Power-Law Modeling of Cancer Cell Fates Driven by Signaling Data to Reveal Drug Effects
Zhang, Fan; Wu, Min; Kwoh, Chee Keong; Zheng, Jie
2016-01-01
Extracellular signals are captured and transmitted by signaling proteins inside a cell. An important type of cellular responses to the signals is the cell fate decision, e.g., apoptosis. However, the underlying mechanisms of cell fate regulation are still unclear, thus comprehensive and detailed kinetic models are not yet available. Alternatively, data-driven models are promising to bridge signaling data with the phenotypic measurements of cell fates. The traditional linear model for data-driven modeling of signaling pathways has its limitations because it assumes that the a cell fate is proportional to the activities of signaling proteins, which is unlikely in the complex biological systems. Therefore, we propose a power-law model to relate the activities of all the measured signaling proteins to the probabilities of cell fates. In our experiments, we compared our nonlinear power-law model with the linear model on three cancer datasets with phosphoproteomics and cell fate measurements, which demonstrated that the nonlinear model has superior performance on cell fates prediction. By in silico simulation of virtual protein knock-down, the proposed model is able to reveal drug effects which can complement traditional approaches such as binding affinity analysis. Moreover, our model is able to capture cell line specific information to distinguish one cell line from another in cell fate prediction. Our results show that the power-law data-driven model is able to perform better in cell fate prediction and provide more insights into the signaling pathways for cancer cell fates than the linear model. PMID:27764199
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.
Anisotropic power-law inflation
Kanno, Sugumi; Soda, Jiro; Watanabe, Masa-aki E-mail: jiro@tap.scphys.kyoto-u.ac.jp
2010-12-01
We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.
Lee, Kelley
2015-01-01
Jeremy Shiffman’s editorial appropriately calls on making all forms of power more apparent and accountable, notably productive power derived from expertise and claims to moral authority. This commentary argues that relationships based on productive power can be especially difficult to reveal in global health policy because of embedded notions about the nature of power and politics. Yet, it is essential to recognize that global health is shot through with power relationships, that they can take many forms, and that their explicit acknowledgement should be part of, rather than factored out of, any reform of global health governance. PMID:25844390
Power Law Distribution in Education
NASA Astrophysics Data System (ADS)
Gupta, Hari M.; Campanha, José R.; Prado, Fernando D.
We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.
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).
Oldenburg, Amy L.; Yu, Xiao; Gilliss, Thomas; Alabi, Oluwafemi; Taylor, Russell M.; Troester, Melissa A.
2015-01-01
The progression of breast cancer is known to be affected by stromal cells within the local microenvironment. Here we study the effect of stromal fibroblasts on the in-place motions (motility) of mammary epithelial cells within organoids in 3D co-culture, inferred from the speckle fluctuation spectrum using optical coherence tomography (OCT). In contrast to Brownian motion, mammary cell motions exhibit an inverse power-law fluctuation spectrum. We introduce two complementary metrics for quantifying fluctuation spectra: the power-law exponent and a novel definition of the motility amplitude, both of which are signal- and position-independent. We find that the power-law exponent and motility amplitude are positively (p<0.001) and negatively (p<0.01) correlated with the density of stromal cells in 3D co-culture, respectively. We also show how the hyperspectral data can be visualized using these metrics to observe heterogeneity within organoids. This constitutes a simple and powerful tool for detecting and imaging cellular functional changes with OCT. PMID:26973862
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 regularities in human language
NASA Astrophysics Data System (ADS)
Mehri, Ali; Lashkari, Sahar Mohammadpour
2016-11-01
Complex structure of human language enables us to exchange very complicated information. This communication system obeys some common nonlinear statistical regularities. We investigate four important long-range features of human language. We perform our calculations for adopted works of seven famous litterateurs. Zipf's law and Heaps' law, which imply well-known power-law behaviors, are established in human language, showing a qualitative inverse relation with each other. Furthermore, the informational content associated with the words ordering, is measured by using an entropic metric. We also calculate fractal dimension of words in the text by using box counting method. The fractal dimension of each word, that is a positive value less than or equal to one, exhibits its spatial distribution in the text. Generally, we can claim that the Human language follows the mentioned power-law regularities. Power-law relations imply the existence of long-range correlations between the word types, to convey an especial idea.
Power Laws and Market Crashes ---Empirical Laws on Bursting Bubbles---
NASA Astrophysics Data System (ADS)
Kaizoji, T.
In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a power-law distribution, P (S > x) ˜ x^{-α}, with an exponent that moves in the range of 1.09 < α < 1.27. Furthermore, we found that as the power-law exponents α approached unity, the bubbles collapsed. This suggests that Zipf's law for stock prices is a sign that bubbles are going to burst.
Hierarchical networks, power laws, and neuronal avalanches.
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 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.
Power-law statistics for avalanches in a martensitic transformation.
Ahluwalia, R; Ananthakrishna, G
2001-04-30
We devise a two-dimensional model that mimics the recently observed power-law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [Vives et al., Phys. Rev. Lett. 72, 1694 (1994)]. We include a threshold mechanism, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis and, more importantly, it shows that the energy is released in the form of avalanches with power-law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.
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.
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.
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.
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.
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.
Kant on causal laws and powers.
Henschen, Tobias
2014-12-01
The aim of the paper is threefold. Its first aim is to defend Eric Watkins's claim that for Kant, a cause is not an event but a causal power: a power that is borne by a substance, and that, when active, brings about its effect, i.e. a change of the states of another substance, by generating a continuous flow of intermediate states of that substance. The second aim of the paper is to argue against Watkins that the Kantian concept of causal power is not the pre-critical concept of real ground but the category of causality, and that Kant holds with Hume that causal laws cannot be inferred non-inductively (that he accordingly has no intention to show in the Second analogy or elsewhere that events fall under causal laws). The third aim of the paper is to compare the Kantian position on causality with central tenets of contemporary powers ontology: it argues that unlike the variants endorsed by contemporary powers theorists, the Kantian variants of these tenets are resistant to objections that neo-Humeans raise to these tenets.
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.
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.
Spectrum of power laws for curved hand movements.
Huh, Dongsung; Sejnowski, Terrence J
2015-07-21
In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the -1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the -1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.
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
The origin of power-law rheology in foams
NASA Astrophysics Data System (ADS)
Hwang, Hyun Joo; Riggleman, Robert; Crocker, John
Soft glassy matter (SGM) such as foams, emulsions, and colloids, exhibit interesting rheological properties that have long defied explanation. In particular, the shear modulus of these materials displays weak power law frequency dependence. To understand the origin of this property in more depth, we have built a three-dimensional, modified Bubble Dynamics model. The bubbles interact with a purely repulsive harmonic potential and ripen according to diffusion-based governing equations. Notably, the bubble motion has a Levy flight character, in addition to being spatially correlated in the form of avalanches. Microrheology studies reveal that the power-law shear modulus is the result of constraint release driven by the bubbles' super-diffusive motion combined with simple yield of the resulting stress. The super-diffusive motion of the bubbles, in turn, is the result of the system taking a fractal path in configuration space. We shall discuss the origins of this fractal scaling.
29 CFR 417.6 - Powers of Administrative Law Judge.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 29 Labor 2 2010-07-01 2010-07-01 false Powers of Administrative Law Judge. 417.6 Section 417.6... Administrative Law Judge. The designated Administrative Law Judge shall have authority: (a) To give notice... other actions authorized by the regulations in this part. The Administrative Law Judge's authority...
43 CFR 4.1121 - Powers of administrative law judges.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Powers of administrative law judges. 4... Evidentiary Hearings § 4.1121 Powers of administrative law judges. (a) Under the regulations of this part, an administrative law judge may— (1) Administer oaths and affirmations; (2) Issue subpoenas; (3) Issue...
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.
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
Small power systems for law enforcement applications
NASA Astrophysics Data System (ADS)
Sims, Paul E.; Mauk, Michael G.; Sulima, Oleg V.
2002-08-01
Recent events have increased interest in the use of sensors by law enforcement and homeland defense related organizations. Autonomous sensors such as those under development for the Unattended Ground Sensor (UGS) program are suitable for some of these applications. The operational lifetime of a UGS depends on the power consumption of the package and the space allocated for batteries. We survey and assess options for powering these devices ina long-term scenario. These alternatives are in various stages of development, and range from conventional batteries and solar cells that are ready for deployment and are now commercially available; to technologies developed for other applications (e.g., power for deep-space probes, man portable power for soldiers, or for sensors in oil drilling bore holes) that would need to be adapted to UGS's; to new and often speculative concepts that are in the laboratory or are still on the drawing board. Ideally, unattended ground sensors do not require servicing, re- energizing or refueling; and are capable of autonomous operation for weeks or even years. Further, UGS's may need to be used covertly, which restricts schemes that would provide a detectable signature. Reliability, ruggedness, cost, weight, size, camouflaging, use of toxic materials and other safety or disposal aspects, restrictions on their deployment (e.g., whether UGS's can be dropped form the air or whether they need to be uprighted or favorably oriented), storage and inventorying considerations, temperature ranges of operation, and complexity of associated electronics are also important issues. In this paper, we will limit the discussion to systems where operating power does not exceed 5 watts since larger systems are commercially available. Some subjectivity in comparisons is perhaps inevitable, but despite the disparate physics upon which these devices are based, a few common criteria can be invoked for discussing their suitability for energy storage and powering UGS
Discovery of power-laws in chemical space.
Benz, Ryan W; Swamidass, S Joshua; Baldi, Pierre
2008-06-01
Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank/ frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80/20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases.
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.
Stochastic dynamics and a power law for measles variability.
Keeling, M; Grenfell, B
1999-01-01
Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size. PMID:10365402
The invariances of power law size distributions.
Frank, Steven A
2016-01-01
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances.
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.
Power law exponents characterizing human DNA
NASA Astrophysics Data System (ADS)
Provata, A.; Oikonomou, Th.
2007-05-01
The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc(S) of size S present long tails Pnc(S)˜S-1-μnc , with exponents μnc ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments Pc(S) in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.
The invariances of power law size distributions
Frank, Steven A.
2016-01-01
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances. PMID:27928497
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.
Helmholtz solitons in power-law optical materials
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-09-15
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.
Stochastic model of Zipf's law and the universality of the power-law exponent.
Yamamoto, Ken
2014-04-01
We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.
