and eventually to transition to turbulence. We visualize a time sequence of images of a section of the flow illuminated with a laser sheet. The SF{sub 6} is premixed with tracer (glycol fog), so the intensity of the light scattered off the curtain grows with the local density. As the curtain evolves towards a fully mixed state, real-space correlations of the density, inferred from scattered light intensity, show the emergence of a power-law behavior, indicative of transition to turbulence. {copyright} {ital 1998} {ital The American Physical Society }

  10. Liquid-metal binary cycles for stationary power

    NASA Technical Reports Server (NTRS)

    Gutstein, M.; Furman, E. R.; Kaplan, G. M.

    1975-01-01

    The use of topping cycles to increase electric power plant efficiency is discussed, with particular attention to mercury and alkali metal Rankine cycle systems that could be considered for topping cycle applications. An overview of this technology, possible system applications, the required development, and possible problem areas is presented.

  11. Power-Law Template for IR Point Source Clustering

    NASA Technical Reports Server (NTRS)

    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

    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.

  12. Power-Law Template for Infrared Point-Source Clustering

    NASA Technical Reports Server (NTRS)

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

    2012-01-01

    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 micron; 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) varies as l (sub -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, ?(sup Beta)B(?, 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.

  13. POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING

    SciTech Connect

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

    2012-06-20

    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.

  14. A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4

    SciTech Connect

    Chakrabarty, Deepto; Nowak, Michael A.; Tomsick, John A.; Boggs, Steven E.; Craig, William W.; Grefenstette, Brian W.; Fürst, Felix; Harrison, Fiona A.; Rana, Vikram; Psaltis, Dimitrios; Bachetti, Matteo; Barret, Didier; Christensen, Finn E.; Hailey, Charles J.; Kaspi, Victoria M.; Miller, Jon M.; Stern, Daniel; Wik, Daniel R.; Zhang, William W.; Wilms, Jörn

    2014-12-20

    The low-mass X-ray binary (LMXB) Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1×10{sup 33} D{sub kpc}{sup 2} erg s{sup –1}, with ≅60% in the thermal component. We clearly detect a cutoff of the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. We show that thermal Comptonization and synchrotron shock origins for the hard X-ray emission are ruled out on physical grounds. However, the hard X-ray spectrum is well fit by a thermal bremsstrahlung model with kT{sub e} = 18 keV, which can be understood as arising either in a hot layer above the neutron star atmosphere or in a radiatively inefficient accretion flow. The power-law cutoff energy may be set by the degree of Compton cooling of the bremsstrahlung electrons by thermal seed photons from the neutron star surface. Lower thermal luminosities should lead to higher (possibly undetectable) cutoff energies. We compare Cen X-4's behavior with PSR J1023+0038, IGR J18245–2452, and XSS J12270–4859, which have shown transitions between LMXB and radio pulsar modes at a similar X-ray luminosity.

  15. Evaluation of Hybrid Air-Cooled Flash/Binary Power Cycle

    SciTech Connect

    Greg Mines

    2005-10-01

    Geothermal binary power plants reject a significant portion of the heat removed from the geothermal fluid. Because of the relatively low temperature of the heat source (geothermal fluid), the performance of these plants is quite sensitive to the sink temperature to which heat is rejected. This is particularly true of air-cooled binary plants. Recent efforts by the geothermal industry have examined the potential to evaporatively cool the air entering the air-cooled condensers during the hotter portions of a summer day. While the work has shown the benefit of this concept, air-cooled binary plants are typically located in regions that lack an adequate supply of clean water for use in this evaporative cooling. In the work presented, this water issue is addressed by pre-flashing the geothermal fluid to produce a clean condensate that can be utilized during the hotter portions of the year to evaporatively cool the air. This study examines both the impact of this pre-flash on the performance of the binary plant, and the increase in power output due to the ability to incorporate an evaporative component to the heat rejection process.

  16. Power law in random multiplicative processes with spatio-temporal correlated multipliers

    NASA Astrophysics Data System (ADS)

    Morita, Satoru

    2016-02-01

    It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time correlation: the local environment and the global environment. In addition, we introduce two simple models through which we analytically and numerically show that the local and global environments yield different trends in the power-law exponent.

  17. Universal fractional noncubic power law for density of metallic glasses.

    PubMed

    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

    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

  18. Multi-scale evaporator architectures for geothermal binary power plants

    SciTech Connect

    Sabau, Adrian S; Nejad, Ali; Klett, James William; Bejan, Adrian

    2016-01-01

    In this paper, novel geometries of heat exchanger architectures are proposed for evaporators that are used in Organic Rankine Cycles. A multi-scale heat exchanger concept was developed by employing successive plenums at several length-scale levels. Flow passages contain features at both macro-scale and micro-scale, which are designed from Constructal Theory principles. Aside from pumping power and overall thermal resistance, several factors were considered in order to fully assess the performance of the new heat exchangers, such as weight of metal structures, surface area per unit volume, and total footprint. Component simulations based on laminar flow correlations for supercritical R134a were used to obtain performance indicators.

  19. 5 CFR 2423.31 - Powers and duties of the Administrative Law Judge at the hearing.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... Law Judge at the hearing. 2423.31 Section 2423.31 Administrative Personnel FEDERAL LABOR RELATIONS... LABOR PRACTICE PROCEEDINGS Hearing Procedures § 2423.31 Powers and duties of the Administrative Law Judge at the hearing. (a) Conduct of hearing. The Administrative Law Judge shall conduct the hearing...

  20. Importance of the specific heat anomaly in the design of binary Rankine cycle power plants

    SciTech Connect

    Pope, W.L.; Doyle, P.A.; Fulton, R.L.; Silvester, L.F.

    1980-05-01

    The transposed critical temperature (TPCT) is shown to be an extremely important thermodynamic property in the selection of working fluids and turbine states for geothermal power plants operating on a closed organic (binary) Rankine cycle. When the optimum working fluid composition and process states are determined for specified source and sink conditions, turbine inlet states consistently lie adjacent to the working fluids' TPCT line for all resource temperatures, constraints, and cost and efficiency factors investigated.

  1. Determination of tidal distortion in the eclipsing binary system V621 Cen by means of deviations from the third Kepler law

    NASA Astrophysics Data System (ADS)

    Iorio, Lorenzo

    2008-10-01

    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.

  2. Money, power, gas and the law: The `big` convergence

    SciTech Connect

    Hollis, S.S.

    1998-06-29

    Nothing ever endures but change, and in the ever whirling wheel of change that is the energy economy and its regulation, massive flux is under way. The key ingredients in this mix--the gas and electric industries, the financial instruments and entities that back them, and the laws and regulations that control and guide them--are in a confluence moving at warp speed. Assets are being divested or monetized. Financial products--not only reserves--are the answer to managing supply risks. Spark spreads--the financial differential between the price of gas as a commodity and gas that has been transformed into electrons--are being traded. Electric restructuring is being patterned on the template of the gas experience. Electronic bulletin boards and trading systems are linking the industries in cyberspace. And the consolidation of these industries has led to the biggest mating game in the energy industries` history, all at a fast-forward pace. Federal and state legislators and regulators swim in the same tank as the voracious entities this article discusses. Faced with unimagined combinations of players, complicated market power questions swirl around the merger and acquisition marriages. And, as the markets push ahead with new ideas, the regulators attempt to shape the process with their own proposals to influence the market of the next millennium. This article discusses some of the major moves and certain key regulatory decisions regarding these landscape-altering initiatives.

  3. Diffusion-limited aggregation with power-law pinning

    NASA Astrophysics Data System (ADS)

    Hentschel, H. G.; Popescu, M. N.; Family, F.

    2004-01-01

    Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth R-γN (where RN is the radius of the N-particle cluster). For γ>1 the growth pattern is in the same universality class as diffusion limited aggregation (DLA), while for γ<1 the resulting patterns have a lower fractal dimension D(γ) than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at γ=1/2, significantly smaller than might be expected from the lower bound αmin≃0.67 of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for D(γ) both close to the breakdown of DLA universality class, i.e., γ≲1, and close to the pinning transition, i.e., γ≳1/2.

  4. Diffusion Limited Aggregation with Power-Law Pinning

    NASA Astrophysics Data System (ADS)

    Hentschel, H. G. E.; Popescu, M. N.; Family, F.

    2004-03-01

    Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth R_N^-γ (where RN is the radius of the N- particle cluster and γ ≥ 1/2). For γ > 1 the growth pattern lies in the same universality class as diffusion limited aggregation (DLA), but for γ < 1 the resulting patterns have a lower effective fractal dimension D(γ) than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that all clusters become pinned for γ ≤ 1/2, significantly smaller than the lower bound α_max ≃ 0.6 of multifractal spectrum of DLA, indicating the appearance of line singularities in the growth pattern. Using multifractal analysis, analytic expressions are established for D(γ) for both growth close to the breakdown of the DLA universality class γ < ˜ 1 and close to the pinning transition γ > ˜ 1/2. We believe these studies give new insights into the development of multifractal singularities in Laplacian growth processes.

  5. Consistency relation in power law G-inflation

    SciTech Connect

    Unnikrishnan, Sanil; Shankaranarayanan, S. E-mail: shanki@iisertvm.ac.in

    2014-07-01

    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 ≤ −8n{sub T}, where r is the tensor-to-scalar-ratio and n{sub T} 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/|n{sub T}| 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 > −8n{sub T} or r ≤ −8n{sub T} depending on the model parameters. However, the subluminal propagation of speed of scalar field perturbations, as required by causality, restricts r ≤ −(32/3) n{sub T}.

  6. Reciprocity and the Emergence of Power Laws in Social Networks

    NASA Astrophysics Data System (ADS)

    Schnegg, Michael

    Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.

  7. Statistical tests for power-law cross-correlated processes

    NASA Astrophysics Data System (ADS)

    Podobnik, Boris; Jiang, Zhi-Qiang; Zhou, Wei-Xing; Stanley, H. Eugene

    2011-12-01

    For stationary time series, the cross-covariance and the cross-correlation as functions of time lag n serve to quantify the similarity of two time series. The latter measure is also used to assess whether the cross-correlations are statistically significant. For nonstationary time series, the analogous measures are detrended cross-correlations analysis (DCCA) and the recently proposed detrended cross-correlation coefficient, ρDCCA(T,n), where T is the total length of the time series and n the window size. For ρDCCA(T,n), we numerically calculated the Cauchy inequality -1≤ρDCCA(T,n)≤1. Here we derive -1≤ρDCCA(T,n)≤1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ρDCCA within which the cross-correlations become statistically significant. For overlapping windows we numerically determine—and for nonoverlapping windows we derive—that the standard deviation of ρDCCA(T,n) tends with increasing T to 1/T. Using ρDCCA(T,n) we show that the Chinese financial market's tendency to follow the U.S. market is extremely weak. We also propose an additional statistical test that can be used to quantify the existence of cross-correlations between two power-law correlated time series.

  8. Common origin of power-law tails in income distributions and relativistic gases

    NASA Astrophysics Data System (ADS)

    Modanese, G.

    2016-01-01

    Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms ("saving propensity") which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the macroscopic distribution for the income or respectively for the energy.

  9. Scale Invariance in Landscape Evolution Models Using Stream Power Laws

    NASA Astrophysics Data System (ADS)

    Kwang, J. S.; Parker, G.

    2014-12-01

    Landscape evolution models (LEM) commonly utilize stream power laws to simulate river incision with formulations such as E = KAmSn, where E is a vertical incision rate [L/T], K is an erodibility constant [L1-2m/T], A is an upstream drainage area [L2], S is a local channel gradient [-], and m and n are positive exponents that describe the basin hydrology. In our reduced complexity model, the landscape approached equilibrium by balancing an incision rate with a constant, uniform, vertical rock uplift rate at every location in the landscape. From our simulations, for a combination of m and n, the landscape exhibited scale invariance. That is, regardless of the size and scale of the basin, the relief and vertical structure of the landscape remained constant. Therefore, the relief and elevation profile of the landscape at equilibrium were only dependent on the coefficients for erodibility and uplift and an equation that described how upstream area, A, increased as the length of a stream increased. In our analytical 1D models, we utilized two equations that described upslope area, (a) A = Bl, where B is the profile width [L], and l is the stream length from the ridge [L] and (b) A = Clh, Hack's Law, where C is a constant [L2-h] and h is a positive exponent. With these equations, (a) m = n and (b) hm = n resulted in scale invariance. In our numerical 2D models, the relationship between A and l was inherent in the actual structure of the drainage network. From our numerical 2D results, scale invariance occurred when 2m = n. Additionally, using reasonable values from the literature for exponents, n, m and h, resulted in singularities at the ridges in the landscape, which caused truncation error. In consequence, the elevation of the ridge increased as the number of grid cells in the domain increased in the numerical model, and the model was unable to converge. These singularities at the ridges appeared when (a) m ≥ n and (b) hm ≥ n in the analytical model and 2m ≥ n in the numerical model. Here we present (1) 1D analytical solutions and (2) 2D numerical solutions that demonstrate scale invariance in LEMs and (3) the consequences of the singularity in 2D LEM numerical simulations. These results will help provide insight about the structure and dynamics of landscapes and drainage networks and shed light on geomorphological empirical relationships.

  10. Numerical tools for obtaining power-law representations of heavy-tailed datasets

    NASA Astrophysics Data System (ADS)

    Mansfield, Marc L.

    2016-01-01

    Many empirical datasets have highly skewed, non-Gaussian, heavy-tailed distributions, dominated by a relatively small number of data points at the high end of the distribution. Consistent with their role as stable distributions, power laws have frequently been proposed to model such datasets. However there are physical situations that require distributions with finite means. Such situations may call for power laws with high-end cutoffs. Here, I present a maximum-likelihood technique for determining an optimal cut-off power law to represent a given dataset. I also develop a new statistical test of the quality of fit. Results are demonstrated for a number of benchmark datasets. Non-power-law datasets can frequently be represented by power laws, but this is a trivial result unless the dataset spans a broad domain. Nevertheless, I demonstrate that there are non-power-law distributions, including broad log-normal distributions, whose tails can be fit to power laws over many orders of magnitude. Therefore, caution is called for whenever power laws are invoked to represent empirical data. Supplementary material in the form of one pdf file available from the Journal web page at: http://dx.doi.org/10.1140/epjb/e2015-60452-3

  11. Power-law tail probabilities of drainage areas in river basins

    USGS Publications Warehouse

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

    2003-01-01

    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.

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

    NASA Astrophysics Data System (ADS)

    Brzezinski, Michal

    2014-07-01

    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.

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

    NASA Astrophysics Data System (ADS)

    Todorova, Lora; Vogt, Bodo

    2011-11-01

    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.

  14. Power-law and exponential rank distributions: A panoramic Gibbsian perspective

    SciTech Connect

    Eliazar, Iddo

    2015-04-15

    Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.

  15. Focusing effect of radially power-law channel on an intense laser beam

    NASA Astrophysics Data System (ADS)

    Tang, Rong-An; Hong, Xue-Ren; Gao, Ji-Ming; Xue, Ju-Kui

    2016-03-01

    To study the focusing effect of the power-law channel, the evolution equation of the laser spot size is derived for the laser propagation in a radially power-law channel by using variational method. It is found that there exists a small critical region of the ratio of the initial laser spot size to the channel radius. Below the critical region, the laser power for constant spot size varies dramatically with the increase of the power-law exponent of the channel and so do other focusing behaviors. Quite opposite behaviors are observed above the critical region.

  16. Power-law modeling based on least-squares minimization criteria.

    PubMed

    Hernández-Bermejo, B; Fairén, V; Sorribas, A

    1999-10-01

    The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system. PMID:10546442

  17. Analytical Derivation of Power Laws in Firm Size Variables from Gibrat's Law and Quasi-inversion Symmetry: A Geomorphological Approach

    NASA Astrophysics Data System (ADS)

    Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu

    2014-03-01

    We start from Gibrat’s law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.

  18. Power-law solution for anisotropic universe in f( G) gravity

    NASA Astrophysics Data System (ADS)

    Fayaz, V.; Hossienkhani, H.; Aghamohammadi, A.

    2015-06-01

    We try to study the theory of modified Gauss-Bonnet gravity in non-isotope universe. It is considered the exact power-law solution in modified gravity models. A f( G) function corresponding with power law solutions for given scale factor are calculated. We show that BI-like power-law solutions only exist for a very special class of f( G) theories. It is shown that transition to phantom phase is happened by applied some bound on free parameters. We also explore the stability issue of modified gravitational models.

  19. Anisotropic power-law solutions for a supersymmetry Dirac-Born-Infeld theory

    NASA Astrophysics Data System (ADS)

    Do, Tuan Q.; Kao, W. F.

    2016-04-01

    A new set of Bianchi type I power-law expanding solutions is obtained for a supersymmetric Dirac-Born-Infeld (SDBI) theory coupled to a gauge field. Stability analysis is also performed to show that this set of power-law expanding solutions is stable. In particular, this set of power-law solutions provides an explicit example to the role played by the supersymmetry correction term. We also show by a general approach that any stable anisotropic solution of SDBI model will turn unstable when a phantom field is introduced. We also show that the result of the scalar perturbation indicates that the SDBI model is a realistic model.

  20. Two universal physical principles shape the power-law statistics of real-world networks

    PubMed Central

    Lorimer, Tom; Gomez, Florian; Stoop, Ruedi

    2015-01-01

    The study of complex networks has pursued an understanding of macroscopic behaviour by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex network generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations. PMID:26202858

  1. Two universal physical principles shape the power-law statistics of real-world networks.

    PubMed

    Lorimer, Tom; Gomez, Florian; Stoop, Ruedi

    2015-01-01

    The study of complex networks has pursued an understanding of macroscopic behaviour by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex network generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations. PMID:26202858

  2. Power-law versus exponential relaxation of 29Si nucleus spins in Si:B crystals

    NASA Astrophysics Data System (ADS)

    Koplak, O. V.; Talantsev, A. D.; Morgunov, R. B.

    2016-02-01

    The Si:B micro-crystals enriched with 29Si isotope have been studied by high resolution nuclear magnetic resonance (NMR) in the 300-800 K temperature range. The recovery of nuclear magnetization saturated by radiofrequency impulses follows pure power-law kinetics at 300 K, while admixture of exponential relaxation takes place at 500 K. The power-law relaxation corresponds to direct electron-nuclear relaxation due to the inhomogeneous distribution of paramagnetic centers, while exponential kinetics corresponds to the nuclear spin diffusion mechanism. The inhomogeneous distribution of deformation defects is a most probable reason of the power-law kinetics of nuclear spin relaxation.

  3. On the origin of power-law X-ray spectra of active galactic nuclei

    NASA Technical Reports Server (NTRS)

    Schlosman, I.; Shaham, J.; Shaviv, G.

    1984-01-01

    In the present analytical model for a power law X-ray continuum production in active galactic nuclei, the dissipation of turbulent energy flux above the accretion disk forms an optically thin transition layer with an inverted temperature gradient. The emitted thermal radiation has a power law spectrum in the 0.1-100 keV range, with a photon energy spectral index gamma of about 0.4-1.0. Thermal X-ray contribution from the layer is 5-10 percent of the total disk luminosity. The gamma value of 0.75 is suggested as a 'natural' power law index for Seyfert galaxies and QSOs.

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

    NASA Technical Reports Server (NTRS)

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

    2006-01-01

    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.

  5. Power-law and intermediate inflationary models in f( T)-gravity

    NASA Astrophysics Data System (ADS)

    Rezazadeh, K.; Abdolmaleki, A.; Karami, K.

    2016-01-01

    We study inflation in the framework of f( T)-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in f( T)-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law f( T) function and investigate the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, the power-law and intermediate inflationary models in f( T)-gravity can be compatible with the observational results of Planck 2015 at 68% CL. We find that in our f( T) setting, the potentials responsible for the both power-law and intermediate inflationary models have the power-law form V( ϕ) ∝ ϕ m but the power m is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of f( T)-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, is that the self-interacting quartic potential V( ϕ) ∝ ϕ 4 which has special reheating properties, can be consistent with the Planck 2015 data in our f( T) scenario while it is ruled out in the standard inflationary scenario.

  6. Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection

    PubMed Central

    Adler, Miri; Mayo, Avi; Alon, Uri

    2014-01-01

    Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling. PMID:25121598

  7. Logarithmic and power law input-output relations in sensory systems with fold-change detection.

    PubMed

    Adler, Miri; Mayo, Avi; Alon, Uri

    2014-08-01

    Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling. PMID:25121598

  8. Analytical time-domain Green’s functions for power-law media

    PubMed Central

    Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

    2008-01-01

    Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

  9. Theoretical implications of wide binary observations

    SciTech Connect

    Wasserman, I.; Weinberg, M.D.

    1987-01-01

    The theoretical implications of the recent Latham, et al. (1984) data on wide binaries are examined. Using a technique for comparing wide binary observations with theoretical semimajor axis distributions, it is concluded that power-law models for the underlying distribution are consistent with observations, implying no sharp cutoffs in the semimajor axis distribution. Repeating the analysis for simple evolutionary models, it is found that the available data do not yet significantly limit the mass of dark matter particles. The detection of six wide binaries by Latham et al. (1984) would require an uncomfortably large local density of wide binaries (semimajor axes of at least about 0.001 pc) for a broad range of theoretical models. The data suggest that wide binaries are predominantly made of F5-K5 stars and that a major fraction of all F5-K5 stars are in wide binaries. 16 references.

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

    NASA Astrophysics Data System (ADS)

    Pisarenko, V.; Sornette, D.

    2006-07-01

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2007-11-01

    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.

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

    PubMed

    Gong, Tao; Shuai, Lan

    2014-01-01

    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 λ 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

  13. Explanation of power law behavior of autoregressive conditional duration processes based on the random multiplicative process.

    PubMed

    Sato, Aki-Hiro

    2004-04-01

    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

  14. Explanation of power law behavior of autoregressive conditional duration processes based on the random multiplicative process

    NASA Astrophysics Data System (ADS)

    Sato, Aki-Hiro

    2004-04-01

    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.

  15. Power-law Relationship in Describing Temporal and Spatial Precipitation Pattern in Turkey

    NASA Astrophysics Data System (ADS)

    Kadiğlu, M.; Şen, Z.

    Wet and dry spell properties of monthly rainfall series at five meteorology stations in Turkey are examined by plotting successive wet and dry month duration versus their number of occurrences on the double-logarithmic paper. Straight line relationships on such graphs show that power-laws govern the pattern of successive persistent wet and dry monthly spells. Functional power law relationships between the number of dry and wet spells for a given monthly period are derived from the available monthly precipitation data. The probability statements for wet and dry period spells are obtained from the power law expressions. Comparison of power-law behaviours at five distinct sites in Turkey provides useful interpretation about the temporal and spatial rainfall pattern. As in temperate areas such as Turkey the rainfall amounts change mostly due to one-month-long dry or wet spells.

  16. The power law for the perception of rotation by airline pilots.

    NASA Technical Reports Server (NTRS)

    Clark, B.; Stewart, J. D.

    1972-01-01

    The purpose of this study was to determine the power laws for the perception of rotation about the three major body axes. Eighteen airline pilots made magnitude estimates of 5-sec pulses of nine angular accelerations having a range of acceleration x time of 10-150 deg/sec. The results showed that (1) the power law with an exponent of 1.4 describes the subjective motion of these pilots for all three major body axes, (2) the power law also describes the perception of motion for individual pilots with a substantial range of exponents, (3) there were significant correlations among the exponents for the three body axes, and (4) the data suggest that the power law over the wide range used may be more complex than implied by a formula with a single exponent.

  17. Tunable power law in the desynchronization events of coupled chaotic electronic circuits

    SciTech Connect

    Oliveira, Gilson F. de Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de

    2014-03-15

    We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.

  18. Power-law behavior in electron transport through a quantum dot with Luttinger liquid leads

    NASA Astrophysics Data System (ADS)

    Yang, Kai-Hua; He, Xian; Wang, Huai-Yu; Liu, Kai-Di; Liu, Bei-Yun

    2014-08-01

    The electron transport of a system consisting of a Kondo dot and two Luttinger liquid (LL) leads is theoretically studied by use of nonequilibrium Green function approach. In the Kondo regime, the zero bias anomaly appears and the density of states of the dot obeys a power-law scaling at positive energy part with an exponent ?/2 = 1/ g - 1, where g reflects the electron interaction in the LL leads. The differential conductance shows a power-law scaling both in bias voltage and in temperature, with the exponent being ?. The power-law temperature dependence of the peak conductance is observed in different temperature regimes. These features are ascribed to the LL correlation in the leads. Our work describes both the zero bias anomaly and power-law scalings within one theoretical frame.

  19. Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model

    PubMed Central

    Teka, Wondimu; Stockton, David; Santamaria, Fidel

    2016-01-01

    We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron. PMID:26937967

  20. Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.

