NASA Astrophysics Data System (ADS)
Ackermann, M.; Asano, K.; Atwood, W. B.; Axelsson, M.; Baldini, L.; Ballet, J.; Barbiellini, G.; Baring, M. G.; Bastieri, D.; Bechtol, K.; Bellazzini, R.; Berenji, B.; Bhat, P. N.; Bissaldi, E.; Blandford, R. D.; Bloom, E. D.; Bonamente, E.; Borgland, A. W.; Bouvier, A.; Bregeon, J.; Brez, A.; Briggs, M. S.; Brigida, M.; Bruel, P.; Buson, S.; Caliandro, G. A.; Cameron, R. A.; Caraveo, P. A.; Carrigan, S.; Casandjian, J. M.; Cecchi, C.; Çelik, Ö.; Charles, E.; Chiang, J.; Ciprini, S.; Claus, R.; Cohen-Tanugi, J.; Connaughton, V.; Conrad, J.; Dermer, C. D.; de Palma, F.; Dingus, B. L.; Silva, E. do Couto e.; Drell, P. S.; Dubois, R.; Dumora, D.; Farnier, C.; Favuzzi, C.; Fegan, S. J.; Finke, J.; Focke, W. B.; Frailis, M.; Fukazawa, Y.; Fusco, P.; Gargano, F.; Gasparrini, D.; Gehrels, N.; Germani, S.; Giglietto, N.; Giordano, F.; Glanzman, T.; Godfrey, G.; Granot, J.; Grenier, I. A.; Grondin, M.-H.; Grove, J. E.; Guiriec, S.; Hadasch, D.; Harding, A. K.; Hays, E.; Horan, D.; Hughes, R. E.; Jóhannesson, G.; Johnson, W. N.; Kamae, T.; Katagiri, H.; Kataoka, J.; Kawai, N.; Kippen, R. M.; Knödlseder, J.; Kocevski, D.; Kouveliotou, C.; Kuss, M.; Lande, J.; Latronico, L.; Lemoine-Goumard, M.; Llena Garde, M.; Longo, F.; Loparco, F.; Lott, B.; Lovellette, M. N.; Lubrano, P.; Makeev, A.; Mazziotta, M. N.; McEnery, J. E.; McGlynn, S.; Meegan, C.; Mészáros, P.; Michelson, P. F.; Mitthumsiri, W.; Mizuno, T.; Moiseev, A. A.; Monte, C.; Monzani, M. E.; Moretti, E.; Morselli, A.; Moskalenko, I. V.; Murgia, S.; Nakajima, H.; Nakamori, T.; Nolan, P. L.; Norris, J. P.; Nuss, E.; Ohno, M.; Ohsugi, T.; Omodei, N.; Orlando, E.; Ormes, J. F.; Ozaki, M.; Paciesas, W. S.; Paneque, D.; Panetta, J. H.; Parent, D.; Pelassa, V.; Pepe, M.; Pesce-Rollins, M.; Piron, F.; Preece, R.; Rainò, S.; Rando, R.; Razzano, M.; Razzaque, S.; Reimer, A.; Ritz, S.; Rodriguez, A. Y.; Roth, M.; Ryde, F.; Sadrozinski, H. F.-W.; Sander, A.; Scargle, J. D.; Schalk, T. L.; Sgrò, C.; Siskind, E. J.; Smith, P. D.; Spandre, G.; Spinelli, P.; Stamatikos, M.; Stecker, F. W.; Strickman, M. S.; Suson, D. J.; Tajima, H.; Takahashi, H.; Takahashi, T.; Tanaka, T.; Thayer, J. B.; Thayer, J. G.; Thompson, D. J.; Tibaldo, L.; Toma, K.; Torres, D. F.; Tosti, G.; Tramacere, A.; Uchiyama, Y.; Uehara, T.; Usher, T. L.; van der Horst, A. J.; Vasileiou, V.; Vilchez, N.; Vitale, V.; von Kienlin, A.; Waite, A. P.; Wang, P.; Wilson-Hodge, C.; Winer, B. L.; Wu, X. F.; Yamazaki, R.; Yang, Z.; Ylinen, T.; Ziegler, M.
2010-06-01
We present detailed observations of the bright short-hard gamma-ray burst GRB 090510 made with the Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) on board the Fermi observatory. GRB 090510 is the first burst detected by the LAT that shows strong evidence for a deviation from a Band spectral fitting function during the prompt emission phase. The time-integrated spectrum is fit by the sum of a Band function with E peak = 3.9 ± 0.3 MeV, which is the highest yet measured, and a hard power-law component with photon index -1.62 ± 0.03 that dominates the emission below ≈20 keV and above ≈100 MeV. The onset of the high-energy spectral component appears to be delayed by ~0.1 s with respect to the onset of a component well fit with a single Band function. A faint GBM pulse and a LAT photon are detected 0.5 s before the main pulse. During the prompt phase, the LAT detected a photon with energy 30.5+5.8 -2.6 GeV, the highest ever measured from a short GRB. Observation of this photon sets a minimum bulk outflow Lorentz factor, Γgsim 1200, using simple γγ opacity arguments for this GRB at redshift z = 0.903 and a variability timescale on the order of tens of ms for the ≈100 keV-few MeV flux. Stricter high confidence estimates imply Γ >~ 1000 and still require that the outflows powering short GRBs are at least as highly relativistic as those of long-duration GRBs. Implications of the temporal behavior and power-law shape of the additional component on synchrotron/synchrotron self-Compton, external-shock synchrotron, and hadronic models are considered.
Ackermann, M.; Bechtol, K.; Berenji, B.; Blandford, R. D.; Bloom, E. D.; Borgland, A. W.; Bouvier, A.; Asano, K.; Atwood, W. B.; Axelsson, M.; Baldini, L.; Bellazzini, R.; Bregeon, J.; Ballet, J.; Baring, M. G.; Bastieri, D.; Bhat, P. N.; Bissaldi, E.; Bonamente, E. E-mail: sylvain.guiriec@lpta.in2p3.f E-mail: ohno@astro.isas.jaxa.j
2010-06-20
We present detailed observations of the bright short-hard gamma-ray burst GRB 090510 made with the Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) on board the Fermi observatory. GRB 090510 is the first burst detected by the LAT that shows strong evidence for a deviation from a Band spectral fitting function during the prompt emission phase. The time-integrated spectrum is fit by the sum of a Band function with E{sub peak} = 3.9 {+-} 0.3 MeV, which is the highest yet measured, and a hard power-law component with photon index -1.62 {+-} 0.03 that dominates the emission below {approx}20 keV and above {approx}100 MeV. The onset of the high-energy spectral component appears to be delayed by {approx}0.1 s with respect to the onset of a component well fit with a single Band function. A faint GBM pulse and a LAT photon are detected 0.5 s before the main pulse. During the prompt phase, the LAT detected a photon with energy 30.5{sup +5.8}{sub -2.6} GeV, the highest ever measured from a short GRB. Observation of this photon sets a minimum bulk outflow Lorentz factor, {Gamma}{approx_gt} 1200, using simple {gamma}{gamma} opacity arguments for this GRB at redshift z = 0.903 and a variability timescale on the order of tens of ms for the {approx}100 keV-few MeV flux. Stricter high confidence estimates imply {Gamma} {approx_gt} 1000 and still require that the outflows powering short GRBs are at least as highly relativistic as those of long-duration GRBs. Implications of the temporal behavior and power-law shape of the additional component on synchrotron/synchrotron self-Compton, external-shock synchrotron, and hadronic models are considered.
NASA Astrophysics Data System (ADS)
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin; Li, Xiaocan
2014-10-01
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density and when the system size is sufficiently large. The power law slope approaches ``-1'' for closed systems and gets softer when particle loss from the acceleration region is included. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection. We demonstrate that both continuous inflow and Fermi-type acceleration lead to the power-law distributions. Finally, we discuss the role of particle anisotropy in particle acceleration during magnetic reconnection. The work shows that hard power-law distributions are a common feature in relativistic magnetic reconnection region, which may be important for explaining the high-energy emissions in systems like pulsars, jets from black holes, and gamma-ray bursts.
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin
2014-10-10
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ ≡ B(2)/(4πnm(e)c(2))>1 and when the system size is sufficiently large. In the limit σ ≫ 1, the spectral index approaches p = 1 and most of the available energy is converted into nonthermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection. PMID:25375716
NASA Astrophysics Data System (ADS)
Guo, Fan; Li, Hui; Daughton, William; Liu, Yi-Hsin
2014-10-01
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ≡B2/(4πnmec2)>1 and when the system size is sufficiently large. In the limit σ≫1, the spectral index approaches p=1 and most of the available energy is converted into nonthermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection.
A HARD X-RAY POWER-LAW SPECTRAL CUTOFF IN CENTAURUS X-4
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.
Evidence for two hard X-ray components in double power-law fits to the 1980 June 7 flare
NASA Technical Reports Server (NTRS)
Smith, Dean F.; Orwig, Larry E.
1988-01-01
The June 7, 1980 flare at 0312 UT was analyzed with double power-law fits on the basis of SMM hard X-ray burst spectrometer data. The flare is found to consist of seven peaks of characteristic time scale of about 8 sec followed by seven valleys which may contain significant peak components because of overlap. It is suggested that the possibility of thermal spectra for the peaks is unlikely. An investigation of the double power-law parameters through the third and fourth peaks revealed a hysteresis effect in the fourth peak. The present results have been interpreted in terms of a trap plus precipitation model.
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.
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Torrilhon, Manuel
2015-08-01
A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence is proven to be convergent to the linearized Boltzmann operator, and it established a connection between the Shakhov model and the linearized collision model. The convergence is demonstrated by solving the spatially homogeneous Boltzmann equation. By observing the magnitudes of the coefficients, simpler models are developed through removing small entries in the coefficient matrices.
NASA Astrophysics Data System (ADS)
Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.
2013-11-01
We explore the nonequilibrium dynamics of a two-dimensional trapped Bose-Einstein condensate excited by a moving red-detuned laser potential. The trap is a combination of a general power-law potential cutoff by a hard wall box potential. The red laser potential is allowed to exit the box potential, leaving the system in a highly nonequilibrium state. This is crucial since the red laser potential squeezes the BEC trapped inside it against the hard wall-boundary at this instant, paving the way for the creation of a shock wave. Once the red laser potential has left the box potential, the Hamiltonian of the system becomes time-independent and the total energy stabilizes. Our systems are simulated by the time-dependent Gross-Ptiaevskii Equation which is numerically solved by the split-step Crank-Nicolson method in real time. It is found that the value at which the total energy stabilizes in the transient stage of the simulation is largely controlled by the initialization process. Before the red laser potential leaves the trap, when the Hamiltonian of the system is still time-dependent, oscillations in the total energy occur if the system is initialized adiabatically by application of a gradually growing and moving red laser potential. If this laser potential is not moving, yet fully present in the initialization process, these oscillations are not observed in the transient stage of the simulation. In addition, the system displays oscillations in the root-mean-square radius of the trapped cloud. The amplitudes of these radial oscillations continue even after the red laser potential leaves the box potential and are used to explore the deviation of the nonstationary states from the corresponding ground states. It is demonstrated that the geometry of the power law potential influences the amplitude of these radial oscillations, reducing them and bringing the systems closer to an equilibrium state. We then argue that by going to tighter trapping geometries, it is not
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.