Rate-Controlling Mechanisms in Five-Power-Law Creep
Michael E. Kassner
2004-04-20
OAK-B135 Rate-Controlling Mechanisms in Five-Power-Law Creep. The initial grant emphasized the rate-controlling processes for five power-law creep. The effort has six aspects: (1) Theory of Taylor hardening from the Frank dislocation network in five power law substructures. (2) The dual dynamical and hardening nature of dislocations in five power law substructures. (3) Determination of the existence of long-range internal stress in five-power law creep dislocation substructures. (4) Dynamic recovery mechanisms associated with dislocation heterogeneities during five power law creep. (5) Versatility of five power law creep concept to other (hcp) crystal structures. (6) Writing of a book on ''Fundamental of Creep in Metals and Alloys'' by M.E. Kassner and Maria-Teresa Perez-Frado (postdoctoral scholar, funded by this project) Elsevier Press, 2004, in press. These areas are consistent with the original goals of this project as delineated in the original proposal to Basic Energy Sciences. The progress in each of these areas will be discussed separately and there will be an attempt to tie each aspect together so as to allow a summary regarding the conclusions with respect to the rate-controlling mechanisms of five power-law creep.
Systematic harmonic power laws inter-relating multiple fundamental constants
NASA Astrophysics Data System (ADS)
Chakeres, Donald; Buckhanan, Wayne; Andrianarijaona, Vola
2017-01-01
Power laws and harmonic systems are ubiquitous in physics. We hypothesize that 2, π, the electron, Bohr radius, Rydberg constant, neutron, fine structure constant, Higgs boson, top quark, kaons, pions, muon, Tau, W, and Z when scaled in a common single unit are all inter-related by systematic harmonic powers laws. This implies that if the power law is known it is possible to derive a fundamental constant's scale in the absence of any direct experimental data of that constant. This is true for the case of the hydrogen constants. We created a power law search engine computer program that randomly generated possible positive or negative powers searching when the product of logical groups of constants equals 1, confirming they are physically valid. For 2, π, and the hydrogen constants the search engine found Planck's constant, Coulomb's energy law, and the kinetic energy law. The product of ratios defined by two constants each was the standard general format. The search engine found systematic resonant power laws based on partial harmonic fraction powers of the neutron for all of the constants with products near 1, within their known experimental precision, when utilized with appropriate hydrogen constants. We conclude that multiple fundamental constants are inter-related within a harmonic power law system.
Development of Jet Noise Power Spectral Laws
NASA Technical Reports Server (NTRS)
Khavaran, Abbas; Bridges, James
2011-01-01
High-quality jet noise spectral data measured at the Aero-Acoustic Propulsion Laboratory (AAPL) at NASA Glenn is used to develop jet noise scaling laws. A FORTRAN algorithm was written that provides detailed spectral prediction of component jet noise at user-specified conditions. The model generates quick estimates of the jet mixing noise and the broadband shock-associated noise (BBSN) in single-stream, axis-symmetric jets within a wide range of nozzle operating conditions. Shock noise is emitted when supersonic jets exit a nozzle at imperfectly expanded conditions. A successful scaling of the BBSN allows for this noise component to be predicted in both convergent and convergent-divergent nozzles. Configurations considered in this study consisted of convergent and convergent- divergent nozzles. Velocity exponents for the jet mixing noise were evaluated as a function of observer angle and jet temperature. Similar intensity laws were developed for the broadband shock-associated noise in supersonic jets. A computer program called sJet was developed that provides a quick estimate of component noise in single-stream jets at a wide range of operating conditions. A number of features have been incorporated into the data bank and subsequent scaling in order to improve jet noise predictions. Measurements have been converted to a lossless format. Set points have been carefully selected to minimize the instability-related noise at small aft angles. Regression parameters have been scrutinized for error bounds at each angle. Screech-related amplification noise has been kept to a minimum to ensure that the velocity exponents for the jet mixing noise remain free of amplifications. A shock-noise-intensity scaling has been developed independent of the nozzle design point. The computer program provides detailed narrow-band spectral predictions for component noise (mixing noise and shock associated noise), as well as the total noise. Although the methodology is confined to single
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 laws in citation distributions: evidence from Scopus.
Brzezinski, Michal
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in "Physics and Astronomy". Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.
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.
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.
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.
Statistical analyses support power law distributions found in neuronal avalanches.
Klaus, Andreas; Yu, Shan; Plenz, Dietmar
2011-01-01
The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
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
Fractal ladder models and power law wave equations.
Kelly, James F; McGough, Robert J
2009-10-01
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.
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
Exploring the effect of power law social popularity on language evolution.
Gong, Tao; Shuai, Lan
2014-01-01
We evaluate the effect of a power-law-distributed social popularity on the origin and change of language, based on three artificial life models meticulously tracing the evolution of linguistic conventions including lexical items, categories, and simple syntax. A cross-model analysis reveals an optimal social popularity, in which the λ value of the power law distribution is around 1.0. Under this scaling, linguistic conventions can efficiently emerge and widely diffuse among individuals, thus maintaining a useful level of mutual understandability even in a big population. From an evolutionary perspective, we regard this social optimality as a tradeoff among social scaling, mutual understandability, and population growth. Empirical evidence confirms that such optimal power laws exist in many large-scale social systems that are constructed primarily via language-related interactions. This study contributes to the empirical explorations and theoretical discussions of the evolutionary relations between ubiquitous power laws in social systems and relevant individual behaviors.
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.
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.
Optical monitoring for power law fluids during spin coating.
Jardim, P L G; Michels, A F; Horowitz, F
2012-01-30
Optical monitoring is applied, in situ and in real time, to non-newtonian, power law fluids in the spin coating process. An analytical exact solution is presented for thickness evolution that well fits to most measurement data. As result, typical rheological parameters are obtained for several CMC (carboximetilcelullose) concentrations and rotation speeds. Optical monitoring thus precisely indicates applicability of the model to power law fluids under spin coating.
Relaxation Dynamics of Non-Power-Law Fluids
NASA Astrophysics Data System (ADS)
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong
2013-12-01
The relaxation of non-Newtonian liquids with non-power-law rheology on partially wetted surfaces is rarely investigated. This study assesses the relaxation behavior of 14 partial wetting systems with non-power-law fluids by sessile drop method. These systems are two carboxymethylcellulose sodium solutions on two kinds of slides, cover glass, and silicon wafer surfaces; three polyethylene glycol (PEG400) + silica nanoparticle suspensions on polymethyl methacrylate and polystyrene surfaces. The dynamic contact angle and moving velocity of contact line relationship data for relaxation drops of the 14 tested systems demonstrate a power-law fluid-like behavior, and the equivalent power exponent for a certain fluid on different solid substrates are uniform. By analyzing the relationship between the equivalent power exponent and shear rate, it is proposed that a fluid regime with shear rates of a few tens of s controls relaxation dynamics.
A generalization of the power law distribution with nonlinear exponent
NASA Astrophysics Data System (ADS)
Prieto, Faustino; Sarabia, José María
2017-01-01
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
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.
A power law approach to orifice flow rate calibration.
Rhinehart, R Russell; Gebreyohannes, Solomon; Sridhar, Upasana Manimegalai; Patrachari, Anirudh; Rahaman, M S
2011-04-01
Although standards for orifice flow meter design, installation, and calibration are supported herein, noncompliant devices exist in many pilot-, lab-scale, and on-board applications. For these, a common calibration practice is to preserve the ideal square root relation and determine a device specific discharge coefficient value. This work provides theoretical and empirical analyses to support relaxing the square root relation between orifice pressure drop and flow rate for noncompliant devices. The resulting power law relation is shown to improve accuracy, precision, and rangeability. Whether a device specific square root or power law model is used, it requires off-line or in-line calibration data. As such, a power law calibration model may only be useful for on-board and small-scale applications.
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.
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.
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.
Edge effect on the power law distribution of granular avalanches.
Lorincz, Kinga A; Wijngaarden, Rinke J
2007-10-01
Many punctuated phenomena in nature are claimed [e.g., by the theory of self-organized criticality (SOC)] to be power-law distributed. In our experiments on a three-dimensional pile of long-grained rice, we find that by only changing the boundary condition of the system, we switch from such power-law-distributed avalanche sizes to quasiperiodic system-spanning avalanches. Conversely, by removing ledges the incidence of system-spanning avalanches is significantly reduced. This may offer a perspective on new avalanche prevention schemes. In addition, our findings may help to explain why the archetype of SOC, the sandpile, was found to have power-law-distributed avalanches in some experiments, while in other experiments quasiperiodic system-spanning avalanches were found.
Universal power law behaviors in genomic sequences and evolutionary models
NASA Astrophysics Data System (ADS)
Martignetti, Loredana; Caselle, Michele
2007-08-01
We study the length distribution of a particular class of DNA sequences known as the 5' untranslated regions exons. These exons belong to the messenger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that in both mice and humans these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model, which may explain this finding. We conjecture that this power law behavior could indeed be a general feature of higher eukaryotes.
Soliton solutions with power-law nonlinearity in inhomogeneous media
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Yu, Fang-Bo
2013-04-01
We construct the relation between the variable coefficient nonlinear Schrödinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schrödinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.
Power Laws, Flicker Noise, and the Barkhausen Effect
1993-10-01
AD-A274 702 AD TECHNICAL REPORT ARCCB-TR-93038 POWER LAWS, FLICKER NOISE, AND THE BARKHAUSEN EFFECT DTIC ELECTE JA~N 211994 3 L.V. MEISEL S D P.J...CATES C&MORD October 1993 Fuel 4. TITLE AND SUBTITU S. FUNDING NUMBERS POWER LAWS. FUCKER NOISE. AND THE BARKHAUSEN EFFECT AMCMS: 611L02.H61L1 6. AUTHOR... Barkhausen effect was studied in three ferromagnetic metals: an amorphous alloy, iron. and alumel. The data exhibit all the characteristics of self
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.