    PubMed

    Teka, Wondimu; Stockton, David; Santamaria, Fidel

    2016-03-01

    We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron. PMID:26937967

  1. On the Nature of the Variability Power Decay towards Soft Spectral States in X-Ray Binaries. Case Study in Cyg X-1

    NASA Technical Reports Server (NTRS)

    Titarchuk, Lev; Shaposhinikov, Nikolai

    2007-01-01

    A characteristic feature of the Fourier Power Density Spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broad band-limited noise, characterized by a constant below some frequency (a "break" frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time to is related to the phenomenological break frequency, while the PDS power-law slope above the "break" is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black hole and neutron star) during an evolution of theses sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power P(sub x), decreases approximately as a square root of the characteristic frequency of the driving oscillations v(sub dr). The RXTE observations of Cyg X-1 allow us to infer P(sub dr), and t(sub o) as a function of v(sub dr). We also apply the basic parameters of observed PDSs, power-law index and low frequency quasiperiodic oscillations. to infer Reynolds (Re) number from the observations using the method developed in our previous paper. Our analysis shows that Re-number increases from values about 10 in low/hard state to that about 70 during the high/soft state. Subject headings: accretion, accretion disks-black hole physics-stars:individual (Cyg X-1) :radiation mechanisms: nonthermal-physical data and processes

  2. Theories of Power, Poverty, and Law: In Commemoration of the Contributions of Peter Bachrach--Power, Law, and Final Thoughts: The Contributions of Peter Bachrach

    ERIC Educational Resources Information Center

    Schneider, Elizabeth M.

    2010-01-01

    I am pleased to be part of this symposium to celebrate the life and work of Peter Bachrach. Although my focus is the relevance of Peter's ideas of power to law, I want to begin with some personal comments as well as raise some final thoughts, drawing on others' contributions. Like so many of Peter's other students, I adored him. Peter's joy in…

  3. An exact thermodynamical model of power-law temperature time scaling

    NASA Astrophysics Data System (ADS)

    Zingales, Massimiliano

    2016-02-01

    In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t) ∝tβ with β ∈ R shows a different evolution of the temperature time rate T ˙ (t) with respect to the temperature time-dependence T(t) . Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the thermal energy flux as soon as the distance increases. In this paper this idea has been exploited showing that such thermodynamical system is represented by an heterogeneous one-dimensional distributed mass one with power-law spatial scaling of its physical properties. The model yields, exactly a power-law evolution (decay) of the temperature field in terms of a real exponent as T ∝tβ (or T ∝t-β) that is related to the power-law spatial scaling of the thermodynamical property of the system. The obtained relation yields a physical ground to the formulation of fractional-order generalization of the Fourier diffusion equation.

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

    PubMed

    Schure, Mark R; Davis, Joe M

    2011-12-30

    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 β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) 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

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

    SciTech Connect

    Jiulin, Du

    2013-09-15

    Transport coefficients in Lorentz plasma with the power-law κ-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 κ-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the κ-parameter, and in the limit of the parameter κ→∞ they are reduced to the standard forms for a Maxwellian distribution.

  6. Statistical interpretation of transient current power-law decay in colloidal quantum dot arrays

    NASA Astrophysics Data System (ADS)

    Sibatov, R. T.

    2011-08-01

    A new statistical model of the charge transport in colloidal quantum dot arrays is proposed. It takes into account Coulomb blockade forbidding multiple occupancy of nanocrystals and the influence of energetic disorder of interdot space. The model explains power-law current transients and the presence of the memory effect. The fractional differential analogue of the Ohm law is found phenomenologically for nanocrystal arrays. The model combines ideas that were considered as conflicting by other authors: the Scher-Montroll idea about the power-law distribution of waiting times in localized states for disordered semiconductors is applied taking into account Coulomb blockade; Novikov's condition about the asymptotic power-law distribution of time intervals between successful current pulses in conduction channels is fulfilled; and the carrier injection blocking predicted by Ginger and Greenham (2000 J. Appl. Phys. 87 1361) takes place.

  7. Gravity darkening in binary stars

    NASA Astrophysics Data System (ADS)

    Espinosa Lara, F.; Rieutord, M.

    2012-11-01

    Context. Interpretation of light curves of many types of binary stars requires the inclusion of the (cor)relation between surface brightness and local effective gravity. Until recently, this correlation has always been modeled by a power law relating the flux or the effective temperature and the effective gravity, namely Teff ∝ geffβ . Aims: We look for a simple model that can describe the variations of the flux at the surface of stars belonging to a binary system. Methods: This model assumes that the energy flux is a divergence-free vector anti-parallel to the effective gravity. The effective gravity is computed from the Roche model. Results: After explaining in a simple manner the old result of Lucy (1967, Z. Astrophys., 65, 89), which says that β ~ 0.08 for solar type stars, we first argue that one-dimensional models should no longer be used to evaluate gravity darkening laws. We compute the correlation between log Teff and log geff using a new approach that is valid for synchronous, weakly magnetized, weakly irradiated binaries. We show that this correlation is approximately linear, validating the use of a power law relation between effective temperature and effective gravity as a first approximation. We further show that the exponent β of this power law is a slowly varying function, which we tabulate, of the mass ratio of the binary star and the Roche lobe filling factor of the stars of the system. The exponent β remains mostly in the interval [0.20,0.25] if extreme mass ratios are eliminated. Conclusions: For binary stars that are synchronous, weakly magnetized and weakly irradiated, the gravity darkening exponent is well constrained and may be removed from the free parameters of the models.

  8. ELECTROMAGNETIC TRANSIENTS POWERED BY NUCLEAR DECAY IN THE TIDAL TAILS OF COALESCING COMPACT BINARIES

    SciTech Connect

    Roberts, L. F.; Ramirez-Ruiz, E.; Kasen, D.; Lee, W. H.

    2011-07-20

    We investigate the possibility that long tidal tails formed during compact object mergers may produce optical transients powered by the decay of freshly synthesized r-process material. Precise modeling of the merger dynamics allows for a realistic determination of the thermodynamic conditions in the ejected debris. We combine hydrodynamic and full nuclear network calculations to determine the resultant r-process abundances and the heating of the material by their decays. The subsequent homologous structure is mapped into a radiative transfer code to synthesize emergent model light curves and determine how their properties (variability and color evolution) depend on the mass ratio and orientation of the merging binary. The radiation emanating from the ejected debris, though less spectacular than a typical supernova, should be observable in transient surveys and we estimate the associated detection rates. We find that it is unlikely that photometry alone will be able to distinguish between different binary mass ratios and the nature of the compact objects, emphasizing the need for spectroscopic follow-up of these events. The case for (or against) compact object mergers as the progenitors of short gamma-ray bursts can be tested if such electromagnetic transients are detected (or not) in coincidence with some bursts, although they may be obscured by on-axis afterglows.

  9. Interim Report: Air-Cooled Condensers for Next Generation Geothermal Power Plants Improved Binary Cycle Performance

    SciTech Connect

    Daniel S. Wendt; Greg L. Mines

    2010-09-01

    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

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

    PubMed

    Tinker, Jesse; Velazquez, Jose Luis Perez

    2014-01-01

    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. PMID:24822039

  11. Non-Cubic Power-law Scaling of Density in Metallic Glasses (Invited)

    NASA Astrophysics Data System (ADS)

    Zeng, Q. C.; Kono, Y.; Lin, Y.; Zeng, Z.; Wang, J.; Sinogeikin, S. V.; Park, C.; Meng, Y.; Yang, W.; Mao, W. L.

    2013-12-01

    Understanding structure-property relationships and dimensionality plays a central role in materials science. A cubic power law relationship between the average interatomic distance and the global density is commonly expected in 'disordered' glasses and has been extensively employed in various measurements. However, this relationship has never been rigorously verified which challenges our understanding of glass materials. Here, by using high pressure as a tuning tool, we rigorously demonstrated that the density of metallic glass (MG) varies with the 2.5 power of its fundamental atomic-level length scale (the inverse of the principal diffraction peak position, 1/q1). This falls between the 3-dimensional density and 1-dimensional length instead of the expected cubic power-law relationship. We further demonstrated the 2.5 power-law is universally valid for MGs of different compositions, as well as the same MG at different pressures. This study includes high quality data from multiple techniques which provides compelling evidence of the non-cubic power-law scaling in MGs. It has important implications not only in the practical measurements of density, or any measurement involving a change in length scale under various environments by correcting the extensively employed cubic power-law, but also in understanding the real atomic packing in glasses by providing a critical new constraint on a structure-property relationship.

  12. Power, Resistance, and Emotional Economies in Women's Relationships with Mothers-in-Law in Chinese Immigrant Families

    ERIC Educational Resources Information Center

    Shih, Kristy Y.; Pyke, Karen

    2010-01-01

    This interview study interrogates how cultural values of filial piety inform Chinese American daughters-in-law's understanding of their relationship and power dynamics with immigrant Chinese American mothers-in-law. Ideals of filial respect accord limited authority to mothers-in-law, who engage other mechanisms of power, such as their domestic…

  13. A more powerful exact test of noninferiority from binary matched-pairs data.

    PubMed

    Lloyd, Chris J; Moldovan, Max V

    2008-08-15

    Assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design. This paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives. There are two new elements presented in this paper. First, we introduce the likelihood ratio statistic as an alternative to the previously proposed score statistic of Nam (Biometrics 1997; 53:1422-1430). Second, we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of Berger and Boos (Am. Stat. Assoc. 1994; 89:1012-1016) or traditional full maximization. Based on an extensive numerical study, we recommend tests based on the score statistic, the nuisance parameter being controlled by estimation followed by maximization. PMID:18314932

  14. Failure analysis report: Heat exchanger tubes geothermal binary power plant, Magma Electric Company, East Mesa, California

    SciTech Connect

    Anliker, Dennis M.; Ellis, Peter F. II

    1982-05-01

    Radian received twelve sections of heat exchanger tubing from the Magma Electric Company's 10MW(e) East Mesa binary geothermal power plant. Three tube sections were received from each of four shell and tube heat exchangers (HX1, Hx6, HX8, and Hx10) of the isobutane vaporizer train. All samples were taken from the upper few rows of tubes. Two months later, four more tube sections were received. These four sections were taken from the lower rows of heat exchangers 1, 6 (two sections), and 10. Radian was requested to investigate the cause of severe pitting failure of these heat exchanger tubes. This report is part of a continuing DOE effort to gain insight into the service life of component materials employed in geothermal energy utilization.

  15. Modified power law equations for vertical wind profiles. [in investigation of windpower plant siting

    NASA Technical Reports Server (NTRS)

    Spera, D. A.; Richards, T. R.

    1979-01-01

    In an investigation of windpower plant siting, equations are presented and evaluated for a wind profile model which incorporates both roughness and wind speed effects, while retaining the basic simplicity of the Hellman power law. These equations recognize the statistical nature of wind profiles and are compatible with existing analytical models and recent wind profile data. Predictions of energy output based on the proposed profile equations are 10% to 20% higher than those made with the 1/7 power law. In addition, correlation between calculated and observed blade loads is significantly better at higher wind speeds when the proposed wind profile model is used than when a constant power model is used.

  16. Interception efficiency in flow of power-law fluids past confined porous bodies

    NASA Astrophysics Data System (ADS)

    Shahsavari, Setareh; McKinley, Gareth

    2014-11-01

    Understanding the flow of power-law fluids through porous media is important for a wide range of filtration and sedimentation processes. In this study, the mobility of power-law fluids through porous media is investigated numerically and we use parametric studies to systematically understand the individual roles of geometrical characteristics, rheological properties as well as flow conditions. In addition, an analytical solution is presented that can be used as a modified Darcy law for generalized Newtonian fluids. Building on this modified Darcy law, the incompressible laminar flow of power-law and Carreau fluids past a confined porous body is modeled numerically. From the simulations we calculate the flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector. Finally, the interception efficiency of power-law fluids are compared with the case of a Newtonian fluid. The focus of this work is principally for flow of inelastic fluids in fibrous media; however, the methodology can also be extended to other porous media.

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

    PubMed

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

    2010-01-01

    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(τ) ~ τ(⁻β) with β 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

  18. Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

    NASA Astrophysics Data System (ADS)

    Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.

    The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.

  19. Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

    PubMed Central

    Lagrue, Clément; Poulin, Robert; Cohen, Joel E.

    2015-01-01

    How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor’s law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution. PMID:25550506

  20. Implications of the Power Law Cutoff Evolution in XTE J1550-564 to the Comptonization Regimes

    NASA Astrophysics Data System (ADS)

    Shaposhnikov, Nikolai; Titarchuk, L.

    2010-05-01

    We present spectral analysis of data collected using RXTE during two periods of X-ray activity in 1998 and 2000 from the Galactic X-ray black hole binary XTE J1550-564. We particularly concentrate on the behavior of the high energy cutoff (folding energy) of the power law part of the spectrum. The 1998 event was very powerful, showing a quick initial transition from low-hard state to very high state. The power law cutoff energy decreased from low-hard to intermediate states and increased again during transition to very high and high-soft states. For the 2000 outburst we also observe the decrease of the cutoff energy during the start of the state transition, similar to that in 1998 outburst, however the increase of the high energy cutoff is not apparent in this track because the source does not reach the real high-soft state in this event. We attribute this difference in the cutoff energy behavior to the different partial contributions of the thermal and non-thermal (bulk motion) Comptonization in photon upscattering. Namely, during the 1998 event higher accretion rate presumably provided more cooling to the Comptonizing media and thus reducing the effectiveness of the thermal upscattering process. Under these conditions the bulk motion should take a leading role in boosting the input soft photons. This observational behavior of the cutoff energy presents an additional evidence of the existence of the converging bulk motion region near the central objects and provides further support for the previously reported index saturations effect as a black hole signature.

  1. Prediction of radio frequency power generation of Neptune's magnetosphere from generalized radiometric Bode's law

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

    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.

  2. Spreading of completely wetting, non-Newtonian fluids with non-power-law rheology.

    PubMed

    Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong; Su, Ay

    2010-08-01

    Spreading non-Newtonian liquids with non-power-law rheology on completely wetting surfaces are seldom investigated. This study assessed the wetting behavior of polydimethylsiloxane (PDMS), a Newtonian fluid, two carboxymethylcellulose (CMC) sodium solutions, a PDMS+2%w/w silica nanoparticle suspension and three polyethylene glycol (PEG400)+5-10%w/w silica nanoparticle suspensions (non-power-law fluids) on a mica surface. The theta(D)-U and R-t data for spreading drops of the six tested, non-power-law fluids can be described by power-law wetting models. We propose that this behavior is attributable to a uniform shear rate (a few tens to a few hundreds of s(-1)) distributed over the thin-film regime that controls spreading dynamics. Estimated film thickness was below the resolution of an optical microscope for direct observation. Approximating a general non-Newtonian fluid spreading as a power-law fluid greatly simplifies theoretical analysis and data interpretation. PMID:20447644

  3. Power law distributions of wildfires across Europe: benchmarking a land surface model with observed data

    NASA Astrophysics Data System (ADS)

    Di Mauro, B.; Fava, F.; Frattini, P.; Camia, A.; Colombo, R.; Migliavacca, M.

    2015-11-01

    Monthly wildfire burned area frequency is here modeled with a power law distribution and scaling exponent across different European biomes are estimated. Data sets, spanning from 2000 to 2009, comprehend the inventory of monthly burned areas from the European Forest Fire Information System (EFFIS) and simulated monthly burned areas from a recent parameterization of a Land Surface Model (LSM), that is the Community Land Model (CLM). Power law exponents are estimated with a Maximum Likelihood Estimation (MLE) for different European biomes. The characteristic fire size (CFS), i.e. the area that most contributes to the total burned area, was also calculated both from EFFIS and CLM data set. We used the power law fitting and the CFS analysis to benchmark CLM model against the EFFIS observational wildfires data set available for Europe. Results for the EFFIS data showed that power law fittings holds for 2-3 orders of magnitude in the Boreal and Continental ecoregions, whereas the distribution of the Alpine, Atlantic are fitted only in the upper tail. Power law instead is not a suitable model for fitting CLM simulations. CLM benchmarking analysis showed that the model strongly overestimates burned areas and fails in reproducing size-frequency distribution of observed EFFIS wildfires. This benchmarking analysis showed that some refinements in CLM structure (in particular regarding the anthropogenic influence) are needed for predicting future wildfires scenarios, since the low spatial resolution of the model and differences in relative frequency of small and large fires can affect the reliability of the predictions.

  4. Constraints on the tensor-to-scalar ratio for non-power-law models

    SciTech Connect

    Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M.P. E-mail: mb435@mrao.cam.ac.uk E-mail: mph@mrao.cam.ac.uk

    2013-08-01

    Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby and Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: r{sub LD} = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

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

    NASA Astrophysics Data System (ADS)

    Fenner, Trevor; Levene, Mark; Loizou, George

    2010-06-01

    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.

  6. Constraints on the tensor-to-scalar ratio for non-power-law models

    NASA Astrophysics Data System (ADS)

    Vázquez, J. Alberto; Bridges, M.; Ma, Yin-Zhe; Hobson, M. P.

    2013-08-01

    Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: rLD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

  7. Double Power Laws in the Event-integrated Solar Energetic Particle Spectrum

    NASA Astrophysics Data System (ADS)

    Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K.

    2016-04-01

    A double power law or a power law with exponential rollover at a few to tens of MeV nucleon-1 of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochastic approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon-1 is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.

  8. Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

    NASA Astrophysics Data System (ADS)

    Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor

    2015-12-01

    The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.

  9. Stochastic Mixing Model with Power Law Decay of Variance

    NASA Technical Reports Server (NTRS)

    Fedotov, S.; Ihme, M.; Pitsch, H.

    2003-01-01

    Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.

  10. Power-law ansatz in complex systems: Excessive loss of information.

    PubMed

    Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming

    2015-12-01

    The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring. PMID:26764792

  11. Power-law ansatz in complex systems: Excessive loss of information

    NASA Astrophysics Data System (ADS)

    Tsai, Sun-Ting; Chang, Chin-De; Chang, Ching-Hao; Tsai, Meng-Xue; Hsu, Nan-Jung; Hong, Tzay-Ming

    2015-12-01

    The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring.

  12. Phase diagram of power law and Lennard-Jones systems: crystal phases.

    PubMed

    Travesset, Alex

    2014-10-28

    An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed. PMID:25362319

  13. Comprehensive Solution for Ultrathin Oxide Reliability Projections Including Novel Explanation for Power-Law Exponent Variations

    NASA Astrophysics Data System (ADS)

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

    2006-01-01

    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/β), 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 β 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.

  14. Pascal (Yang Hui) triangles and power laws in the logistic map

    NASA Astrophysics Data System (ADS)

    Velarde, Carlos; Robledo, Alberto

    2015-04-01

    We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic-band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.

  15. Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction

    NASA Astrophysics Data System (ADS)

    Hayat, Tasawar; Rashid, Madiha; Imtiaz, Maria; Alsaedi, Ahmed

    2015-11-01

    This paper deals with the boundary layer flow of nanofluid over power-law stretched surface. Analysis has been carried out in the presence of applied magnetic field and chemical reaction. Heat and mass transfer characteristics are studied using heat and mass convective conditions. The governing partial differential equations are transferred to the nonlinear ordinary differential equations. Convergent series solutions are obtained for fluid velocity, temperature and concentrations fields. Influences of pertinent parameters including Hartman number, thermal and concentration Biot numbers and chemical reaction parameters are discussed on the velocity, temperature and concentration profiles. Graphical result are presented and discussed. Computations for local Nusselt and Sherwood numbers are carried out. It is observed that the heat transfer rate is enhanced by increasing power-law index, thermal Biot number and chemical reaction parameter while mass transfer rate increases for power-law index and chemical reaction parameter.

  16. Phase diagram of power law and Lennard-Jones systems: Crystal phases

    SciTech Connect

    Travesset, Alex

    2014-10-28

    An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.

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

    NASA Technical Reports Server (NTRS)

    Zdziarski, A. A.

    1985-01-01

    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.

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

    PubMed Central

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

    2012-01-01

    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. PMID:22496595

  19. Tornado outbreak variability follows Taylor's power law of fluctuation scaling and increases dramatically with severity

    NASA Astrophysics Data System (ADS)

    Tippett, Michael K.; Cohen, Joel E.

    2016-02-01

    Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from `outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related.

  20. Power law distribution of the duration and magnitude of recessions in capitalist economies: breakdown of scaling

    NASA Astrophysics Data System (ADS)

    Ormerod, Paul; Mounfield, Craig

    2001-04-01

    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.

  1. Thermodynamics of Ideal Bose Gas Under Generic Power Law Potential in d-dimensions

    NASA Astrophysics Data System (ADS)

    Faruk, M. M.

    Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.

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

    NASA Astrophysics Data System (ADS)

    Mitsoulis, E.; Zisis, Th.

    2014-05-01

    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.

  3. Power-law defect energy in a single-crystal gradient plasticity framework: a computational study

    NASA Astrophysics Data System (ADS)

    Bayerschen, E.; Böhlke, T.

    2016-03-01

    A single-crystal gradient plasticity model is presented that includes a power-law type defect energy depending on the gradient of an equivalent plastic strain. Numerical regularization for the case of vanishing gradients is employed in the finite element discretization of the theory. Three exemplary choices of the defect energy exponent are compared in finite element simulations of elastic-plastic tricrystals under tensile loading. The influence of the power-law exponent is discussed related to the distribution of gradients and in regard to size effects. In addition, an analytical solution is presented for the single slip case supporting the numerical results. The influence of the power-law exponent is contrasted to the influence of the normalization constant.

  4. Generating Discrete Power-Law Distributions from a Death- Multiple Immigration Population Process

    NASA Astrophysics Data System (ADS)

    Matthews, J. O.; Jakeman, E.; Hopcraft, K. I.

    2003-04-01

    We consider the evolution of a simple population process governed by deaths and multiple immigrations that arrive with rates particular to their order. For a particular choice of rates, the equilibrium solution has a discrete power-law form. The model is a generalization of a process investigated previously where immigrants arrived in pairs [1]. The general properties of this model are discussed in a companion paper. The population is initiated with precisely M individuals present and evolves to an equilibrium distribution with a power-law tail. However the power-law tails of the equilibrium distribution are established immediately, so that moments and correlation properties of the population are undefined for any non-zero time. The technique we develop to characterize this process utilizes external monitoring that counts the emigrants leaving the population in specified time intervals. This counting distribution also possesses a power-law tail for all sampling times and the resulting time series exhibits two features worthy of note, a large variation in the strength of the signal, reflecting the power-law PDF; and secondly, intermittency of the emissions. We show that counting with a detector of finite dynamic range regularizes naturally the fluctuations, in effect `clipping' the events. All previously undefined characteristics such as the mean, autocorrelation and probabilities to the first event and time between events are well defined and derived. These properties, although obtained by discarding much data, nevertheless possess embedded power-law regimes that characterize the population in a way that is analogous to box averaging determination of fractal-dimension.

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

    NASA Astrophysics Data System (ADS)

    Kashi, Amit; Soker, Noam; Moskovitz, Nitsan

    2013-12-01

    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.

  6. Stability of natural convection of power-law fluid and non-Darcy flow in porous media

    NASA Astrophysics Data System (ADS)

    Kong, Xiangyan; Chen, Guoquan; Wu, Jianbing; Li, Peichao; Lu, Detang; Xu, Xianzhi

    2001-03-01

    In the present work the effect of the power law exponent of power-law fluid and non-Darcy number of non-Darcy flow on stability of natural convection in porous media are studied. The computation analysis of effect of power-law exponent of power-law fluid and non-Darcy number of non-Darcy flow in the rectangular duct on the transition Rayleigh number Ra*, which means the convective model transiting from stationary state to periodic solution. The duct has filled a porous medium saturated with the power-law non-Newtonian fluid or Newtonian fluid for non-Darcy flow, in which there is uniform internal heat generation per unit volume q. In this paper the relationship between the transition Rayleigh number Ra* and the power-law exponent n, Ra* and non-Darcy number Be, are shown. To these two aspects, the transition route from steady to chaotic convection is also obtained.

  7. Perimeter-area power-law relationship of pores in sedimentary rocks and implications for permeability

    SciTech Connect

    Schlueter, E.M.; Zimmerman, R.W.; Cook, N.G.W.; Witherspoon, P.A.

    1994-12-31

    Perimeter-area power-law relationships of pores in five sedimentary rocks are determined from scanning electron photomicrographs of thin sections. These relationships for the pores of four sandstones were found to lie between 1.43 and 1.49, while that of an Indiana limestone was found to be 1.67. The authors discuss how the perimeter-area power-law relationship of pores, along with a pore-size distribution, can be used to estimate the hydraulic permeability.

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

    NASA Astrophysics Data System (ADS)

    Song, Qiwu; Huang, Guangli; Tan, Baolin

    2012-05-01

    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.

  9. The Extent of Power-law Energy Spectra in Collisionless Relativistic Magnetic Reconnection in Pair Plasmas

    NASA Astrophysics Data System (ADS)

    Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; Nalewajko, K.; Begelman, M. C.

    2016-01-01

    Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron-positron plasmas, for a wide range of upstream magnetizations σ and system sizes L. The particle spectra are well-represented by a power law {γ }-α , with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. For large L and σ, the power-law index α approaches about 1.2.