NASA Astrophysics Data System (ADS)
Hong, Byoung Hee; Lee, Kyoung Eun; Lee, Jae Woo
2007-01-01
We consider the scaling behaviors for fluctuations of the number of Korean firms bankrupted in the period from 1 August 2002 to 28 October 2003. We observe a power law for the distribution of the number of the bankrupted firms. The Pareto exponent is close to unity. We also consider the daily increments of the number of firms bankrupted. The probability distribution of the daily increments for the firms bankrupted follows the Gaussian distribution in central part and has a fat tail. The tail parts of the probability distribution of the daily increments for the firms bankrupted follow a power law.
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.
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. PMID:21946780
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.
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.
Power-law distributions in noisy dynamical systems
NASA Astrophysics Data System (ADS)
Wilkinson, Michael; Guichardaz, Robin; Pradas, Marc; Pumir, Alain
2015-09-01
We consider a dynamical system which is non-autonomous, has a stable attractor and which is perturbed by an additive noise. We establish that under some quite typical conditions, the intermittent fluctuations from the attractor have a probability distribution with power-law tails. We show that this results from a stochastic cascade of amplification of fluctuations due to transient periods of instability. The exponent of the power-law is interpreted as a negative fractal dimension, and is explicitly determined, using numerics or perturbation expansion, in the case of a model of colloidal particles in one-dimension.
Power law inflation with electromagnetism
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.
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.
Power Law Distributions in Two Community Currencies
NASA Astrophysics Data System (ADS)
Kichiji, N.; Nishibe, M.
2007-07-01
The purpose of this paper is to highlight certain newly discovered social phenomena that accord with Zipf's law, in addition to the famous natural and social phenomena including word frequencies, earthquake magnitude, city size, income1 etc. that are already known to follow it. These phenomena have recently been discovered within the transaction amount (payments or receipts) distributions within two different Community Currencies (CC) that had been initiated as social experiments. One is a local CC circulating in a specific geographical area, such as a town. The other is a virtual CC used among members who belong to a certain community of interest (COI) on the Internet. We conducted two empirical studies to estimate the economic vitalization effects they had on their respective local economies. The results we found were that the amount of transactions (payments and receipts) of the two CCs was distributed according to a power-law distribution with a unity rank exponent. In addition, we found differences between the two CCs with regard to the shapes of their distribution over a low-transaction range. The result may originate from the difference in methods of issuing CCs or in the magnitudes of the minimum-value unit; however, this result calls for further investigation.
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.
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.
Power-Law Tails from Dynamical Comptonization in Converging Flows
NASA Astrophysics Data System (ADS)
Turolla, Roberto; Zane, Silvia; Titarchuk, Lev
2002-09-01
The effects of bulk motion Comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semianalytical, diffusion approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates when photon diffusion holds. Our semianalytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method, we find that although the power-law tail at extremely large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Γ=3 at large accretion rates, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft seed photons when the accretion rate is either quite low (<~5 in Eddington units) or sufficiently high (>~10). On the other hand, the spatial distribution of source photons controls the photon index at intermediate accretion rates, when Γ switches from the first to the second mode. Our analysis confirms that a hard tail with photon index Γ<3 is produced by the upscattering of primary photons onto infalling electrons if the central object is a black hole.
Universal power law for the spectrum of breaking Riemann waves
NASA Astrophysics Data System (ADS)
Pelinovsky, Dmitry; Pelinovsky, Efim; Kartashova, Elena; Talipova, Tatiana
2014-05-01
The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation with arbitrary nonlinearity. This equation describe the long surface and internal wave in the coastal zone. The spectrum of spatial amplitudes at the breaking time has an power asymptotic decay with exponent - 4/3. This spectrum is formed by the singularity of the form like x1/3 in the wave shape at the breaking time. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg-de Vries equations.
Power law analysis of the human microbiome.
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
Fractal power law in literary English
NASA Astrophysics Data System (ADS)
Gonçalves, L. L.; Gonçalves, L. B.
2006-02-01
We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.
Variational Principle for the Pareto Power Law
NASA Astrophysics Data System (ADS)
Chakraborti, Anirban; Patriarca, Marco
2009-11-01
A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system.
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.
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.
Variational principle for the Pareto power law.
Chakraborti, Anirban; Patriarca, Marco
2009-11-27
A mechanism is proposed for the appearance of power-law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system. PMID:20366128
Relativity, nonextensivity, and extended power law distributions.
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
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.
Power law deformation of Wishart Laguerre ensembles of random matrices
NASA Astrophysics Data System (ADS)
Akemann, Gernot; Vivo, Pierpaolo
2008-09-01
We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of β, in terms of the orthogonal polynomials of the standard Wishart-Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Marčenko-Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on β and the difference M-N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart-Laguerre ensembles. To illustrate these findings, the generalized Marčenko-Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices.
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.
Power-law Decay and the Ergodic-Nonergodic Transition in Simple Fluids
NASA Astrophysics Data System (ADS)
Spyridis, Paul; Mazenko, Gene F.
2014-02-01
It is well known that mode coupling theory (MCT) leads to a two-step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic theory developed in the Fundamental Theory of Statistical Particle Dynamics (Mazenko in Phys Rev E 81(6):061102, 2010). We show how the power-law exponents can be computed in the second-order approximation where we treat hard-sphere fluids with statics described by the Percus-Yevick solution.
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.
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.
Study on local resistance of non-Newtonian power law fluid in elbow pipes
NASA Astrophysics Data System (ADS)
Zhang, Hao; Xu, Tiantian; Zhang, Xinxin; Wang, Yuxiang; Wang, Yuancheng; Liu, Xueting
2016-06-01
This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved 90° bend pipe with circular cross-sections, which are widely used in industrial applications. By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained. To explore the change rule the experiment is carried out by changing the Reynolds number, the wall roughness and different diameter ratio of elbow pipe. The variation of the local resistance coefficient with the Reynolds number, the diameter ratio and the wall roughness is presented comprehensively in the paper. The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid; the wall roughness has a significant impact on the local resistance coefficient. As the pipe wall roughness increasing, the coefficient of local resistance force will increase. The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow, which increases the kinetic energy dissipation of the main flow. This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.
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.
Universal Power Law Governing Pedestrian Interactions
NASA Astrophysics Data System (ADS)
Karamouzas, Ioannis; Skinner, Brian; Guy, Stephen J.
2014-12-01
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.
Power laws and fragility in flow networks☆
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
Power-law parametrized quintessence model
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.
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.
Power-law spatial dispersion from fractional Liouville equation
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.
López de Haro, Mariano; Tejero, Carlos F; Santos, Andrés
2013-04-28
The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures. PMID:23635104
Power law scaling in synchronization of brain signals depends on cognitive load
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
The power law as an emergent property.
Anderson, R B
2001-10-01
Recent work has shown that the power function, a ubiquitous characteristic of learning, memory, and sensation, can emerge from the arithmetic averaging of exponential curves. In the present study, the forgetting process was simulated via computer to determine whether power curves can result from the averaging of other types of component curves. Each of several simulations contained 100 memory traces that were made to decay at different rates. The resulting component curves were then arithmetically averaged to produce an aggregate curve for each simulation. The simulations varied with respect to the forms of the component curves: exponential, range-limited linear, range-limited logarithmic, or power. The goodness of the aggregate curve's fit to a power function relative to other functions increased as the amount of intercomponent slope variability increased, irrespective of component-curve type. Thus, the power law's ubiquity may reflect the pervasiveness of slope variability across component functions. Moreover, power-curve emergence may constitute a methodological artifact, an explanatory construct, or both, depending on the locus of the effect. PMID:11820749
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.
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning. PMID:25711183
Constraints on the tensor-to-scalar ratio for non-power-law models
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.
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.
NASA Astrophysics Data System (ADS)
Dexter, Jason; Blaes, Omer
2014-03-01
We propose a new model of the steep power-law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, the inner radii of radiation pressure dominated accretion discs are expected to (i) become effectively optically thin and (ii) produce significant luminosities. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energies. These spectra sum together to form a steep power-law tail to the spectrum. A given photon energy on this tail corresponds to a narrow range in radius, so that local vertical oscillations of the disc naturally produce high-quality high-frequency quasi-periodic oscillations (HFQPOs) in the hard X-ray band. The two lowest order modes have a robust frequency ratio of sqrt{7/3}˜eq 1.53. This model explains the appearance of steep power-law spectra and HFQPOs at high luminosity, the 3:2 HFQPO frequency ratios, and their association with the power-law spectral component. We predict an increase in QPO quality factor when the power spectrum is restricted to a narrower photon energy band, and an increase in HFQPO frequency at higher X-ray energies or lower luminosities. Future X-ray telescopes could detect additional HFQPOs from higher order modes. We demonstrate how this model could be used to measure black hole spin from HFQPOs, and qualitatively estimate the spin of GRO J1655-40 as a/M ˜ 0.4-0.7.
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.
Resurrecting power law inflation in the light of Planck results
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.
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.
Fractional power-law spatial dispersion in electrodynamics
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.
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.
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.
Power-law defect energy in a single-crystal gradient plasticity framework: a computational study
NASA Astrophysics Data System (ADS)
Bayerschen, E.; Böhlke, T.
2016-07-01
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.
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.
Magnetic characterization of HSLA steel by power-law decay exponents of Barkhausen emission signal
NASA Astrophysics Data System (ADS)
Tarafder, M.; Chattoraj, I.; Nasipuri, M.; Mitra, A.
2009-04-01
The general trend of magnetic behaviour of materials is that the mechanically hard materials are also magnetically hard. However for the high strength low alloy (HSLA) steel tempered at various aging temperatures, the correlation was reported as negative. The anomaly could not be explained by the magnetic parameters like RMS voltage calculated from the Barkhausen emission signal and the coercivity from the magnetic hysteresis loop. This paper reports another magnetic parameter known as power-law decay exponent which shows excellent correlation with the mechanical properties and thus explains the progressive evolution of the microstructural constituents in HSLA steel.
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.
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.
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.
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.
Power-Law entropy corrected holographic dark energy model
NASA Astrophysics Data System (ADS)
Sheykhi, Ahmad; Jamil, Mubasher
2011-10-01
Among various scenarios to explain the acceleration of the universe expansion, the holographic dark energy (HDE) model has got a lot of enthusiasm recently. In the derivation of holographic energy density, the area relation of the black hole entropy plays a crucial role. Indeed, the power-law corrections to entropy appear in dealing with the entanglement of quantum fields in and out the horizon. Inspired by the power-law corrected entropy, we propose the so-called "power-law entropy-corrected holographic dark energy" (PLECHDE) in this Letter. We investigate the cosmological implications of this model and calculate some relevant cosmological parameters and their evolution. We also briefly study the so-called "power-law entropy-corrected agegraphic dark energy" (PLECADE).