Medical practices display power law behaviors similar to spoken languages
2013-01-01
Background Medical care commonly involves the apprehension of complex patterns of patient derangements to which the practitioner responds with patterns of interventions, as opposed to single therapeutic maneuvers. This complexity renders the objective assessment of practice patterns using conventional statistical approaches difficult. Methods Combinatorial approaches drawn from symbolic dynamics are used to encode the observed patterns of patient derangement and associated practitioner response patterns as sequences of symbols. Concatenating each patient derangement symbol with the contemporaneous practitioner response symbol creates “words” encoding the simultaneous patient derangement and provider response patterns and yields an observed vocabulary with quantifiable statistical characteristics. Results A fundamental observation in many natural languages is the existence of a power law relationship between the rank order of word usage and the absolute frequency with which particular words are uttered. We show that population level patterns of patient derangement: practitioner intervention word usage in two entirely unrelated domains of medical care display power law relationships similar to those of natural languages, and that–in one of these domains–power law behavior at the population level reflects power law behavior at the level of individual practitioners. Conclusions Our results suggest that patterns of medical care can be approached using quantitative linguistic techniques, a finding that has implications for the assessment of expertise, machine learning identification of optimal practices, and construction of bedside decision support tools. PMID:24007376
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.
The power laws of nanoscale forces under ambient conditions.
Lai, Chia-Yun; Olukan, Tuza; Santos, Sergio; Al Ghaferi, Amal; Chiesa, Matteo
2015-12-25
We report a power law derived from experimental atomic force microscopy (AFM) data suggesting a nano to mesoscale transition in force-distance dependencies. Our results are in relative agreement with the Hamaker and Lifshitz theories for van der Waals forces for the larger tip radii only.
Constraints on cosmological parameters in power-law cosmology
NASA Astrophysics Data System (ADS)
Rani, Sarita; Altaibayeva, A.; Shahalam, M.; Singh, J. K.; Myrzakulov, R.
2015-03-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H0 (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H0 average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → -1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.
Constraints on cosmological parameters in power-law cosmology
Rani, Sarita; Singh, J.K.; Altaibayeva, A.; Myrzakulov, R.; Shahalam, M. E-mail: aziza.bibol@mail.ru E-mail: jainendrrakumar@rediffmail.com
2015-03-01
In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters H{sub 0} (Hubble constant) and q (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of ΛCDM . We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on i.e. H{sub 0} average and q average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard ΛCDM model as q → −1. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.
Second law analysis of a conventional steam power plant
NASA Astrophysics Data System (ADS)
Liu, Geng; Turner, Robert H.; Cengel, Yunus A.
1993-11-01
A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.
Second law analysis of a conventional steam power plant
NASA Technical Reports Server (NTRS)
Liu, Geng; Turner, Robert H.; Cengel, Yunus A.
1993-01-01
A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.
The speed–curvature power law in Drosophila larval locomotion
2016-01-01
We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species. PMID:28120807
Scaling range of power laws that originate from fluctuation analysis
NASA Astrophysics Data System (ADS)
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A0378-437110.1016/j.physa.2013.01.049 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Scaling range of power laws that originate from fluctuation analysis.
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R^{2} of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
Power law cosmology model comparison with CMB scale information
NASA Astrophysics Data System (ADS)
Tutusaus, Isaac; Lamine, Brahim; Blanchard, Alain; Dupays, Arnaud; Zolnierowski, Yves; Cohen-Tanugi, Johann; Ealet, Anne; Escoffier, Stéphanie; Le Fèvre, Olivier; Ilić, Stéphane; Pisani, Alice; Plaszczynski, Stéphane; Sakr, Ziad; Salvatelli, Valentina; Schücker, Thomas; Tilquin, André; Virey, Jean-Marc
2016-11-01
Despite the ability of the cosmological concordance model (Λ CDM ) to describe the cosmological observations exceedingly well, power law expansion of the Universe scale radius, R (t )∝tn, has been proposed as an alternative framework. We examine here these models, analyzing their ability to fit cosmological data using robust model comparison criteria. Type Ia supernovae (SNIa), baryonic acoustic oscillations (BAO) and acoustic scale information from the cosmic microwave background (CMB) have been used. We find that SNIa data either alone or combined with BAO can be well reproduced by both Λ CDM and power law expansion models with n ˜1.5 , while the constant expansion rate model (n =1 ) is clearly disfavored. Allowing for some redshift evolution in the SNIa luminosity essentially removes any clear preference for a specific model. The CMB data are well known to provide the most stringent constraints on standard cosmological models, in particular, through the position of the first peak of the temperature angular power spectrum, corresponding to the sound horizon at recombination, a scale physically related to the BAO scale. Models with n ≥1 lead to a divergence of the sound horizon and do not naturally provide the relevant scales for the BAO and the CMB. We retain an empirical footing to overcome this issue: we let the data choose the preferred values for these scales, while we recompute the ionization history in power law models, to obtain the distance to the CMB. In doing so, we find that the scale coming from the BAO data is not consistent with the observed position of the first peak of the CMB temperature angular power spectrum for any power law cosmology. Therefore, we conclude that when the three standard probes (SNIa, BAO, and CMB) are combined, the Λ CDM model is very strongly favored over any of these alternative models, which are then essentially ruled out.
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
Power-law behavior of power spectra in low Prandtl number Rayleigh-Bénard convection.
Paul, M R; Cross, M C; Fischer, P F; Greenside, H S
2001-10-08
The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.
Power-law rheology controls aftershock triggering and decay
Zhang, Xiaoming; Shcherbakov, Robert
2016-01-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established. PMID:27819355
Power-law rheology controls aftershock triggering and decay
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Shcherbakov, Robert
2016-11-01
The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.
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 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.
Power law behavior of the zigzag transition in Yukawa clusters
Sheridan, T. E.; Magyar, Andrew L.
2010-11-15
We provide direct experimental evidence that the width of a Yukawa cluster exhibits power law behavior during the one-dimensional (1D) to two-dimensional (2D) zigzag transition. Configurations of small dusty (complex) plasma clusters confined in a biharmonic potential well are characterized as the well anisotropy is varied. When the anisotropy is large the particles are in a 1D straight-line configuration. As the anisotropy is decreased the cluster undergoes a zigzag transition to a 2D configuration. The measured dependence of cluster width on anisotropy follows a power law. A second transition from the zigzag to an elliptical configuration is also observed. The results are in very good agreement with a model of identical particles interacting through a Yukawa potential.
Probability distributions and confidence intervals for simulated power law noise.
Ashby, Neil
2015-01-01
A method for simulating power law noise in clocks and oscillators is presented based on modification of the spectrum of white phase noise, then Fourier transforming to the time domain. Symmetric real matrices are introduced whose traces-the sums of their eigenvalues-are equal to the Allan variances, in overlapping or non-overlapping forms, as well as for the corresponding forms of the modified Allan variance. We show that the standard expressions for spectral densities, and their relations to Allan variance, are obtained with this method. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval τ, and hence for estimating confidence in the measurements. Examples are presented for the common power-law noises. Extension to other variances such as the Hadamard variance, and variances with dead time, are discussed.
COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS
Mota, David F.; Winther, Hans A.
2011-05-20
In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to {Lambda}CDM, but can in some special cases enhance the growth of the linear perturbations at low redshifts. For the models we consider, it is found that this region of the parameter space is ruled out by local gravity constraints. Imposing a coupling to dark matter only, the local constraints are avoided, and it is possible to have observable signatures on the linear matter perturbations.
Lévy flights with power-law absorption.
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.
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 cosmology, SN Ia, and BAO
Dolgov, Aleksander; Halenka, Vitali; Tkachev, Igor E-mail: vithal@umich.edu
2014-10-01
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime a(t) ∼ t{sup β} with β close to 3/2 in a spatially flat universe is a good fit to these data.
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) .
Development of Jet Noise Power Spectral Laws Using SHJAR Data
NASA Technical Reports Server (NTRS)
Khavaran, Abbas; Bridges, James
2009-01-01
High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.
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.
SHJAR Jet Noise Data and Power Spectral Laws
NASA Technical Reports Server (NTRS)
Khavaran, Abbas; Bridges, James
2009-01-01
High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. The measured spectral data are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of 0.0 to 10.0. The measured data are reported as lossless (i.e., atmospheric attenuation is added to measurements), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter (200-in.) arc. Following the work of Viswanathan, velocity power factors are evaluated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit and the confidence margins for the two regression parameters are studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. As an immediate application of the velocity power laws, spectral density in shockcontaining jets are decomposed into components attributed to jet mixing noise and shock noise. From this analysis, jet noise prediction tools can be developed with different spectral components derived from different physics.
Event-scale power law recession analysis: quantifying methodological uncertainty
NASA Astrophysics Data System (ADS)
Dralle, David N.; Karst, Nathaniel J.; Charalampous, Kyriakos; Veenstra, Andrew; Thompson, Sally E.
2017-01-01
The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship
Power-law time distribution of large earthquakes.
Mega, Mirko S; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea; Vinciguerra, Sergio
2003-05-09
We study the statistical properties of time distribution of seismicity in California by means of a new method of analysis, the diffusion entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent mu=2.06+/-0.01. We propose the long-range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes.
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 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.
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.
Conductivity scaling in supercritical percolation of nanoparticles--not a power law.
Li, Jiantong; Östling, Mikael
2015-02-28
The power-law behavior widely observed in supercritical percolation systems of conductive nanoparticles may merely be a phenomenological approximation to the true scaling law not yet discovered. In this work, we derive a comprehensive yet simple scaling law and verify its extensive applicability to various experimental and numerical systems. In contrast to the power law which lacks theoretical backing, the new scaling law is explanatory and predictive, and thereby helpful to gain more new insights into percolation systems of conductive nanoparticles.
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.
Implitcation of a Power-Law Climate Response Function
NASA Astrophysics Data System (ADS)
Hébert, R.
2015-12-01
A study of global mean temperature is presented assuming that the climate response function to anthropogenic forcing is a power law. This general form allows for long-range dependancies with only 3 parameter while remaining within the linear forcing paradigm. This establish a one-to-one relation between the scaling exponent H and the ratio of the Transient Climate Response, TCR, and the Equilibrium Climate Sensitivity, ECS. The scaling exponent of the power law is estimated by a regression of temperature as a function of forcing and by a spectral analysis of the temperature and the forcing. We consider for the analysis 5 different datasets of historical global mean temperature and 100 CMIP5 RCP runs distributed among the 4 scenarios. We find that the error function for the estimate on historical temperature is very wide and thus, many scaling exponent can be used without meaningful changes in the fit residuals of historical temperatures; their response in the year 2100 on the other hand, is very broad. CMIP5 runs allow a narrower estimate of H which can then be used to estimate the ECS by dividing the TCR estimated from the historical data.