  10. One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase

    SciTech Connect

    Dalmonte, M.; Pupillo, G.; Zoller, P.

    2010-10-01

    We study one-dimensional fermionic and bosonic gases with repulsive power-law interactions 1/|x|{sup {beta}}, with {beta}>1, in the framework of Tomonaga-Luttinger liquid (TLL) theory. We obtain an accurate analytical expression linking the TLL parameter to the microscopic Hamiltonian, for arbitrary {beta} and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the TLL unstable towards the formation of a cascade of lattice solids with fractional filling, a 'Luttinger staircase'. Several of these quantum phases and phase transitions are realized with ground state polar molecules and weakly bound magnetic Feshbach molecules.

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

    SciTech Connect

    Paul, B. C.; Beesham, A.

    2006-11-03

    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.

  12. The equivalence of isothermal and non-isothermal power law distributions with temperature duality

    NASA Astrophysics Data System (ADS)

    Zheng, Yahui; Du, Jiulin

    2015-06-01

    The concept of temperature duality states that the physical temperature and Lagrange temperature both have physical sense in the nonextensive system. By use of this concept, the isothermal power law distribution and the non-isothermal power law distribution are equivalent to each other when the detailed balance is satisfied. Also, the polytropic equation in stellar system and self-gravitating gaseous system can be deduced from both of these two distributions. This indicates that the polytropic system exhibits some 'equilibrium' configuration which, in the stellar system, is probably the result of so called 'violent relaxation'.

  13. Effect of Body Perturbations on Hypersonic Flow Over Slender Power Law Bodies

    NASA Technical Reports Server (NTRS)

    Mirels, Harold; Thornton, Philip R.

    1959-01-01

    Hypersonic-slender-body theory, in the limit as the free-stream Mach number becomes infinite, is used to find the effect of slightly perturbing the surface of slender two-dimensional and axisymmetric power law bodies, The body perturbations are assumed to have a power law variation (with streamwise distance downstream of the nose of the body). Numerical results are presented for (1) the effect of boundary-layer development on two dimensional and axisymmetric bodies, (2) the effect of very small angles of attack (on tow[dimensional bodies), and (3) the effect of blunting the nose of very slender wedges and cones.

  14. Numerical Simulations of Power Law Heating Functions for Quiescent Loops: Stability and Observables

    NASA Astrophysics Data System (ADS)

    Martens, P. C.; Winter, H. D.; Munetsi-Mugomba, K.

    2007-12-01

    We present the numerical simulations of quiescent coronal loops with heating functions that are power law functions of pressure and temperature. These simulations are made using a time-dependent, 1D hydrodynamics code with heating functions that are treated as dynamic variables which are constantly re- evaluated during the loops' lifetimes. These numerical simulations provide a stability test for the analytical solutions formulated by Martens (2007, submitted) for the same heating functions. TRACE and XRT datasets are simulated to determine if present observables can provide adequate information to discriminate between power law heating functions.

  15. Power law distribution of the frequency of demises of US firms

    NASA Astrophysics Data System (ADS)

    Cook, William; Ormerod, Paul

    2003-06-01

    Both theoretical and applied economics have a great deal to say about many aspects of the firm, but the literature on the extinctions, or demises, of firms is very sparse. We use a publicly available data base covering some 6 million firms in the US and show that the underlying statistical distribution which characterises the frequency of firm demises-the disappearances of firms as autonomous entities-is closely approximated by a power law. The exponent of the power law is, intriguingly, close to that reported in the literature on the extinction of biological species.

  16. Power-law behavior in a cascade process with stopping events: a solvable model.

    PubMed

    Yamamoto, Ken; Yamazaki, Yoshihiro

    2012-01-01

    The present paper proposes a stochastic model to be solved analytically, and a power-law-like distribution is derived. This model is formulated based on a cascade fracture with the additional effect that each fragment at each stage of a cascade ceases fracture with a certain probability. When the probability is constant, the exponent of the power-law cumulative distribution lies between -1 and 0, depending not only on the probability but the distribution of fracture points. Whereas, when the probability depends on the size of a fragment, the exponent is less than -1, irrespective of the distribution of fracture points. The applicability of our model is also discussed. PMID:22400550

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

    PubMed

    Kendal, Wayne S; Jørgensen, Bent

    2011-12-01

    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

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

    NASA Astrophysics Data System (ADS)

    Kendal, Wayne S.; Jørgensen, Bent

    2011-12-01

    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.

  19. Power law and log law velocity distributions in the wall bounded turbulent flows on transitional rough walls: New approach to universal scaling

    NASA Astrophysics Data System (ADS)

    Afzal, Noor

    2006-11-01

    An alternate two layers theory, based on four new scalings for transitional wall roughness variables, is presented for large appropriate roughness Reynolds numbers. For velocity profile the matching of inner and outer layers in the overlap region, by Izakson-Millikan-Kolmogorov hypothesis (Afzal, N. 2005 Proc. Royal Society A: PME 461, 1889-1910) leads to functional solutions that are universal log laws, as well as universal power laws, that explicitly independent of transitional wall roughness, having same constants as in smooth wall case. The universal log or power laws velocity profile and skin friction, if expressed in terms of traditional Reynolds numbers also yield log law and power laws that depend on surface roughness. The skin friction, in traditional variables, is predicted by a single relation for inflectional type of Nikuradse roughness for sand grain type roughness data and Colebrook commercial monotonic roughness. The extensive experimental data for various types of wall transitional roughness provide very good support to present theory of universal log laws as well as new predictions in traditional log laws . The experimental data from various sources (Osaka and Mochizuki, Kameda et al, Antonia and Krogstad, Smalley et al, Schultz and Flack and Leonardi et al for boundary layers and Nikuradse, Shockling and Bakken for pipes/Channels) provide strong support to the new scaling for log and power laws. Moody type diagram for inflectional roughness for boundary layer and pipe flows are presented.

  20. From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature

    NASA Astrophysics Data System (ADS)

    Reed, William J.; Hughes, Barry D.

    2002-12-01

    We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes of incomes, cities, internet files, biological taxa, and in gene family and protein family frequencies.

  1. Inverse free steering law for small satellite attitude control and power tracking with VSCMGs

    NASA Astrophysics Data System (ADS)

    Malik, M. S. I.; Asghar, Sajjad

    2014-01-01

    Recent developments in integrated power and attitude control systems (IPACSs) for small satellite, has opened a new dimension to more complex and demanding space missions. This paper presents a new inverse free steering approach for integrated power and attitude control systems using variable-speed single gimbal control moment gyroscope. The proposed inverse free steering law computes the VSCMG steering commands (gimbal rates and wheel accelerations) such that error signal (difference in command and output) in feedback loop is driven to zero. H? norm optimization approach is employed to synthesize the static matrix elements of steering law for a static state of VSCMG. Later these matrix elements are suitably made dynamic in order for the adaptation. In order to improve the performance of proposed steering law while passing through a singular state of CMG cluster (no torque output), the matrix element of steering law is suitably modified. Therefore, this steering law is capable of escaping internal singularities and using the full momentum capacity of CMG cluster. Finally, two numerical examples for a satellite in a low earth orbit are simulated to test the proposed steering law.

  2. Geomorphological and hydrological implications of a given hydraulic geometry relationship, beyond the power-law

    NASA Astrophysics Data System (ADS)

    Kim, JongChun; Paik, Kyungrock

    2015-04-01

    Channel geometry and hydraulic characteristics of a given river network, i.e., spatio-temporal variability of width, depth, and velocity, can be described as power functional relationships of flow discharge, named 'hydraulic geometry' (Leopold and Maddock, 1953). Many studies have focused on the implication of this power-law itself, i.e., self-similarity, and accordingly its exponents. Coefficients of the power functional relationships, on the contrary, have received little attention. They are often regarded as empirical constants, determined by 'best fitting' to the power-law without significant scientific implications. Here, we investigate and claim that power-law coefficients of hydraulic geometry relationships carry vital information of a given river system. We approach the given problem on the basis of 'basin hydraulic geometry' formulation (Stall and Fok, 1968) which decomposes power-law coefficients into more elementary constants. The linkage between classical power-law relationship (Leopold and Maddock, 1953) and the basin hydraulic geometry is provided by Paik and Kumar (2004). On the basis of this earlier study, it can be shown that coefficients and exponents of power-law hydraulic geometry are interrelated. In this sense, we argue that more elementary constants that constitute both exponents and coefficients carry important messages. In this presentation, we will demonstrate how these elementary constants vary over a wide range of catchments provided from Stall and Fok (1968) and Stall and Yang (1970). Findings of this study can provide new insights on fundamental understanding about hydraulic geometry relationships. Further, we expect that this understanding can help interpretation of hydraulic geometry relationship in the context of flood propagation through a river system as well. Keywords: Hydraulic geometry; Power-law; River network References Leopold, L. B., & Maddock, T. J. (1953). The hydraulic geometry of stream channels and some physiographic implications. U. S. Geological Survey Professional Paper, 252. Paik, K., & Kumar, P. (2004). Hydraulic geometry and the nonlinearity of the network instantaneous response, Water Resource Research, 40, W03602. Stall, J. B., & Fok, Y. S. (1968). Hydraulic geometry of Illinois streams. University of Illinois Water Resources Center Research Report, 15. Stall, J. B., & Yang, C. T. (1970). Hydraulic geometry of 12 selected stream systems of the United States. University of Illinois Water Resources Center Research Report, 32.

  3. Boiling Temperature vs. Composition. An Almost-Exact Explicit Equation for a Binary Mixture Following Raoult's Law.

    ERIC Educational Resources Information Center

    Cardinali, Mario Emilio; Giomini, Claudio

    1989-01-01

    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)

  4. Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media

    NASA Astrophysics Data System (ADS)

    Tan, Xiao-Hua; Li, Xiao-Ping; Zhang, Lie-Hui; Liu, Jian-Yi; Cai, Jianchao

    2015-09-01

    A transient flow model for power-law fluid in fractal porous media is derived by combining transient flow theory with the fractal properties of tortuous capillaries. Pressure changes of transient flow for power-law fluid in fractal porous media are related to pore fractal dimension, tortuosity fractal dimension and the power-law index. Additionally, the starting pressure gradient model of power-law fluid in fractal porous media is established. Good agreement between the predictions of the present model and that of the traditional empirical model is obtained, the sensitive parameters that influence the starting pressure gradient are specified and their effects on the starting pressure gradient are discussed.

  5. Thermodynamic laws, economic methods and the productive power of energy

    NASA Astrophysics Data System (ADS)

    Kümmel, Reiner; Ayres, Robert U.; Lindenberger, Dietmar

    2010-07-01

    Energy plays only a minor role in orthodox theories of economic growth, because standard economic equilibrium conditions say that the output elasticity of a production factor, which measures the factor's productive power, is equal to the factor's share in total factor cost. Having commanded only a tiny cost share of about 5 percent so far, energy is often neglected altogether. On the other hand, energy conversion in the machines of the capital stock has been the basis of industrial growth. How can the physically obvious economic importance of energy be reconciled with the conditions for economic equilibrium, which result from the maximization of profit or overall welfare? We show that these equilibrium conditions no longer yield the equality of cost shares and output elasticities, if the optimization calculus takes technological constraints on the combinations of capital, labor, and energy into account. New econometric analyses of economic growth in Germany, Japan, and the USA yield output elasticities that are for energy much larger and for labor much smaller than their cost shares. Social consequences are discussed.

  6. Power loss in open cavity diodes and a modified Child-Langmuir law

    SciTech Connect

    Biswas, Debabrata; Kumar, Raghwendra; Puri, R.R.

    2005-09-15

    Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.

  7. AC losses in superconductors with a power-law constitutive relation

    NASA Astrophysics Data System (ADS)

    Agassi, Y. D.

    2015-10-01

    The observed constitutive relation between the electrical field and current density in cuprates high temperature superconductors is a power-law of the current. This functional dependence is presumably related to the giant flux-creep domain. It is shown that this constitutive relation reflects the statistical spread of the pinning potential associated with creep motion of vortex bundles. The AC losses emanating from a power-law constitutive relation are calculated in an approach focused on the superconductor's electric field. For a slab geometry in the presence of a parallel AC magnetic field or transport current, the calculated AC-loss scaling laws are consistent with BSCCO data and the critical state model. Extensions of the approach are briefly discussed.

  8. Study on power law along meridian line for progressive addition lenses

    NASA Astrophysics Data System (ADS)

    Wu, Quanying; Qian, Lin; Yu, Jingchi; Chen, Hao; Wang, Yuanyuan

    2008-12-01

    The surface curvature of the progressive addition lenses varies gradually from the distance-viewing area to the near-viewing area. The curvature of the principal meridional curve varies progressively from point to point to provide a predetermined dioptric focal power at each point according to a predetermined power law. Several kinds of power laws along meridian line including linear combination and polynomials, are illustrated. The details for determining the coefficient and order of the polynomial are also introduced. Based on different power laws along meridian lines, the results of the computer evaluation are given out. Progressive addition lenses corresponding to different forms of meridional power laws have been manufactured with Satisloh VFT-compact machine. The lenses manufactured have been measured using the Class Plus lens analyzer to provide sphere, cylinder, and axis values across the surface of the lens, and distortion distributions are also presented. The results of measurement indicate that the performances of progressive addition lenses are consistent with those of the computer evaluation. These results are shown that the lenses have more wide distance-viewing or near-viewing areas and short corridor but with higher level of astigmatism in the peripheral areas while the curvature along the median line is constant in the distance zone and the rate of meridional dioptric variation is quicker, on the contrary, the lenses have more narrow distance-viewing or near-viewing areas and long corridor. The comparison and analysis prove that determining the power law along the meridian line is an important task in designs for progressive addition lenses.

  9. 5 CFR 2423.24 - Powers and duties of the Administrative Law Judge during prehearing proceedings.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 5 Administrative Personnel 3 2012-01-01 2012-01-01 false Powers and duties of the Administrative Law Judge during prehearing proceedings. 2423.24 Section 2423.24 Administrative Personnel FEDERAL LABOR RELATIONS AUTHORITY, GENERAL COUNSEL OF THE FEDERAL LABOR RELATIONS AUTHORITY AND FEDERAL SERVICE IMPASSES PANEL FEDERAL LABOR RELATIONS...

  10. 22 CFR 1423.19 - Duties and powers of the Administrative Law Judge.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... 22 Foreign Relations 2 2012-04-01 2009-04-01 true Duties and powers of the Administrative Law Judge. 1423.19 Section 1423.19 Foreign Relations FOREIGN SERVICE LABOR RELATIONS BOARD; FEDERAL LABOR RELATIONS AUTHORITY; GENERAL COUNSEL OF THE FEDERAL LABOR RELATIONS AUTHORITY; AND THE FOREIGN SERVICE IMPASSE DISPUTES PANEL FOREIGN SERVICE...

  11. 24 CFR 1720.140 - Administrative law judge, powers and duties.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Administrative law judge, powers and duties. 1720.140 Section 1720.140 Housing and Urban Development Regulations Relating to Housing and Urban Development (Continued) OFFICE OF ASSISTANT SECRETARY FOR HOUSING-FEDERAL...

  12. 24 CFR 26.32 - Powers and duties of the Administrative Law Judge (ALJ).

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Powers and duties of the Administrative Law Judge (ALJ). 26.32 Section 26.32 Housing and Urban Development Office of the Secretary, Department of Housing and Urban Development HEARING PROCEDURES Hearings Pursuant to the...

  13. A theory of power-law distributions in financial market fluctuations.

    PubMed

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

    2003-05-15

    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 trades. Surprisingly, the exponents that characterize these power laws are similar for different types and sizes of markets, for different market trends and even for different countries--suggesting that a generic theoretical basis may underlie these phenomena. Here we propose a model, based on a plausible set of assumptions, which provides an explanation for these empirical power laws. Our model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants. Starting from an empirical characterization of the size distribution of those large market participants (mutual funds), we show that the power laws observed in financial data arise when the trading behaviour is performed in an optimal way. Our model additionally explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades. PMID:12748636

  14. Imaging viscoelastic properties of live cells by AFM: power-law rheology on the nanoscale.

    PubMed

    Hecht, Fabian M; Rheinlaender, Johannes; Schierbaum, Nicolas; Goldmann, Wolfgang H; Fabry, Ben; Schäffer, Tilman E

    2015-06-21

    We developed force clamp force mapping (FCFM), an atomic force microscopy (AFM) technique for measuring the viscoelastic creep behavior of live cells with sub-micrometer spatial resolution. FCFM combines force-distance curves with an added force clamp phase during tip-sample contact. From the creep behavior measured during the force clamp phase, quantitative viscoelastic sample properties are extracted. We validate FCFM on soft polyacrylamide gels. We find that the creep behavior of living cells conforms to a power-law material model. By recording short (50-60 ms) force clamp measurements in rapid succession, we generate, for the first time, two-dimensional maps of power-law exponent and modulus scaling parameter. Although these maps reveal large spatial variations of both parameters across the cell surface, we obtain robust mean values from the several hundreds of measurements performed on each cell. Measurements on mouse embryonic fibroblasts show that the mean power-law exponents and the mean modulus scaling parameters differ greatly among individual cells, but both parameters are highly correlated: stiffer cells consistently show a smaller power-law exponent. This correlation allows us to distinguish between wild-type cells and cells that lack vinculin, a dominant protein of the focal adhesion complex, even though the mean values of viscoelastic properties between wildtype and knockout cells did not differ significantly. Therefore, FCFM spatially resolves viscoelastic sample properties and can uncover subtle mechanical signatures of proteins in living cells. PMID:25891371

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

    ERIC Educational Resources Information Center

    Bauer, Ben

    2009-01-01

    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…

  16. Fingering instability in the flow of a power-law fluid on a rotating disc

    NASA Astrophysics Data System (ADS)

    Arora, Akash; Doshi, Pankaj

    2016-01-01

    A computational study of the flow of a non-Newtonian power law fluid on a spinning disc is considered here. The main goal of this work is to examine the effect of non-Newtonian nature of the fluid on the flow development and associated contact line instability. The governing mass and momentum balance equations are simplified using the lubrication theory. The resulting model equation is a fourth order non-linear PDE which describes the spatial and temporal evolutions of film thickness. The movement of the contact line is modeled using a constant angle slip model. To solve this moving boundary problem, a numerical method is developed using a Galerkin/finite element method based approach. The numerical results show that the spreading rate of the fluid strongly depends on power law exponent n. It increases with the increase in the shear thinning character of the fluid (n < 1) and decreases with the increase in shear thickening nature of the fluid (n > 1). It is also observed that the capillary ridge becomes sharper with the value of n. In order to examine the stability of these ridges, a linear stability theory is also developed for these power law fluids. The dispersion relationship depicting the growth rate for a given wave number has been reported and compared for different power-law fluids. It is found that the growth rate of the instability decreases as the fluid becomes more shear thinning in nature, whereas it increases for more shear thickening fluids.

  17. 30 CFR 44.22 - Administrative law judges; powers and duties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Administrative law judges; powers and duties. 44.22 Section 44.22 Mineral Resources MINE SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR FILING AND OTHER ADMINISTRATIVE REQUIREMENTS RULES OF PRACTICE FOR PETITIONS FOR MODIFICATION OF MANDATORY SAFETY STANDARDS Hearings §...

  18. 29 CFR 1955.12 - Administrative law judge; powers and duties.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 29 Labor 9 2010-07-01 2010-07-01 false Administrative law judge; powers and duties. 1955.12 Section 1955.12 Labor Regulations Relating to Labor (Continued) OCCUPATIONAL SAFETY AND HEALTH ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) PROCEDURES FOR WITHDRAWAL OF APPROVAL OF STATE PLANS Notice of Formal Proceeding § 1955.12 Administrative...

  19. 5 CFR 2423.24 - Powers and duties of the Administrative Law Judge during prehearing proceedings.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 5 Administrative Personnel 3 2010-01-01 2010-01-01 false Powers and duties of the Administrative Law Judge during prehearing proceedings. 2423.24 Section 2423.24 Administrative Personnel FEDERAL LABOR RELATIONS AUTHORITY, GENERAL COUNSEL OF THE FEDERAL LABOR RELATIONS AUTHORITY AND FEDERAL SERVICE IMPASSES PANEL FEDERAL LABOR RELATIONS...

  20. Gas-Solid Transition of Quantum Particles Interacting with Inverse-Power-Law Repulsive Potential

    NASA Astrophysics Data System (ADS)

    Yamashita, Kohei; Kwon, Yongkyung; Koike, Yukio; Hirashima, Dai S.

    2014-04-01

    We study the gas-solid phase diagram of quantum particles interacting with the inverse-power-law repulsive interaction. It is found that the solid phase is promoted by the quantum effect in the intermediate region where the quantum effect is not yet dominant but is nonnegligible. We further find that a weak minimum in the coexistence pressure curve appears at low temperatures.

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

    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.

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

    PubMed

    Freed, Andrew M; Bürgmann, Roland

    2004-07-29

    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

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

    NASA Astrophysics Data System (ADS)

    Karlický, M.

    2014-01-01

    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 ωpe is much higher than the electron-cyclotron frequency ωce, the Fourier power spectra are interpreted to be those of the electron plasma density in zebra radio sources.

  4. The inverse system method applied to the derivation of power system nonlinear control laws

    NASA Astrophysics Data System (ADS)

    Li, Donghai; Jiang, Xuezhi; Li, Liqin; Xie, Maoging; Guo, Jingrong

    1997-05-01

    The differential geometric method has been applied to a series of power system nonlinear control problems effectively. However a set of differential equations must be solved for obtaining the required diffeomorphic transformation. Therefore the derivation of control laws is very complicated. In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly, so it is unnecessary to solve a set of differential equations. In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems. Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation, so control laws can be obtained easily and the application to engineering is very convenient. Authors of this paper take steam valving control of power system as a typical case to be studied. It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method. The conclusion will simplify the control law derivations of steam valving, excitation, converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.

  5. Deposition from evaporating drops: Power laws and new morphologies in coffee stains

    NASA Astrophysics Data System (ADS)

    Freed-Brown, Julian E.

    We investigate the structure of stains formed through evaporative deposition in sessile drops. Commonly, the deposited stain has a high surface density near the three phase contact line of the drying drop and much less solute in the bulk of the drop. This is known as the ``coffee ring effect'' and primarily arises due to contact line pinning. While many features of the stain depend on subtle physical phenomena within the drop, the coffee ring effect stands out as a robust feature that persists in many varied experimental realizations. In 2009, Witten predicted another robust feature of deposited stains: an asymptotic regime where a robust power law governs the fadeout profile of the stain into the interior of the drop. This power law is only controlled by geometric properties at a single point and the power does not vary along the contact line. We investigate the approach to this power law using numerical methods. For many evaporation profiles (including common experimental ones) the numerics show good agreement with the power law prediction. However, we demonstrate an intuitive scheme to construct evaporation profiles that subvert the power law prediction. We find that, in general, the approach to the power law cannot be known without full knowledge of the evaporation and height profile. We also extend this work in another way. We apply the basic arguments of the coffee ring effect to the case where the drop has a receding contact line. Here, we develop a new theoretical framework for deposition that has not previously been studied. In this context, the surface density profile can be directly calculated. Unlike a pinned contact line, receding contact lines push fluid into the interior of the drop. This effect can be overcome by strong evaporation near the contact line, but in general the intuition from contact line pinning is reversed. Following Witten's example, we find that the surface density of the stain near the center of the drop goes as eta ∝ rnu, where nu is a geometric property determined by the evaporation and height at the stagnation point. We demonstrate analytic and numeric calculations within this new framework and find novel stain morphologies that resemble recent experiments.

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

    NASA Astrophysics Data System (ADS)

    Ord, A.; Hobbs, B. E.

    2011-12-01

    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.

  7. Superdiffusive transport and the power law distribution of pitch angle scattering times in solar wind turbulence

    NASA Astrophysics Data System (ADS)

    Zimbardo, G.; Perri, S.

    2012-12-01

    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., = 2Da*tα with α > 1 for superdiffusion, as well as on the shock compression ratio.

  8. Second-order small-disturbance solutions for hypersonic flow over power-law bodies

    NASA Technical Reports Server (NTRS)

    Townsend, J. C.

    1975-01-01

    Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.

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

    PubMed

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

    2012-04-01

    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

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

    SciTech Connect

    Yu Wenfei; Zhang Wenda

    2013-06-20

    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.

  11. Evaluation of the Impact of Off-Design Operation on an Air-Cooled Binary Power Plant

    SciTech Connect

    Mines, Gregory Lee

    2002-09-01

    Geothermal power plants are designed and constructed to provide a rated power output at specific resource and ambient conditions. Due to both diurnal and seasonal changes in the ambient air temperature, as well as a decline in resource productivity over time, plants seldom operate at these "design" conditions. This paper examines the impact of "off- design" operation of an air-cooled binary geothermal power plant. An available energy analysis is used to evaluate operation at these conditions. This evaluation identifies those portions of the power cycle that are most sensitive to changing resource and ambient conditions, as well as where improvements in cycle component or system performance would have the largest impact in increasing power output.