Fractal ladder models and power law wave equations
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
Intramolecular vibrational dephasing obeys a power law at intermediate times
Gruebele, M.
1998-01-01
Experimental intramolecular vibrational dephasing transients for several large organic molecules are reanalyzed. Fits to the experimental data, as well as full numerical quantum calculations with a factorized potential surface for all active degrees of freedom of fluorene indicate that power law decays, not exponentials, occur at intermediate times. The results support a proposal that power law decays describe vibrational dephasing dynamics in large molecules at intermediate times because of the local nature of energy flow. PMID:9600900
Singularity problems of the power law for modeling creep compliance
NASA Technical Reports Server (NTRS)
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
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.
KAPPA DISTRIBUTION MODEL FOR HARD X-RAY CORONAL SOURCES OF SOLAR FLARES
Oka, M.; Ishikawa, S.; Saint-Hilaire, P.; Krucker, S.; Lin, R. P.
2013-02-10
Solar flares produce hard X-ray emission, the photon spectrum of which is often represented by a combination of thermal and power-law distributions. However, the estimates of the number and total energy of non-thermal electrons are sensitive to the determination of the power-law cutoff energy. Here, we revisit an 'above-the-loop' coronal source observed by RHESSI on 2007 December 31 and show that a kappa distribution model can also be used to fit its spectrum. Because the kappa distribution has a Maxwellian-like core in addition to a high-energy power-law tail, the emission measure and temperature of the instantaneous electrons can be derived without assuming the cutoff energy. Moreover, the non-thermal fractions of electron number/energy densities can be uniquely estimated because they are functions of only the power-law index. With the kappa distribution model, we estimated that the total electron density of the coronal source region was {approx}2.4 Multiplication-Sign 10{sup 10} cm{sup -3}. We also estimated without assuming the source volume that a moderate fraction ({approx}20%) of electrons in the source region was non-thermal and carried {approx}52% of the total electron energy. The temperature was 28 MK, and the power-law index {delta} of the electron density distribution was -4.3. These results are compared to the conventional power-law models with and without a thermal core component.
Indentation of a Power Law Creeping Solid
NASA Astrophysics Data System (ADS)
Bower, A. F.; Fleck, N. A.; Needleman, A.; Ogbonna, N.
1993-04-01
The aim of this paper is to establish a rigorous theoretical basis for interpreting the results of hardness tests on creeping specimens. We investigate the deformation of a creeping half-space with uniaxial stress-strain behaviour dot{ɛ}=dot{ɛ}0(σ /σ 0)m, which is indented by a rigid punch. Both axisymmetric and plane indenters are considered. The shape of the punch is described by a general expression which includes most indenter profiles of practical importance. Two methods are used to solve the problem. The main results are found using a transformation method suggested by R. Hill. It is shown that the creep indentation problem may be reduced to a form which is independent of the geometry of the punch, and depends only on the material properties through m. The reduced problem consists of a nonlinear elastic half-space, which is indented to a unit depth by a rigid flat punch of unit radius (in the axisymmetric case), or unit semi-width (in the plane case). Exact solutions are given for m = 1 and m = ∞ . For m between these two limits, the reduced problem has been solved using the finite element method. The results enable the load on the indenter and the contact radius to be calculated in terms of the indentation depth and rate of penetration. The stress, strain and displacement fields in the half-space may also be deduced. The accuracy of the solution is demonstrated by comparing the results with full-field finite element calculations. The predictions of the theory are shown to be consistent with experimental observations of hardness tests on creeping materials reported in the literature.
Arif, Saqib; Ali, Tahira Mohsin; Ul Afzal, Qurat; Ahmed, Mubarik; Siddiqui, Asim Jamal; Hasnain, Abid
2014-06-01
The effects of water extractable pentosans (WEP) and water unextractable pentosans (WUP) on pasting properties in flours of eight different hard white spring wheat (HWSW) cultivars was studied. WEP and WUP isolated from a hard wheat flour were added to each of the cultivars at 1% and 2% level. The results indicated that WEP exhibited a pronounced effect on pasting properties as compared to WUP and variety. Univariate analysis of variance (ANOVA) was used to evaluate sources of variation. The variety significantly (P < 0.001) influenced all the pasting parameters. WUP caused significant (P < 0.001) variation in paste viscosities (except breakdown). WEP influenced more pronouncedly the hot paste, cold paste, breakdown and setback viscosities with F values-221.802, 214.286, 98.073 and 120.159, respectively. Variety-by-WEP interaction exhibited significant (P < 0.01) influence on pasting time, peak, hot paste and cold paste viscosities. Whereas, variety-by-WUP interaction only significantly (P < 0.001) influenced the pasting- time and -temperature. Duncan's test was used to analyze the significant difference (P < 0.05) within the variety. The results revealed that WUP did not induce significant (P < 0.05) influence on all the pasting parameters, whereas, WEP influenced significantly (P < 0.05) the paste viscosities of some of the varieties. It was also found that the addition of WEP remarkably reduced the setback, hot paste, cold paste viscosities and increased the breakdown viscosity in all cultivar flours. The effect of WEP was greater at higher level of supplementation on paste viscosities. PMID:24876638
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.
Zhang, G; Torquato, S
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space R^{d} has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g(2)(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation
NASA Astrophysics Data System (ADS)
Zhang, G.; Torquato, S.
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space Rd has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.74.061308 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g2(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed “decorrelation” principle, and the degree of “hyperuniformity” (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the
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.
Statistical tests for power-law cross-correlated processes.
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, ρ(DCCA)(T,n), where T is the total length of the time series and n the window size. For ρ(DCCA)(T,n), we numerically calculated the Cauchy inequality -1 ≤ ρ(DCCA)(T,n) ≤ 1. Here we derive -1 ≤ ρ DCCA)(T,n) ≤ 1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ρ(DCCA) 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 ρ(DCCA)(T,n) tends with increasing T to 1/T. Using ρ(DCCA)(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. PMID:22304166
Power-law ansatz in complex systems: Excessive loss of information.
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
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.
Distortion of power law blinking with binning and thresholding
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.
Power-law relations in random networks with communities
NASA Astrophysics Data System (ADS)
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.
2016-07-01
Most random graph models are locally tree-like—do not contain short cycles—rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ . In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ =γ -1 .
Between disorder and order: A case study of power law
NASA Astrophysics Data System (ADS)
Cao, Yong; Zhao, Youjie; Yue, Xiaoguang; Xiong, Fei; Sun, Yongke; He, Xin; Wang, Lichao
2016-08-01
Power law is an important feature of phenomena in long memory behaviors. Zipf ever found power law in the distribution of the word frequencies. In physics, the terms order and disorder are Thermodynamic or statistical physics concepts originally and a lot of research work has focused on self-organization of the disorder ingredients of simple physical systems. It is interesting what make disorder-order transition. We devise an experiment-based method about random symbolic sequences to research regular pattern between disorder and order. The experiment results reveal power law is indeed an important regularity in transition from disorder to order. About these results the preliminary study and analysis has been done to explain the reasons.
Statistical Models of Power-law Distributions in Homogeneous Plasmas
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.
Robust Statistical Detection of Power-Law Cross-Correlation
NASA Astrophysics Data System (ADS)
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-06-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram.
Power-law hereditariness of hierarchical fractal bones.
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
PLMaddon: a power-law module for the Matlab SBToolbox.
Vera, Julio; Sun, Cheng; Oertel, Yvonne; Wolkenhauer, Olaf
2007-10-01
PLMaddon is a General Public License (GPL) software module designed to expand the current version of the SBToolbox (a Matlab toolbox for systems biology; www.sbtoolbox.org) with a set of functions for the analysis of power-law models, a specific class of kinetic models, set in ordinary differential equations (ODE) and in which the kinetic orders can have positive/negative non-integer values. The module includes functions to generate power-law Taylor expansions of other ODE models (e.g. Michaelis-Menten type models), as well as algorithms to estimate steady-states. The robustness and sensitivity of the models can also be analysed and visualized by computing the power-law's logarithmic gains and sensitivities. PMID:17495997
General 2.5 power law of metallic glasses.
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
General 2.5 power law of metallic glasses
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.
2016-01-01
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
Power-law relations in random networks with communities.
Stegehuis, Clara; van der Hofstad, Remco; van Leeuwaarden, Johan S H
2016-07-01
Most random graph models are locally tree-like-do not contain short cycles-rendering them unfit for modeling networks with a community structure. We introduce the hierarchical configuration model (HCM), a generalization of the configuration model that includes community structures, while properties such as the size of the giant component, and the size of the giant percolating cluster under bond percolation can still be derived analytically. Viewing real-world networks as realizations of HCM, we observe two previously undiscovered power-law relations: between the number of edges inside a community and the community sizes, and between the number of edges going out of a community and the community sizes. We also relate the power-law exponent τ of the degree distribution with the power-law exponent of the community-size distribution γ. In the case of extremely dense communities (e.g., complete graphs), this relation takes the simple form τ=γ-1. PMID:27575143
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.
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
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.
Power-law creep from discrete dislocation dynamics.
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
A consistency relation for power law inflation in DBI models
NASA Astrophysics Data System (ADS)
Spaliński, Michał
2007-07-01
Brane inflation in string theory leads to a new realization of power law inflation which can give rise to significant non-gaussianity. This can happen for any throat geometry if the scalar potential is appropriate. This Letter presents a consistency relation connecting the running of the nonlinearity parameter characterizing the non-gaussianity and the scalar and tensor indices. The relationship is valid assuming that the throat geometry and scalar potential support power law inflation, regardless of the level of non-gaussianity.
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 λ(1)<λ<λ(2), 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 λ(2). 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 λ(c)=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. PMID:27078381
Power law corrections to BTZ black hole entropy
NASA Astrophysics Data System (ADS)
Singh, Dharm Veer
2015-11-01
We study the quantum scalar field in the background of BTZ black hole and evaluate the entanglement entropy of the nonvacuum states. The entropy is proportional to the area of event horizon for the ground state, but the area law is violated in the case of nonvacuum states (first excited state and mixed states) and the corrections scale as power law.
Power laws of wealth, market order volumes and market returns
NASA Astrophysics Data System (ADS)
Solomon, Sorin; Richmond, Peter
2001-10-01
Using the Generalized Lotka Volterra model adapted to deal with mutiagent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a ‘fair’ market, the wealth distribution among individual investors fulfills a power law. We then argue that ‘fair play’ for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent α∼ {3}/{2}. In particular, we relate it to the average number of individuals L depending on the average wealth: α∼ L/( L-1). Then we connect it to certain power exponents characterizing the stock markets. We find that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent β∼α∼ {3}/{2}. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order γ∼2 α∼3. These results are consistent with recent experimental measurements of these power law exponents (S. Maslov, M. Mills, Physica A 299 (2001) 234 for β; P. Gopikrishnan et al., Phys. Rev. E 60 (1999) 5305 for γ).