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 distributions from additive preferential redistributions
NASA Astrophysics Data System (ADS)
Ree, Suhan
2006-02-01
We introduce a nongrowth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed N -particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.
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.
Brain Network Dynamics Adhere to a Power Law
Tomasi, Dardo G.; Shokri-Kojori, Ehsan; Volkow, Nora D.
2017-01-01
The temporal dynamics of complex networks such as the Internet are characterized by a power scaling between the temporal mean and dispersion of signals at each network node. Here we tested the hypothesis that the temporal dynamics of the brain networks are characterized by a similar power law. This realization could be useful to assess the effects of randomness and external modulators on the brain network dynamics. Simulated data using a well-stablished random diffusion model allowed us to predict that the temporal dispersion of the amplitude of low frequency fluctuations (ALFF) and that of the local functional connectivity density (lFCD) scale with their temporal means. We tested this hypothesis in open-access resting-state functional magnetic resonance imaging datasets from 66 healthy subjects. A robust power law emerged from the temporal dynamics of ALFF and lFCD metrics, which was insensitive to the methods used for the computation of the metrics. The scaling exponents (ALFF: 0.8 ± 0.1; lFCD: 1.1 ± 0.1; mean ± SD) decreased with age and varied significantly across brain regions; multimodal cortical areas exhibited lower scaling exponents, consistent with a stronger influence of external inputs, than limbic and subcortical regions, which exhibited higher scaling exponents, consistent with a stronger influence of internal randomness. Findings are consistent with the notion that external inputs govern neuronal communication in the brain and that their relative influence differs between brain regions. Further studies will assess the potential of this metric as biomarker to characterize neuropathology. PMID:28261049
Passive mechanical behavior of human neutrophils: power-law fluid.
Tsai, M A; Frank, R S; Waugh, R E
1993-01-01
The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c
Deviation from power law of the global seismic moment distribution
NASA Astrophysics Data System (ADS)
Serra, Isabel; Corral, Álvaro
2017-01-01
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to the global CMT earthquake catalog. Although the Tap distribution does not introduce any significant improvement of fit respect the PL, the truncated gamma does. Simulated samples of this distribution, with parameters β = 0.68 and mc = 9.15 and reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, are able to explain the temporal heterogeneity of global seismicity both before and after the great Sumatra-Andaman earthquake of 2004.
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.
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.
Deviation from power law of the global seismic moment distribution
Serra, Isabel; Corral, Álvaro
2017-01-01
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law (PL) distribution with two statistical models that incorporate an exponential tail, the so-called tapered Gutenberg-Richter (Tap) and the truncated gamma, when fitted to the global CMT earthquake catalog. Although the Tap distribution does not introduce any significant improvement of fit respect the PL, the truncated gamma does. Simulated samples of this distribution, with parameters β = 0.68 and mc = 9.15 and reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, are able to explain the temporal heterogeneity of global seismicity both before and after the great Sumatra-Andaman earthquake of 2004. PMID:28053311
Power-law resistivity, magnetic relaxation and ac susceptibility
Gilchrist, J.; van der Beek, C.J.
1994-07-01
The nonlinear diffusion of magnetic flux into a superconducting sample can be studied by measuring the relaxation of the magnetisation after application of a step field or by measuring the ac susceptibility, {chi}{sub 1} and its third harmonic, {chi}{sub 3}, or preferably both methods covering different time scales. Each has been analysed recently for a field-cooled sample of a material whose creep activation energy depends logarithmically on current density, J corresponding to a power-law relation between electric field, E and J. Here, results are compared, using a universal scaling depth. Maximum {chi}{sub 1}{double_prime} {vert_bar}{chi}{sub 3}{vert_bar} and values occur, and also the magnetisation has relaxed to half its initial value when the scaling depth is comparable to the sample half-thickness.
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-law versus log-law in wall-bounded turbulence: A large-eddy simulation perspective
NASA Astrophysics Data System (ADS)
Cheng, W.; Samtaney, R.
2014-01-01
The debate whether the mean streamwise velocity in wall-bounded turbulent flows obeys a log-law or a power-law scaling originated over two decades ago, and continues to ferment in recent years. As experiments and direct numerical simulation can not provide sufficient clues, in this study we present an insight into this debate from a large-eddy simulation (LES) viewpoint. The LES organically combines state-of-the-art models (the stretched-vortex model and inflow rescaling method) with a virtual-wall model derived under different scaling law assumptions (the log-law or the power-law by George and Castillo ["Zero-pressure-gradient turbulent boundary layer," Appl. Mech. Rev. 50, 689 (1997)]). Comparison of LES results for Reθ ranging from 105 to 1011 for zero-pressure-gradient turbulent boundary layer flows are carried out for the mean streamwise velocity, its gradient and its scaled gradient. Our results provide strong evidence that for both sets of modeling assumption (log law or power law), the turbulence gravitates naturally towards the log-law scaling at extremely large Reynolds numbers.
NASA Astrophysics Data System (ADS)
Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.
2014-09-01
We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.
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.
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.
NASA Astrophysics Data System (ADS)
Gómez-Aguilar, J. F.; Atangana, Abdon
2017-01-01
Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems.
Multiple short time power laws in the orientational relaxation of nematic liquid crystals.
Jose, Prasanth P; Bagchi, Biman
2006-11-14
Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
NASA Astrophysics Data System (ADS)
Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco
2015-06-01
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
Crossover of two power laws in the anomalous diffusion of a two lipid membrane
Bakalis, Evangelos E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco E-mail: francesco.zerbetto@unibo.it; Venturini, Alessandro
2015-06-07
Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.
5 CFR 2423.31 - Powers and duties of the Administrative Law Judge at the hearing.
Code of Federal Regulations, 2013 CFR
2013-01-01
... Law Judge at the hearing. 2423.31 Section 2423.31 Administrative Personnel FEDERAL LABOR RELATIONS... LABOR PRACTICE PROCEEDINGS Hearing Procedures § 2423.31 Powers and duties of the Administrative Law Judge at the hearing. (a) Conduct of hearing. The Administrative Law Judge shall conduct the hearing...
NASA Astrophysics Data System (ADS)
Stewart, Michael; Morgenstern, Uwe
2013-04-01
Understanding runoff generation is important for management of freshwater systems. Determining transit time distributions of streamwaters and how they change with discharge gives information on the flowpaths and recharge sources of streams - vital information for determining the responses of streams to stressors such as pollution, landuse change, or climate change. This work takes a first look at unique information on how transit time distributions change with discharge in some New Zealand catchments. Transit time distributions of streamwaters have been determined from tritium measurements on single samples in this work. This allows changes with stream discharge to be observed, in contrast to previous isotope studies which have given averaged transit time distributions based on series of samples. In addition, tritium reveals the wide spectrum of ages present in streams whereas oxygen-18 or chloride variations only show the younger ages (Stewart et al., 2010). It was found that the mean transit time (MTT) data could be reasonably represented by straight lines in log-log plots, indicating power law relationships between MTT and discharge. Similar power law behaviour has been observed for the rock forming elements such as silica in streamwaters (Godsey et al., 2009). Case studies are presented for two New Zealand catchments, both with volcanic ash substrates. Toenepi is a dairy catchment near Hamilton, which shows well-constrained power law relationships between MTT and discharge, and between silica concentration and discharge (Morgenstern et al., 2010). Baseflow MTTs vary from 2.5 to 157 years. Tutaeuaua is a pastoral farming catchment near Taupo. Results for nested catchments along the stream also show power law relationships for both MTT and silica with discharge. Streamwater MTTs vary from 1 to 11 years. The results indicate that (1) relatively old waters dominate many streams, (2) streamwater ages vary with discharge, and (3) age, like silica, varies according to
Power-law cross-correlations estimation under heavy tails
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2016-11-01
We examine the performance of six estimators of the power-law cross-correlations-the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator-under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the α-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.
Money, power, gas and the law: The `big` convergence
Hollis, S.S.
1998-06-29
Nothing ever endures but change, and in the ever whirling wheel of change that is the energy economy and its regulation, massive flux is under way. The key ingredients in this mix--the gas and electric industries, the financial instruments and entities that back them, and the laws and regulations that control and guide them--are in a confluence moving at warp speed. Assets are being divested or monetized. Financial products--not only reserves--are the answer to managing supply risks. Spark spreads--the financial differential between the price of gas as a commodity and gas that has been transformed into electrons--are being traded. Electric restructuring is being patterned on the template of the gas experience. Electronic bulletin boards and trading systems are linking the industries in cyberspace. And the consolidation of these industries has led to the biggest mating game in the energy industries` history, all at a fast-forward pace. Federal and state legislators and regulators swim in the same tank as the voracious entities this article discusses. Faced with unimagined combinations of players, complicated market power questions swirl around the merger and acquisition marriages. And, as the markets push ahead with new ideas, the regulators attempt to shape the process with their own proposals to influence the market of the next millennium. This article discusses some of the major moves and certain key regulatory decisions regarding these landscape-altering initiatives.
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|.
Evaluation of detection model performance in power-law noise
NASA Astrophysics Data System (ADS)
Burgess, Arthur E.
2001-06-01
Two alternative forced-choice (2AFC) nodule detection performances of a number of model observers were evaluated for detection of simulated nodules in filtered power-law (1/f3) noise. The models included the ideal observer, the channelized Fisher-Hotelling (FH) model with two different basis function sets, the non-prewhitening matched filter with an eye filter (NPWE), and the Rose model with no DC response (RoseNDC). Detectability of the designer nodule signal was investigated. It has equation s((rho) )equalsA*Rect((rho) /2)(1-(rho) 2)v, where (rho) is a normalized distance (r/R), R is the nodule radius and A is signal amplitude. The nodule profile can be changed (designed) by changing the value of v. For example, the result is a sharp-edged, flat-topped disc for v equal to zero and the projection of a sphere for v equal to 0.5. Human observer experiments were done with nodules based on v equal to 0, 0.5 and 1.5. For the v equal to 1.5 case, human results could be well fitted using a variety of models. The human CD diagram slopes were -0.12, +0.27 and +0.44 for v equal to 0, 0.5 and 1.5 respectively.
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.
NASA Astrophysics Data System (ADS)
Hong, S. Lee; Bodfish, James W.; Newell, Karl M.