  12. Evaluation of the Impact of Off-Design Operation on an Air-Cooled Binary Power Plant

    SciTech Connect

    Mines, G.L.

    2002-06-17

    Geothermal power plants are designed and constructed to provide a rated power output at specific resource and ambient conditions. Due to both diurnal and seasonal changes in the ambient air temperature, as well as a decline in resource productivity over time, plants seldom operate at these ''design'' conditions. This paper examines the impact of ''off- design'' operation of an air-cooled binary geothermal power plant. An available energy analysis is used to evaluate operation at these conditions. This evaluation identifies those portions of the power cycle that are most sensitive to changing resource and ambient conditions, as well as where improvements in cycle component or system performance would have the largest impact in increasing power output.

  13. Pacific Northwest Electric Power Planning and Conservation Act, with Index (Public Law 96-501).

    SciTech Connect

    Not Available

    1991-12-01

    The Pacific Northwest Electric Power Planning and Conservation Act was enacted by the Senate and House of Representatives of the United States of America. It was enacted to assist the electrical consumers of the Pacific Northwest through use of the Federal columbia River Power System to achieve cost-effective energy conservation, to encourage the development of renewable energy resources, to establish a representative regional power planning process, to assure the region of an efficient and adequate power supply, and for other purposes. Contents of the Act are: short title and table of contents; purposes; definitions; regional planning and participation; sale of power; conservation and resource acquisition; rates; amendments to existing law; administrative provisions; savings provisions; effective date; and severability.

  14. Mapping Power Law Distributions in Digital Health Social Networks: Methods, Interpretations, and Practical Implications

    PubMed Central

    2015-01-01

    Background Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. Objectives The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. Methods Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. Results All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R 2 values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). Conclusions This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers. PMID:26111790

  15. Modelling memory processes and Internet response times: Weibull or power-law?

    NASA Astrophysics Data System (ADS)

    Chessa, Antonio G.; Murre, Jaap M. J.

    2006-07-01

    The Weibull distribution is proposed as a model for response times. Theoretical support is offered by classical results for extreme-value distributions. Fits of the Weibull distribution to response time data in different contexts show that this distribution (and the exponential distribution on small time-scales) perform better than the often-suggested power-law and logarithmic function. This study suggests that the power-law can be viewed as an approximation, at neural level, for the aggregate strength of superposed memory traces that have different decay rates in distinct parts of the brain. As we predict, this view does not find support at the level of induced response processes. The distinction between underlying and induced processes might also be considered in other fields, such as engineering, biology and physics.

  16. MHD boundary layer flow of a power-law nanofluid with new mass flux condition

    NASA Astrophysics Data System (ADS)

    Khan, Masood; Khan, Waqar Azeem

    2016-02-01

    An analysis is carried out to study the magnetohydrodynamic (" separators=" MHD ) boundary layer flow of power-law nanofluid over a non-linear stretching sheet. In the presence of a transverse magnetic field, the flow is generated due to non-linear stretching sheet. By using similarity transformations, the governing boundary layer equations are reduced into a system of ordinary differential equations. A recently proposed boundary condition requiring zero nanoparticle mass flux is employed in the flow analysis of power-law fluid. The reduced coupled differential equations are then solved numerically by the shooting method. The variations of dimensionless temperature and nanoparticle concentration with various parameters are graphed and discussed in detail. Numerical values of physical quantities such as the skin-friction coefficient and the reduced local Nusselt number are computed in tabular form.

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

    NASA Technical Reports Server (NTRS)

    Fiorito, Ralph; Titarchuk, Lev

    2004-01-01

    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.

  18. Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions

    NASA Astrophysics Data System (ADS)

    Kuo, Huan-Yu; Wu, Kuo-An

    2015-12-01

    We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α ≤1 is identical to that of the all-to-all coupling case. For α >1 , oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations.

  19. Market reaction to a bid-ask spread change: A power-law relaxation dynamics

    NASA Astrophysics Data System (ADS)

    Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N.

    2009-07-01

    We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.

  20. Two-phase power-law modeling of pipe flows displaying shear-thinning phenomena

    SciTech Connect

    Ding, Jianmin; Lyczkowski, R.W.; Sha, W.T.

    1993-12-31

    This paper describes work in modeling concentrated liquid-solids flows in pipes. COMMIX-M, a three-dimensional transient and steady-state computer program developed at Argonne National Laboratory, was used to compute velocities and concentrations. Based on the authors` previous analyses, some concentrated liquid-solids suspension flows display shear-thinning rather than Newtonian phenomena. Therefore, they developed a two-phase non-Newtonian power-law model that includes the effect of solids concentration on solids viscosity. With this new two-phase power-law solids-viscosity model, and with constitutive relationships for interfacial drag, virtual mass effect, shear lift force, and solids partial-slip boundary condition at the pipe walls, COMMIX-M is capable of analyzing concentrated three-dimensional liquid-solids flows.

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

    NASA Astrophysics Data System (ADS)

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

    2002-05-01

    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.

  2. Market reaction to a bid-ask spread change: a power-law relaxation dynamics.

    PubMed

    Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N

    2009-07-01

    We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread. PMID:19658779

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

    PubMed

    McKenzie, Donald; Kennedy, Maureen C

    2012-01-01

    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

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

    SciTech Connect

    Batista, C. E. M.; Zimdahl, W.

    2010-07-15

    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.

  5. Behaviour of microscale gas flows based on a power-law free path distribution function

    NASA Astrophysics Data System (ADS)

    Dongari, Nishanth; Zhang, Yonghao; Reese, Jason M.

    2011-05-01

    We investigate a power-law form for the probability distribution function of free paths of dilute gas molecules in a confined region. A geometry-dependent effective molecular mean free path (MFP) model is then derived for a planar wall confinement, by taking into account the boundary limiting effects on the molecular paths. The power-law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier-Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure-driven Poiseuille gas flows in micro-channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data.

  6. Casimir effect of an ideal Bose gas trapped in a generic power-law potential

    NASA Astrophysics Data System (ADS)

    Lin, Tongling; Su, Guozhen; Wang, Qiuping A.; Chen, Jincan

    2012-05-01

    The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T<=Tc (where Tc is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T>Tc, the Casimir force is an exponential decay function; and when TGtTc, the Casimir force vanishes.

  7. Flow of a power-law fluid over a rotating disk revisited

    NASA Astrophysics Data System (ADS)

    Andersson, H. I.; de Korte, E.; Meland, R.

    2001-02-01

    The von Kármán swirling flow due to a rotating disk admits similarity solutions even in the case of a power-law fluid. The non-linearities introduced by the rheological model may deteriorate the numerical solutions of the resulting set of ordinary differential equations with increasing departure from Newtonian behaviour. The reliability of earlier numerical results are nevertheless approved, except for highly shear-thinning fluids (the power-law index n<0.5) for which a severe ambiguity in the solutions is revealed and ascribed to a breakdown of the boundary layer approximation. This phenomenon makes it impossible to determine the pumping action of the disk. For highly shear-thickening fluids, on the other hand, new accurate results are provided beyond the parameter range considered earlier, i.e. for 1.5< n⩽2.0.

  8. Creep substructure formation in sodium chloride single crystals in the power law and exponential creep regimes

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

    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.

  10. Hypersonic aerodynamic characteristics of a family of power-law, wing body configurations

    NASA Technical Reports Server (NTRS)

    Townsend, J. C.

    1973-01-01

    The configurations analyzed are half-axisymmetric, power-law bodies surmounted by thin, flat wings. The wing planform matches the body shock-wave shape. Analytic solutions of the hypersonic small disturbance equations form a basis for calculating the longitudinal aerodynamic characteristics. Boundary-layer displacement effects on the body and the wing upper surface are approximated. Skin friction is estimated by using compressible, laminar boundary-layer solutions. Good agreement was obtained with available experimental data for which the basic theoretical assumptions were satisfied. The method is used to estimate the effects of power-law, fineness ratio, and Mach number variations at full-scale conditions. The computer program is included.

  11. Determination of the creep exponent of a power-law creep solid using indentation tests

    NASA Astrophysics Data System (ADS)

    Cao, Yanping

    2007-06-01

    Based on dimensional analysis, we analysed the indentation of a rigid indenter into a power-law creep solid for which the relationship between the stress and the strain rate is given by σ=bdot{\\varepsilon}n . It is shown that under a described condition the creep exponent n can be determined without invoking the detail knowledge of the indenter profile and the shape of the indented solid. The result reported herein should be useful for interpreting the data of nanoindentation into a power-law creep solid in the case that the indented solid is not a flat half-space and/or the indenter has tip defects. The performance of the simple method to evaluate the creep exponent is examined by using numerical experiments and its limitations also discussed.

  12. Exact solutions of unsteady boundary layer equations for power-law non-Newtonian fluids

    NASA Astrophysics Data System (ADS)

    Polyanin, A. D.

    2015-08-01

    A number of new exact solutions (with the generalized and functional separation of variables) of unsteady equations of a planar and asymmetric boundary layer of power-law non-Newtonian fluids are described. To find the solutions, the Crocco transformation reducing the order of the equations considered and simpler point transformations are used. Two theorems allowing one to generalize exact solutions of the unsteady axisymmetric boundary layer equations including additional arbitrary functions into them are proven.

  13. Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields

    SciTech Connect

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

    2010-12-31

    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.

  14. A power-law distribution for tenure lengths of sports managers

    NASA Astrophysics Data System (ADS)

    Aidt, Toke S.; Leong, Bernard; Saslaw, William C.; Sgroi, Daniel

    2006-10-01

    We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.

  15. Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

    NASA Technical Reports Server (NTRS)

    Howell, L. W., Jr.

    2003-01-01

    A simple power law model consisting of a single spectral index, sigma(sub 2), 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 sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(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: (Pl) 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 be 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 stained in practice are investigated.

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

    NASA Astrophysics Data System (ADS)

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

    2007-01-01

    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.

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

    PubMed

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

    2010-12-31

    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

  18. Study of Entropy-corrected Logarithmic and Power-law Versions of Pilgrim Dark Energy

    NASA Astrophysics Data System (ADS)

    Saha, Pameli; Debnath, Ujjal

    2016-03-01

    In the present work, first, we have described pilgrim dark energy, entropy-corrected pilgrim dark energy for logarithmic and power law versions. Secondly, we have done the work on the aforementioned entropy-corrected versions by choosing an interacting framework with cold dark matter and three cutoffs such as Hubble, event and conformal age of the universe. We have also made the analysis of w_{de}-w^' }_{de} and point out freezing region and thawing region in that plane.

  19. Power-law distributions for a trapped ion interacting with a classical buffer gas.

    PubMed

    DeVoe, Ralph G

    2009-02-13

    Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This provides a statistical explanation for the previously observed transition from cooling to heating. Monte Carlo results approximate a Tsallis distribution over a wide range of parameters and have ab initio agreement with experiment. PMID:19257583

  20. Spectral properties of empirical covariance matrices for data with power-law tails

    NASA Astrophysics Data System (ADS)

    Burda, Zdzisław; Görlich, Andrzej T.; Wacław, Bartłomiej

    2006-10-01

    We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the system. The method is applicable to a class of random matrices with radial measures including those with heavy (power-law) tails in the probability distribution. As an example we apply it to a multivariate Student distribution.

  1. Phenomenological Blasius-type friction equation for turbulent power-law fluid flows.

    PubMed

    Anbarlooei, H R; Cruz, D O A; Ramos, F; Silva Freire, A P

    2015-12-01

    We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed. PMID:26764803

  2. Phenomenological Blasius-type friction equation for turbulent power-law fluid flows

    NASA Astrophysics Data System (ADS)

    Anbarlooei, H. R.; Cruz, D. O. A.; Ramos, F.; Silva Freire, A. P.

    2015-12-01

    We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.

  3. The Power Laws of Violence against Women: Rescaling Research and Policies

    PubMed Central

    Kappler, Karolin E.; Kaltenbrunner, Andreas

    2012-01-01

    Background Violence against Women –despite its perpetuation over centuries and its omnipresence at all social levels– entered into social consciousness and the general agenda of Social Sciences only recently, mainly thanks to feminist research, campaigns, and general social awareness. The present article analyzes in a secondary analysis of German prevalence data on Violence against Women, whether the frequency and severity of Violence against Women can be described with power laws. Principal Findings Although the investigated distributions all resemble power-law distributions, a rigorous statistical analysis accepts this hypothesis at a significance level of 0.1 only for 1 of 5 cases of the tested frequency distributions and with some restrictions for the severity of physical violence. Lowering the significance level to 0.01 leads to the acceptance of the power-law hypothesis in 2 of the 5 tested frequency distributions and as well for the severity of domestic violence. The rejections might be mainly due to the noise in the data, with biases caused by self-reporting, errors through rounding, desirability response bias, and selection bias. Conclusion Future victimological surveys should be designed explicitly to avoid these deficiencies in the data to be able to clearly answer the question whether Violence against Women follows a power-law pattern. This finding would not only have statistical implications for the processing and presentation of the data, but also groundbreaking consequences on the general understanding of Violence against Women and policy modeling, as the skewed nature of the underlying distributions makes evident that Violence against Women is a highly disparate and unequal social problem. This opens new questions for interdisciplinary research, regarding the interplay between environmental, experimental, and social factors on victimization. PMID:22768348

  4. Power-law relationships for estimating mass, fuel consumption and costs of energy conversion equipments.

    PubMed

    Caduff, Marloes; Huijbregts, Mark A J; Althaus, Hans-Joerg; Hendriks, A Jan

    2011-01-15

    To perform life-cycle assessment studies, data on the production and use of the products is required. However, often only few data or measurements are available. Estimation of properties can be performed by applying scaling relationships. In many disciplines, they are used to either predict data or to search for underlying patterns, but they have not been considered in the context of product assessments hitherto. The goal of this study was to explore size scaling for commonly used energy conversion equipment, that is, boilers, engines, and generators. The variables mass M, fuel consumption Q, and costs C were related to power P. The established power-law relationships were M = 10(0.73.. 1.89)P(0.64.. 1.23) (R(2) ≥ 0.94), Q = 10(0.06.. 0.68)P(0.82.. 1.02) (R(2) ≥ 0.98) and C = 10(2.46.. 2.86)P(0.83.. 0.85) (R(2) ≥ 0.83). Mass versus power and costs versus power showed that none of the equipment types scaled isometrically, that is, with a slope of 1. Fuel consumption versus power scaled approximately isometrically for steam boilers, the other equipments scaled significantly lower than 1. This nonlinear scaling behavior induces a significant size effect. The power laws we established can be applied to scale the mass, fuel consumption and costs of energy conversion equipments up or down. Our findings suggest that empirical scaling laws can be used to estimate properties, particularly relevant in studies focusing on early product development for which generally only little information is available. PMID:21133374

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

    NASA Technical Reports Server (NTRS)

    Orlandini, Mauro; Morfill, G. E.

    1992-01-01

    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.

  6. Power-law behavior in complex organizational communication networks during crisis

    NASA Astrophysics Data System (ADS)

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

    2011-08-01

    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 γ 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.

  7. Explaining the power-law distribution of human mobility through transportation modality decomposition

    NASA Astrophysics Data System (ADS)

    Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu

    2015-03-01

    Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.

  8. Explaining the power-law distribution of human mobility through transportation modality decomposition.

    PubMed

    Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu

    2015-01-01

    Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns. PMID:25779306

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

    NASA Astrophysics Data System (ADS)

    Bernstein, Noam

    2012-08-01

    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.

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

    NASA Astrophysics Data System (ADS)

    Saichev, A.; Sornette, D.

    2010-01-01

    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.

  11. Cyclotron Maser Emission from Power-law Electrons with Strong Pitch-angle Anisotropy

    NASA Astrophysics Data System (ADS)

    Zhao, G. Q.; Feng, H. Q.; Wu, D. J.; Chen, L.; Tang, J. F.; Liu, Q.

    2016-05-01

    Energetic electrons with power-law spectra are commonly observed in astrophysics. This paper investigates electron cyclotron maser emission (ECME) from the power-law electrons, in which strong pitch-angle anisotropy is emphasized. The electron distribution function proposed in this paper can describe various types of pitch-angle anisotropy. Results show that the emission properties of ECME, including radiation growth, propagation, and frequency properties, depend considerably on the types of electron pitch-angle anisotropy, and different wave modes show different dependences on the pitch angle of electrons. In particular, the maximum growth rate of the X2 mode rapidly decreases with respect to the electron pitch-angle cosine μ 0 at which the electron distribution peaks, while the growth rates for other modes (X1, O1, O2) initially increase before decreasing as μ 0 increases. Moreover, the O mode, as well as the X mode, can be the fastest growth mode, in terms of not only the plasma parameter but also the type of electron pitch-angle distribution. This result presents a significant extension of the recent researches on ECME driven by the lower energy cutoff of power-law electrons, in which the X mode is generally the fastest growth mode.

  12. Power-law creep consolidation of Metal Matrix Composites. Ph.D. Thesis

    SciTech Connect

    Crow, P.D.

    1994-01-01

    The development of high strength composites for use in high temperature environments demands a whole new class of material systems. Among the promising materials to meet these new challenges are metal matrix composites (MMC`s). The problems involved in producing usable MMC`s are enormous. Typically, ceramic fibers are coated with a metal matrix by a process such as plasma spray deposition or sputtering. Even if these processes perform well, they result in intermediate materials which are not useful in engineering applications, due in part to the presence of residual porosity. Further processing is required to compact these intermediate materials into fully dense components. The dissertation is concerned with a phase of consolidation processes featuring the isolation of pores from one another and power-law creep as the dominant mechanism by which densification occurs. Using existing constitutive models for the behavior of fully dense power-law creeping materials, the effect of pores (voids) and reinforcing on the consolidation of MMC`s is investigated. Novel in the work is the presentation of a two-dimensional constitutive relation, through a potential, for a porous matrix containing cusped pores. The potential expressing this constitutive relation will provide the stress-strain rate response under symmetric in-plane loading of an MMC densifying due to power-law creep.

  13. Mobility of power-law and Carreau fluids through fibrous media

    NASA Astrophysics Data System (ADS)

    Shahsavari, Setareh; McKinley, Gareth H.

    2015-12-01

    The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ ≃0.65 , the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.

  14. Mobility of power-law and Carreau fluids through fibrous media.

    PubMed

    Shahsavari, Setareh; McKinley, Gareth H

    2015-12-01

    The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers. PMID:26764809

  15. Detection of two power-law tails in the probability distribution functions of massive GMCs

    NASA Astrophysics Data System (ADS)

    Schneider, N.; Bontemps, S.; Girichidis, P.; Rayner, T.; Motte, F.; André, Ph.; Russeil, D.; Abergel, A.; Anderson, L.; Arzoumanian, D.; Benedettini, M.; Csengeri, T.; Didelon, P.; Di Francesco, J.; Griffin, M.; Hill, T.; Klessen, R. S.; Ossenkopf, V.; Pezzuto, S.; Rivera-Ingraham, A.; Spinoglio, L.; Tremblin, P.; Zavagno, A.

    2015-11-01

    We report the novel detection of complex high column density tails in the probability distribution functions (PDFs) for three high-mass star-forming regions (CepOB3, MonR2, NGC 6334), obtained from dust emission observed with Herschel. The low column density range can be fitted with a lognormal distribution. A first power-law tail starts above an extinction (AV) of ∼6-14. It has a slope of α 1.3-2 for the &ρ ≈ r-α profile for an equivalent density distribution (spherical or cylindrical geometry), and is thus consistent with free-fall gravitational collapse. Above AV ∼40, 60, and 140, we detect an excess that can be fitted by a flatter power-law tail with α > 2. It correlates with the central regions of the cloud (ridges/hubs) of size ∼;1 pc and densities above 104 cm-3. This excess may be caused by physical processes that slow down collapse and reduce the flow of mass towards higher densities. Possible are: (1) rotation, which introduces an angular momentum barrier, (2) increasing optical depth and weaker cooling, (3) magnetic fields, (4) geometrical effects, and (5) protostellar feedback. The excess/second power-law tail is closely linked to high-mass star-formation though it does not imply a universal column density threshold for the formation of (high-mass) stars.

  16. Tornado outbreak variability follows Taylor's power law of fluctuation scaling and increases dramatically with severity

    PubMed Central

    Tippett, Michael K.; Cohen, Joel E.

    2016-01-01

    Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from ‘outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954–2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210

  17. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

    USGS Publications Warehouse

    Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.

    2011-01-01

    Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.

  18. Tornado outbreak variability follows Taylor's power law of fluctuation scaling and increases dramatically with severity.

    PubMed

    Tippett, Michael K; Cohen, Joel E

    2016-01-01

    Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210

  19. Empirical analysis on the connection between power-law distributions and allometries for urban indicators

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

    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.

  20. Accuracy analysis of measurements on a stable power-law distributed series of events

    NASA Astrophysics Data System (ADS)

    Matthews, J. O.; Hopcraft, K. I.; Jakeman, E.; Siviour, G. B.

    2006-11-01

    We investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined. The model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events. This leads to a scale-free discrete random process where customary measures, such as mean value and variance, do not exist. However, converting the number of events occurring in fixed time intervals to a 1-bit 'clipped' process allows the construction of well-behaved statistics that still retain vestiges of the original power-law and fluctuation properties. These statistics include the clipped mean and correlation function, from measurements of which both the power-law index of the distribution of events and the time constant of its fluctuations can be deduced. We report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process. This indicates that, for a fixed experiment time, the error on measurements of the sample mean is minimized by an optimum choice of the number of samples. It is shown furthermore that this choice is sensitive to the power-law index and that the approach to Poisson statistics is dominated by rare events or 'outliers'. Our results are supported by numerical simulation.

  1. Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel.

    PubMed

    Zhao, Cunlu; Yang, Chun

    2013-03-01

    EOF of non-Newtonian power-law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first-order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz-Smoluchowski velocity of power-law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz-Smoluchowski velocity over planar surfaces or in parallel-plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non-Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power-law fluids is proposed under a combined DC and AC electric field. PMID:23229874

  2. DC CIRCUIT POWERED BY ORBITAL MOTION: MAGNETIC INTERACTIONS IN COMPACT OBJECT BINARIES AND EXOPLANETARY SYSTEMS

    SciTech Connect

    Lai Dong

    2012-09-20

    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.

  3. Self-similar rupture of thin free films of power-law fluids

    NASA Astrophysics Data System (ADS)

    Thete, Sumeet Suresh; Anthony, Christopher; Basaran, Osman A.; Doshi, Pankaj

    2015-08-01

    The rupture of a thin free film of a power-law fluid under the competing influences of destabilizing van der Waals pressure and stabilizing surface tension pressure is analyzed. In such a fluid, viscosity decreases with the deformation rate raised to the n -1 power where 0

  4. Preliminary limits on deviation from the inverse-square law of gravity in the solar system: a power-law parameterization

    NASA Astrophysics Data System (ADS)

    Liu, Meng-Yao; Zhong, Ze-Hao; Han, Yi-Chen; Wang, Xiao-Yu; Yang, Zong-Shui; Xie, Yi

    2014-08-01

    New physics beyond the standard model of particles might cause a deviation from the inverse-square law of gravity. In some theories, it is parameterized by a power-law correction to the Newtonian gravitational force, which might originate from the simultaneous exchange of particles or modified and extended theories of gravity. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain preliminary limits on this correction. In our estimation, we take the Lense-Thirring effect due to the Sun's angular momentum into account. The parameters of the power-law correction and the uncertainty of the Sun's quadrupole moment are simultaneously estimated with the method of minimizing ?2. From INPOP10a, we find N = 0.605 for the exponent of the power-law correction. However, from EPM2011, we find that, although it yields N = 3.001, the estimated uncertainty in the Sun's quadrupole moment is much larger than the value given by current observations. This might be caused by the intrinsic nonlinearity in the power-law correction, which makes the estimation very sensitive to the supplementary advances of the perihelia.

  5. Streamwater ages derived from tritium show power law variation with discharge like silica concentrations

    NASA Astrophysics Data System (ADS)

    Stewart, Michael; Morgenstern, Uwe

    2013-04-01

    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.

  6. Non-linear power law approach for spatial and temporal pattern analysis of salt marsh evolution

    NASA Astrophysics Data System (ADS)

    Taramelli, A.; Cornacchia, L.; Valentini, E.; Bozzeda, F.