Weather-driven model indicative of spatiotemporal power laws.
Song, Weiguo; Zheng, Hongyang; Wang, Jian; Ma, Jian; Satoh, Kohyu
2007-01-01
In the traditional Drossel-Schwabl forest fire model (DS model), the frequency distributions of fire size and fire interval follow a power law and an exponential law, respectively. However, it is found that the frequency-interval distribution of actual forest fires is not exponential, but a power law with periodical fluctuations which may be caused by the daily cycle of weather parameters. Therefore, a weather driven forest fire model (WD model) is built considering actual hourly weather records, with which the fire igniting probability is calculated. The simulation results indicate that the frequency-interval distribution of the WD model agrees with that of actual forest fire data and, at the same time, the frequency-size distributions of the WD and the DS models are in accordance with each other. In the further analysis of the temporal property of weather data, it is found that the change of weather data also exhibits a power-law relation with periodic fluctuations, implying that the external driving from weather parameters is the essential reason for the power-law distribution of fire intervals. The results suggest that natural systems may be coupled with each other and that the decoupling of systems is important to identifying system characteristics. PMID:17358226
Electrokinetically modulated peristaltic transport of power-law fluids.
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
Input-anticipating critical reservoirs show power law forgetting of unexpected input events.
Mayer, Norbert Michael
2015-05-01
Usually reservoir computing shows an exponential memory decay. This letter investigates under which circumstances echo state networks can show a power law forgetting. That means traces of earlier events can be found in the reservoir for very long time spans. Such a setting requires critical connectivity exactly at the limit of what is permissible according to the echo state condition. However, for general matrices, the limit cannot be determined exactly from theory. In addition, the behavior of the network is strongly influenced by the input flow. Results are presented that use certain types of restricted recurrent connectivity and anticipation learning with regard to the input, where power law forgetting can indeed be achieved. PMID:25774542
Effects of sorghum flour addition on chemical and rheological properties of hard white winter wheat
Technology Transfer Automated Retrieval System (TEKTRAN)
This study was carried out to investigate the chemical and rheological properties of different blends prepared using hard white winter wheat and whole or decorticated sorghum. Whole and decorticated sorghum were used to replace 5, 10, 15, and 20% of wheat flour. Wheat samples had higher protein, moi...
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws
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.
A spatial network explanation for a hierarchy of urban power laws
NASA Astrophysics Data System (ADS)
Andersson, Claes; Hellervik, Alexander; Lindgren, Kristian
2005-01-01
Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unified in the same model: transportation costs and multiplicative growth. The model is an elaboration of a previously reported complex network model of geographical land value evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: land value per unit area, cluster areas, aggregated land value per cluster and cluster area/perimeter ratios. It is found that transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.
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
Diffusion with stochastic resetting at power-law times
NASA Astrophysics Data System (ADS)
Nagar, Apoorva; Gupta, Shamik
2016-06-01
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ˜τ-(1 +α );α >0 ? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α <1 , to one that is time independent for α >1 . The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.
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.
On estimating the exponent of power-law frequency distributions.
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
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.
Diffusion with stochastic resetting at power-law times.
Nagar, Apoorva; Gupta, Shamik
2016-06-01
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α<1, to one that is time independent for α>1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment. PMID:27415186
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.
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.
Power-law behavior in social and economical phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Keizo; Miyazima, Sasuke
2004-12-01
We have already found power-law behavior in various phenomena such as high-tax payer, population distribution, name distribution, passenger number at stations, student number in a university from high schools, and so on. We can explain why these phenomena show such interesting behaviors by doing simulations based on adequate models. We have come to the conclusion that there are fractal structures underlying those phenomena.
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.
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) .
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.
Estimation of shear modulus in media with power law characteristics.
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
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.
Robust Statistical Detection of Power-Law Cross-Correlation
Blythe, Duncan A. J.; Nikulin, Vadim V.; Müller, Klaus-Robert
2016-01-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630
Model selection for identifying power-law scaling.
Ton, Robert; Daffertshofer, Andreas
2016-08-01
Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present. PMID:26774613
Automated piecewise power-law modeling of biological systems.
Machina, Anna; Ponosov, Arkady; Voit, Eberhard O
2010-09-01
Recent trends suggest that future biotechnology will increasingly rely on mathematical models of the biological systems under investigation. In particular, metabolic engineering will make wider use of metabolic pathway models in stoichiometric or fully kinetic format. A significant obstacle to the use of pathway models is the identification of suitable process descriptions and their parameters. We recently showed that, at least under favorable conditions, Dynamic Flux Estimation (DFE) permits the numerical characterization of fluxes from sets of metabolic time series data. However, DFE does not prescribe how to convert these numerical results into functional representations. In some cases, Michaelis-Menten rate laws or canonical formats are well suited, in which case the estimation of parameter values is easy. However, in other cases, appropriate functional forms are not evident, and exhaustive searches among all possible candidate models are not feasible. We show here how piecewise power-law functions of one or more variables offer an effective default solution for the almost unbiased representation of uni- and multivariate time series data. The results of an automated algorithm for their determination are piecewise power-law fits, whose accuracy is only limited by the available data. The individual power-law pieces may lead to discontinuities at break points or boundaries between sub-domains. In many practical applications, these boundary gaps do not cause problems. Potential smoothing techniques, based on differential inclusions and Filippov's theory, are discussed in Appendix A. PMID:20060428
Robust Statistical Detection of Power-Law Cross-Correlation.
Blythe, Duncan A J; Nikulin, Vadim V; Müller, Klaus-Robert
2016-01-01
We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram. PMID:27250630
Spectrum of power laws for curved hand movements
Huh, Dongsung; Sejnowski, Terrence J.
2015-01-01
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
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.
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
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
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
Scaling, dimensional analysis, and hardness measurements
NASA Astrophysics Data System (ADS)
Cheng, Yang-Tse; Cheng, Che-Min; Li, Zhiyong
2000-03-01
Hardness is one of the frequently used concepts in tribology. For nearly one hundred years, indentation experiments have been performed to obtain the hardness of materials. Recent years have seen significant improvements in indentation equipment and a growing need to measure the mechanical properties of materials on small scales. However, questions remain, including what properties can be measured using instrumented indention techniques and what is hardness? We discuss these basic questions using dimensional analysis together with finite element calculations. We derive scaling relationships for loading and unloading curve, initial unloading slope, contact depth, and hardness. Hardness is shown to depend on elastic, as well as plastic properties of materials. The conditions for "piling-up" and "sinking-in" of surface profiles in indentation are obtained. The methods for estimating contact area are examined. The work done during indentation is also studied. A relationship between hardness, elastic modulus, and the work of indentation is revealed. This relationship offers a new method for obtaining hardness and elastic modulus. In addition, we demonstrate that stress-strain relationships may not be uniquely determined from loading/unloading curves alone using a conical or pyramidal indenter. The dependence of hardness on indenter geometry is also studied. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and "indentation size effect" is established.
Mobile hard substrata - An additional biodiversity source in a high latitude shallow subtidal system
NASA Astrophysics Data System (ADS)
Balazy, Piotr; Kuklinski, Piotr
2013-03-01
This study demonstrates the importance of a hard mobile substratum (hermit crab shells) for Arctic biodiversity. Based on previous observations from other geographic regions we hypothesized that this niche at high latitudes would support a higher biodiversity of epifauna than might be predicted from similar substrata. We test whether the hermit crab epifauna is specific to that substratum providing unique biodiversity components to the local community. From four study sites in Isfjorden (78°N), West Spitsbergen and two study sites in Northern Norway (69°N) we collected approximately 50 each of hermit crabs, gastropods and pebbles, of visually similar surface area using SCUBA diving. Hermit crab shells were colonized by a larger number of epifaunal species than either gastropods or pebbles, even when they were of a larger size. Among 87 taxa found on all the three substrata, 22 occurred only on hermit crab shells. Except for two study sites hermit crab shells also supported more individuals. This study shows that the contribution of shells carried by hermit crabs to high-latitude, shallow-subtidal diversity is higher than might be predicted by their surface area alone and that hermit crabs modify, maintain and create a unique habitat. This is the result of a number of factors interacting positively on the presence of epifauna including shell surface heterogeneity and the complex influence of the crab host.
Analysis of the proof test with power law assumptions
NASA Astrophysics Data System (ADS)
Hanson, Thomas A.
1994-03-01
Prooftesting optical fiber is required to assure a minimum strength over all lengths of fiber. This is done as the fiber is wound onto a spool by applying a tensile stress over a length of fiber as it passes a stress region. The failure of weak flaws assures a minimum strength of lengths that survive the test. Flaw growth is assumed to follow the power law. Distributions of initial flaw size are assumed to be of the Weibull type. Experimental data are presented to validate these assumptions.
Inflation in the generalized inverse power law scenario
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.
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.
Power-law photoluminescence decay in quantum dots
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.
Analytical Limit Distributions from Random Power-Law Interactions
NASA Astrophysics Data System (ADS)
Zaid, Irwin; Mizuno, Daisuke
2016-07-01
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated.
Power laws, discontinuities and regional city size distributions
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.
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
A graph-dynamic model of the power law of practice and the problem-solving fan-effect.
Shrager, J; Hogg, T; Huberman, B A
1988-10-21
Numerous human learning phenomena have been observed and captured by individual laws, but no unified theory of learning has succeeded in accounting for these observations. A theory and model are proposed that account for two of these phenomena: the power law of practice and the problem-solving fan-effect. The power law of practice states that the speed of performance of a task will improve as a power of the number of times that the task is performed. The power law resulting from two sorts of problem-solving changes, addition of operators to the problem-space graph and alterations in the decision procedure used to decide which operator to apply at a particular state, is empirically demonstrated. The model provides an analytic account for both of these sources of the power law. The model also predicts a problem-solving fan-effect, slowdown during practice caused by an increase in the difficulty of making useful decisions between possible paths, which is also found empirically. PMID:3175664
Inference of Statistical Patterns in Complex Geosystems: Fitting Power-law Distributions.
NASA Astrophysics Data System (ADS)
Deluca, Anna; Corral, Alvaro
2014-05-01
Power-law distributions contain precious information about a large variety of physical processes. Although there are sound theoretical grounds for these distributions, the empirical evidence giving support to power laws has been traditionally weak. Recently, Clauset et al. have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method fails to recognize true (simulated) power-law tails in some instances, rejecting the power-law hypothesis. Moreover, the method does not perform well when it is extended to power-law distributions with an upper truncation. We present an alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. We will test the performance of our method on several empirical data which were previously analyzed with less systematic approaches.
Power Law Distributions of Patents as Indicators of Innovation
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
Power Law Distributions of Patents as Indicators of Innovation
NASA Astrophysics Data System (ADS)
O'Neale, Dion; Hendy, Shaun
2013-03-01
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. Such figures however give an overly simplistic measure of innovation within a country. Here we present evidence that the distribution of patents amongst applicants within many countries is well-fitted to a power law distribution with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.