2006-03-01
We investigated the relationship between macroscopic entropy and microscopic complexity of the dynamics of body rocking and sitting still across adults with stereotyped movement disorder and mental retardation (profound and severe) against controls matched for age, height, and weight. This analysis was performed through the examination of center of pressure (COP) motion on the mediolateral (side-to-side) and anteroposterior (fore-aft) dimensions and the entropy of the relative phase between the two dimensions of motion. Intentional body rocking and stereotypical body rocking possessed similar slopes for their respective frequency spectra, but differences were revealed during maintenance of sitting postures. The dynamics of sitting in the control group produced lower spectral slopes and higher complexity (approximate entropy). In the controls, the higher complexity found on each dimension of motion was related to a weaker coupling between dimensions. Information entropy of the relative phase between the two dimensions of COP motion and irregularity (complexity) of their respective motions fitted a power-law function, revealing a relationship between macroscopic entropy and microscopic complexity across both groups and behaviors. This power-law relation affords the postulation that the organization of movement and posture dynamics occurs as a fractal process.
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.
Deformation of a Capsule in a Power-Law Shear Flow.
Tian, Fang-Bao
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
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
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
An Analytical Model of Wave-Induced Longshore Current Based on Power Law Wave Height Decay.
1988-01-01
34I ANALYtTICAL MODEL OF NAVE-INDUCED LON6SHORE CURRENT BASED ON PONE* LAW.. (U) COASTAL ENG INEERING RESEAKNH CENTER VICKSBURG NS J N SMITH ET AL...j . - .L .V . : ; * AN ANALYTICAL MODEL OF WAVE-INDUCED ~ z * LONGSHORE CURRENT BASED ON POWER LAW * - WAVE HEIGHT DECAY by Jane McKee...I_ I IF 31592 11. TITLE (Include Security Classfication) • An Analytical Model of Wave-Induced Longshore Current Based on Power Law . Wave
Power law distribution in high frequency financial data? An econometric analysis
NASA Astrophysics Data System (ADS)
Todorova, Lora; Vogt, Bodo
2011-11-01
Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov-Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks.
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
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.
NASA Astrophysics Data System (ADS)
Echeverria, J. C.; Rodriguez, E.; Aguilar-Cornejo, M.; Alvarez-Ramirez, J.
2016-10-01
In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA.
Chimera patterns induced by distance-dependent power-law coupling in ecological networks
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard
2016-09-01
This paper reports the occurrence of several chimera patterns and the associated transitions among them in a network of coupled oscillators, which are connected by a long-range interaction that obeys a distance-dependent power law. This type of interaction is common in physics and biology and constitutes a general form of coupling scheme, where by tuning the power-law exponent of the long-range interaction the coupling topology can be varied from local via nonlocal to global coupling. To explore the effect of the power-law coupling on collective dynamics, we consider a network consisting of a realistic ecological model of oscillating populations, namely the Rosenzweig-MacArthur model, and show that the variation of the power-law exponent mediates transitions between spatial synchrony and various chimera patterns. We map the possible spatiotemporal states and their scenarios that arise due to the interplay between the coupling strength and the power-law exponent.
Power law olivine crystal size distributions in lithospheric mantle xenoliths
NASA Astrophysics Data System (ADS)
Armienti, P.; Tarquini, S.
2002-12-01
Olivine crystal size distributions (CSDs) have been measured in three suites of spinel- and garnet-bearing harzburgites and lherzolites found as xenoliths in alkaline basalts from Canary Islands, Africa; Victoria Land, Antarctica; and Pali Aike, South America. The xenoliths derive from lithospheric mantle, from depths ranging from 80 to 20 km. Their textures vary from coarse to porphyroclastic and mosaic-porphyroclastic up to cataclastic. Data have been collected by processing digital images acquired optically from standard petrographic thin sections. The acquisition method is based on a high-resolution colour scanner that allows image capturing of a whole thin section. Image processing was performed using the VISILOG 5.2 package, resolving crystals larger than about 150 μm and applying stereological corrections based on the Schwartz-Saltykov algorithm. Taking account of truncation effects due to resolution limits and thin section size, all samples show scale invariance of crystal size distributions over almost three orders of magnitude (0.2-25 mm). Power law relations show fractal dimensions varying between 2.4 and 3.8, a range of values observed for distributions of fragment sizes in a variety of other geological contexts. A fragmentation model can reproduce the fractal dimensions around 2.6, which correspond to well-equilibrated granoblastic textures. Fractal dimensions >3 are typical of porphyroclastic and cataclastic samples. Slight bends in some linear arrays suggest selective tectonic crushing of crystals with size larger than 1 mm. The scale invariance shown by lithospheric mantle xenoliths in a variety of tectonic settings forms distant geographic regions, which indicate that this is a common characteristic of the upper mantle and should be taken into account in rheological models and evaluation of metasomatic models.
Exponential and power-law mass distributions in brittle fragmentation
NASA Astrophysics Data System (ADS)
Åström, J. A.; Linna, R. P.; Timonen, J.; Møller, Peder Friis; Oddershede, Lene
2004-08-01
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size s scales as s-(2D-1)/Df1(-(2/λ)Ds)+f2(-s0-1(λ+s1/D)D) , where D is the Euclidean dimension of the space, λ is the penetration depth, and f1 and f2 can be approximated by exponential functions. Simulation results and experiments can both be described by this theoretical fragment-size distribution. The typical largest fragment size s0 was found to diverge at the minimum strain required for fragmentation as it is inversely related to the density of initially formed cracks. Our results also indicate that scaling of s0 close to this divergence depends on, e.g., loading conditions, and thus is not universal. At the same time, the density of fragment surface vanishes as L-1 , L being the linear dimension of the brittle solid. The results obtained provide an explanation as to why the fragment-size distributions found in nature can have two components, an exponential as well as a power-law component, with varying relative weights.
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.
Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators
NASA Astrophysics Data System (ADS)
Casteels, W.; Storme, F.; Le Boité, A.; Ciuti, C.
2016-03-01
We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states; in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a nonadiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in the presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.
Fluctuation power spectra reveal dynamical heterogeneity of peptides
NASA Astrophysics Data System (ADS)
Khatri, Bhavin; Yew, Zu Thur; Krivov, Sergei; McLeish, Tom; Paci, Emanuele
2010-07-01
Characterizing the conformational properties and dynamics of biopolymers and their relation to biological activity and function is an ongoing challenge. Single molecule techniques have provided a rich experimental window on these properties, yet they have often relied on simple one-dimensional projections of a multidimensional free energy landscape for a practical interpretation of the results. Here, we study three short peptides with different structural propensity (α helical, β hairpin, and random coil) in the presence (or absence) of a force applied to their ends using Langevin dynamics simulation and an all-atom model with implicit solvation. Each peptide produces fluctuation power spectra with a characteristic dynamic fingerprint consistent with persistent structural motifs of helices, hairpins, and random coils. The spectra for helix formation shows two well-defined relaxation modes, corresponding to local relaxation and cooperative coil to uncoil interconversion. In contrast, both the hairpin and random coil are polymerlike, showing a broad and continuous range of relaxation modes giving characteristic power laws of ω-5/4 and ω-3/2, respectively; the -5/4 power law for hairpins is robust and has not been previously observed. Langevin dynamics simulations of diffusers on a potential of mean force derived from the atomistic simulations fail to reproduce the fingerprints of each peptide motif in the power spectral density, demonstrating explicitly that such information is lacking in such one-dimensional projections. Our results demonstrate the yet unexploited potential of single molecule fluctuation spectroscopy to probe more fine scaled properties of proteins and biological macromolecules and how low dimensional projections may cause the loss of relevant information.
Power-law modeling based on least-squares minimization criteria.
Hernández-Bermejo, B; Fairén, V; Sorribas, A
1999-10-01
The power-law formalism has been successfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a wider range of concentration values than the classical power-law. Although the implications of this alternative approach remain to be established, our results show that the predicted steady-state using the least-squares power-law is closest to the actual steady-state of the target system.
Mathematical modeling of genome evolution: Where do the power laws come from
NASA Astrophysics Data System (ADS)
Koonin, Eugene
2003-03-01
Power law distributions appear in numerous biological, physical, social and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interaction partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium were derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models were found and their appearance depending on model parameters was investigated. It was proved that the power law asymptotics appears if, and only if, the model is balanced, i.e., domain duplication (birth) and deletion (death) rates are asymptotically equal up to the second order. It was further proved that any power asymptotic with the degree not equal to -1 can appear only if the assumption of independence of the birth/death rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, were
Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales
NASA Technical Reports Server (NTRS)
Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.
2006-01-01
The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.
AEGIS: A MULTIWAVELENGTH STUDY OF SPITZER POWER-LAW GALAXIES
Park, S. Q.; Barmby, P.; Willner, S. P.; Ashby, M. L. N.; Fazio, G. G.; Georgakakis, A.; Ivison, R. J.; Konidaris, N. P.; Rosario, D. J.; Nandra, K.
2010-07-10
This paper analyzes a sample of 489 Spitzer/Infrared Array Camera (IRAC) sources in the Extended Groth Strip (EGS), whose spectral energy distributions fit a red power law (PL) from 3.6 to 8.0 {mu}m. The median redshift for sources with known redshifts is (z) = 1.6. Though all or nearly all of the sample galaxies are likely to be active galactic nuclei (AGNs), only 33% were detected in the EGS X-ray survey (AEGIS-X) using 200 ks Chandra observations. The detected sources are X-ray luminous with L {sub X}>10{sup 43} erg s{sup -1} and moderately to heavily obscured with N {sub H}>10{sup 22} cm{sup -2}. Stacking the X-ray-undetected sample members yields a statistically significant X-ray signal, suggesting that they are on average more distant or more obscured than sources with X-ray detections. The ratio of X-ray to mid-infrared fluxes suggests that a substantial fraction of the sources undetected in X-rays are obscured at the Compton-thick level, in contrast to the X-ray-detected sources, all of which appear to be Compton thin. For the X-ray-detected PL sources with redshifts, an X-ray luminosity L {sub X} {approx} 10{sup 44} erg s{sup -1} marks a transition between low-luminosity, blue sources dominated by the host galaxy to high-luminosity, red PL sources dominated by nuclear activity. X-ray-to-optical ratios, infrared variability, and 24 {mu}m properties of the sample are consistent with the identification of infrared PL sources as active nuclei, but a rough estimate is that only 22% of AGNs are selected by the PL criteria. Comparison of the PL selection technique and various IRAC color criteria for identifying AGNs confirms that high-redshift samples selected via simple IRAC colors may be heavily contaminated by starlight-dominated objects.