    2013-11-01

    Many complex systems on the Earth surface show non-equilibrium fluctuations, often determining the spontaneous evolution towards a critical state. In this context salt marshes are characterized by complex patterns both in geomorphological and ecological features, which often appear to be strongly correlated. A striking feature in salt marshes is vegetation distribution, which can self-organize in patterns over time and space. Self-organized patchiness of vegetation can often give rise to power law relationships in the frequency distribution of patch sizes. In cases where the whole distribution does not follow a power law, the variance of scale in its tail may often be disregarded. To this end, the research aims at how changes in the main climatic and hydrodynamic variables may influence such non-linearity, and how numerical thresholds can describe this. Since it would be difficult to simultaneously monitor the presence and typology of vegetation and channel sinuosity through in situ data, and even harder to analyze them over medium to large time-space scales, remote sensing offers the ability to analyze the scale invariance of patchiness distributions. Here, we focus on a densely vegetated and channelized salt marsh (Scheldt estuary Belgium-the Netherlands) by means of the sub-pixel analysis on satellite images to calculate the non-linearity in the values of the power law exponents due to the variance of scale. The deviation from power laws represents stochastic conditions under climate drivers that can be hybridized on the basis of a fuzzy Bayesian generative algorithm. The results show that the hybrid approach is able to simulate the non-linearity inherent to the system and clearly show the existence of a link between the autocorrelation level of the target variable (i.e. size of vegetation patches), due to its self-organization properties, and the influence exerted on it by the external drivers (i.e. climate and hydrology). Considering the results of the stochastic model, high uncertainties can be associated to the short term climate influence on the saltmarshes, and the medium-long term spatial and temporal trends seem to be dominated by vegetation with its evolution in time and space. The evolution of vegetation patches (under power law) and channel sinuosity can then be used to forecast potential deviation from steady states in intertidal systems, taking into account the climatic and hydrological regimes.

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

    SciTech Connect

    Jaouadi, A.; Telmini, M.; Charron, E.

    2011-02-15

    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.

  8. Power-law dynamics in neuronal and behavioral data introduce spurious correlations.

    PubMed

    Schaworonkow, Natalie; Blythe, Duncan A J; Kegeles, Jewgeni; Curio, Gabriel; Nikulin, Vadim V

    2015-08-01

    Relating behavioral and neuroimaging measures is essential to understanding human brain function. Often, this is achieved by computing a correlation between behavioral measures, e.g., reaction times, and neurophysiological recordings, e.g., prestimulus EEG alpha-power, on a single-trial-basis. This approach treats individual trials as independent measurements and ignores the fact that data are acquired in a temporal order. It has already been shown that behavioral measures as well as neurophysiological recordings display power-law dynamics, which implies that trials are not in fact independent. Critically, computing the correlation coefficient between two measures exhibiting long-range temporal dependencies may introduce spurious correlations, thus leading to erroneous conclusions about the relationship between brain activity and behavioral measures. Here, we address data-analytic pitfalls which may arise when long-range temporal dependencies in neural as well as behavioral measures are ignored. We quantify the influence of temporal dependencies of neural and behavioral measures on the observed correlations through simulations. Results are further supported in analysis of real EEG data recorded in a simple reaction time task, where the aim is to predict the latency of responses on the basis of prestimulus alpha oscillations. We show that it is possible to "predict" reaction times from one subject on the basis of EEG activity recorded in another subject simply owing to the fact that both measures display power-law dynamics. The same is true when correlating EEG activity obtained from different subjects. A surrogate-data procedure is described which correctly tests for the presence of correlation while controlling for the effect of power-law dynamics. PMID:25930148

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

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

    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 ξ (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 ξ (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.

  10. Thermal analysis of a reactive generalized Couette flow of power law fluids between concentric cylindrical pipes

    NASA Astrophysics Data System (ADS)

    Makinde, O. D.

    2014-12-01

    In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.

  11. On the Nonlinear Effects in Focused Ultrasound Beams with Frequency Power Law Attenuation

    NASA Astrophysics Data System (ADS)

    Jiménez, N.; Redondo, J.; Sánchez-Morcillo, V.; Iglesias, P. C.; Camarena, F.

    When finite amplitude ultrasound propagation is considered, changes in spatial features of focused ultrasound beams can be observed. These nonlinear effects typically appear in thermoviscous fluids as focal displacements, beam-width variations or gain changes. However, in soft-tissue media, the frequency dependence of the attenuation doesn't obey a squared law. In this way, these complex media response leads to weak dispersion that prevents the cumulative processes of energy transfer to higher harmonics. In this work we explore the influence of different frequency power law attenuation responses and its influence on the self-defocusing effects in focused ultrasound beams. Thus, we numerically explore the spatial field distributions produced by low-Fresnel number devices and High Intensity Focused Ultrasound (HIFU) radiating trough different soft-tissue media.

  12. Transport ac loss of elliptical thin strips with a power-law E(J) relation

    NASA Astrophysics Data System (ADS)

    Jia, Chen-Xi; Chen, Du-Xing; Li, Shuo; Fang, Jin

    2015-10-01

    The transport ac loss Q of an elliptical thin strip of critical current I c with a power-law relation E\\propto {J}n is accurately computed as a function of current amplitude I m and frequency f. The resulting Q({I}m) is normalized to q({i}m) following the Norris critical-state formula, and converted to {q}*({i}m*) at a critical frequency f c based on a transport scaling law. Having a set of {q}*({i}m*) at several values of n as a base, a general expression of {q}*({i}m*,n) is obtained, which can be used to easily calculate q({i}m) for any practical purposes.

  13. A Control Law Design Method Facilitating Control Power, Robustness, Agility, and Flying Qualities Tradeoffs: CRAFT

    NASA Technical Reports Server (NTRS)

    Murphy, Patrick C.; Davidson, John B.

    1998-01-01

    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.

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

    NASA Astrophysics Data System (ADS)

    Koonin, Eugene

    2003-03-01

    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.

  15. MHD thermosolutal marangoni convection heat and mass transport of power law fluid driven by temperature and concentration gradient

    NASA Astrophysics Data System (ADS)

    Jiao, Chengru; Zheng, Liancun; Ma, Lianxi

    2015-08-01

    This paper studies the magnetohydrodynamic (MHD) thermosolutal Marangoni convection heat and mass transfer of power-law fluids driven by a power law temperature and a power law concentration which is assumed that the surface tension varies linearly with both the temperature and concentration. Heat and mass transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection-diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient and the mass diffusion depends non-linearly on both the concentration and the concentration gradient with modified Fourier heat conduction for power law fluid. The governing equations are reduced to nonlinear ordinary differential equations by using suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM). The transport characteristics of velocity, temperature and concentration fields are analyzed in detail.

  16. Crossover from exponential to power-law scaling for human mobility pattern in urban, suburban and rural areas

    NASA Astrophysics Data System (ADS)

    Liu, Hsing; Chen, Ying-Hsing; Lih, Jiann-Shing

    2015-05-01

    Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution.

  17. a, b careful: The challenge of scale invariance for comparative analyses in power law models of the streamflow recession

    NASA Astrophysics Data System (ADS)

    Dralle, David; Karst, Nathaniel; Thompson, Sally E.

    2015-11-01

    The falling limb of the hydrograph—the streamflow recession—is frequently well approximated by power law functions, in the form dq/dt = -aqb, so that recessions are often characterized in terms of their power law parameters (a, b). The empirical determination and interpretation of the parameter a is typically biased by the presence of a ubiquitous mathematical artifact resulting from the scale-free properties of the power law function. This reduces the information available from recession parameter analysis and creates several heretofore unaddressed methodological "pitfalls." This letter outlines the artifact, demonstrates its genesis, and presents an empirical rescaling method to remove artifact effects from fitted recession parameters. The rescaling process reveals underlying climatic patterns obscured in the original data and, we suggest, could maximize the information content of fitted power laws.

  18. Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential, Soma Membrane Current and Single-Neuron Contribution to the EEG

    PubMed Central

    Pettersen, Klas H.; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T.

    2014-01-01

    Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation. PMID:25393030

  19. Lower Energy Cutoff Behavior of Negative Power-Law Electrons and Electron-Cyclotron Maser Emission

    NASA Astrophysics Data System (ADS)

    Tang, J. F.

    2014-01-01

    The electron-cyclotron maser (ECM) emission is one of the most important radio emission mechanisms in astrophysics. It was first pointed out in the late 1950s. Because of the limitation of the nonrelativistic resonant condition, it is difficult to produce an amplified radiation that can escape from plasma. The ECM instability has been extensively applied to various coherent radio-burst phenomena since Wu & Lee (1979) utilized the weakly relativistic resonant condition. Several loss-cone like electron distribution functions have been put forward. Astrophysical observations demonstrate that energetic electrons usually have a negative power-law distribution. However, the negative power-law spectrum of energetic electrons can depress the ECM instability effectively. We need a new and more effective mechanism to drive the radiation. In this thesis, we investigate the ECM emission driven by the lower energy cutoff behavior of power-law electrons, and the effects of anisotropy of energetic electrons in velocity space on ECM. Firstly, Chapter 1 introduces the general knowledge of the observational characteristics of solar radio bursts, and the excitation mechanisms of radio emission. Then, combining with the observations of hard X-ray spectrum, in Chapter 2 we overview the properties of energetic electrons driving the radio emission, and discuss the lower energy cutoff behavior of the negative power-law electrons. We suggest a hyperbolic tangent function to describe the lower energy cutoff behavior. In Chapter 3 we discuss the ECM driven by the lower energy cutoff behavior, and the effects of anisotropy in velocity space on the ECM instability. It is found that: (1) even with isotropic distribution, the power-law electrons with the steepness cutoff can efficiently excite the ECM instability; (2) same as the isotropy case, the power-law electrons with anisotropic distributions can also excite ECM instability efficiently, which have an important effect on the ECM emission. Energetic electrons observed in situ are ubiquitous in the near Earth space plasmas. They are commonly modeled as the so-called Kappa distribution. In Chapter 4 we investigate the ECM instability in space plasmas driven by the Kappa loss-cone distribution. Chapter 5 reports a novel kind of fine structures in solar radio bursts, solar microwave drifting spikes (SMDSs) on 2004 November 3, and makes statistical analysis of microwave spikes on 2006 December 13. We investigate the observational parameters of SMDSs observed on 2004 November 3. The electrons trapped within the solitary kinetic Alfven waves (SKAWs) can be accelerated by the SKAW electric fields, and directly trigger the observed SMDSs by the ECM mechanism. According to the GOES soft X-ray observations, the flare on 2006 December 13 can be separated into the rising phase, peak phase, and decay phase. We make statistical analysis of the observational parameters of the radio spikes, which occurred in all the three phases, and investigate their temporal evolution. Finally, the summary of the whole thesis and outlook are presented in Chapter 6.

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

    NASA Astrophysics Data System (ADS)

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

    2011-08-01

    We use three methods to identify power law scaling of (natural) log air permeability data collected by Tidwell and Wilson (1999) on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), extended power-law scaling also known as Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on qth-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. Most analyses of this type published to date concern time series or one-dimensional transects of spatial data associated with a unique measurement (support) scale. We consider log air permeability data having diverse support scales on the faces of a cube. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents ξ(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 (Guadagnini and Neuman, 2011; Guadagnini et al., 2011) 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. ESS and G-ESS ratios between scaling exponents ξ(q) associated with various orders q show no distinct dependence on support volume or on two out of three Cartesian directions (there being no distinct power law scaling in the third direction). The finding by Tidwell and Wilson (1999) 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 size scales show nonlinear (multifractal) variations in ξ(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, ξ(q), of tfBm vary linearly with q we conclude, in accord with Neuman (2010a, b, 2011), 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 is 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. Our estimate of lower cutoff is consistent with a theoretical support scale of the data.

  1. Extended Power-Law Scaling of Air Permeabilities Measured on a Block of Tuff

    NASA Astrophysics Data System (ADS)

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

    2011-12-01

    We use three methods to identify power law scaling of (natural) log air permeability data collected by Tidwell and Wilson (1999) on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), extended power-law scaling also known as Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on qth-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. Most analyses of this type published to date concern time series or one-dimensional transects of spatial data associated with a unique measurement (support) scale. We consider log air permeability data having diverse support scales on the faces of a cube. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents ξ(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 (Guadagnini and Neuman, 2011; Guadagnini et al., 2011) 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. ESS and G-ESS ratios between scaling exponents ξ(q) associated with various orders q show no distinct dependence on support volume or on two out of three Cartesian directions (there being no distinct power law scaling in the third direction). The finding by Tidwell and Wilson (1999) 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 size scales show nonlinear (multifractal) variations in ξ(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, ξ(q), of tfBm vary linearly with q we conclude, in accord with Neuman (2010a, 2010b, 2011), 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 is 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. Our estimate of lower cutoff is consistent with a theoretical support scale of the data.

  2. Power of quantitative trait locus mapping for polygenic binary traits using generalized and regression interval mapping in multi-family half-sib designs.

    PubMed

    Kadarmideen, H N; Janss, L L; Dekkers, J C

    2000-12-01

    A generalized interval mapping (GIM) method to map quantitative trait loci (QTL) for binary polygenic traits in a multi-family half-sib design is developed based on threshold theory and implemented using a Newton-Raphson algorithm. Statistical power and bias of QTL mapping for binary traits by GIM is compared with linear regression interval mapping (RIM) using simulation. Data on 20 paternal half-sib families were simulated with two genetic markers that bracketed an additive QTL. Data simulated and analysed were: (1) data on the underlying normally distributed liability (NDL) scale, (2) binary data created by truncating NDL data based on three thresholds yielding data sets with three different incidences, and (3) NDL data with polygenic and QTL effects reduced by a proportion equal to the ratio of the heritabilities on the binary versus NDL scale (reduced-NDL). Binary data were simulated with and without systematic environmental (herd) effects in an unbalanced design. GIM and RIM gave similar power to detect the QTL and similar estimates of QTL location, effects and variances. Presence of fixed effects caused differences in bias between RIM and GIM, where GIM showed smaller bias which was affected less by incidence. The original NDL data had higher power and lower bias in QTL parameter estimates than binary and reduced-NDL data. RIM for reduced-NDL and binary data gave similar power and estimates of QTL parameters, indicating that the impact of the binary nature of data on QTL analysis is equivalent to its impact on heritability. PMID:11204977

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

    NASA Astrophysics Data System (ADS)

    Selvam, A. M.

    2014-06-01

    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.

  4. Self-similar rupture of thin free films of power law fluids

    NASA Astrophysics Data System (ADS)

    Thete, Sumeet; Anthony, Christopher; Basaran, Osman; Doshi, Pankaj

    2015-11-01

    Rupture of a thin sheet (free film) of a power law fluid under the competing influences of destabilizing van der Waals pressure (vdWP) and stabilizing surface tension pressure (STP) is analyzed. In such a fluid, viscosity is not constant but decreases with the deformation rate raised to the n - 1 power where 0 < n <= 1 is the power law exponent (n = 1 for a Newtonian fluid). It is shown that when 1 > n > 6 / 7 , film rupture occurs under a balance between vdWP, inertial stress (IS), and viscous stress (VS), and the film thickness decreases as τ n / 3 and the lateral length scale as τ 1 - n / 2 where τ is time remaining to rupture. When n < 6 / 7 , the dominant balance changes so that VS becomes negligible and the film ruptures under the competition between vdWP, IS, and STP. In this new regime, film thickness and lateral length vary as τ 2 / 7 and τ 4 / 7.

  5. A binary solvent of water and propanol for use in high-average power dye lasers

    NASA Astrophysics Data System (ADS)

    Ray, A. K.; Sinha, S.; Kundu, S.; Kumar, S.; Dasgupta, K.

    2007-05-01

    Water is an inherently safe solvent for laser dyes and posses far better photo thermal characteristics in comparison to the commonly used organic solvents in dye lasers. However, water solution of dye needs a suitable deaggregating additive to suppress non-radiative dimers and to achieve similar laser efficiency. We have carried out systematic studies on comparative performances of dye lasers, pumped by low-repetition-rate Nd-YAG, as well as high-repetition-rate copper vapour lasers using Rhodamine 6G dye solutions in ethanol and various binary solvents of water. Among different additives in water, for the first time, the results of our studies on the application of water solvent in dye lasers could clearly establish that binary solvent comprising of normal or heavy water and about 18% to 25% n-propanol has produced similar efficiency, better photochemical stability and superior thermo-optic properties than ethanol solvent in high-repetition rate oscillator-amplifier operation.

  6. Air-chemistry "turbulence": power-law scaling and statistical regularity

    NASA Astrophysics Data System (ADS)

    Hsu, H.-M.; Lin, C.-Y.; Guenther, A.; Tribbia, J. J.; Liu, S. C.

    2011-08-01

    With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, plain/hill, and industrial/agricultural locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, and intermediate (20 ~ 30 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of -5/3 and -1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. These exponents are mostly independent of the averages and standard deviations of time series measured at various geographic settings, i.e., the spatial inhomogeneities. In other words, they possess dominant universal structures. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, -3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are important structural information, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.

  7. Effects of diversity and procrastination in priority queuing theory: the different power law regimes.

    PubMed

    Saichev, A; Sornette, D

    2010-01-01

    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 approximately 1/t(alpha) with 0power law tail approximately 1/t(1/2), 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(alpha), with alpha is an element of (0.5,infinity), 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. PMID:20365433

  8. Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators

    NASA Astrophysics Data System (ADS)

    Casteels, W.; Storme, F.; Le Boité, A.; Ciuti, C.

    2016-03-01

    We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states; in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a nonadiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in the presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.

  9. Integrating connectivity, power law, and alternative stable state paradigms of dryland ecosystem structure and dynamics

    NASA Astrophysics Data System (ADS)

    Okin, Gregory; D'Odorico, Paolo

    2013-04-01

    Drylands are important ecosystems that cover about 40% of the Earth's land surface and provide goods and services for about 30% of the Earth's inhabitants. Dryland vegetation is almost universally patchy reflecting the resource limitation endemic to these areas and this patchiness unquestionably results from some type of self-organization. Understanding the function of these ecosystems is critical for their effective management and for understanding how they will be affected by changes in climate and land use as well as by invasion of non-native species. There are three main paradigms that have emerged in the literature to explain dryland ecosystem structure and dynamics. The connectivity paradigm posits that spatiotemporal patterns of vegetation observed in drylands are a result of the lateral movement of resources and disturbance along connected pathways. Other authors have examined the impact of local-scale interactions that give rise to large-scale patterns in the form of power law distributions of vegetation patches. Deviation from power law distributions as a sign of imminent, catastrophic change has been a common thread in this line of research. The sudden and often irreversible change observed in dryland ecosystems has led others to emphasize the importance of feedbacks that lead to the existence of alternative stable states and hysteresis in drylands. This latter view is closely aligned with the state-and-transition model approach. Here we show, through a series of conceptual and mathematical model arguments, that these three approaches - connectivity, power law distributions, and alternative stable states - can in many circumstances be considered equivalent. They are, in essence, different facets of a common set underlying processes. This transdisciplinary, integrated perspective should help understand how spatial processes interact to create pattern and patchiness in dryalnds as well as other ecosystems worldwide.

  10. Protein family and fold occurrence in genomes: power-law behaviour and evolutionary model.

    PubMed

    Qian, J; Luscombe, N M; Gerstein, M

    2001-11-01

    Global surveys of genomes measure the usage of essential molecular parts, defined here as protein families, superfamilies or folds, in different organisms. Based on surveys of the first 20 completely sequenced genomes, we observe that the occurrence of these parts follows a power-law distribution. That is, the number of distinct parts (F) with a given genomic occurrence (V) decays as F=aV(-b), with a few parts occurring many times and most occurring infrequently. For a given organism, the distributions of families, superfamilies and folds are nearly identical, and this is reflected in the size of the decay exponent b. Moreover, the exponent varies between different organisms, with those of smaller genomes displaying a steeper decay (i.e. larger b). Clearly, the power law indicates a preference to duplicate genes that encode for molecular parts which are already common. Here, we present a minimal, but biologically meaningful model that accurately describes the observed power law. Although the model performs equally well for all three protein classes, we focus on the occurrence of folds in preference to families and superfamilies. This is because folds are comparatively insensitive to the effects of point mutations that can cause a family member to diverge beyond detectable similarity. In the model, genomes evolve through two basic operations: (i) duplication of existing genes; (ii) net flow of new genes. The flow term is closely related to the exponent b and can accommodate considerable gene loss; however, we demonstrate that the observed data is reproduced best with a net inflow, i.e. with more gene gain than loss. Moreover, we show that prokaryotes have much higher rates of gene acquisition than eukaryotes, probably reflecting lateral transfer. A further natural outcome from our model is an estimation of the fold composition of the initial genome, which potentially relates to the common ancestor for modern organisms. Supplementary material pertaining to this work is available from www.partslist.org/powerlaw. PMID:11697896

  11. Cascade failure analysis of power grid using new load distribution law and node removal rule

    NASA Astrophysics Data System (ADS)

    Ren, Hai-Peng; Song, Jihong; Yang, Rong; Baptista, Murilo S.; Grebogi, Celso

    2016-01-01

    The power grid is a directional complex network of generators, substations, and consumers. We propose a new load distribution law to emulate the power grid. We assume that the power flow is transferred through all the paths connecting generators and consumers according to their efficiency. The initial generation of generators and the initial loads of substations are calculated according to the path efficiency and the load of the consumers. If a node fails, it is removed from the power grid, and all paths passing through it will fail to transfer power. In that case, the loads of the corresponding consumers are redistributed within the whole network. During the failure cascading and propagation procedure, our node removal rule is to remove the first overload node along the opposite direction of power flow, then the network distributes load and goes on the cascade procedure. Our new removal rule for nodes does suppress the large scale cascading failures. This work would be very helpful for designing the protective relay system and the tolerant parameters of the grid.

  12. Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated

    NASA Astrophysics Data System (ADS)

    Langlois, Dominic; Cousineau, Denis; Thivierge, J. P.

    2014-01-01

    The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.

  13. Rationalization of Creep Data of Creep-Resistant Steels on the Basis of the New Power Law Creep Equation

    NASA Astrophysics Data System (ADS)

    Wang, Q.; Yang, M.; Song, X. L.; Jia, J.; Xiang, Z. D.

    2016-05-01

    The conventional power law creep equation (Norton equation) relating the minimum creep rate to creep stress and temperature cannot be used to predict the long-term creep strengths of creep-resistant steels if its parameters are determined only from short-term measurements. This is because the stress exponent and activation energy of creep determined on the basis of this equation depend on creep temperature and stress and these dependences cannot be predicted using this equation. In this work, it is shown that these problems associated with the conventional power law creep equation can be resolved if the new power law equation is used to rationalize the creep data. The new power law creep equation takes a form similar to the conventional power law creep equation but has a radically different capability not only in rationalizing creep data but also in predicting the long-term creep strengths from short-term test data. These capabilities of the new power law creep equation are demonstrated using the tensile strength and creep test data measured for both pipe and tube grades of the creep-resistant steel 9Cr-1.8W-0.5Mo-V-Nb-B (P92 and T92).

  14. Fast and Accurate Fourier Series Solutions to Gravitational Lensing by a General Family of Two-Power-Law Mass Distributions

    NASA Astrophysics Data System (ADS)

    Chae, Kyu-Hyun

    2002-04-01

    Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two-power-law ellipsoidal mass distributions are presented. The cusped two-power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and η models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two-power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e.g., 10-5). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two-power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single-power-law mass model are made publicly available.

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

    SciTech Connect

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

    2010-10-01

    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.

  16. An explanation for the universal 3.5 power-law observed in currency markets

    NASA Astrophysics Data System (ADS)

    Johnson, Nicholas A.; Johnson, Neil F.

    We present a mathematical theory to explain a recent empirical finding in the Physics literature (Zhao et al., 2013) in which the distributions of waiting-times between discrete events were found to exhibit power-law tails with an apparent universal exponent: α ∼ 3.5 . This new theory provides the first ever qualitative and quantitative explanation of Zhao et al.'s surprising finding. It also provides a mechanistic description of the origin of the observed universality, assigning its cause to the emergence of dynamical feedback processes between evolving clusters of like-minded agents.

  17. Hysteresis and creep: Comparison between a power-law model and Kuhnen's model

    NASA Astrophysics Data System (ADS)

    Oliveri, Alberto; Stellino, Flavio; Parodi, Mauro; Storace, Marco

    2016-04-01

    In this paper we analyze some properties of a recently proposed model of hysteresis and creep (related to a circuit model, whose only nonlinear element is based on a power law) and compare it with the well-known Kuhnen's model. A first qualitative comparison relies on the analysis of the behavior of the elementary cell of each model. Their responses to step inputs (which allow to better evidence the creep effect) are analyzed and compared. Then, a quantitative comparison is proposed, based on the fitting performances of the two models on experimental data measured from a commercial piezoelectric actuator.

  18. Power-law scaling in Bénard-Marangoni convection at large Prandtl numbers

    NASA Astrophysics Data System (ADS)

    Boeck, Thomas; Thess, André

    2001-08-01

    Bénard-Marangoni convection at large Prandtl numbers is found to exhibit steady (nonturbulent) behavior in numerical experiments over a very wide range of Marangoni numbers Ma far away from the primary instability threshold. A phenomenological theory, taking into account the different character of thermal boundary layers at the bottom and at the free surface, is developed. It predicts a power-law scaling for the nondimensional velocity (Peclet number) and heat flux (Nusselt number) of the form Pe~Ma2/3, Nu~Ma2/9. This prediction is in good agreement with two-dimensional direct numerical simulations up to Ma=3.2×105.