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.
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.
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, Rǎzvan; 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 β in the log-log domain. It has been suggested that the magnitude of the power-law spectrum coefficient β is related to mass lesion detection performance. We assessed β 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 β 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 β highly depends on the reconstruction algorithm; the highest β values were found for SBP, followed by reconstruction with FBP, while the lowest β values were found for SIRT. In contrast to previous studies, we found that β is not always lower in reconstructed DBT slices, compared to 2D projections and this depends on the reconstruction algorithm. All β values estimated in DBT slices reconstructed with SBP were larger than β 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.
Power-law distribution of gene expression fluctuations
NASA Astrophysics Data System (ADS)
Nacher, J. C.; Ochiai, T.
2008-09-01
Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.
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.
Power-law Growth and Punctuated Equilibrium Dynamics in Water Resources Systems
NASA Astrophysics Data System (ADS)
Parolari, A.; Katul, G. G.; Porporato, A. M.
2015-12-01
The global rise in population-driven water scarcity and recent appreciation of strong dynamic coupling between human and natural systems has called for new approaches to predict the future sustainability of regional and global water resources systems. The dynamics of coupled human-water systems are driven by a complex set of social, environmental, and technological factors. Present projections of water resources systems range from a finite carrying capacity regulated by accessible freshwater, or `peak renewable water,' to punctuated evolution with new supplied and improved efficiency gained from technological and social innovation. However, these projections have yet to be quantified from observations or in a comprehensive theoretical framework. Using data on global water withdrawals and storage capacity of regional water supply systems, non-trivial dynamics are identified in water resources systems development over time, including power-law growth and punctuated equilibria. Two models are introduced to explain this behavior: (1) a delay differential equation and (2) a power-law with log-periodic oscillations, both of which rely on past conditions (or system memory) to describe the present rate of growth in the system. In addition, extension of the first model demonstrates how system delays and punctuated equilibria can emerge from coupling between human population growth and associated resource demands. Lastly, anecdotal evidence is used to demonstrate the likelihood of power-law growth in global water use from the agricultural revolution 3000 BC to the present. In a practical sense, the presence of these patterns in models with delayed oscillations suggests that current decision-making related to water resources development results from the historical accumulation of resource use decisions, technological and social changes, and their consequences.
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.
Optimal numerical flux of power-law fluids in some partially full pipes
NASA Astrophysics Data System (ADS)
Lefton, Lew; Wei, Dongming; Liu, Yu
2014-07-01
Consider the steady state pressure driven flow of a power-law fluid in a partially filled straight pipe. It is known that an increase in flux can be achieved for a fixed pressure by partially filling the pipe and having the remaining volume either void or filled with a less viscous, lubricating fluid. If the pipe has circular cross section, the fluid level which maximizes flux is the level which avoids contact with exactly 25% of the boundary. This result can be proved analytically for Newtonian fluids and has been verified numerically for certain non-Newtonian models. This paper provides a generalization of this work numerically to pipes with non-circular cross sections which are partially full with a power-law fluid. A simple and physically plausible geometric condition is presented which can be used to approximate the fluid level that maximizes flux in a wide range of pipe geometries. Additional increases in flux for a given pressure can be obtained by changing the shape of the pipe but leaving the perimeter fixed. This computational analysis of flux as a function of both fluid level and pipe geometry has not been considered to our knowledge. Fluxes are computed using a special discretization scheme, designed to uncover general properties which are only dependent on fluid level and/or pipe cross-sectional geometry. Computations use finite elements and take advantage of the variational structure inherent in the power-law model. A minimization technique for approximating the critical points of the associated non-linear energy functional is used. In particular, the numerical scheme for the non-linear partial differential equation has been proved to be convergent with known error estimates. The numerical results obtained in this work can be useful for designing pipes and canals for transportation of non-Newtonian fluids, such as those in chemical engineering and food processing engineering.
Shah-Khan, M.Z.
1981-10-01
Results of the research work show that the addition of 0.1% yttrium does not significantly change the mechanical properties of the AL1 alloy with temperature (even though the yttrium-doped samples did show a slight increase in yield stress and hardness for tests above 700/sup 0/C); the room temperature strength of the undoped AL1 alloy increases upon annealing at temperatures above 600/sup 0/C; and the room temperature uniform and fracture strains of the undoped AL1 alloy decrease upon annealing at temperatures above 600/sup 0/C.
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.
Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements.
Schaal, S; Sternad, D
2001-01-01
The 2/3 power law, the nonlinear relationship between tangential velocity and radius of curvature of the end-effector trajectory, is thought to be a fundamental constraint of the central nervous system in the formation of rhythmic endpoint trajectories. However, studies on the 2/3 power law have been confined largely to planar drawing patterns of relatively small size. With the hypothesis that this strategy overlooks nonlinear effects that are constitutive in movement generation, the present experiments tested the validity of the power law in elliptical patterns that were not confined to a planar surface and which were performed by the unconstrained 7-degrees of freedom (DOF) arm, with significant variations in pattern size and workspace orientation. Data were recorded from five human subjects where the seven joint angles and the endpoint trajectories were analyzed. Additionally, an anthropomorphic 7-DOF robot arm served as a "control subject" whose endpoint trajectories were generated on the basis of the human joint angle data, modeled as simple harmonic oscillations. Analyses of the endpoint trajectories demonstrate that the power law is systematically violated with increasing pattern size, in both exponent and the goodness of fit. The origins of these violations can be explained analytically based on smooth, rhythmic trajectory formation and the kinematic structure of the human arm. We conclude that, in unconstrained rhythmic movements, the power law seems to be a by-product of a movement system that favors smooth trajectories, and that it is unlikely to serve as a primary movement-generating principle. Our data rather suggest that subjects employed smooth oscillatory pattern generators in joint space to realize the required movement patterns. PMID:11204414
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.
Optimized dynamical decoupling for power-law noise spectra
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.
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.
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.
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.
Power law tails in the Italian personal income distribution
NASA Astrophysics Data System (ADS)
Clementi, F.; Gallegati, M.
2005-05-01
We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977-2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of our analysis show a shift of the distribution and a change of the indexes specifying it over time. As regards the first issue, we test the hypothesis that the evolution of both gross domestic product and personal income is governed by similar mechanisms, pointing to the existence of correlation between these quantities. The fluctuations of the shape of income distribution are instead quantified by establishing some links with the business cycle phases experienced by the Italian economy over the years covered by our dataset.
There is more than a power law in Zipf.
Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano
2012-01-01
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf's Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto's or Benford's, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf's law for the largest cities. This pathology is reflected in the fact that Zipf's Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call 'coherence' and it corresponds to a 'screening' between various elements of the set. We show how it should be accounted for when fitting Zipf's Law. PMID:23139862
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.
Exponential and power laws in public procurement markets
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav; Skuhrovec, Jiri
2012-07-01
We analyze for the first time a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40000 public procurements in the Czech Republic between 2006 and 2011, focusing on the distributional properties of the variables of interest. We uncover several scaling laws —the exponential law for the number of bidders, and the power laws for the total revenues and total spendings of the participating companies, which even follows Zipf's law for the 100 most spending institutions. We propose an analogy between extensive and non-extensive systems in physics and the public procurement market situations. Through an entropy maximization, such analogy yields some interesting results and policy implications with respect to the Maxwell-Boltzmann and Pareto distributions in the analyzed quantities.
Analytical Limit Distributions from Random Power-Law Interactions.
Zaid, Irwin; Mizuno, Daisuke
2016-07-15
Nature is full of power-law interactions, e.g., gravity, electrostatics, and hydrodynamics. When sources of such fields are randomly distributed in space, the superposed interaction, which is what we observe, is naively expected to follow a Gauss or Lévy distribution. Here, we present an analytic expression for the actual distributions that converge to novel limits that are in between these already-known limit distributions, depending on physical parameters, such as the concentration of field sources and the size of the probe used to measure the interactions. By comparing with numerical simulations, the origin of non-Gauss and non-Lévy distributions are theoretically articulated. PMID:27472105
Bootstrap Percolation in Power-Law Random Graphs
NASA Astrophysics Data System (ADS)
Amini, Hamed; Fountoulakis, Nikolaos
2014-04-01
A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remains so forever. The parameter is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse this process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent , where , then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function such that with the following property. Assuming that is the number of vertices of the underlying random graph, if , then the process does not evolve at all, with high probability as grows, whereas if , then there is a constant such that, with high probability, the final set of infected vertices has size at least . This behaviour is in sharp contrast with the case where the underlying graph is a random graph with . It follows from an observation of Balogh and Bollobás that in this case if the number of initially infected vertices is sublinear, then there is lack of evolution of the process. It turns out that when the maximum degree is , then depends also on . But when the maximum degree is , then.
Bose-Einstein condensation in dark power-law laser traps
NASA Astrophysics Data System (ADS)
Jaouadi, A.; Gaaloul, N.; Viaris de Lesegno, B.; Telmini, M.; Pruvost, L.; Charron, E.
2010-08-01
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.
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.
Bose-Einstein condensation in dark power-law laser traps
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.
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.
Shape of gas flow paths causes power law tailing
NASA Astrophysics Data System (ADS)
Kawanishi, T.; Sakami, A.; Hayashi, Y.
2004-12-01
In soil and/or groundwater remediation, we often see prolonged tailings: continuous outflow of low concentration pollutants for very long time, and in many cases power low behavior of late-time time-concentration curves. We considered that this kind of tailing can be caused by the shape of the gaseous flow introduced in saturated/unsaturated porous media. When gas is introduced to porous media, like air-sparging or soil vapor extraction, the shape of the gas flow path would be tree-like, or to some extent "fractal." So, there would be a distribution of the distance that a solute would have to travel by diffusion before getting to a gas/water interface, and we might expect that the distribution of this "diffusion distance" would be power-law-like. In order to see if tailing can be caused by this mechanism, simple column experiments were carried out. A column, 64 mm in inner diameter and 240 mm in height, was prepared and was packed with 1mm diameter glass beads. Nitrogen gas containing 5 % CO2 and 5% He was supplied from the bottom of the column, and after the water in the column is approximately saturated with CO2, the sparging gas was changed to pure nitrogen. The CO2 and He concentrations in the effluent gas was monitored and recorded. As the result, we saw tailing: the double-log plots of the concentration vs. time relationship was practically linear, and the absolute value of the slope in the double-log charts were 1.28, 0.95 and 0.83 according to the gas flow rates of 40, 80 and 120 ml/min, respectively. Slope less than 1.00 showed that these tailings cannot be explained by Freundlich-type adsorption behavior. Model analysis showed that this power low time-concentration behavior with the slope of approximately -1.0 can be explained by the power law distribution of diffusion distance \\textit{a} with PDF p(\\textit{a}) proportional to \\textit{a}^{-1}.
Glitch observation and hard X-ray power law measurement in PSR J1119-6127
NASA Astrophysics Data System (ADS)
Archibald, R. F.; Tendulkar, S. P.; Scholz, P. A.; Kaspi, V. M.