Simple inflationary quintessential model. II. Power law potentials
NASA Astrophysics Data System (ADS)
de Haro, Jaume; Amorós, Jaume; Pan, Supriya
2016-09-01
The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive
Transition from Exponential to Power Law Income Distributions in a Chaotic Market
NASA Astrophysics Data System (ADS)
Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.
Fitting power-laws in empirical data with estimators that work for all exponents
Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan
2017-01-01
Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes. PMID:28245249
Fitting power-laws in empirical data with estimators that work for all exponents.
Hanel, Rudolf; Corominas-Murtra, Bernat; Liu, Bo; Thurner, Stefan
2017-01-01
Most standard methods based on maximum likelihood (ML) estimates of power-law exponents can only be reliably used to identify exponents smaller than minus one. The argument that power laws are otherwise not normalizable, depends on the underlying sample space the data is drawn from, and is true only for sample spaces that are unbounded from above. Power-laws obtained from bounded sample spaces (as is the case for practically all data related problems) are always free of such limitations and maximum likelihood estimates can be obtained for arbitrary powers without restrictions. Here we first derive the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces. We then show that an almost identical estimator also works perfectly for continuous data. We implemented this ML estimator and discuss its performance with previous attempts. We present a general recipe of how to use these estimators and present the associated computer codes.
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2017-02-01
Boundary-layer solutions to Banks' problem for the flow induced by power-law stretching of a plate are obtained for two generalizations that include arbitrary transverse plate shearing motion. In one extension an arbitrary transverse shearing motion is the product of the power-law stretching. In the other extension the streamwise stretching coordinate is added to an arbitrary transverse shearing and together raised to the power of stretching. In addition we find that Banks' power law stretching may be accompanied by orthogonal power-law shear. In all cases, the original boundary-value problem of Banks [1] is recovered. Results are illustrated with velocity profiles both at the plate and at fixed height in the fluid above the plate.
Blinking in quantum dots: The origin of the grey state and power law statistics
NASA Astrophysics Data System (ADS)
Ye, Mao; Searson, Peter C.
2011-09-01
Quantum dot (QD) blinking is characterized by switching between an “on” state and an “off” state, and a power-law distribution of on and off times with exponents from 1.0 to 2.0. The origin of blinking behavior in QDs, however, has remained a mystery. Here we describe an energy-band model for QDs that captures the full range of blinking behavior reported in the literature and provides new insight into features such as the gray state, the power-law distribution of on and off times, and the power-law exponents.
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.
The double power law in human collaboration behavior: The case of Wikipedia
NASA Astrophysics Data System (ADS)
Kwon, Okyu; Son, Woo-Sik; Jung, Woo-Sung
2016-11-01
We study human behavior in terms of the inter-event time distribution of revision behavior on Wikipedia, an online collaborative encyclopedia. We observe a double power law distribution for the inter-editing behavior at the population level and a single power law distribution at the individual level. Although interactions between users are indirect or moderate on Wikipedia, we determine that the synchronized editing behavior among users plays a key role in determining the slope of the tail of the double power law distribution.
NASA Astrophysics Data System (ADS)
Alderweireld, Thomas; Nuyts, Jean
2004-01-01
The technique of Padé approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more “microscopic” level.
Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
Adler, Miri; Mayo, Avi; Alon, Uri
2014-01-01
Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling. PMID:25121598
14 CFR 406.109 - Administrative law judges-powers and limitations.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 14 Aeronautics and Space 4 2011-01-01 2011-01-01 false Administrative law judges-powers and limitations. 406.109 Section 406.109 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... Rules of Practice in FAA Space Transportation Adjudications § 406.109 Administrative law...
14 CFR 406.109 - Administrative law judges-powers and limitations.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 4 2010-01-01 2010-01-01 false Administrative law judges-powers and limitations. 406.109 Section 406.109 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... Rules of Practice in FAA Space Transportation Adjudications § 406.109 Administrative law...
14 CFR 406.109 - Administrative law judges-powers and limitations.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 4 2014-01-01 2014-01-01 false Administrative law judges-powers and limitations. 406.109 Section 406.109 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... Rules of Practice in FAA Space Transportation Adjudications § 406.109 Administrative law...
14 CFR 406.109 - Administrative law judges-powers and limitations.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 4 2013-01-01 2013-01-01 false Administrative law judges-powers and limitations. 406.109 Section 406.109 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... Rules of Practice in FAA Space Transportation Adjudications § 406.109 Administrative law...
14 CFR 406.109 - Administrative law judges-powers and limitations.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 4 2012-01-01 2012-01-01 false Administrative law judges-powers and limitations. 406.109 Section 406.109 Aeronautics and Space COMMERCIAL SPACE TRANSPORTATION, FEDERAL AVIATION... Rules of Practice in FAA Space Transportation Adjudications § 406.109 Administrative law...
Power law relation between particle concentrations and their sizes in the blood plasma
NASA Astrophysics Data System (ADS)
Kirichenko, M. N.; Chaikov, L. L.; Zaritskii, A. R.
2016-08-01
This work is devoted to the investigation of sizes and concentrations of particles in blood plasma by dynamic light scattering (DLS). Blood plasma contains many different proteins and their aggregates, microparticles and vesicles. Their sizes, concentrations and shapes can give information about donor's health. Our DLS study of blood plasma reveals unexpected dependence: with increasing of the particle sizes r (from 1 nm up to 1 μm), their concentrations decrease as r-4 (almost by 12 orders). We found also that such dependence was repeated for model solution of fibrinogen and thrombin with power coefficient is -3,6. We believe that this relation is a fundamental law of nature that shows interaction of proteins (and other substances) in biological liquids.
Charged Noncommutative Wormhole Solutions via Power-Law f(T) Models
NASA Astrophysics Data System (ADS)
Rani, Shamaila; Jawad, Abdul; Bilal Amin, M.
2016-10-01
In this paper, we explore static spherically symmetric charged wormhole solutions in extended teleparallel gravity taking power-law f(T) models. We consider noncommutative geometry under Lorentzian distribution. In order to obtain matter components, we develop field equations using effective energy-momentum tensor for non-diagonal tetrad. We explore solutions by considering various viable power-law f(T) models, which also include teleparallel gravity case. The violation of energy conditions obtain by exotic matter to form wormhole solutions in teleparallel case while, physical acceptable wormhole solutions exist for charged noncommutative wormhole solutions for some cases of power-law models. The effective energy-momentum tensor and charge are responsible for the violation of the energy conditions. Also, we check the equilibrium condition for these solutions. The equilibrium condition meets for the teleparallel case and some power-law solutions while remaining solutions are either in less equilibrium or in disequilibrium situation.
Convex and concave successions of power-law decays in small-angle scattering
NASA Astrophysics Data System (ADS)
Anitas, E. M.
2016-08-01
The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with fractal iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: convex/concave - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power- law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.
Hydrodynamics of Newtonian and power-law fluids in microchannel with superhydrophobic wall
NASA Astrophysics Data System (ADS)
Vagner, S. A.; Patlazhan, S. A.
2016-11-01
The flow peculiarities of the Newtonian and Carreau-Yasuda power-law fluids in a microchannel with the striped superhydrophobic wall is studied numerically. The driving forces leading to deviation of streamlines from the channel axis are analyzed.
Sato, Aki-Hiro
2004-04-01
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
NASA Astrophysics Data System (ADS)
Sato, Aki-Hiro
2004-04-01
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
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.
Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems
NASA Astrophysics Data System (ADS)
Rodin, Aleksandr; Fogler, Michael
2011-03-01
Observation of power-law dependence of conductance on temperature and voltage has been reported for a wide variety of low-dimensional systems(nano-wires, nano-tubes, and conducting polymers). This behavior has been attributed to the Luttinger liquid effects expected in a pure one-dimensional wire. However, the systems studied were neither one-dimensional nor defect-free. Using numerical simulations we show that the power-law behavior can arise from variable-range hopping in an ensemble of non-interacting disordered wires connected in parallel. This power-law behavior holds in restricted ranges of voltage and temperature, typical of experimental situations. Physically, it comes from rare, but highly conducting hopping paths that appear by chance in some members of the ensemble. The power-law exponents and their dependence on system parameters are consistent with the great majority of available empirical data. Supported by Grant NSF DMR-0706654.
Enhanced discriminability for nonbiological motion violating the two-thirds power law.
Salomon, Roy; Goldstein, Ariel; Vuillaume, Laurène; Faivre, Nathan; Hassin, Ran R; Blanke, Olaf
2016-06-01
The two-thirds power law describes the relationship between velocity and curvature in human motor movements. Interestingly, this motor law also affects visual motion perception, in which stimuli moving according to the two-thirds power law are perceived to have a constant velocity compared to stimuli actually moving at constant velocity. Thus, visual motion adhering to biological motion principles causes a kinematic illusion of smooth and velocity-invariant motion. However, it is yet unclear how this motion law affects the discrimination of visual stimuli and if its encoding requires attention. Here we tested the perceptual discrimination of stimuli following biological (two-thirds power law) or nonbiological movement under conditions in which the stimuli were degraded or masked through continuous flash suppression. Additionally, we tested subjective perception of naturalness and velocity consistency. Our results show that the discriminability of a visual target is inversely related to the perceived "naturalness" of its movement. Discrimination of stimuli following the two-thirds power law required more time than the same stimuli moving at constant velocity or nonecological variants of the two-thirds power law and was present for both masked and degraded stimuli.
Analytical study of solitons in the fiber waveguide with power law nonlinearity
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah
2017-01-01
This work deals with the existence of exact soliton solutions in fiber waveguide with power law nonlinearity. The propagation equation that is the resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity is studied by three analytical methods. The integration tools are the extended trial equation method, exp(-Φ(ξ)) -expansion method and extended G‧ / G - expansion method. The presented results show that analytical optical solitons can exist in this setting.
Deformation of a Capsule in a Power-Law Shear Flow
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values. PMID:27840656
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
ERIC Educational Resources Information Center
Schneider, Elizabeth M.