  19. Additivity property and emergence of power laws in nonequilibrium steady states.

    PubMed

    Das, Arghya; Chatterjee, Sayani; Pradhan, Punyabrata; Mohanty, P K

    2015-11-01

    We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena. PMID:26651647

  20. Scattering at the Anderson transition: Power-law banded random matrix model

    NASA Astrophysics Data System (ADS)

    Méndez-Bermúdez, J. A.; Varga, I.

    2006-09-01

    We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal-insulator transition. We focus on the scaling of Wigner delay times τ and resonance widths Γ . We find that the typical values of τ and Γ (calculated as the geometric mean) scale with the system size L as τtyp∝LD1 and Γtyp∝L-(2-D2) , where D1 is the information dimension and D2 is the correlation dimension of eigenfunctions of the corresponding closed system.

  1. Modeling explosion generated Scholte waves in sandy sediments with power law dependent shear wave speed.

    PubMed

    Soloway, Alexander G; Dahl, Peter H; Odom, Robert I

    2015-10-01

    Experimental measurements of Scholte waves from underwater explosions collected off the coast of Virginia Beach, VA in shallow water are presented. It is shown here that the dispersion of these explosion-generated Scholte waves traveling in the sandy seabed can be modeled using a power-law dependent shear wave speed profile and an empirical source model that determines the pressure time-series at 1 m from the source as a function of TNT-equivalent charge weight. PMID:26520346

  2. Steady thermal explosion with power-law thermal absorptivity in microannuli: wavy-roughness effect

    NASA Astrophysics Data System (ADS)

    Zotin Kwang-Hua, Chu

    2009-07-01

    We obtain the approximate solutions for the steady temperature profiles of materials with a temperature-dependent thermal absorptivity inside a microannulus with wavy-rough surfaces considering a quasilinear partial differential equation by the boundary perturbation approach. Our numerical results show that the wave number as well as the small amplitude of the wavy roughness will influence the net temperature significantly especially near the inner wall of a microannulus. Meanwhile we observed that the critical Frank-Kamanestkii parameter depends on the small-amplitude wavy-roughness for specific power-law of thermal absorptivity. Our results could be applied to the relevant fields in MicroElectroMechanical System (MEMS).

  3. Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps.

    PubMed

    Grossmann, S; Holthaus, M

    1997-11-10

    After discussing the idea underlying the Maxwell's Demon ensemble, we employ this ensemble for calculating fluctuations of ideal Bose gas condensates in traps with power-law single-particle energy spectra. Two essentially different cases have to be distinguished. If the heat capacity is continuous at the condensation point, the fluctuations of the number of condensate particles vanish linearly with temperature, independent of the trap characteristics. In this case, microcanonical and canonical fluctuations are practically indistinguishable. If the heat capacity is discontinuous, the fluctuations vanish algebraically with temperature, with an exponent determined by the trap, and the micro-canonical fluctuations are lower than their canonical counterparts. PMID:19373412

  4. Thermodynamics of Ideal Fermi Gas Under Generic Power Law Potential in d-dimensions

    NASA Astrophysics Data System (ADS)

    Faruk, M. M.; Bhuiyan, G. M.

    Thermodynamics of ideal Fermi gas trapped in an external generic power law potential $U=\\sum_{i=1} ^d c_i |\\frac{x_i}{a_i}|^{n_i}$ are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. These properties are explored deeply in the degenerate limit ($\\mu>> K_BT$), where the thermodynamic properties are greatly dominated by Pauli exclusion principle. Pressure and energy along with the isothermal compressibilty is non zero at $T=0K$, denoting trapped Fermi system is quite live even at absolute zero temperature. The nonzero value of compressibilty denotes zero point pressure is not just a constant but depends on volume.

  5. Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

    NASA Astrophysics Data System (ADS)

    Mercan, Kadir; Demir, Çiğdem; Civalek, Ömer

    2016-01-01

    In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

  6. Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

    NASA Technical Reports Server (NTRS)

    Howell, L. W.

    2002-01-01

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2012-01-01

    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, ξ(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 ξ(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, ξ(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.

  8. Forces acting on a stationary sphere in power-law fluid flow near the wall

    NASA Astrophysics Data System (ADS)

    Bocharov, O. B.; Kushnir, D. Yu.

    2016-01-01

    The analysis and evaluation of the forces acting on the particle in a linear shear flow of power-law fluid (PLF) in the presence of the wall were performed. Using the results of a series of computations for a model problem with a spherical particle near a flat wall in the Reynolds number range of 0-200 and the distance to the wall from 0 to 20 particle diameters, the correlation formulas for calculating the coefficients of drag force and lift force were obtained. Special attention was paid to the behavior of the forces acting on the particle approaching the wall.

  9. Crossover of two power laws in the anomalous diffusion of a two lipid membrane

    SciTech Connect

    Bakalis, Evangelos E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco E-mail: francesco.zerbetto@unibo.it; Venturini, Alessandro

    2015-06-07

    Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.

  10. Solitary and shock waves in discrete strongly nonlinear double power-law materials

    NASA Astrophysics Data System (ADS)

    Herbold, E. B.; Nesterenko, V. F.

    2007-06-01

    A laminar metamaterial supporting strongly nonlinear solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. The force-displacement relationship of a compressed o-ring is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into three separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.

  11. Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

    NASA Astrophysics Data System (ADS)

    Takesue, Shinji; Mitsudo, Tetsuya; Hayakawa, Hisao

    2003-07-01

    We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a ω-3/2 power spectrum. This is successfully applied to the totally asymmetric simple exclusion process with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and the discreteness of the system is not effective.

  12. Orbital period variability in the eclipsing pulsar binary PSR B1957+20: Evidence for a tidally powered star

    NASA Technical Reports Server (NTRS)

    Applegate, James H.; Shaham, Jacob

    1994-01-01

    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.

  13. Improved short-time propagator for repulsive inverse-power-law potentials

    NASA Astrophysics Data System (ADS)

    Lolle, Lene I.; Gray, C. G.; Poll, J. D.; Basile, A. G.

    1991-02-01

    Recently Makri and Miller have shown that the standard Trotter approximation for the short-time propagator K( x0, x, t) can be greatly improved by writing K( x0, x, t) in exponential form and then systematically expanding the exponent in powers of the time t. The Makri-Miller method is based on the assumption that in the semiclassical limit, there is a unique classical path which connects the initial point x0 to the final point x in the time t. We show that for potentials such as repulsive inverse power-laws, which admit two classical paths connecting the given end points in the given time, further improvement can be made by expanding the exponents of the two terms corresponding to the two paths. Numerical tests for the inverse square potential, for which analytic results are available for comparison, show that such further improvements can be substantial. The tests are carried out for real, imaginary, and complex times.

  14. Evaluation of flow rate for a one-dimensional lava flow with power-law rheology

    NASA Astrophysics Data System (ADS)

    Piombo, Antonello; Dragoni, Michele

    2009-11-01

    During the emplacement lava behaves as a non-Newtonian, pseudoplastic fluid. Laboratory experiments on lava samples suggest that a power-law constitutive equation may be appropriate. We consider a horizontally unbounded, isothermal layer of lava, flowing down a slope driven by the gravity force. We consider a constitutive equation where shear stress is proportional to strain rate raised to a power n, ranging from 0 to 1, and we take into account the temperature dependence of the rheological parameters. Formulae are obtained relating the lava rheology to the geometric and dynamic parameters of a lava flow. Under the model assumptions, if we know the temperature dependence of the rheological parameters, these formulae allow to evaluate the flow rate from the field measurements of the temperature, and the thickness or the surface velocity of a lava flow.

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

    PubMed

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

    2013-06-01

    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 α=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. PMID:23848757

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

    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.

  17. Quantifying two-dimensional nonstationary signal with power-law correlations by detrended fluctuation analysis

    NASA Astrophysics Data System (ADS)

    Fan, Qingju; Wu, Yonghong

    2015-08-01

    In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.

  18. The Common Law Power of the Legislature: Insurer Conversions and Charitable Funds

    PubMed Central

    Horwitz, Jill R; Fremont-Smith, Marion R

    2005-01-01

    New York's Empire Blue Cross and Blue Shield conversion from nonprofit to for-profit form has considerable legal significance. Three aspects of the conversion make the case unique: the role of the state legislature in directing the disposition of the conversion assets, the fact that it made itself the primary beneficiary of those assets, and the actions of the state attorney general defending the state rather than the public interest in the charitable assets. Drawing on several centuries of common law rejecting the legislative power to direct the disposition of charitable funds, this article argues that the legislature lacked power to control the conversion and direct the disposition of its proceeds and that its actions not only undermined the nonprofit form but also raised constitutional concerns. PMID:15960770

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

    NASA Astrophysics Data System (ADS)

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

    2005-12-01

    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.

  20. Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

    NASA Astrophysics Data System (ADS)

    Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun

    2015-01-01

    Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass meff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation νt and change in spectral index for scalar perturbation νst to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of ns=0.96 by having a non-zero value of effective mass of the inflaton field m2eff/H2. The analysis with WP + Planck likelihood shows a non-zero detection of m2eff/H2 with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m2eff/H2 = -0.0237 ± 0.0135 which is consistent with zero.

  1. Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

    NASA Technical Reports Server (NTRS)

    Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

    2015-01-01

    Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

  2. Metabolic Engineering with power-law and linear-logarithmic systems.

    PubMed

    Marin-Sanguino, Alberto; Torres, Nestor V; Mendoza, Eduardo R; Oesterhelt, Dieter

    2009-03-01

    Metabolic Engineering aims to improve the performance of biotechnological processes through rational manipulation rather than random mutagenesis of the organisms involved. Such a strategy can only succeed when a mathematical model of the target process is available. Simplifying assumptions are often needed to cope with the complexity of such models in an efficient way, and the choice of such assumptions often leads to models that fall within a certain structural template or formalism. The most popular formalisms can be grouped in two categories: power-law and linear-logarithmic. As optimization and analysis of a model strongly depends on its structure, most methods in Metabolic Engineering have been defined within a given formalism and never used in any other. In this work, the four most commonly used formalisms (two power-law and two linear-logarithmic) are placed in a common framework defined within Biochemical Systems Theory. This framework defines every model as matrix equations in terms of the same parameters, enabling the formulation of a common steady state analysis and providing means for translating models and methods from one formalism to another. Several Metabolic Engineering methods are analysed here and shown to be variants of a single equation. Particularly, two problem solving philosophies are compared: the application of the design equation and the solution of constrained optimization problems. Generalizing the design equation to all the formalisms shows it to be interchangeable with the direct solution of the rate law in matrix form. Furthermore, optimization approaches are concluded to be preferable since they speed the exploration of the feasible space, implement a better specification of the problem and exclude unrealistic results. Beyond consolidating existing knowledge and enabling comparison, the systematic approach adopted here can fill the gaps between the different methods and combine their strengths. PMID:19174172

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

    NASA Technical Reports Server (NTRS)

    Weisskopf, Martin C.

    2008-01-01

    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.

  4. Vortex Lattice Metastability and Power Law Dynamics in MgB2

    NASA Astrophysics Data System (ADS)

    Rastovski, Catherine; Kuhn, S. J.; Smith, K.; Eskildsen, M. R.; Debeer-Schmitt, L.; Dewhurst, C. D.; Gannon, W. J.; Zhigadlo, N. D.; Karpinski, J.

    2014-03-01

    Previous small-angle neutron scattering (SANS) studies of the vortex lattice (VL) of MgB2 with H ∥ c found a triangular VL which undergoes a field-driven 30° reorientation transition, forming three distinct ground state phases. A high degree of metastability exists between the VL phases of MgB2 that cannot be attributed to vortex pinning and may be a result of the jamming of VL domains [C. Rastovski et al., Phys. Rev. Lett. 111, 107002 (2013)]. To further investigate the effect of vortex motion on the metastable to ground state VL transition, we applied a small AC magnetic field parallel or perpendicular to the vortices to ``shake'' the lattice. The metastable VL volume fraction decreased with a two-step power law dependence on the number of applied AC cycles. The slow and then fast power law decay of the metastable state may indicate first nucleation and then growth of ground state VL domains. This work was supported by the Department of Energy, Basic Energy Sciences under Award No. DE-FG02-10ER46783.

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

    NASA Astrophysics Data System (ADS)

    Sornette, D.

    2002-06-01

    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 rδ, 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> rδ 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.

  6. Moduli of curve families and (quasi-)conformality of power-law entropies

    NASA Astrophysics Data System (ADS)

    Kalogeropoulos, Nikos

    2016-03-01

    We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the calculations of the moduli of curve families for a cylinder and for an annulus in ℝn. The underlying motivation for these studies is that the definitions and some properties of the modulus of a curve family resembles those of the Tsallis entropy, when the latter is seen from a micro-canonical viewpoint. We comment on the origin of the conjectured invariance of the Tsallis entropy under Möbius transformations of the non-extensive (entropic) parameter. Needing techniques applicable to both locally Euclidean and fractal classes of spaces, we examine the behavior of the Tsallis functional, via the modulus, under quasi-conformal maps. We comment on properties of such maps and their possible significance for the dynamical foundations of power-law entropies.

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

    PubMed Central

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

    2013-01-01

    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

  8. Power law scaling and ``Dragon-Kings'' in distributions of intraday financial drawdowns

    NASA Astrophysics Data System (ADS)

    Filimonov, Vladimir; Sornette, Didier

    2015-05-01

    We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of epsilon-drawdowns and epsilon-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (dragon-kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.

  9. Ruling out the power-law form of the scalar primordial spectrum

    SciTech Connect

    Hazra, Dhiraj Kumar; Shafieloo, Arman; Smoot, George F.; Starobinsky, Alexei A. E-mail: arman@apctp.org E-mail: alstar@landau.ac.ru

    2014-06-01

    Combining Planck CMB temperature [1] and BICEP2 B-mode polarization data [2,3] we show qualitatively that, assuming inflationary consistency relation, the power-law form of the scalar primordial spectrum is ruled out at more than 3σ CL. This is an important finding, since the power-law form of the scalar primordial spectrum is one of the main assumptions of concordance model of cosmology and also a direct prediction of many inflationary scenarios. We show that a break or step in the form of the primordial scalar perturbation spectrum, similar to what we studied recently analyzing Planck data [4], can address both Planck and BICEP2 results simultaneously. Our findings also indicate that the data may require more flexibilities than what running of scalar spectral index can provide. Finally we show that an inflaton potential, originally appeared in [5], can generate both the step and the break model of scalar primordial spectrum in two different limits. The discussed potential is found to be favored by Planck data but marginally disfavored by BICEP2 results as it produces slightly lower amplitude of tensor primordial spectrum. Hence, if the tensor-to-scalar ratio (r) quoted by BICEP2 persists, it is of importance that we generate inflationary models with large r and at the same time provide suppression in scalar primordial spectrum at large scales.

  10. The MLP distribution: a modified lognormal power-law model for the stellar initial mass function

    NASA Astrophysics Data System (ADS)

    Basu, Shantanu; Gil, M.; Auddy, Sayantan

    2015-05-01

    This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modelling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.

  11. Underestimating extreme events in power-law behavior due to machine-dependent cutoffs

    NASA Astrophysics Data System (ADS)

    Radicchi, Filippo

    2014-11-01

    Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subject to severe machine-dependent limitations. As a result, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, which are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies, they also pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.

  12. Lifetimes of metastable ion clouds in a Paul trap: Power-law scaling

    NASA Astrophysics Data System (ADS)

    Weiss, D. K.; Nam, Y. S.; Blümel, R.

    2016-04-01

    It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime τ¯m of the metastable cloud follows a power law, τ¯m˜(γ-γc) -β , where γc is the value of the damping constant at which the transition occurs. The exponent β depends on the trap control parameter q , but is independent of both the number of particles N stored in the trap and the trap control parameter a , which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given a and q , γc scales approximately like γc=C ln[ln(N ) ] +D as a function of N , where C and D are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.

  13. Spectral function of the Tomonaga-Luttinger model revisited: Power laws and universality

    NASA Astrophysics Data System (ADS)

    Markhof, L.; Meden, V.

    2016-02-01

    We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum dependence of the two-particle interaction V (q ) . Usually, V (q ) is assumed to be a constant and integrals are regularized in the ultraviolet "by hand" employing an ad hoc procedure. As the momentum dependence of the interaction is irrelevant in the renormalization group sense, this does not affect the universal low-energy properties of the model, e.g., exponents of power laws, if all energy scales are sent to zero. If, however, the momentum k is fixed away from the Fermi momentum kF, with |k - kF| setting a nonvanishing energy scale, the details of V (q ) start to matter. We provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys power-law scaling of the momentum-resolved spectral function as a function of energy. Even for |k - kF| much smaller than the momentum-space range of the interaction the spectral line shape depends on the details of V (q ) . The significance of our results for universality in the Luttinger liquid sense, for experiments on quasi-one-dimensional metals, and for recent results on the spectral function of one-dimensional correlated systems taking effects of the curvature of the single-particle dispersion into account ("nonlinear LL phenomenology") is discussed.

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

    NASA Astrophysics Data System (ADS)

    Ormerod, Paul

    2002-11-01

    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.

  15. Power-law optical conductivity from unparticles: Application to the cuprates

    NASA Astrophysics Data System (ADS)

    Limtragool, Kridsanaphong; Phillips, Philip

    2015-10-01

    We calculate the optical conductivity by using several models for unparticle or scale-invariant matter. Within a Gaussian action for unparticles that is gauged with Wilson lines, we find that the conductivity computed from the Kubo formalism with vertex corrections yields no nontrivial deviation from the free-theory result. This result obtains because, at the Gaussian level, unparticles are just a superposition of particle fields and hence any transport property must be consistent with free theory. Beyond the Gaussian approach, we adopt the continuous-mass formulation of unparticles and calculate the Drude conductivity directly. We show that unparticles in this context can be tailored to yield an algebraic conductivity that scales as ω-2 /3 with the associated phase angle between the imaginary and real parts of arctanσ/2σ1=60∘ , as is seen in the cuprates. Given the recent results [J. High Energy Phys. 4, 40 (2014), 10.1007/JHEP04(2014)040; J. High Energy Phys. 7, 24 (2015), 10.1007/JHEP07(2015)024; arXiv:1506.06769] that gravitational crystals lack a power-law optical conductivity, this constitutes the first consistent account of the ω-2 /3 conductivity and the phase angle seen in optimally doped cuprates. Our results indicate that, at each frequency in the scaling regime, excitations on all energy scales contribute. Hence, incoherence is at the heart of the power law in the optical conductivity in strongly correlated systems such as the cuprates.

  16. Escort mean values and the characterization of power-law-decaying probability densities

    NASA Astrophysics Data System (ADS)

    Tsallis, C.; Plastino, A. R.; Alvarez-Estrada, R. F.

    2009-04-01

    Escort mean values (or q-moments) constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like power laws. They naturally appear in the study of many complex dynamical systems, particularly those obeying nonextensive statistical mechanics, a current generalization of the Boltzmann-Gibbs theory. They recover standard mean values (or moments) for q =1. Here we discuss the characterization of a (non-negative) probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities, provided that all of them converge. This opens the door to a natural extension of the well-known characterization, for the q =1 instance, of a distribution in terms of the standard moments, provided that all of them have finite values. This question would be specially relevant in connection with probability densities having divergent values for all nonvanishing standard moments higher than a given one (e.g., probability densities asymptotically decaying as power laws), for which the standard approach is not applicable. The Cauchy-Lorentz distribution, whose second and higher even order moments diverge, constitutes a simple illustration of the interest of this investigation. In this context, we also address some mathematical subtleties with the aim of clarifying some aspects of an interesting nonlinear generalization of the Fourier transform, namely, the so-called q-Fourier transform.

  17. Influence of the power law index on the fiber breakage during injection molding by numerical simulations

    NASA Astrophysics Data System (ADS)

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

    2013-04-01

    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.

  18. Polarized Synchrotron Emissivities and Absorptivities for Relativistic Thermal, Power-law, and Kappa Distribution Functions

    NASA Astrophysics Data System (ADS)

    Pandya, Alex; Zhang, Zhaowei; Chandra, Mani; Gammie, Charles F.

    2016-05-01

    Synchrotron emission and absorption determine the observational appearances of many astronomical systems. In this paper, we describe a numerical scheme for calculating synchrotron emissivities and absorptivities in all four Stokes parameters for arbitrary gyrotropic electron distribution functions, building on earlier work by Leung, Gammie, and Noble. We use this technique to evaluate the emissivities and the absorptivities for a thermal (Maxwell–Jüttner), isotropic power-law, and an isotropic kappa distribution function. The latter contains a power-law tail at high particle energies that smoothly merges with a thermal core at low energies, as is characteristic of observed particle spectra in collisionless plasmas. We provide fitting formulae and error bounds on the fitting formulae for use in codes that solve the radiative transfer equation. The numerical method and the fitting formulae are implemented in a compact C library called symphony. We find that the kappa distribution has a source function that is indistinguishable from a thermal spectrum at low frequency and transitions to the characteristic self-absorbed synchrotron spectrum, \\propto {ν }5/2, at high frequency; the linear polarization fraction for a thermal spectrum is near unity at high frequency; and all distributions produce O(10%) circular polarization at low frequency for lines of sight sufficiently close to the magnetic field vector.

  19. Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks

    NASA Astrophysics Data System (ADS)

    Cota, Wesley; Ferreira, Silvio C.; Ódor, Géza

    2016-03-01

    We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space λ1<λ <λ2 , suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at λ2. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at λc=0 . Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.

  20. THE POWER-LAW SPECTRA OF ENERGETIC PARTICLES DURING MULTI-ISLAND MAGNETIC RECONNECTION

    SciTech Connect

    Drake, J. F.; Swisdak, M.; Fermo, R. E-mail: swisdak@umd.edu

    2013-01-20

    Power-law distributions are a near-universal feature of energetic particle spectra in the heliosphere. Anomalous cosmic rays (ACRs), super-Alfvenic ions in the solar wind, and the hardest energetic electron spectra in flares all have energy fluxes with power laws that depend on energy E approximately as E {sup -1.5}. We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omnidirectional particle distribution f (v, t) that is solved in closed form to reveal v {sup -5} (corresponding to an energy flux varying as E {sup -1.5}) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state, the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems.

  1. Transition from Exponential to Power Law Income Distributions in a Chaotic Market

    NASA Astrophysics Data System (ADS)

    Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo

    Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

  2. Sudden expansion of the Lieb-Liniger gas from power-law traps

    NASA Astrophysics Data System (ADS)

    Kheruntsyan, Karen; Campbell, A. S.; Gangardt, D. M.

    2015-05-01

    We study free expansion of an interacting one-dimensional Bose gas (described, in the uniform limit, by the integrable Lieb-Liniger model) in a confinement quench scenario of being suddenly released from the ground state of the trapping potential. We consider the general case of power-law traps and, by using the stationary phase and local density approximations, show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the thermodynamic Bethe ansatz equations. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the known scaling solutions of the hydrodynamic approach corresponding to self-similar expansion. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the shape variation of the density profile during the evolution on the trap anharmonicity. We also characterize dynamical fermionization of an expanding cloud in terms of its first- and second-order coherences describing phase and density fluctuations.

  3. Bose-Einstein condensation in dark power-law laser traps

    SciTech Connect

    Jaouadi, A.; Gaaloul, N.; Viaris de Lesegno, B.; Pruvost, L.; Telmini, M.; Charron, E.

    2010-08-15

    We investigate theoretically an original route to achieve Bose-Einstein condensation using dark power-law laser traps. We propose to create such traps with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling their azimuthal order l allows for the exploration of a multitude of power-law trapping situations in one, two, and three dimensions, ranging from the usual harmonic trap to an almost square-well potential, in which a quasihomogeneous Bose gas can be formed. The usual cigar-shaped and disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take the generic form of a 'finger' or of a 'hockey puck' in such Laguerre-Gaussian traps. In addition, for a fixed atom number, higher transition temperatures are obtained in such configurations when compared with a harmonic trap of the same volume. This effect, which results in a substantial acceleration of the condensation dynamics, requires a better but still reasonable focusing of the Laguerre-Gaussian beams.

  4. Power-law scaling for macroscopic entropy and microscopic complexity: Evidence from human movement and posture

    NASA Astrophysics Data System (ADS)

    Hong, S. Lee; Bodfish, James W.; Newell, Karl M.

    2006-03-01

    We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.

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

    PubMed

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

    2014-05-01

    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

  6. Extended power-law scaling of self-affine signals exhibiting apparent multifractality

    NASA Astrophysics Data System (ADS)

    Guadagnini, Alberto; Neuman, Shlomo P.

    2011-07-01

    Many earth and environmental variables appear to scale as multiplicative (multifractal) processes with spatial or temporal increments possessing Gaussian or heavy-tailed distributions. The behavior, characterized by power-law scaling, is typically limited to intermediate ranges of separation scales (lags) considered, in the case of fully developed turbulence, to be dominated by inertia. It has been established empirically that, in numerous cases (e.g. turbulence, diffusion-limited aggregates, natural images, kinetic surface roughening, fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel-bed mobility, barometric pressure, low-energy cosmic rays, cosmic microwave background radiation, metal-insulator transition, irregularities in human heartbeat time series, turbulence in edge magnetized plasma of fusion devices and turbulent boundary layers of the Earth's magnetosphere), this range of lags can be enlarged significantly, at both ends of the spectrum, via a procedure known as Extended Self-Similarity (ESS). We demonstrate numerically that a similar procedure extends the power-law scaling range over which additive (self-affine) signals exhibit apparent multifractality. We conclude that signals appearing to exhibit either standard or extended (such as those listed) multifractal scaling may potentially represent self-affine processes.