2016-07-01
We report on Swift-XRT, NuSTAR and Fermi spectral and timing observations of PSR J1119-6127, a rotation-powered high magnetic field pulsar that showed a magnetar-like burst on 2016 July 28, 01:27:51 UT (ATel #9274, ATel #9282).
NASA Astrophysics Data System (ADS)
Rubinstein, Robert
2015-11-01
It is well known that collision models based on an assumed intermolecular potential (IPL, LJ, ...) can be successfully replaced by simplified surrogates (VHS, VSS, VS, ...) in DSMC calculations. But these surrogates only reproduce certain gross properties of the molecular model, for example, the temperature dependence of the viscosity; they do not approximate, and even mis-state, the details of the particle interactions. The success of the simplified models in problems at finite Knudsen number, where the Navier-Stokes approximation is not valid, may therefore seem surprising. To understand this success in a very special case, we showed that the first seven relaxation rates of the linearized Boltzmann equation for Maxwellian molecules are well approximated by the corresponding relaxation rates of its VHS surrogate. We will show that this analysis can be extended in somewhat less generality to IPL interactions, and to some extent to more realistic models including LJ. We believe that this analysis can help address the more general problem of identifying the properties of the collision model that dominate the predictions of the Boltzmann equation.
Power law distributions and dynamic behaviour of stock markets
NASA Astrophysics Data System (ADS)
Richmond, P.
2001-04-01
A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t' = 2Dδ t-t' and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψ ϕ - ln G(ϕ)} where Ψ ϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ2 - cϕ3 and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ>>ɛ, a distribution function with power law tails, viz: P ϕ = exp{ 2bϕ-cϕ2 /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D | J|.
Consistency relation in power law G-inflation
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}.
Universal fractional noncubic power law for density of metallic glasses.
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
Folding of a finite length power law layer
NASA Astrophysics Data System (ADS)
Schmid, Daniel W.; Podladchikov, Yuri Y.; Marques, Fernando O.
2004-03-01
Folding of an isolated finite length power law layer embedded in a Newtonian viscous matrix is investigated and compared to conventional folding experiments where the layer is of infinite length or in direct contact with lateral boundaries. The approach employed is a combination of the complex potential method for the basic state and the thin plate approximation for the linear stability analysis and is verified by finite element models. The resulting theory reveals that the aspect ratio of a layer has a first-order influence on the development of folds. The aspect ratio competes with the effective viscosity contrast for dominant influence on the folding process. If the aspect ratio is substantially larger than the effective viscosity contrast, the conventional theories are applicable. In other situations, where the aspect ratio is smaller than the effective viscosity contrast, substantial corrections must be taken into account, which lead to a new folding mode that is mainly characterized by decreasing growth rates with increasing effective viscosity contrast (relative to the far-field shortening rate). This new folding mode helps explain the absence of large wavelength to thickness ratio folds in nature, which may be due to the limitations of aspect ratios rather than large effective viscosity contrasts.
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.
There is More than a Power Law in Zipf
Cristelli, Matthieu; Batty, Michael; Pietronero, Luciano
2012-01-01
The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the relation between the frequency of a set of objects or events and their size. It is assumed to be one of many manifestations of an underlying power law like Pareto’s or Benford’s, but contrary to popular belief, from a distribution of, say, city sizes and a simple random sampling, one does not obtain Zipf’s law for the largest cities. This pathology is reflected in the fact that Zipf’s Law has a functional form depending on the number of events N. This requires a fundamental property of the sample distribution which we call ‘coherence’ and it corresponds to a ‘screening’ between various elements of the set. We show how it should be accounted for when fitting Zipf’s Law. PMID:23139862
Diffusion-limited aggregation with power-law pinning.
Hentschel, H G E; 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(-gamma)(N) (where R(N) is the radius of the N-particle cluster). For gamma>1 the growth pattern is in the same universality class as diffusion limited aggregation (DLA), while for gamma<1 the resulting patterns have a lower fractal dimension D(gamma) 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 gamma=1/2, significantly smaller than might be expected from the lower bound alpha(min) approximately 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(gamma) both close to the breakdown of DLA universality class, i.e., gamma less, similar 1, and close to the pinning transition, i.e., gamma greater, similar 1/2. PMID:14995617
High-Energy X-Ray Timing Experiment Detections of Hard X-Ray Tails in Scorpius X-1
NASA Astrophysics Data System (ADS)
D'Amico, Flavio; Heindl, William A.; Rothschild, Richard E.; Gruber, Duane E.
2001-02-01
We report the detection of a nonthermal hard X-ray component from Sco X-1 based on the analysis of 20-220 keV spectra obtained with the High-Energy X-Ray Timing Experiment on board the Rossi X-Ray Timing Explorer satellite. We find that the addition of a power-law component to a thermal bremsstrahlung model is required to achieve a good fit in five of 16 observations analyzed. Using Proportional Counter Array data, we were able to track the movement of the source along the Z diagram, and we found that the presence of the hard X-ray tail is not confined to a specific Z position. However, we do observe an indication that the power-law index hardens with increasing M, as indicated from the position on the Z diagram. We find that the derived nonthermal luminosities are ~10% of that derived for the brightest of the atoll sources.
Kitahama, Yasutaka; Araki, Daichi; Yamamoto, Yuko S; Itoh, Tamitake; Ozaki, Yukihiro
2015-09-01
For single colloidal Ag nanoaggregates, covered with either large or small amounts of citrate anions, blinking surface-enhanced Raman scattering (SERS) of anionic thiacyanine was measured and analyzed by a truncated power law. The power law without and with an exponential function reproduces a probability distribution for bright and dark SERS events versus their duration times, respectively. On the Ag surface, except for junctions of the nanoaggregate with a large or small amount of the citrate anions, two-dimensional fast or one-dimensional slow random walk of the anionic thiacyanine, respectively, was estimated by the exponents and the truncation times in the power law for the dark SERS events. In addition, the power law exponents for the bright SERS events were derived to be of similar values, indicating a similar molecular random walk near the junction, which may be dominated evenly by a surface-plasmon-enhanced electromagnetic field on the same-sized Ag nanoaggregate. Thus, not only the bright SERS, but also the dark SERS molecular behaviour on the Ag surface was investigated by the truncated power law analysis. PMID:25571862
Power law signature of media exposure in human response waiting time distributions
NASA Astrophysics Data System (ADS)
Crane, Riley; Schweitzer, Frank; Sornette, Didier
2010-05-01
We study the humanitarian response to the destruction brought by the tsunami generated by the Sumatra earthquake of December 26, 2004, as measured by donations, and find that it decays in time as a power law ˜1/tα with α=2.5±0.1 . This behavior is suggested to be the rare outcome of a priority queuing process in which individuals execute tasks at a rate slightly faster than the rate at which new tasks arise. We believe this to be an empirical evidence documenting the recently predicted [G. Grinstein and R. Linsker, Phys. Rev. E 77, 012101 (2008)] regime, and provide additional independent evidence that suggests that this “highly attentive regime” arises as a result of the intense focus placed on this donation “task” by the media.
Molecular clouds have power-law probability distribution functions (not log-normal)
NASA Astrophysics Data System (ADS)
Alves, Joao; Lombardi, Marco; Lada, Charles
2015-08-01
We investigate the shape of the probability distribution of column densities (PDF) in molecular clouds. Through the use of low-noise, extinction-calibrated Planck-Herschel 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 0.2mag, 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≃0.1mag, limiting our ability to investigate more complex models for the shape of the cloud PDF.
Power-law tail probabilities of drainage areas in river basins
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.
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
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2015-03-01
The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).
Investigating dynamics of inhibitory and feedback loops in ERK signalling using power-law models.
Vera, Julio; Rath, Oliver; Balsa-Canto, Eva; Banga, Julio R; Kolch, Walter; Wolkenhauer, Olaf
2010-11-01
The investigation of the structure and dynamics of signal transduction systems through data-based mathematical models in ordinary differential equations or other paradigms has proven to be a successful approach in recent times. Extending this concept, we here analysed the use of kinetic models based on power-law terms with non-integer kinetic orders in the validation of hypotheses concerning regulatory structures in signalling systems. We integrated pre-existent biological knowledge, hypotheses and experimental quantitative data into a power-law model to validate the existence of certain regulatory loops in the Ras/Raf-1/MEK/ERK pathway, a MAPK pathway involved in the transduction of mitogenic and differentiation signals. Towards this end, samples of a human mammary epithelial cell line (MCF-10A) were used to obtain time-series data, characterising the behaviour of the system after epidermal growth factor stimulation in different scenarios of expression for the critical players of the system regarding the investigated loops (e.g., the inhibitory protein RKIP). The mathematical model was calibrated using a computational procedure that included: analysis of structural identifiability, global ranking of parameters to detect the most sensitivity ones towards the experimental setup, model calibration using global optimization methods to find the parameter values that better fit the data, and practical identifiability analysis to estimate the confidence in the estimated values for the parameters. The obtained model was used to perform computational simulations concerning the role of the investigated regulatory loops in the time response of the signalling pathway. Our findings suggest that the special regularity in the structure of the power-law terms make them suitable for a data-based validation of regulatory loops in signalling pathways. The model-based analysis performed identified RKIP as an actual inhibitor of the activation of the ERK pathway, but also suggested
NASA Astrophysics Data System (ADS)
Ata, Shingo; Murata, Masayuki; Gotoh, Yoshihiro
2003-08-01
Many services have recently been offered based on a peer-to-peer (P2P) communication model. Peers connect to each other and build an overlaid logical network and available services are communicated over this network. The robustness of the P2P network against frequent peer failure must be considered. This includes when the peers leave the network and this directly affects the stability of the entire logical network. Replication of the content is one of the most useful techniques to increase robustness. However, the overall effectiveness of replication is heavily dependent on the topology of the logical network. As topology of networks, including the Internet and P2P, follows a Power-Law distribution pattern, we first investigate the effect of the logical network topology (especially of the Power-Law characteristics) on replication methods. We use a search method called "n-walkers random walk" in which multiple queries move randomly across the P2P logical network. We use a "path replication method," to create replicas at all the intermediate nodes on the path between the requesting and responding nodes. Through simulations experiments, we observed that peers with a large number of degrees (e.g., degree > 10) make four times as many replicas as peers with a small number of degrees. In addition, replicas on large degree's peers are used ten times as frequently as those on peers with small degrees. Based on these observations, we propose a query forwarding method that considers the Power-Law property of the network topology in order to improve the performance of the P2P service. In our method the queries are transmitted with different probabilities, dependending on the degree of each adjacent node. Our simulation results show that our proposed method can greatly improve the query performance by considering the characteristics of Power-Law. Our method reduces the average hop count in finding replicas by up to 60% compared with the random forwarding method.
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.
Fractal scaling and power-law landslide distribution in a micromodel of geomorphological evolution
NASA Astrophysics Data System (ADS)
Czirók, A.; Somfai, E.; Vicsek, T.