2010-01-01
I am pleased to be part of this symposium to celebrate the life and work of Peter Bachrach. Although my focus is the relevance of Peter's ideas of power to law, I want to begin with some personal comments as well as raise some final thoughts, drawing on others' contributions. Like so many of Peter's other students, I adored him. Peter's joy in…
NASA Astrophysics Data System (ADS)
Zeng, Hong-Li; Zhu, Chen-Ping; Guo, Yan-Dong; Teng, Ao; Jia, Jing; Kong, Hui; Zhou, Rui; Yang, Juan-Ping; Li, Su-Quan
2015-04-01
A co-evolutionary neuronal network model based on previous ones is proposed, and both functional and structural properties are numerically calculated. Recent experiments have revealed power-law behavior in electrocorticogram (ECoG) spectrum related with synaptic plasticity and reorganization. In the present neuronal network model, the network starts its evolution from the initial configuration of random network which is the least biased and without special structure, and the interaction rules among neurons are modified from both models by Bornholdt's and Arcangelis' groups to simulate the process of synaptic development and maturation. The system exhibits dynamic small-world structure which is the result of evolution instead of the assumption beforehand. Meanwhile, the power spectrum of electrical signals reproduces the power-law behavior with the exponent 2.0 just as what is experimentally measured in ECoG spectrum. Moreover, the power spectrum of the average degree per neuron over time also exhibits power-law behavior, with the exponent 2.0 again over more than 5 orders of magnitude. Different from previous results, our network exhibits assortative degree-degree correlation which is expected to be checked by experiments.
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.
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.
Taylor's power law of fluctuation scaling and the growth-rate theorem.
Cohen, Joel E
2013-09-01
Taylor's law (TL), a widely verified empirical relationship in ecology, states that the variance of population density is approximately a power-law function of mean density. The growth-rate theorem (GR) states that, in a subdivided population, the rate of change of the overall growth rate is proportional to the variance of the subpopulations' growth rates. We show that continuous-time exponential change implies GR at every time and, asymptotically for large time, TL with power-law exponent 2. We also show why diverse population-dynamic models predict TL in the limit of large time by identifying simple features these models share: If the mean population density and the variance of population density are (exactly or asymptotically) non-constant exponential functions of a parameter (e.g., time), then the variance of density is (exactly or asymptotically) a power-law function of mean density.
Astronomy phenomenological analysis of redshift-distance power laws
NASA Astrophysics Data System (ADS)
Segal, I. E.; Nicoll, J. F.
The traditional astronomical literature accepts the linear redshift-distance law on the basis of its internal consistency with accepted models of the history of the universe more than on nontrivial clearly objective tests of the linear law for directly observed quantities. The reluctance to depend on such tests rested historically on the assumed large variation in the intrinsic luminosity of extragalactic objects and a distrust of curve-fitting and statistics. But such tests are eminently feasible on the basis of modern objectively specified samples and up-to-date statistical methodology. This paper compares red-shift distance relations of the form z=k r, for real values of p. Data from the visible, infrared, radio, and X-ray bands are examined. The deviation of predicted and observed apparent magnitudes, (a), and the difference between observed and predicated slope of the magnitude-log (z) plots, (b), are used to compare values of p. In summary, the p=1 values (corresponding to standard linear law) are more deviant than any other value of p, 1
ERIC Educational Resources Information Center
Walker, W. R.; Cox, W. E.
1978-01-01
Presents a literature review of the legal issues relative to water quality covering publications of 1977. Consideration is given to federal laws, Supreme Court cases, and the impact of federal environmental laws on local government. A list of 47 references is also presented. (HM)
Takahashi, Ryosuke; Okajima, Takaharu
2015-10-26
We present multi-frequency force modulation atomic force microscopy (AFM) for mapping the complex shear modulus G* of living cells as a function of frequency over the range of 50–500 Hz in the same measurement time as the single-frequency force modulation measurement. The AFM technique enables us to reconstruct image maps of rheological parameters, which exhibit a frequency-dependent power-law behavior with respect to G{sup *}. These quantitative rheological measurements reveal a large spatial variation in G* in this frequency range for single cells. Moreover, we find that the reconstructed images of the power-law rheological parameters are much different from those obtained in force-curve or single-frequency force modulation measurements. This indicates that the former provide information about intracellular mechanical structures of the cells that are usually not resolved with the conventional force measurement methods.
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.
NASA Astrophysics Data System (ADS)
Buschmann, Matthias
2000-03-01
The paper presents an analysis of two-dimensional zero pressure gradient (ZPG) turbulent boundary layers (TBL) with regard to the application of power laws. Only TBL with low Reynolds number 300 < Reδ2 < 6200 are taken into account. It is found that a certain region of the mean velocity profile can be described with a power law of the formu +=C Pow{*}y +a. This power law region is not a priori identical with the overlap region. An algorithm for the determination of the wall skin friction using the power law is proposed. The method was applied with good result to ZPG TBL and to adverse pressure gradient (APG) TBL. To bridge the gap between the wall and the power law region an approach for the turbulent viscosity is suggested.
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.
Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts
NASA Astrophysics Data System (ADS)
Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.
The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.
The fractal nature of nature: power laws, ecological complexity and biodiversity.
Brown, James H; Gupta, Vijay K; Li, Bai-Lian; Milne, Bruce T; Restrepo, Carla; West, Geoffrey B
2002-01-01
Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science. PMID:12079523
The fractal nature of nature: power laws, ecological complexity and biodiversity.
Brown, James H; Gupta, Vijay K; Li, Bai-Lian; Milne, Bruce T; Restrepo, Carla; West, Geoffrey B
2002-05-29
Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self-similar or fractal-like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science.
Power laws from individual differences in learning and forgetting: mathematical analyses.
Murre, Jaap M J; Chessa, Antonio G
2011-06-01
It has frequently been claimed that learning performance improves with practice according to the so-called "Power Law of Learning." Similarly, forgetting may follow a power law. It has been shown on the basis of extensive simulations that such power laws may emerge through averaging functions with other, nonpower function shapes. In the present article, we supplement these simulations with a mathematical proof that power functions will indeed emerge as a result of averaging over exponential functions, if the distribution of learning rates follows a gamma distribution, a uniform distribution, or a half-normal function. Through a number of simulations, we further investigate to what extent these findings may affect empirical results in practice.
ERIC Educational Resources Information Center
Shih, Kristy Y.; Pyke, Karen
2010-01-01
This interview study interrogates how cultural values of filial piety inform Chinese American daughters-in-law's understanding of their relationship and power dynamics with immigrant Chinese American mothers-in-law. Ideals of filial respect accord limited authority to mothers-in-law, who engage other mechanisms of power, such as their domestic…
Interception efficiency in flow of power-law fluids past confined porous bodies
NASA Astrophysics Data System (ADS)
Shahsavari, Setareh; McKinley, Gareth
2014-11-01
Understanding the flow of power-law fluids through porous media is important for a wide range of filtration and sedimentation processes. In this study, the mobility of power-law fluids through porous media is investigated numerically and we use parametric studies to systematically understand the individual roles of geometrical characteristics, rheological properties as well as flow conditions. In addition, an analytical solution is presented that can be used as a modified Darcy law for generalized Newtonian fluids. Building on this modified Darcy law, the incompressible laminar flow of power-law and Carreau fluids past a confined porous body is modeled numerically. From the simulations we calculate the flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector. Finally, the interception efficiency of power-law fluids are compared with the case of a Newtonian fluid. The focus of this work is principally for flow of inelastic fluids in fibrous media; however, the methodology can also be extended to other porous media.
Decomposition of Heart Rate Variability Spectrum into a Power-Law Function and a Residual Spectrum.
Kuo, Jane; Kuo, Cheng-Deng
2016-01-01
The power spectral density (PSD) of heart rate variability (HRV) contains a power-law relationship that can be obtained by plotting the logarithm of PSD against the logarithm of frequency. The PSD of HRV can be decomposed mathematically into a power-law function and a residual HRV (rHRV) spectrum. Almost all rHRV measures are significantly smaller than their corresponding HRV measures except the normalized high-frequency power (nrHFP). The power-law function can be characterized by the slope and Y-intercept of linear regression. Almost all HRV measures except the normalized low-frequency power have significant correlations with the Y-intercept, while almost all rHRV measures except the total power [residual total power (rTP)] do not. Though some rHRV measures still correlate significantly with the age of the subjects, the rTP, high-frequency power (rHFP), nrHFP, and low-/high-frequency power ratio (rLHR) do not. In conclusion, the clinical significances of rHRV measures might be different from those of traditional HRV measures. The Y-intercept might be a better HRV measure for clinical use because it is independent of almost all rHRV measures. The rTP, rHFP, nrHFP, and rLHR might be more suitable for the study of age-independent autonomic nervous modulation of the subjects.
Direct simulation Monte Carlo of rarefied hypersonic flow on power law shaped leading edges
NASA Astrophysics Data System (ADS)
Santos, Wilson Fernando Nogueira Dos
A numerical study of several parameters that influence the flowfield structure, aerodynamic surface quantities and shock wave structure at rarefied hypersonic flow conditions is conducted on power law shaped leading edges. The calculations are performed with a detailed computer code that properly accounts for nonequilibrium effects and that has been demonstrated to yield excellent comparisons with flight- and ground-test data. The flowfield structure, aerodynamic surface quantities and shock wave structure of power law shaped leading edges are examined in order to provide information on how well these shapes could stand as possible candidates for blunting geometries of hypersonic leading edges. Newtonian flow analysis has shown that these shapes exhibit both blunt and sharp aerodynamic properties. Moreover, computational investigation of minimum-drag bodies at supersonic and moderate hypersonic speeds has indicated that power law shapes for certain exponents yield the lowest wave drag. These qualities make power law shapes strong candidates for leading edge design. A very detailed description of the impact on the flow properties, such as velocity, density, temperature and pressure, has been presented separately in the vicinity of the nose of the leading edges due to changes in their shapes. Numerical solutions show that the shape of the leading edge disturbed the flowfield far upstream, where the domain of influence decreased as the leading edge became aerodynamically sharp. A detailed procedure is presented to predict the pressure gradient along the body surface in a rarefied environment. Numerical solutions show that the pressure gradient behavior follows that predicted by Newtonian theory. It is found that the pressure gradient along the body surface goes to zero at the nose of the leading edge for power law exponents less than 2/3, a characteristic of a blunt body. It is finite for power law exponent of 2/3 and goes to minus infinite for power law exponents
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.
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.
Spreading of completely wetting, non-Newtonian fluids with non-power-law rheology.