  7. Power and Nonpower Laws of Passive Scalar Moments Convected by Isotropic Turbulence

    NASA Astrophysics Data System (ADS)

    Gotoh, Toshiyuki; Watanabe, Takeshi

    2015-09-01

    The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at Rλ=805 and Sc=0.72 is studied by using direct numerical simulation with N =40963 grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the n th-order moments of the scalar increment δ θ (r ) do not obey a simple power law, but have the local scaling exponents ξnθ+βnlog (r /r*) with βn>0 . In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments.

  8. Power and nonpower laws of passive scalar moments convected by isotropic turbulence.

    PubMed

    Gotoh, Toshiyuki; Watanabe, Takeshi

    2015-09-11

    The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at R_{λ}=805 and Sc=0.72 is studied by using direct numerical simulation with N=4096^{3} grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the nth-order moments of the scalar increment δθ(r) do not obey a simple power law, but have the local scaling exponents ξ_{n}^{θ}+β_{n}log(r/r_{*}) with β_{n}>0. In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments. PMID:26406833

  9. Universal correlations and power-law tails in financial covariance matrices

    NASA Astrophysics Data System (ADS)

    Akemann, G.; Fischmann, J.; Vivo, P.

    2010-07-01

    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 data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.

  10. Scaling law and general expression for transport ac loss of a rectangular thin strip with power-law E(J) relation

    NASA Astrophysics Data System (ADS)

    Chen, Du-Xing; Li, Shuo; Fang, Jin

    2015-12-01

    Transport ac loss Q of a superconducting rectangular thin strip obeying a power-law relation E∝Jn as a function of current amplitude Im may be, following Norris, expressed by normalized quantities as q(im). A scaling law is deduced that if Icf, Ic and f being the critical current and frequency, is multiplied by a positive constant C, then im and qm are multiplied by C 1 /(n - 1)and C 2 /(n - 1) , respectively. Based on this scaling law and the well-known Norris formula, the general function of q(im, n, f) is obtained graphically or analytically for any practical purpose, after accurate numerical computations on a set of q(im) at several values of n and a fixed value of f.

  11. A new exact and more powerful unconditional test of no treatment effect from binary matched pairs.

    PubMed

    Lloyd, Chris J

    2008-09-01

    We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization, producing what I call an E+M P-value. The E+M P-value based on McNemar's statistic is shown numerically to dominate previous suggestions, including partially maximized P-values as described in Berger and Sidik (2003, Statistical Methods in Medical Research 12, 91-108). The latter method, however, may have computational advantages for large samples. PMID:18047530

  12. Design and off-design operation of a dual-boiling binary geothermal power plant

    SciTech Connect

    Bliem, C.J. Jr.

    1980-01-01

    The design of a 5 MW(e) geothermal plant using a binary fluid process is described. The second fluid is isobutane. This plant is presently under construction at Raft River, Idaho. A mathematical simulation of the plant is discussed. The heat exchangers were modeled by dividing them into segments in the direction of flow to permit local adjustments in heat transfer coefficients and fluid properties. Sensitivity of plant performance to geofluid temperature and flow rate, heat exchanger fouling and cooling water temperatures were investigated. Conventional correlations were used for the heat transfer coefficients except for the condensing coefficient, which was obtained from a recent study at Lawrence Berkeley Laboratory.

  13. 29 CFR 102.35 - Duties and powers of administrative law judges; stipulations of cases to administrative law...

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... engaged in or is engaging in an unfair labor practice affecting commerce as set forth in the complaint or..., provides for a decision by the Board. A statement of the issues presented should be set forth in the... administrative law judge (or the Board) will set a time for the filing of briefs. In proceedings before...

  14. 29 CFR 102.35 - Duties and powers of administrative law judges; stipulations of cases to administrative law...

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... engaged in or is engaging in an unfair labor practice affecting commerce as set forth in the complaint or..., provides for a decision by the Board. A statement of the issues presented should be set forth in the... administrative law judge (or the Board) will set a time for the filing of briefs. In proceedings before...

  15. 29 CFR 102.35 - Duties and powers of administrative law judges; stipulations of cases to administrative law...

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... engaged in or is engaging in an unfair labor practice affecting commerce as set forth in the complaint or..., provides for a decision by the Board. A statement of the issues presented should be set forth in the... administrative law judge (or the Board) will set a time for the filing of briefs. In proceedings before...

  16. Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses

    NASA Technical Reports Server (NTRS)

    Wijers, Ralph A. M. J.; Lubin, Lori M.

    1994-01-01

    We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.

  17. Evidence for Power Law in the Spectrum of the Coronal Ly-alpha Line

    NASA Astrophysics Data System (ADS)

    Telloni, Daniele; Antonucci, Ester; Bruno, Roberto; D'Amicis, Raffaella

    Long time series of the intensity of the hydrogen Lyα line revealed the existence of f-2 power spectra in the corona at low and mid latitudes and very close to the Sun, at 1.7 solar radii. These observations are performed with the UltraViolet Coronagraph Spectrometer (UVCS) on board the Solar and Heliospheric Observatory (SoHO). A preliminary analysis indicates that this scaling extends for more than a decade and terminates at higher frequencies with a flat spectrum indicating the presence of white-noise fluctuations. The frequency corresponding to the knee which separates these two different spectral regimes moves to lower and lower values for observations performed at higher and higher heliographic latitudes. Low-frequency power spectra with a f-2 dependence may be due rapid changes (jumps) in the time series. If these coherent structures are removed from the time series, hydrogen coronal intensity power spectra seem to show a power law following the f-1 scaling which would suggest that 1/f interplanetary noise originates in corona.

  18. New multi-parametric analytical approximations of exponential distribution with power law tails for new cars sells and other applications

    NASA Astrophysics Data System (ADS)

    Garanina, O. S.; Romanovsky, M. Yu.

    2015-06-01

    A multi-parametric family of exponential distributions with various power law tails is introduced and is shown to describe adequately the known distributions of incomes and wealth as well as the recently measured distributions of new car sales. The three or four-parametric families are characterized by effective temperature in the exponential part, the power exponent in the power-law asymptotic part, the coefficient for the transition between the above two parts, and the starting value, if it is not equal to zero. Since the new car sales distributions are found to correspond to known distributions of incomes, the latter may be inferred from the former.

  19. Anomalous power law distribution of total lifetimes of branching processes: application to earthquake aftershock sequences.

    PubMed

    Saichev, A; Sornette, D

    2004-10-01

    We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes ("aftershocks"). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake ("productivity" or "fertility"), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities mu is characterized by a power law approximately 1/ mu(1+gamma) and the bare Omori law for the memory of previous triggering mothers decays slowly as approximately 1/ t(1+theta;) , with 0law approximately 1/ t(1+theta;) into approximately 1/ t(1+theta;/gamma) stems from the nonlinear amplification due to the heavy-tailed distribution of fertilities and the critical nature of the branching cascade process. In the subcritical case n<1 , the crossover from approximately 1/ t(1+theta;/gamma) at early times to approximately 1/ t(1+theta;) at longer times is described. More generally, our results apply to any stochastic branching process with a power-law distribution of offspring per parent and a long memory. PMID:15600476

  20. Anomalous power law distribution of total lifetimes of branching processes: Application to earthquake aftershock sequences

    SciTech Connect

    Saichev, A.; Sornette, D.

    2004-10-01

    We consider a general stochastic branching process, which is relevant to earthquakes, and study the distributions of global lifetimes of the branching processes. In the earthquake context, this amounts to the distribution of the total durations of aftershock sequences including aftershocks of arbitrary generation number. Our results extend previous results on the distribution of the total number of offspring (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We consider a branching model of triggered seismicity, the epidemic-type aftershock sequence model, which assumes that each earthquake can trigger other earthquakes ('aftershocks'). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake ('productivity' or 'fertility'), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities {mu} is characterized by a power law {approx}1/{mu}{sup 1+{gamma}} and the bare Omori law for the memory of previous triggering mothers decays slowly as {approx}1/t{sup 1+{theta}}, with 0<{theta}<1 relevant for earthquakes. Using the tool of generating probability functions and a quasistatic approximation which is shown to be exact asymptotically for large durations, we show that the density distribution of total aftershock lifetimes scales as {approx}1/t{sup 1+{theta}}{sup sol{gamma}} when the average branching ratio is critical (n=1). The coefficient 1<{gamma}=b/{alpha}<2 quantifies the interplay between the exponent b{approx_equal}1 of the Gutenberg-Richter magnitude distribution {approx}10{sup -bm} and the increase {approx}10{sup {alpha}}{sup m} of the number of aftershocks with mainshock magnitude m (productivity), with 0.5<{alpha}<1. The renormalization of the bare Omori decay law {approx}1/t{sup 1+{theta}} into {approx}1/t{sup 1+{theta}}{sup sol{gamma}} stems from the nonlinear amplification due to the heavy-tailed distribution of fertilities and the critical nature of the branching cascade process. In the subcritical case n<1, the crossover from {approx}1/t{sup 1+{theta}}{sup sol{gamma}} at early times to {approx}1/t{sup 1+{theta}} at longer times is described. More generally, our results apply to any stochastic branching process with a power-law distribution of offspring per parent and a long memory.

  1. Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons

    PubMed Central

    Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves

    2009-01-01

    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 Vm 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 Vm 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

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

    SciTech Connect

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

    2013-01-15

    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.

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

    PubMed Central

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

    2013-01-01

    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−β, where k and β are fit coefficients and f is spatial frequency, the exponent β 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−β. The energy dependence of k and β were analyzed. Results: For the 20 mastectomy specimen based numerical phantoms used in the study, the exponent β 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−β, β was independent of E and k(E) = k1[μg(E) − μa(E)]2, where k1 is a constant, and μg(E) and μa(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. PMID:23298092

  4. From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies

    NASA Astrophysics Data System (ADS)

    Soesoo, Alvar; Bons, Paul D.

    2015-07-01

    Magma is generated by partial melting from micrometre-scale droplets at the source and may accumulate to form >100 km-scale plutons. Magma accumulation thus spans well over ten orders of magnitude in scale. Here we provide measurements of migmatitic leucosomes and granitic veins in drill cores from the Estonian Proterozoic basement and outcrops at Masku in SW Finland and Montemor-o-Novo, central Portugal. Despite the differences in size and number of measured leucosomes and magmatic veins, differences in host rock types and metamorphic grades, the cumulative width distribution of the studied magmatic leucosomes/veins follows a power law with exponents usually between 0.7 and 1.8. Published maps of the SE Australian Lachlan Fold Belt were used to investigate the distribution of granitoid pluton sizes. The granites occupy ca. 22 % of the 2.6 × 105 km2 area. The cumulative pluton area distributions show good power law distributions with exponents between 0.6 and 0.8 depending on pluton area group. Using the self-affine nature of pluton shapes, it is possible to estimate the total volume of magma that was expelled from the source in the 2.6 × 105 km2 map area, giving an estimated 0.8 km3 of magma per km2. It has been suggested in the literature that magma batches in the source merge to form ever-bigger batches in a self-organized way. This leads to a power law for the cumulative distribution of magma volumes, with an exponent m V between 1 for inefficient melt extraction, and 2/3 for maximum accumulation efficiency as most of the volume resides in the largest batches that can escape from the source. If m V ≥ 1, the mass of the magma is dominated by small batches; in case m = 2/3, about 50 % of all magma in the system is placed in a single largest batch. Our observations support the model that the crust develops a self-organized critical state during magma generation. In this state, magma batches accumulate in a non-continuous, step-wise manner to form ever-larger accumulations. There is no characteristic length or time scale in the partial melting process or its products. Smallest melt segregations and >km-scale plotuns form the end members of a continuous chain of mergers of magma batches.

  5. A computational analysis of natural convection in a vertical channel with a modified power law non-Newtonian fluid

    SciTech Connect

    Lee, S.R.; Irvine, T.F. Jr.; Greene, G.A.

    1998-04-01

    An implicit finite difference method was applied to analyze laminar natural convection in a vertical channel with a modified power law fluid. This fluid model was chosen because it describes the viscous properties of a pseudoplastic fluid over the entire shear rate range likely to be found in natural convection flows since it covers the shear rate range from Newtonian through transition to simple power law behavior. In addition, a dimensionless similarity parameter is identified which specifies in which of the three regions a particular system is operating. The results for the average channel velocity and average Nusselt number in the asymptotic Newtonian and power law regions are compared with numerical data in the literature. Also, graphical results are presented for the velocity and temperature fields and entrance lengths. The results of average channel velocity and Nusselt number are given in the three regions including developing and fully developed flows. As an example, a pseudoplastic fluid (carboxymethyl cellulose) was chosen to compare the different results of average channel velocity and Nusselt number between a modified power law fluid and the conventional power law model. The results show, depending upon the operating conditions, that if the correct model is not used, gross errors can result.

  6. An Improved Catalog of Halo Wide Binary Candidates

    NASA Astrophysics Data System (ADS)

    Allen, Christine; Monroy-Rodríguez, Miguel A.

    2014-08-01

    We present an improved catalog of halo wide binaries compiled from an extensive literature search. Most of our binaries stem from the common proper motion binary catalogs by Allen et al. and Chanamé & Gould, but we have also included binaries from the lists of Ryan and Zapatero-Osorio & Martín. All binaries were carefully checked and their distances and systemic radial velocities are included when available. Probable membership to the halo population was tested by means of reduced proper motion diagrams for 251 candidate halo binaries. After eliminating obvious disk binaries, we ended up with 211 probable halo binaries, 150 of which have radial velocities available. We compute galactic orbits for these 150 binaries and calculate the time they spend within the galactic disk. Considering the full sample of 251 candidate halo binaries as well as several subsamples, we find that the distribution of angular separations (or expected major semiaxes) follows a power law f(a) ~ a -1 (Oepik's relation) up to different limits. For the 50 most disk-like binaries, those that spend their entire lives within z = ±500 pc, this limit is found to be 19,000 AU (0.09 pc), while for the 50 most halo-like binaries, those that spend on average only 18% of their lives within z = ±500 pc, the limit is 63,000 AU (0.31 pc). In a companion paper, we employ this catalog to establish limits on the masses of the halo massive perturbers (massive compact halo objects).

  7. An improved catalog of halo wide binary candidates

    SciTech Connect

    Allen, Christine; Monroy-Rodríguez, Miguel A.

    2014-08-01

    We present an improved catalog of halo wide binaries compiled from an extensive literature search. Most of our binaries stem from the common proper motion binary catalogs by Allen et al. and Chanamé and Gould, but we have also included binaries from the lists of Ryan and Zapatero-Osorio and Martín. All binaries were carefully checked and their distances and systemic radial velocities are included when available. Probable membership to the halo population was tested by means of reduced proper motion diagrams for 251 candidate halo binaries. After eliminating obvious disk binaries, we ended up with 211 probable halo binaries, 150 of which have radial velocities available. We compute galactic orbits for these 150 binaries and calculate the time they spend within the galactic disk. Considering the full sample of 251 candidate halo binaries as well as several subsamples, we find that the distribution of angular separations (or expected major semiaxes) follows a power law f(a) ∼ a {sup –1} (Oepik's relation) up to different limits. For the 50 most disk-like binaries, those that spend their entire lives within z = ±500 pc, this limit is found to be 19,000 AU (0.09 pc), while for the 50 most halo-like binaries, those that spend on average only 18% of their lives within z = ±500 pc, the limit is 63,000 AU (0.31 pc). In a companion paper, we employ this catalog to establish limits on the masses of the halo massive perturbers (massive compact halo objects).

  8. Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling

    PubMed Central

    Cohen, Joel E.; Xu, Meng

    2015-01-01

    Taylor’s law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species’ population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)b, a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared. PMID:25852144

  9. Random sampling of skewed distributions implies Taylor's power law of fluctuation scaling.

    PubMed

    Cohen, Joel E; Xu, Meng

    2015-06-23

    Taylor's law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species' population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)(b), a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared. PMID:25852144

  10. Thermodynamics of charged rotating dilaton black branes with power-law Maxwell field

    NASA Astrophysics Data System (ADS)

    Zangeneh, M. Kord; Sheykhi, A.; Dehghani, M. H.

    2015-10-01

    In this paper, we construct a new class of charged rotating dilaton black brane solutions, with a complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime, such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both the canonical and the grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of the Maxwell field on the thermal stability of the solutions. We find that, for α ≤ 1, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For α >1, the solutions can encounter an unstable phase depending on the metric parameters.

  11. Power-law sensitivity to initial conditions within a logisticlike family of maps: Fractality and nonextensivity

    NASA Astrophysics Data System (ADS)

    Costa, U. M. S.; Lyra, M. L.; Plastino, A. R.; Tsallis, C.

    1997-07-01

    Power-law sensitivity to initial conditions, characterizing the behavior of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear one-dimensional logisticlike maps xt+1=1-a\\|xt\\|z (z>1 0law Δx(0)-->0[Δx(t)/Δx(0)]=[1+(1-q)λqt]1/(1-q) (equal to eλ1t for q=1, and proportional, for large t, to t1/(1-q) for q≠1 q∈R is the entropic index appearing in the recently introduced nonextensive generalized statistics). The relation between the parameter q and the fractal dimension df of the onset-to-chaos attractor is revealed: q appears to monotonically decrease from 1 (Boltzmann-Gibbs, extensive, limit) to -∞ when df varies from 1 (nonfractal, ergodiclike, limit) to zero.

  12. Modification of Buckley-Leverett and JBN methods for power-law fluids

    SciTech Connect

    Salman, M.; Baghdikian, S.Y.; Handy, L.L.; Yortsos, Y.C.

    1990-05-01

    In of non-Newtonian fluids for mobility control is a standard operation in oil recovery. While the description of the fluid theology during the simultaneous flow of two immiscible phases is in general complicated, significant progress is possible when one of the fluids is of the power-law type. In the latter case the standard methods for flow description and analysis of experimental data must be modified. This paper results such an approach for one-dimensional immiscible displacement. We consider the application of the Buckley-Leverett method and the modification of the JBN technique for measurement of relative permeabilities. The effects of rate and fluid rheology on the displacement features are investigated. It is shown that substantial errors may arise by the direct use of the original JBN method in interpreting unsteady-state experiments. A general modification of the technique is also proposed. 14 refs., 5 figs.

  13. Vertical-channel free convection with a power-law fluid

    SciTech Connect

    Irvine, T.F. Jr.; Wu, K.C.; Schneider, W.J.

    1982-01-01

    A finite-difference solution is presented of the velocity and temperature fields for the flow of an Ostwald-de-Waele (power law) fluid between two vertical isothermal parallel plates under the influence of free convection. Two quantities are of particular interest: the total heat transferred from the plates and the average velocity between the plates. Although these quantities can be presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers, there is an important difference compared to the similar problem involving Newtonian fluids. In the present case, the generalized Prandtl number is not a fluid property but contains a geometric factor and thus the geometry of the system must be specified before the Prandtl number is fixed. The results and the manner in which they can be used are illustrated by a numerical example.

  14. Onsager vortex formation in Bose-Einstein condensates in two-dimensional power-law traps

    NASA Astrophysics Data System (ADS)

    Groszek, Andrew J.; Simula, Tapio P.; Paganin, David M.; Helmerson, Kristian

    2016-04-01

    We study computationally dynamics of quantized vortices in two-dimensional superfluid Bose-Einstein condensates confined in highly oblate power-law traps. We have found that the formation of large-scale Onsager vortex clusters prevalent in steep-walled traps is suppressed in condensates confined by harmonic potentials. However, the shape of the trapping potential does not appear to adversely affect the evaporative heating efficiency of the vortex gas. Instead, the suppression of Onsager vortex formation in harmonic traps can be understood in terms of the energy of the vortex configurations. Furthermore, we find that the vortex-antivortex pair annihilation that underpins the vortex evaporative heating mechanism requires the interaction of at least three vortices. We conclude that experimental observation of Onsager vortices should be the most apparent in flat or inverted-bottom traps.

  15. Radiatively driven winds for different power law spectra. [for explaining narrow and broad quasar absorption lines

    NASA Technical Reports Server (NTRS)

    Beltrametti, M.

    1980-01-01

    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.

  16. Pattern formation and Turing instability in an activator-inhibitor system with power-law coupling

    NASA Astrophysics Data System (ADS)

    dos S. Silva, F. A.; Viana, R. L.; Lopes, S. R.

    2015-02-01

    We investigate activator-inhibitor systems in two spatial dimensions with a non-local coupling, for which the interaction strength decreases with the lattice distance as a power-law. By varying a single parameter we can pass from a local (Laplacian) to a global (all-to-all) coupling type. We derived, from a linear stability analysis of the Fourier spatial modes, a set of conditions for the occurrence of a Turing instability, by which a spatially homogeneous pattern can become unstable. In nonlinear systems the growth of these modes is limited and pattern formation is possible. We have studied some qualitative features of the patterns formed in non-local coupled activator-inhibitor systems described by the Meinhardt-Gierer equations.

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

    NASA Astrophysics Data System (ADS)

    Sinha, Sitabhra

    2006-01-01

    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.

  18. Peristaltic Creeping Flow of Power Law Physiological Fluids through a Nonuniform Channel with Slip Effect.

    PubMed

    Chaube, M K; Tripathi, D; Bég, O Anwar; Sharma, Shashi; Pandey, V S

    2015-01-01

    A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth. PMID:27057132

  19. Power-law approach to steady state in open lattices of noninteracting electrons

    NASA Astrophysics Data System (ADS)

    Medvedyeva, M. V.; Kehrein, S.

    2014-11-01

    We address the question of how a nonequilibrium steady state (NESS) is reached in the Lindbladian dynamics of an open quantum system. We develop an expansion of the density matrix in terms of the NESS excitations, each of which has its own (exponential) decay rate. However, when the decay rates tend to zero for many NESS excitations (the spectral gap of the Liouvillian is closed in the thermodynamic limit), the long-time dynamics of the system can exhibit a power-law behavior. This relaxation to NESS expectation values is determined by the density of states close to zero spectral gap and the value of the operator in these states. We illustrate this main idea on the example of the lattice of noninteracting fermions coupled to Markovian leads at infinite bias voltage. The current comes towards its NESS value starting from a typical initial state as τ-3 /2. This behavior is universal and independent of the space dimension.

  20. Extreme power law in a driven many-particle system without threshold dynamics.

    PubMed

    Mani, Roman; Böttcher, Lucas; Herrmann, Hans J; Helbing, Dirk

    2014-10-01

    We study a one-dimensional system of spatially extended particles, which are attached to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by Gaussian noise and to have dissipative, energy-conserving, or antidissipative (pinball-like) interactions, when the particle density exceeds a critical threshold. While each particle in separation shows a well-behaved behavior characterized by a Gaussian velocity distribution, the interaction of particles at high densities can cause an avalanchelike momentum and energy transfer, which can generate extreme (steep) power laws without a well-defined variance and mean value. Specifically, the velocity variance increases dramatically towards the free boundaries of the driven many-particle system. The model might also have some relevance for better understanding of crowd disasters. Our results suggest that these are most likely caused by passive momentum transfers, not by active pushing. PMID:25375483

  1. Slow synaptic dynamics in a network: From exponential to power-law forgetting

    NASA Astrophysics Data System (ADS)

    Luck, J. M.; Mehta, A.

    2014-09-01

    We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√t relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.

  2. Unification of Small and Large Time Scales for Biological Evolution: Deviations from Power Law

    NASA Astrophysics Data System (ADS)

    Chowdhury, Debashish; Stauffer, Dietrich; Kunwar, Ambarish

    2003-02-01

    We develop a unified model that describes both “micro” and “macro” evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the “microevolution” over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the “macroevolution” over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.

  3. Conductance statistics for the power-law banded random matrix model

    NASA Astrophysics Data System (ADS)

    Martínez-Mendoza, A. J.; Méndez-Bermúdez, J. A.; Varga, Imre

    2010-12-01

    We study numerically the conductance statistics of the one-dimensional (1D) Anderson model with random long-range hoppings described by the Power-law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single-mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT)∝TM2/2, for T⋘Ttyp = exp, for both the critical and the non-critical samples; and (ii) at criticality there is a smooth crossover from localized-like to delocalized-like behavior in the transport properties of the PBRM model by decreasing the fractality of its eigenstates.