Recent analyses of geographical data have shown that mountains can be well described in terms of fractals, which raises the fundamental question about the mechanisms producing fractal surfaces in geomorphological evolution. Because the formation of mountain ranges takes place over an extremely long period of time, direct observations of erosion mechanisms are hardly feasible. Therefore, we expect that model experiments on the erosion of mountain ridges taking place on a limited time scale should contribute significantly to our understanding of the emergence of fractal structures in geomorphological phenomena. During the watering of an initially smooth ridge made of a mixture of silica sand and earthy soil the surface evolves into a shape analogous to actual mountain profiles with self-affine geometry. For the exponents describing, respectively, the spatial and the temporal scaling of the surface width, α=0.78+/-0.05 and β=0.8+/-0.06 have been obtained. The former value is in a very good agreement with α=0.8+/-0.1 calculated for genuine transect profiles. The processes in our micromodel can be well described in terms of self-organized criticality: The system evolves into a critical state, where surface roughening takes place due to power-law distributed landslides.
NASA Astrophysics Data System (ADS)
Dralle, D.; Karst, N.; Thompson, S. E.
2015-12-01
Multiple competing theories suggest that power law behavior governs the observed first-order dynamics of streamflow recessions - the important process by which catchments dry-out via the stream network, altering the availability of surface water resources and in-stream habitat. Frequently modeled as: dq/dt = -aqb, recessions typically exhibit a high degree of variability, even within a single catchment, as revealed by significant shifts in the values of "a" and "b" across recession events. One potential source of this variability lies in underlying, hard-to-observe fluctuations in how catchment water storage is partitioned amongst distinct storage elements, each having different discharge behaviors. Testing this and competing hypotheses with widely available streamflow timeseries, however, has been hindered by a power law scaling artifact that obscures meaningful covariation between the recession parameters, "a" and "b". Here we briefly outline a technique that removes this artifact, revealing intriguing new patterns in the joint distribution of recession parameters. Using long-term flow data from catchments in Northern California, we explore temporal variations, and find that the "a" parameter varies strongly with catchment wetness. Then we explore how the "b" parameter changes with "a", and find that measures of its variation are maximized at intermediate "a" values. We propose an interpretation of this pattern based on statistical mechanics, meaning "b" can be viewed as an indicator of the catchment "microstate" - i.e. the partitioning of storage - and "a" as a measure of the catchment macrostate (i.e. the total storage). In statistical mechanics, entropy (i.e. microstate variance, that is the variance of "b") is maximized for intermediate values of extensive variables (i.e. wetness, "a"), as observed in the recession data. This interpretation of "a" and "b" was supported by model runs using a multiple-reservoir catchment toy model, and lends support to the
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.
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.
POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING
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.
Two universal physical principles shape the power-law statistics of real-world networks
NASA Astrophysics Data System (ADS)
Lorimer, Tom; Gomez, Florian; Stoop, Ruedi
2015-07-01
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.
Two universal physical principles shape the power-law statistics of real-world networks
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
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.
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.
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.
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State.
Stoop, Ruedi; Gomez, Florian
2016-07-15
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information. PMID:27472144
Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State
NASA Astrophysics Data System (ADS)
Stoop, Ruedi; Gomez, Florian
2016-07-01
The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.
Song, M.H.
1981-10-01
The effect of the addition of yttrium on the elevated temperature tensile properties and hardness of an Fe-34% Ni-12% Cr candidate LMFBR cladding and duct alloy was investigated. Tensile tests were performed from room temperature to 800/sup 0/C in 100/sup 0/C steps at strain rates of 2.2 x 10/sup -3/ and 2.2 x 10/sup -4/ sec/sup -1/. Hardness tests were performed from room temperature to 850/sup 0/C in 50/sup 0/C steps. The addition of 0.1% yttrium decreased the yield stress and ultimate tensile stress in the test temperature range employed. Hardness also decreased over this test temperature range. In tensile tests, dynamic strain aging behavior occurred both for the undoped and doped alloy in the temperature range from 200 to 600/sup 0/C and 300 to 600/sup 0/C for the lower and higher strain rate, respectively.
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
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.
Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping
NASA Astrophysics Data System (ADS)
Lobos, Alejandro M.; Tezuka, Masaki; García-García, Antonio M.
2013-10-01
In a one-dimensional (1D) superconductor, zero-temperature quantum fluctuations destroy phase coherence. Here we put forward a mechanism which can restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard model with power-law hopping using Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, noninteger spatial dimensionality deff. For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppresses fluctuations and restores superconducting long-range order for any deff>1, at zero temperature. A detailed DMRG analysis fully supports these findings. These results are also of direct relevance to quantum magnetism as our model can be mapped onto an S=1/2 XXZ spin chain with power-law decaying couplings, which can be studied experimentally with cold-ion-trap techniques.
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.
Emergence of Power-Law in Spatial Epidemics Using Cellular Automation
NASA Astrophysics Data System (ADS)
Li, Li; Sun, Gui-Quan; Jin, Zhen
We analyze a spatial susceptible-infected epidemic model using cellular automata and investigate the relations between the power-law distribution of patch sizes and the regime of invasion. The obtained results show that, when the invasion is in the form of coexistence of stable target and spiral wave, power-law will emerge, which may provide a new insight into the control of disease.
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.
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
Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model
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
Analytical time-domain Green’s functions for power-law media
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
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.
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.
Why credit risk markets are predestined for exhibiting log-periodic power law structures
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Leker, Jens
2014-01-01
Recent research has established the existence of log-periodic power law (LPPL) patterns in financial institutions’ credit default swap (CDS) spreads. The main purpose of this paper is to clarify why credit risk markets are predestined for exhibiting LPPL structures. To this end, the credit risk prediction of two variants of logistic regression, i.e. polynomial logistic regression (PLR) and kernel logistic regression (KLR), are firstly compared to the standard logistic regression (SLR). In doing so, the question whether the performances of rating systems based on balance sheet ratios can be improved by nonlinear transformations of the explanatory variables is resolved. Building on the result that nonlinear balance sheet ratio transformations hardly improve the SLR’s predictive power in our case, we secondly compare the classification performance of a multivariate SLR to the discriminative powers of probabilities of default derived from three different capital market data, namely bonds, CDSs, and stocks. Benefiting from the prompt inclusion of relevant information, the capital market data in general and CDSs in particular increasingly outperform the SLR while approaching the time of the credit event. Due to the higher classification performances, it seems plausible for creditors to align their investment decisions with capital market-based default indicators, i.e., to imitate the aggregate opinion of the market participants. Since imitation is considered to be the source of LPPL structures in financial time series, it is highly plausible to scan CDS spread developments for LPPL patterns. By establishing LPPL patterns in governmental CDS spread trajectories of some European crisis countries, the LPPL’s application to credit risk markets is extended. This novel piece of evidence further strengthens the claim that credit risk markets are adequate breeding grounds for LPPL patterns.
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 3
NASA Technical Reports Server (NTRS)
Smalheer, C. V.
1973-01-01
The chemistry of lubricant additives is discussed to show what the additives are chemically and what functions they perform in the lubrication of various kinds of equipment. Current theories regarding the mode of action of lubricant additives are presented. The additive groups discussed include the following: (1) detergents and dispersants, (2) corrosion inhibitors, (3) antioxidants, (4) viscosity index improvers, (5) pour point depressants, and (6) antifouling agents.
NASA Astrophysics Data System (ADS)
Rovatti, L.; Lemke, J. N.; Emami, A.; Stejskal, O.; Vedani, M.
2015-12-01
Fe-based hardfacing alloys containing high volume fraction of hard phases are a suitable material to be deposited as wear resistant thick coatings. In the case of alloys containing high amount of interstitial alloying elements, a key factor affecting the performance is dilution with the substrate induced by the coating process. The present research was focused on the analysis of V-bearing Fe-based alloys after calibrated carbon and vanadium additions (in the range from 3 to 5 wt.%) to a commercial Fe-C-B-Ni hardfacing alloy. Vanadium carbides with a petal-like morphology were observed in the high-V hypereutectic alloys allowing to reach hardness values above 700 HV. The solidification range shifted to higher temperatures with increasing amount of vanadium addition and in the case of hypereutectic alloys, the gap remains close to that of the original alloy. In the last step of the research, the microstructural evolution after dilution was analyzed by casting the V-rich alloys on a steel substrate. The dilution, caused by the alloying element diffusion and the local melting of the substrate, modified the microstructure and the hardness for a relevant volume fraction of the hardfacing alloys. In particular, the drop of interstitial elements induced the transition from the hypereutectic to the hypoeutectic microstructure and the formation of near-spherical V-rich carbides. Even after dilution, the hardness of the new alloys remained higher than that measured in the original Fe-C-B-Ni alloy.
Apparent power-law distributions in animal movements can arise from intraspecific interactions
Breed, Greg A.; Severns, Paul M.; Edwards, Andrew M.
2015-01-01
Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight. PMID:25519992
A stable and robust calibration scheme of the log-periodic power law model
NASA Astrophysics Data System (ADS)
Filimonov, V.; Sornette, D.
2013-09-01
We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time tc, defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.
Effects of power law primordial magnetic field on big bang nucleosynthesis
NASA Astrophysics Data System (ADS)
Yamazaki, Dai G.; Kusakabe, Motohiko
2012-12-01
Big bang nucleosynthesis (BBN) is affected by the energy density of a primordial magnetic field (PMF). For an easy derivation of constraints on models for PMF generations, we assume a PMF with a power law (PL) distribution in wave number defined with a field strength, a PL index, and maximum and minimum scales at a generation epoch. We then show a relation between PL-PMF parameters and the scale invariant (SI) strength of PMF for the first time. We perform a BBN calculation including PMF effects, and show abundances as a function of baryon to photon ratio η. The SI strength of the PMF is constrained from observational constraints on abundances of He4 and D. The minimum abundance of Li7/H as a function of η slightly moves to a higher Li7/H value at a larger η value when a PMF exists during BBN. We then discuss degeneracies between the PL-PMF parameters in the PMF effect. In addition, we assume a general case in which both the existence and the dissipation of PMF are possible. It is then found that an upper limit on the SI strength of the PMF can be derived from a constraint on He4 abundance, and that a lower limit on the allowed Li7 abundance is significantly higher than those observed in metal-poor stars.
NASA Astrophysics Data System (ADS)
Inglis, A. R.; Ireland, J.; Dominique, M.
2015-01-01
The nature of quasi-periodic pulsations (QPPs) in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPPs is needed. We adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power-law properties of flare signals. Using data from the PROBA2/Large Yield Radiometer, Fermi/Gamma-ray Burst Monitor, Nobeyama Radioheliograph, and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as QPP events. Additionally, we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum. However, for the flare of 1998 May 8, strong evidence for an explicit oscillation with P ≈ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh/HXT data. We conclude that, most likely, many previously analyzed events in the literature may be similarly described by power laws in the flare Fourier power spectrum, without invoking a narrowband, oscillatory component. Hence the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.
Inglis, A. R.; Ireland, J.; Dominique, M.