  4. An Optimal Power-Law for Synchrony and Lognormally Synaptic Weighted Hub Networks

    NASA Astrophysics Data System (ADS)

    Yasuomi, D. Sato

    2013-09-01

    Details about the structure of a network model are revealed at the spontaneous spike activity level, in which the power-law of synchrony is optimized to that observed in the CA3 hippocampal slice cultures. The network model is subject to spike noise with exponentially distributed interspike intervals. The excitatory (E) and/or inhibitory (I) neurons interact through synapses whose weights show a log-normal distribution. The spike behavior observed in the network model with the appropriate log-normal distributed synaptic weights fits best to that observed in the experiment. The best-fit is then achieved with high activities of I neurons having a hub-like structure, in which the I neurons, subject to optimized spike noise, are intensively projected from low active E neurons.

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

    NASA Technical Reports Server (NTRS)

    Zdziarski, A. A.

    1984-01-01

    Pair equilibrium in thermal plasmas emitting power law photon spectra by repeated Compton scatterings of a soft photon source active galactic nuclei was studied. Dependence of the spectral index on optical thickness and on temperature of the plasma is discussed. The equation for pair equilibrium is solved for the maximum steady luminosity. Analytical solutions for the subrelativistic region, and for the ultrarelativistic region are found. In the transrelativistic region the solutions are expressed by single integrals over the pair production cross sections, performed numerically. The constraints on soft photon source imposed by the condition that the soft photon flux cannot exceed the black-body flux are considered. For the Comptonized synchrotron radiation model a relation between magnetic field strength and output luminosity is found.

  6. Ideal-Modified Bosonic Gas Trapped in AN Arbitrary Three-Dimensional Power-Law Potential

    NASA Astrophysics Data System (ADS)

    Castellanos, E.; Lämmerzahl, C.

    2012-10-01

    We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic three-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. In addition, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.

  7. Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

    NASA Astrophysics Data System (ADS)

    Campbell, A. S.; Gangardt, D. M.; Kheruntsyan, K. V.

    2015-03-01

    We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.

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

    NASA Astrophysics Data System (ADS)

    Marklof, Jens; Strömbergsson, Andreas

    2014-06-01

    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.

  9. Sudden expansion of a one-dimensional bose gas from power-law traps.

    PubMed

    Campbell, A S; Gangardt, D M; Kheruntsyan, K V

    2015-03-27

    We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations. PMID:25860753

  10. Modified bosonic gas trapped in a generic 3-dim power law potential

    NASA Astrophysics Data System (ADS)

    Castellanos, E.; Laemmerzahl, C.

    2014-04-01

    We analyze the consequences caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the condensation temperature is shifted as a consequence of such deformation and show that this fact could be used to provide bounds on the deformation parameters. Additionally, we show that the shift in the condensation temperature, described as a non-trivial function of the number of particles and the trap parameters, could be used as a criterion to analyze the effects caused by a deformed dispersion relation in weakly interacting systems and also in finite size systems.

  11. Architectures engender crises: The emergence of power laws in social networks

    NASA Astrophysics Data System (ADS)

    Tohmé, Fernando; Larrosa, Juan M. C.

    2016-05-01

    Recent financial crises posed a number of questions. The most salient were related to the cogency of derivatives and other sophisticated hedging instruments. One claim is that all those instruments rely heavily on the assumption that events in the world are guided by normal distributions while, instead, all the evidence shows that they actually follow fat-tailed power laws. Our conjecture is that it is the very financial architecture that engenders extreme events. Not on purpose but just because of its complexity. That is, the system has an internal connection structure that is able to propagate and enhance initially small disturbances. The final outcome ends up not being correlated with its triggering event. To support this claim, we appeal to the intuition drawn from the behavior of social networks. Most of the interesting cases constitute scale-free structures. In particular, we contend, those that arise from strategic decisions of the agents.

  12. Dominance of the suppressed: Power-law size structure in tropical forests.

    PubMed

    Farrior, C E; Bohlman, S A; Hubbell, S; Pacala, S W

    2016-01-01

    Tropical tree size distributions are remarkably consistent despite differences in the environments that support them. With data analysis and theory, we found a simple and biologically intuitive hypothesis to explain this property, which is the foundation of forest dynamics modeling and carbon storage estimates. After a disturbance, new individuals in the forest gap grow quickly in full sun until they begin to overtop one another. The two-dimensional space-filling of the growing crowns of the tallest individuals relegates a group of losing, slow-growing individuals to the understory. Those left in the understory follow a power-law size distribution, the scaling of which depends on only the crown area-to-diameter allometry exponent: a well-conserved value across tropical forests. PMID:26744402

  13. Analytical probability density function for the statistics of the ENSO phenomenon: Asymmetry and power law tail

    NASA Astrophysics Data System (ADS)

    Bianucci, M.

    2016-01-01

    This letter has two main goals. The first one is to give a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the El Ninõ-Southern Oscillation (ENSO) phenomenon. The second one is to obtain, from the theory, an analytical expression for the equilibrium density function of the anomaly sea surface temperature, an expression that fits the data from observations well, reproducing the asymmetry and the power law tail of the histograms of the NIÑO3 index. We succeed in these tasks exploiting some recent theoretical results of the author in the field of the dynamical origin of the stochastic processes. More precisely, we apply this approach to the celebrated recharge oscillator model (ROM), weakly interacting by a multiplicative term, with a general deterministic complex forcing (Madden-Julian Oscillations, westerly wind burst, etc.), and we obtain a Fokker-Planck equation that describes the statistical behavior of the ROM.

  14. Peristaltic Creeping Flow of Power Law Physiological Fluids through a Nonuniform Channel with Slip Effect

    PubMed Central

    Chaube, M. K.; Tripathi, D.; Bég, O. Anwar; Sharma, Shashi; Pandey, V. S.

    2015-01-01

    A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth. PMID:27057132

  15. Power Law Versus Exponential Form of Slow Crack Growth of Advanced Structural Ceramics: Dynamic Fatigue

    NASA Technical Reports Server (NTRS)

    Choi, Sung R.; Gyekenyesi, John P.

    2002-01-01

    The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.

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

    PubMed

    Yan, H; Guo, Hao

    2012-01-01

    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 et al. [Phys. Rev. Lett. 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. PMID:22400551

  17. Collision-dependent power law scalings in two dimensional gyrokinetic turbulence

    SciTech Connect

    Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.

    2014-08-15

    Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.

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

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

    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 sleeper spectra at higher energies.

  19. Supernova-blast waves in wind-blown bubbles, turbulent, and power-law ambient media

    NASA Astrophysics Data System (ADS)

    Haid, S.; Walch, S.; Naab, T.; Seifried, D.; Mackey, J.; Gatto, A.

    2016-05-01

    Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media (densities of 0.1 ≥ n0 [cm-3 ≥ 100) with uniform (and with stellar wind blown bubbles), power-law, and turbulent (Mach numbers M from 1 - 100) density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with n(r) ˜ r-2 (for n(r) > nfloor) the amount of momentum injection is solely regulated by the background density nfloor and compares to nuni = nfloor. However, in turbulent ambient media with log-normal density distributions the momentum input can increase by a factor of 2 (compared to the homogeneous case) for high Mach numbers. The average momentum boost can be approximated as p_{_turb}/p_{0} =23.07 (n_{_{0,turb}}/1 cm^{-3})^{-0.12} + 0.82 (ln (1+b2M2))^{1.49}(n_{_{0,turb}}/1 cm^{-3})^{-1.6}. The velocity distributions are broad as gas can be accelerated to high velocities in low-density channels. The model values agree with results from recent, computationally expensive, three-dimensional simulations of SN explosions in turbulent media.

  20. Ecohydrological significance of observed power-law distributions of tree canopy cluster sizes for savanna vegetation

    NASA Astrophysics Data System (ADS)

    Scanlon, T. M.; Caylor, K. K.; Rodriguez-Iturbe, I.

    2004-05-01

    Savanna ecosystems are characterized by sparse tree cover, the pattern of which can provide insight into the processes by which these systems are shaped and maintained. Since water is often considered to be the limiting factor for savanna vegetation, we used mean wet season rainfall (MWSR) as the basis for the selection of six sites along the Kalahari Transect, a north-south aridity gradient in southern Africa. MWSR ranged from 879 mm to 216 mm from the wettest to most arid site, and the corresponding fractional tree cover ranged from 0.65 to 0.04. IKONOS satellite images, having a resolution of 4m in the multi-spectral bands, were acquired for each of these sites and tree canopies were identified by merging the remotely-sensed normalized difference vegetation index data with information taken from ground-based surveys. Analysis of the tree canopy cluster size distributions showed the wettest site to deviate from a power-law distribution as a result of the fractional cover being above the four-neighbor percolation threshold for a square lattice. Four of the five other sites, however, were characterized by distinct power-law distributions, despite having substantially disparate fractional covers. Simple random neutral models were insufficient in describing the tree clustering patterns of the observed savanna landscape, leading us to seek fundamental interactions that could explain the consistent spatial organization. In particular, our cellular automata approach focuses on water use by the savanna vegetation, and how annual variability in this limiting resource can lead to emergent pattern formation.

  1. Deterministic excitable media under Poisson drive: power law responses, spiral waves, and dynamic range.

    PubMed

    Ribeiro, Tiago L; Copelli, Mauro

    2008-05-01

    When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h , the interplay between creation and annihilation of excitable waves leads to an average activity F . It has recently been suggested that in the low-stimulus regime (h approximately 0) the response function F(h) of hypercubic deterministic systems behaves as a power law, F approximately h{m} . Moreover, the response exponent m has been predicted to depend only on the dimensionality d of the lattice, m=1/(1+d) [T. Ohta and T. Yoshimura, Physica D 205, 189 (2005)]. In order to test this prediction, we study the response function of excitable lattices modeled by either coupled Morris-Lecar equations or Greenberg-Hastings cellular automata. We show that the prediction is verified in our model systems for d=1 , 2, and 3, provided that a minimum set of conditions is satisfied. Under these conditions, the dynamic range-which measures the range of stimulus intensities that can be coded by the network activity-increases with the dimensionality d of the network. The power law scenario breaks down, however, if the system can exhibit self-sustained activity (spiral waves). In this case, we recover a scenario that is common to probabilistic excitable media: as a function of the conductance coupling G among the excitable elements, the dynamic range is maximized precisely at the critical value G_{c} above which self-sustained activity becomes stable. We discuss the implications of these results in the context of neural coding. PMID:18643106

  2. A growth model for directed complex networks with power-law shape in the out-degree distribution

    PubMed Central

    Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.

    2015-01-01

    Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141

  3. A growth model for directed complex networks with power-law shape in the out-degree distribution.

    PubMed

    Esquivel-Gómez, J; Stevens-Navarro, E; Pineda-Rico, U; Acosta-Elias, J

    2015-01-01

    Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141

  4. Secondary electron emissions and dust charging currents in the nonequilibrium dusty plasma with power-law distributions

    SciTech Connect

    Gong Jingyu; Du Jiulin

    2012-06-15

    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.

  5. The power-law distribution of gene family size is driven by the pseudogenisation rate's heterogeneity between gene families.

    PubMed

    Hughes, Timothy; Liberles, David A

    2008-05-15

    Genome sequencing has shown that the number of homologous gene families of a given size declines rapidly with family size. A power-law has been shown to provide the best mathematical description of this relationship. However, it remains unclear what evolutionary forces drive this observation. We use models of gene duplication, pseudogenisation and accumulation of replacement substitutions, which have been validated and parameterised using genomic data, to build a model of homologous gene evolution. We use this model to simulate the evolution of the distribution of gene family size and show that the power-law distribution is driven by the pseudogenisation rate's heterogeneity across gene families and its correlation within families. Moreover, we show that gene duplication and pseudogenisation are necessary and sufficient for the emergence of the power-law. PMID:18378100

  6. IMPACT OF TYPE Ia SUPERNOVA EJECTA ON A HELIUM-STAR BINARY COMPANION

    SciTech Connect

    Pan, Kuo-Chuan; Ricker, Paul M.; Taam, Ronald E. E-mail: pmricker@astro.illinois.ed

    2010-05-20

    The impact of Type Ia supernova (SN) ejecta on a helium-star companion is investigated via high-resolution, two-dimensional hydrodynamic simulations. For a range of helium-star models and initial binary separations, it is found that the mass unbound in the interaction, {delta}M{sub ub}, is related to the initial binary separation, a, by a power law of the form {delta}M{sub ub} {proportional_to} a{sup m} . This power-law index is found to vary from -3.1 to -4.0, depending on the mass of the helium star. The small range of this index brackets values found previously for hydrogen-rich companions, suggesting that the dependence of the unbound mass on orbital separation is not strongly sensitive to the nature of the binary companion. The kick velocity is also related to the initial binary separation by a power law with an index in a range from -2.7 to -3.3, but the power-law index differs from those found in previous studies for hydrogen-rich companions. The space motion of the companion after the SN is dominated by its orbital velocity in the pre-SN binary system. The level of Ni/Fe contamination of the companion resulting from the passage of the SN ejecta is difficult to estimate, but an upper limit on the mass of bound nickel is found to be {approx}5 x 10{sup -4} M{sub sun}.

  7. Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

    SciTech Connect

    Mukherjee, Suvodip; Das, Santanu; Souradeep, Tarun; Joy, Minu E-mail: santanud@iucaa.ernet.in E-mail: tarun@iucaa.ernet.in

    2015-01-01

    Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m{sub eff} for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation ν{sub t} and change in spectral index for scalar perturbation ν{sub st} to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of n{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.

  8. Power law relationship between cell cycle duration and cell volume in the early embryonic development of Caenorhabditis elegans

    PubMed Central

    Arata, Yukinobu; Takagi, Hiroaki; Sako, Yasushi; Sawa, Hitoshi

    2015-01-01

    Cell size is a critical factor for cell cycle regulation. In Xenopus embryos after midblastula transition (MBT), the cell cycle duration elongates in a power law relationship with the cell radius squared. This correlation has been explained by the model that cell surface area is a candidate to determine cell cycle duration. However, it remains unknown whether this second power law is conserved in other animal embryos. Here, we found that the relationship between cell cycle duration and cell size in Caenorhabditis elegans embryos exhibited a power law distribution. Interestingly, the powers of the time-size relationship could be grouped into at least three classes: highly size-correlated, moderately size-correlated, and potentially a size-non-correlated class according to C. elegans founder cell lineages (1.2, 0.81, and <0.39 in radius, respectively). Thus, the power law relationship is conserved in Xenopus and C. elegans, while the absolute powers in C. elegans were different from that in Xenopus. Furthermore, we found that the volume ratio between the nucleus and cell exhibited a power law relationship in the size-correlated classes. The power of the volume relationship was closest to that of the time-size relationship in the highly size-correlated class. This correlation raised the possibility that the time-size relationship, at least in the highly size-correlated class, is explained by the volume ratio of nuclear size and cell size. Thus, our quantitative measurements shed a light on the possibility that early embryonic C. elegans cell cycle duration is coordinated with cell size as a result of geometric constraints between intracellular structures. PMID:25674063

  9. In search of temporal power laws in the orientational relaxation near isotropic-nematic phase transition in model nematogens

    NASA Astrophysics Data System (ADS)

    Jose, Prasanth P.; Bagchi, Biman

    2004-06-01

    Recent Kerr relaxation experiments by Gottke et al. [J. Chem. Phys. 116, 360 (2002); 116, 6339 (2002)] have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, κ (κ≃3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t-α) with exponent α˜2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

  10. Fitting power-law distributions to geomorphological frequency-magnitude data: a good fingerprint for self-organised criticality?

    NASA Astrophysics Data System (ADS)

    Eadie, Chris; Favis-Mortlock, Dave

    2010-05-01

    Frequency-magnitude analysis has long been a staple of geomorphology. However, in recent years increased awareness of self-organised criticality (SOC) has led geomorphologists to look at frequency-magnitude relationships in a new light. One fingerprint of SOC is a power-law frequency-magnitude relationship. Many geomorphological studies claim to have identified such a relationship, and thus suggest that SOC has a role in determining the dynamics of many kinds of geomorphological systems. If so, there are clear implications for the management of these systems, particularly with regard to extreme events. But how conclusive is the evidence for SOC in geomorphological systems? This paper does not provide an answer. It does, however, question the methodology which is commonly used to determine whether geomorphological frequency-magnitude data are a good fit to a power-law distribution, and hence whether this SOC fingerprint is present. The great majority of published studies which claim to have found a power-law in measured data have done so by fitting a straight line to the data as plotted on log-log axes. One of two techniques is invariably used to estimate the fit: simple visual inspection, or least-squares-based linear regression. Least-squares-based linear regression is of course more objective than visual assessment. Nonetheless, several studies point out that the use of least squares for linear regression in log-log cartesian space is problematic, giving rise to systematically biased estimates of the fit: e.g. Goldstein et al. (2004) calculated that the associated error could be as much as 36 %. This has implications for all studies which use linear regression to fit power-law lines. A number of authors in the statistical literature (most notably Clauset et al., 2009) have recently proposed alternative, more robust, methods. These include logarithmic binning, linear fitting of only the first five points, least squares probability density function, least squares cumulative density function, and maximum likelihood estimation (MLE). Some of these approaches can be extended to determine whether a power-law is indeed the best fit, or whether the data would be better fitted by another tail-heavy distribution, such as the log-normal or the exponential. This paper presents the results obtained by fitting power-laws to Irish river flow data using MLE. Additional tests were also carried out to ascertain whether the power-law is a statistically appropriate model for the data. Results show that a power-law distribution cannot be ruled out for 19 of the 36 rivers in this study.

  11. Magnetized plasma sheath with two positive ions where collision frequencies have a power law dependency on ions velocities

    NASA Astrophysics Data System (ADS)

    Masoudi, S. Farhad; Khoramabadi, Mansor

    2015-09-01

    We study the dynamics of collisional magnetized plasma sheath with two species of positive ions by using the plasma fluid model. The basic equations of the fluid model are solved numerically where the sheath is in the external magnetic field and the elastic collision between ions and neutrals has been taken into account. In our model, we assume that the collisional momentum transferring cross section has a power law dependency on ion flow velocity. Our analysis demonstrates that the sheath dynamics are sensitive to the power law dependency, especially for the ion with greater density.

  12. A simple marriage model for the power-law behaviour in the frequency distributions of family names

    NASA Astrophysics Data System (ADS)

    Wu, Hao-Yun; Chou, Chung-I.; Tseng, Jie-Jun

    2011-01-01

    In many countries, the frequency distributions of family names are found to decay as a power law with an exponent ranging from 1.0 to 2.2. In this work, we propose a simple marriage model which can reproduce this power-law behaviour. Our model, based on the evolution of families, consists of the growth of big families and the formation of new families. Preliminary results from the model show that the name distributions are in good agreement with empirical data from Taiwan and Norway.

  13. Hydrodynamics-Based Functional Forms of Activity Metabolism: A Case for the Power-Law Polynomial Function in Animal Swimming Energetics

    PubMed Central

    Papadopoulos, Anthony

    2009-01-01

    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 describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined. PMID:19333397

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

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

    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.

  15. Wave-speed dispersion associated with an attenuation obeying a frequency power law.

    PubMed

    Buckingham, Michael J

    2015-11-01

    An attenuation scaling as a power of frequency, |ω|(β), over an infinite bandwidth is neither analytic nor square-integrable, thus calling into question the application of the Kramers-Krönig dispersion relations for determining the frequency dependence of the associated phase speed. In this paper, three different approaches are developed, all of which return the dispersion formula for the wavenumber, K(ω). The first analysis relies on the properties of generalized functions and the causality requirement that the impulse response, k(t), the inverse Fourier transform of -iK(ω), must vanish for t < 0. Second, a wave equation is introduced that yields the phase-speed dispersion associated with a frequency-power-law attenuation. Finally, it is shown that, with minor modification, the Kramers-Krönig dispersion relations with no subtractions (the Plemelj formulas) do in fact hold for an attenuation scaling as |ω|(β), yielding the same dispersion formula as the other two derivations. From this dispersion formula, admissible values of the exponent β are established. Physically, the inadmissible values of β, which include all the integers, correspond to attenuation-dispersion pairs whose Fourier components cannot combine in such a way as to make the impulse response, k(t), vanish for t < 0. There is no upper or lower limit on the value that β may take. PMID:26627763

  16. A Recommended Procedure for Estimating the Cosmic Ray Spectral Parameter of a Simple Power Law

    NASA Technical Reports Server (NTRS)

    Howell, Leonard W.; Rose, M. Franklin (Technical Monitor)

    2000-01-01

    A simple power law model consisting of a single spectral index a(f(sub i)) is believed to be an adequate description of the galactic cosmic ray (GQ proton flux at energies below 1013 eV. Two procedures for estimating a(f(sub i)), referred as (1) the method of moments, and (2) maximum likelihood, are developed and their statistical performance compared. I concluded that the maximum likelihood procedure attains the most desirable statistical properties and is hence the recommended statistic estimation procedure for estimating a1. The maximum likelihood procedure is then generalized for application to a set of real cosmic ray data and thereby makes this approach applicable to existing cosmic ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution, as well as inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic ray detector because they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose practical limits to the design envelope.

  17. Power Law Behavior and Self-Similarity in Modern Industrial Accidents

    NASA Astrophysics Data System (ADS)

    Lopes, António M.; Tenreiro Machado, J. A.

    Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

  18. Uncertainty in Power Law Analysis: Influences of Sample Size, Measurement Error, and Analysis Methods

    NASA Astrophysics Data System (ADS)

    Hui, D.; Luo, Y.; Jackson, R. B.

    2005-12-01

    A power function, Y=Y0 Mbeta, can be used to describe the relationship of physiological variables with body size over a wide range of scales, typically many orders of magnitude. One of the key issues in the renewed power law debate is whether the allometric scaling exponent β equals 3/4 or 2/3. The analysis could be remarkably affected by sampling size, measurement error, and analysis methods, but these effects have not been explored systematically. We investigated the influences of these three factors based on a data set of 626 pairs of base metabolic rate and mass in mammals with the calculated β=0.711. Influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo approach. Results showed that estimated parameter b varied considerably from sample to sample. For example, when the sample size was n=63, b varied from 0.582 to 0.776. Even though the original data set did not support either β=3/4 or β=2/3, we found that 39.0% of the samples supported β=2/3, 35.4% of the samples supported β=3/4. Influence of measurement error on parameter estimations was also tested using Bayesian theory. Virtual data sets were created using the mass in the above-mentioned data set, with given parameters α and β (β=2/3 or β=3/4) and certain measurement error in base metabolic rate and/or mass. Results showed that as measurement error increased, more estimated bs were found to be significantly different from the parameter β. When measurement error (i.e., standard deviation) was 20% and 40% of the measured mass and base metabolic rate, 15.4% and 14.6% of the virtual data sets were found to be significant different from the parameter β=3/4 and β=2/3, respectively. Influence of different analysis methods on parameter estimations was also demonstrated using the original data set and the pros and cons of these methods were further discussed. We urged cautions in interpreting the power law analysis, especially from a small data sample, and in selecting analysis methods.

  19. Power-law decay characteristic of coda envelopes revealed from the analysis of regional earthquakes

    NASA Astrophysics Data System (ADS)

    Lee, W.; Sato, H.

    2005-12-01

    So far, coda envelopes for wide frequency bands with long lapse time range have been described by bending curves which have several systematic changes in decay rate with lapse time. However, for NS component seismograms of regional earthquakes, applying the Hilbert Transform to make envelope curves and taking regression analysis on the envelopes in period bands from 24 s to 1/6 s for a wide lapse time range up to 4,000 s instead of measuring the peak amplitudes of the coda used previously, we found coda envelopes show the feature of ``power-law'' decay and there is no systematic change of decay gradient except for once occurring around ScS arrival with lapse time. 157 seismic events recorded by 11 IRIS broadband seismic network stations during the period from 1988 to 2005 with focal depths shallower than 50 km (shallow events) and deeper than 150 km (deep events) and with epicentral distance less than 1,000 km from individual seismic station were collected in this study. The moment magnitude of selected events ranges from 4.7 to 7.8. The ``power-law'' decay characteristic of seismic envelopes indicates that the power spectrum of seismic coda could be simply expressed as of the form P( T, t) ~ t - α, where t is lapse time and T is central period. We find that α = 1.6-6.2 for before ScS arrival in all period bands and 0.6-5.3 for after ScS arrival ranging from 24 s to 3/2 s periods. The coda decay gradient at short periods is steeper than that at longer periods for both cases of before and after ScS arrival. In particular, a clear offset of coda amplitude associated with ScS arrival appears in Turkey, Kyrgyzstan and Bolivia at 4-8 s and 8-16 s period bands. These coda decay gradient change and offset behavior in coda envelopes around ScS arrival are not clear in seismograms of shallow events. The simple and distinct characteristics of seismic coda envelopes could provide reliable information to determine physical values such as seismic source parameters and to identify the regional difference of medium heterogeneity in the deep Earth.

  20. Instability of collective excitations and power laws of an attractive Bose-Einstein condensate in an anharmonic trap

    NASA Astrophysics Data System (ADS)

    Debnath, P. K.; Chakrabarti, Barnali

    2010-10-01

    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.PRLTAO0031-900710.1103/PhysRevLett.80.1576 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of (1-(A)/(Acr)), A is the number of condensate atoms and Acr 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.