2015-01-10
The nature of quasi-periodic pulsations (QPPs) in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPPs is needed. We adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power-law properties of flare signals. Using data from the PROBA2/Large Yield Radiometer, Fermi/Gamma-ray Burst Monitor, Nobeyama Radioheliograph, and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as QPP events. Additionally, we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum. However, for the flare of 1998 May 8, strong evidence for an explicit oscillation with P ≈ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh/HXT data. We conclude that, most likely, many previously analyzed events in the literature may be similarly described by power laws in the flare Fourier power spectrum, without invoking a narrowband, oscillatory component. Hence the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.
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.
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.
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.
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
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. PMID:26764669
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.
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.
Power-law decay of the view times of scientific courses on YouTube
NASA Astrophysics Data System (ADS)
Gao, Lingling
2012-11-01
The temporal power-law decay is one class of interesting decay processes, usually indicating a long-time correlation and benefiting for a system to perform functions in various time-scales. In this work, I collect the data of the view times versus lectures of some scientific courses on YouTube, according to some special principles. These data can reflect the dynamical property of the spontaneous learning behavior, influenced by the decay of learning interest. The view times versus lectures show an obviously power-law decay process. The power approximates to 1, a universal constant. This finding brings the learning process into the interesting power-law family. It will be of interest in the fields of the human dynamics, psychology and education.
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.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
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.
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.
Two-phase flow in porous media: power-law scaling of effective permeability
NASA Astrophysics Data System (ADS)
Grøva, Morten; Hansen, Alex
2011-09-01
A recent experiment has reported power-law scaling of effective permeability of two-phase flow with respect to capillary number for a two-dimensional model porous medium. In this paper, we consider the simultaneous flow of two phases through a porous medium under steady-state conditions, fixed total flow-rate and saturation, using a two-dimensional network simulator. We obtain power-law exponents for the scaling of effective permeability with respect to capillary number. The simulations are performed both for viscosity matched fluids and for a high viscosity ratio resembling that of air and water. Good power-law behaviour is found for both cases. Different exponents are found, depending on saturation.
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.
Power-law and exponential rank distributions: A panoramic Gibbsian perspective
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.
Statistical evidence for power law temporal correlations in exploratory behaviour of rats.
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
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.
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.
Huang, Zhifu Xing, Jiandong; Lv, Liangliang
2013-01-15
The effects of tungsten additions of 0%, 1.12%, 2.04%, and 3.17% (in wt.%) on the morphology, fracture toughness and micro-hardness of Fe{sub 2}B in Fe-B-C cast alloy were investigated. The results indicate that, with the increase of tungsten addition, the morphology and distribution of Fe{sub 2}B have no change and a new W-containing phase, except the (Fe, W){sub 2}B with a certain tungsten solution, does not form, and that the fracture toughness of Fe{sub 2}B increases first and then decreases, while the hardness increases first and then has a little change. Compared with the fracture toughness (3.8 MPa{center_dot}m{sup 1/2}) of Fe{sub 2}B without tungsten addition, the toughness at 2.04 wt.% tungsten can be improved by about above 80% and achieves about 6.9 MPa{center_dot}m{sup 1/2}, and variation characteristics of hardness and toughness of Fe{sub 2}B were also testified by viewing the indentation marks and cracks on the Fe{sub 2}B, respectively. - Highlights: Black-Right-Pointing-Pointer Poor toughness of Fe2B decreases obviously the wear resistance of the alloy. Black-Right-Pointing-Pointer As W content increases, Fe2B's toughness increases first and then decreases. Black-Right-Pointing-Pointer As W content increases, Fe2B's hardness first increases and then has little change. Black-Right-Pointing-Pointer The toughness at 2.04 % W can be improved by above 80% more than that at 0% W.
Non-power law behavior of the radial profile of phase-space density of halos
Popolo, A. Del
2011-07-01
We study the pseudo phase-space density, ρ(r)/σ{sup 3}(r), of ΛCDM dark matter halos with and without baryons (baryons+DM, and pure DM), by using the model introduced in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay. We examine the radial dependence of ρ(r)/σ{sup 3}(r) over 9 orders of magnitude in radius for structures on galactic and cluster of galaxies scales. We find that ρ(r)/σ{sup 3}(r) is approximately a power-law only in the range of halo radius resolved by current simulations (down to 0.1% of the virial radius) while it has a non-power law behavior below the quoted scale, with inner profiles changing with mass. The non-power-law behavior is more evident for halos constituted both of dark matter and baryons while halos constituted just of dark matter and with angular momentum chosen to reproduce a Navarro-Frenk-White (NFW) density profile, are characterized by an approximately power-law behavior. The results of the present paper lead to conclude that density profiles of the NFW type are compatible with a power-law behavior of ρ(r)/σ{sup 3}(r), while those flattening to the halo center, like those found in Del Popolo (2009) or the Einasto profile, or the Burkert profile, cannot produce radial profile of the pseudo-phase-space density that are power-laws at all radii. The results argue against universality of the pseudo phase-space density and as a consequence argue against universality of density profiles constituted by dark matter and baryons as also discussed in Del Popolo (2009)
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.
Power Law Inflation and the Cosmic No Hair Theorem in Brane World
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.
Time-dependent Kramers escape rate in overdamped system with power-law distribution
NASA Astrophysics Data System (ADS)
Zhou, Yanjun; Yin, Cangtao
2016-05-01
The probability distribution of Brownian particles moving in an overdamped complex system follows the generalized Smoluchowski equation, which can be rigorously proven that the exact time-dependent solution for this equation follows Tsallis form. Time-dependent escape rate in overdamped system with power-law distributions is then established based on the flux over population theory. The stationary state escape rate in overdamped system with power-law distribution which has been obtained before based on mean first passage time theory is recovered from time-dependent escape rate as time toward infinity.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; Nalewajko, K.; Begelman, M. C.
2015-12-30
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 ${\\gamma }^{-\\alpha }$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to σ and L, respectively. As a result, for large L and σ, the power-law index α approaches about 1.2.
Evidence of microstructure evolution in solid elastic media based on a power law analysis
NASA Astrophysics Data System (ADS)
Scalerandi, M.; Idjimarene, S.; Bentahar, M.; El Guerjouma, R.
2015-05-01
Complex and consolidated granular media or microcracked composites and metals usually exhibit a high level of nonlinearity in their elastic response already at low amplitudes of excitation. To quantify it, a proper nonlinear indicator y is introduced and its dependence on the excitation amplitude x is studied. The dependence of y on x is found in experiments to be a power law. Here we show that the different power law exponents measured for different materials could be predicted by proper classes of discrete models. An application is presented to link the exponent evolution and the changes of the microstructure due to the progression of damage mechanically induced.
Broken Power-law Distributions from Low Coronal Compression Regions or Shocks
NASA Astrophysics Data System (ADS)
Schwadron, N. A.; Lee, M. A.; Gorby, M.; Lugaz, N.; Spence, H. E.; Desai, M.; Török, T.; Downs, C.; Linker, J.; Lionello, R.; Mikić, Z.; Riley, P.; Giacalone, J.; Jokipii, J. R.; Kota, J.; Kozarev, K.
2015-09-01
Coronal Mass Ejection (CME) expansion regions low in the corona (< 2 - 3 Rs) are highly efficient for the acceleration of energetic particles. Because the acceleration occurs over a finite spatial region, there is a regime where particles diffuse away and escape from the acceleration sites, leading to the formation of broken power-law distributions. This paper highlights recent results indicating that CME expansion and acceleration in the low corona may cause rapid particle acceleration and create large solar energetic particle events with broken power-law distributions.
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.
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.
One-Dimensional Quantum Liquids with Power-Law Interactions: The Luttinger Staircase
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.
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.
Thermal distribution in high power optical devices with power-law thermal conductivity
NASA Astrophysics Data System (ADS)
Zhou, Chuanle; Grayson, M.
2012-01-01
We introduce a power-law approximation to model non-linear ranges of the thermal conductivity, and under this approximation derive a simple analytical expression for calculating the temperature profile in high power quantum cascade lasers and light emitting diodes. The thermal conductivity of a type II InAs/GaSb superlattice (T2SL) is used as an example, having negative or positive power-law exponents depending on the thermal range of interest. The result is an increase or decrease in the temperature, respectively, relative to the uniform thermal conductivity assumption.
Transport coefficients in Lorentz plasmas with the power-law kappa-distribution
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.
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.
Giorgi, Maria Cecília Caldas; Aguiar, Flávio Henrique Baggio; Soares, Luís Eduardo Silva; Martin, Airton Abrahão; Liporoni, Priscila Christiane Suzy; Paulillo, Luís Alexandre Maffei Sartini
2012-01-01
Objective: The purpose of this study was to evaluate the degree of conversion (DC) using FT-Raman spectroscopy and the Knoop hardness (KHN) of composites cured by second and third-generation LED light curing-units (LCU), Radii Cal and Ultralume 5. Methods: Three composites (Filtek Supreme XT, Filtek Z350, and Esthet X) were selected for this study. KHN testing (n=10) was performed with 10 indentations for the top (T) and bottom (B) surfaces. For DC (n=10), both the T and B surfaces were analyzed. Results: For KHN, the three composites differed in hardens. There was a “LCU-surface” interaction, in which Radii Cal showed significantly greater hardens in the B surface. For DC, there was a “composite-surface-LCU” interaction. For the “composite” factor, there was no significant difference between the groups, except for Supreme XT-Radii Cal (T or B surfaces). For the “LCU” factor there was a significant difference for Supreme XT T surface, Ultralume 5 obtained a higher DC. For the Z350 T surface, a significant difference in the DC in which Radii Cal obtained better results. For the “surface” factor, all groups presented T surfaces with a higher DC than the B surfaces, the sole exceptions involved Esthet X-Radii Cal and Z350-Ultralume 5. Conclusion: Knowledge regarding composite composition and the characteristics of LCUs are important for effective polymerization. PMID:23077419
Thermodynamics of higher dimensional topological dilation black holes with a power-law Maxwell field
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Sheykhi, A.; Dehghani, M. H.
2015-02-01
In this paper, we extend the study on the nonlinear power-law Maxwell field to dilaton gravity. We introduce the (n +1 ) -dimensional action in which gravity is coupled to a dilaton and power-law nonlinear Maxwell field, and we obtain the field equations by varying the action. We construct a new class of higher dimensional topological black hole solutions of Einstein-dilaton theory coupled to a power-law nonlinear Maxwell field and investigate the effects of the nonlinearity of the Maxwell source as well as the dilaton field on the properties of the spacetime. Interestingly enough, we find that the solutions exist provided one assumes three Liouville-type potentials for the dilaton field, and in the case of the Maxwell field, one of the Liouville potentials vanishes. After studying the physical properties of the solutions, we compute the mass, charge, electric potential and temperature of the topological dilaton black holes. We also study the thermodynamics and thermal stability of the solutions and disclose the effects of the dilaton field and the power-law Maxwell field on the thermodynamics of these black holes. Finally, we comment on the dynamical stability of the obtained solutions in four dimensions.
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...