Min, Qi; Duan, Yuan-Yuan; Wang, Xiao-Dong; Liang, Zhan-Peng; Lee, Duu-Jong; Su, Ay
2010-08-01
Spreading non-Newtonian liquids with non-power-law rheology on completely wetting surfaces are seldom investigated. This study assessed the wetting behavior of polydimethylsiloxane (PDMS), a Newtonian fluid, two carboxymethylcellulose (CMC) sodium solutions, a PDMS+2%w/w silica nanoparticle suspension and three polyethylene glycol (PEG400)+5-10%w/w silica nanoparticle suspensions (non-power-law fluids) on a mica surface. The theta(D)-U and R-t data for spreading drops of the six tested, non-power-law fluids can be described by power-law wetting models. We propose that this behavior is attributable to a uniform shear rate (a few tens to a few hundreds of s(-1)) distributed over the thin-film regime that controls spreading dynamics. Estimated film thickness was below the resolution of an optical microscope for direct observation. Approximating a general non-Newtonian fluid spreading as a power-law fluid greatly simplifies theoretical analysis and data interpretation.
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.
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.
NASA Astrophysics Data System (ADS)
Millon, M. A.; Goertz, C. K.
1988-01-01
Magnetospheric radio frequency emission power has been shown to vary as a function of both solar wind and planetary values such as magnetic field by Kaiser and Desch. Planetary magnetic fields have been shown to scale with planetary variables such as density and angular momentum by numerous researchers. This paper combines two magnetic scaling laws (Busse's and Curtis Ness') with the radiometric law to yield "Bode's"-type laws governing planetary radio emission. Further analysis allows the reduction of variables to planetary mass and orbital distance. These generalized laws are then used to predict the power output of Neptune to be about 1.6×107W; with the intensity peaking at about 3 MHz.
Stochastic Mixing Model with Power Law Decay of Variance
NASA Technical Reports Server (NTRS)
Fedotov, S.; Ihme, M.; Pitsch, H.
2003-01-01
Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.
On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy
NASA Astrophysics Data System (ADS)
Ahnen, Max L.
2017-02-01
The high-energy non-thermal universe is dominated by power-law-like spectra. Therefore, results in high-energy astronomy are often reported as parameters of power-law fits, or, in the case of a non-detection, as an upper limit assuming the underlying unseen spectrum behaves as a power law. In this paper, I demonstrate a simple and powerful one-to-one relation of the integral upper limit in the two-dimensional power-law parameter space into the spectrum parameter space and use this method to unravel the so-far convoluted question of the sensitivity of astroparticle telescopes.
Thermodynamics of (2 +1 )-dimensional charged black holes with power-law Maxwell field
NASA Astrophysics Data System (ADS)
Dehghani, M.
2016-11-01
In this work, the three-dimensional nonlinearly charged black holes have been considered with a power-law modified electromagnetic theory. The black hole solutions to Einstein's three-dimensional field equations with a negative cosmological constant have been constructed in the presence of power-law nonlinear electrodynamics. Through the physical and mathematical interpretation of the solutions, a new class of asymptotically anti-de Sitter (AdS) black hole solutions has been introduced. The area law, surface gravity, and Gauss's law are utilized to obtain the entropy, temperature, and electric charge of the new AdS black holes, respectively. The quasilocal mass of the solutions has been calculated based on the counterterm method. A Smarr-type formula for the mass as a function of entropy and charge has been obtained. It has been shown that the thermodynamical quantities satisfy the first law of thermodynamics for the new AdS black holes. Also, it has been found that in order for the Smarr mass formula to be compatible with the first law of black hole thermodynamics, the cosmological parameter Λ should be treated as a thermodynamical variable and the generalized first law of thermodynamics has been introduced. Through the canonical ensemble method, the black hole remnant or phase transitions have been investigated regarding the black hole heat capacity. It has been found that the AdS black hole solutions we just obtained are thermodynamically stable.
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.
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.
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.
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.
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.
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.
Analysis of electroosmotic flow of power-law fluids in a slit microchannel.
Zhao, Cunlu; Zholkovskij, Emilijk; Masliyah, Jacob H; Yang, Chun
2008-10-15
Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.
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.
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.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
NASA Astrophysics Data System (ADS)
Travesset, Alex
2014-10-01
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.
Tippett, Michael K; Cohen, Joel E
2016-02-29
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.
Heat transfer analysis in an annular cone subjected to power law variations
NASA Astrophysics Data System (ADS)
Salman Ahmed, N. J.; Al-Rashed, Abdullah A. A. A.; Yunus Khan, T. M.; Kamangar, Sarfaraz; Athani, Abdulgaphur; Anjum Badruddin, Irfan
2016-09-01
Present study deals with the analysis of heat transfer and fluid flow behavior in an annular cone fixed with saturated porous medium. The inner surface of the cone is assumed to have power law variable wall temperature. The governing partial differential equations are solved using well known Finite Element Method (FEM). The coupled nonlinear differential equations are converted into the algebraic equations by using Galerkin method. A 3 noded triangular element is used to divide the porous domain into smaller segments. The effects of various geometrical parameters on the cone angle are presented. It is found that the effect of cone angle on the heat transfer characteristics and fluid flow behavior is considerably significant. The fluid moment is found to shift towards the upper side of cone with increase in the power law coefficient. The fluid velocity decreases with increase in the power law coefficient.
Breast tumor subgroups reveal diverse clinical prognostic power
Liu, Zhaoqi; Zhang, Xiang-Sun; Zhang, Shihua
2014-01-01
Predicting the outcome of cancer therapies using molecular features and clinical observations is a key goal of cancer biology, which has been addressed comprehensively using whole patient datasets without considering the effect of tumor heterogeneity. We hypothesized that molecular features and clinical observations have different prognostic abilities for different cancer subtypes, and made a systematic study using both clinical observations and gene expression data. This analysis revealed that (1) gene expression profiles and clinical features show different prognostic power for the five breast cancer subtypes; (2) gene expression data of the normal-like subgroup contains more valuable prognostic information and survival associated contexts than the other subtypes, and the patient survival time of the normal-like subtype is more predictable based on the gene expression profiles; and (3) the prognostic power of many previously reported breast cancer gene signatures increased in the normal-like subtype and reduced in the other subtypes compared with that in the whole sample set. PMID:24499868
Spherical collapse model and cluster number counts in power-law f(T) gravity
NASA Astrophysics Data System (ADS)
Malekjani, M.; Basilakos, S.; Heidari, N.
2017-04-01
We study the spherical collapse model in the framework of spatially flat power law f(T) ∝ (- T)b gravity model. We find that the linear and non-linear growth of spherical overdensities of this particular f(T) model are affected by the power-law parameter b. Finally, we compute the predicted number counts of virialized haloes in order to distinguish the current f(T) model from the expectations of the concordance Λ cosmology. Specifically, the present analysis suggests that the f(T) gravity model with positive (negative) b predicts more (less) virialized objects with respect to those of Λ cold dark matter.
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.
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|(β), with β>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 β 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.
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.
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.
Power-law electrokinetic behavior as a direct probe of effective surface viscosity
NASA Astrophysics Data System (ADS)
Uematsu, Yuki; Netz, Roland R.; Bonthuis, Douwe Jan
2017-02-01
An exact solution to the Poisson-Boltzmann and Stokes equations is derived to describe the electric double layer with inhomogeneous dielectric and viscosity profiles in a lateral electric field. In the limit of strongly charged surfaces and low salinity, the electrokinetic flow magnitude follows a power law as a function of the surface charge density. Remarkably, the power-law exponent is determined by the interfacial dielectric constant and viscosity, the latter of which has eluded experimental determination. Our approach provides a novel method to extract the effective interfacial viscosity from standard electrokinetic experiments. We find good agreement between our theory and experimental data.
Evidence for power-law dominated noise in vacuum deposited CaF2.
Luhman, D R; Hallock, R B
2004-06-25
We have studied the surface roughness of CaF2 vacuum deposited on glass using atomic force microscopy for film coverages spanning an order of magnitude. We find the roughness exponent alpha=0.88+/-0.03, the growth exponent beta=0.75+/-0.03, and the dynamic exponent z=alpha/beta=1.17+/-0.06. Multifractality is also present, along with power-law behavior in the nearest neighbor height difference probability distribution. The results indicate noise dominated by a power-law distribution with exponent micro+1 approximately 4.6.
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.
NASA Astrophysics Data System (ADS)
Lillo, F.
2007-02-01
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons.
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.
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Channel geometry and hydraulic characteristics of a given river network, i.e., spatio-temporal variability of width, depth, and velocity, can be described as power functional relationships of flow discharge, named 'hydraulic geometry' (Leopold and Maddock, 1953). Many studies have focused on the implication of this power-law itself, i.e., self-similarity, and accordingly its exponents. Coefficients of the power functional relationships, on the contrary, have received little attention. They are often regarded as empirical constants, determined by 'best fitting' to the power-law without significant scientific implications. Here, we investigate and claim that power-law coefficients of hydraulic geometry relationships carry vital information of a given river system. We approach the given problem on the basis of 'basin hydraulic geometry' formulation (Stall and Fok, 1968) which decomposes power-law coefficients into more elementary constants. The linkage between classical power-law relationship (Leopold and Maddock, 1953) and the basin hydraulic geometry is provided by Paik and Kumar (2004). On the basis of this earlier study, it can be shown that coefficients and exponents of power-law hydraulic geometry are interrelated. In this sense, we argue that more elementary constants that constitute both exponents and coefficients carry important messages. In this presentation, we will demonstrate how these elementary constants vary over a wide range of catchments provided from Stall and Fok (1968) and Stall and Yang (1970). Findings of this study can provide new insights on fundamental understanding about hydraulic geometry relationships. Further, we expect that this understanding can help interpretation of hydraulic geometry relationship in the context of flood propagation through a river system as well. Keywords: Hydraulic geometry; Power-law; River network References Leopold, L. B., & Maddock, T. J. (1953). The hydraulic geometry of stream channels and some physiographic
Thermodynamic laws, economic methods and the productive power of energy
NASA Astrophysics Data System (ADS)
Kümmel, Reiner; Ayres, Robert U.; Lindenberger, Dietmar
2010-07-01
Energy plays only a minor role in orthodox theories of economic growth, because standard economic equilibrium conditions say that the output elasticity of a production factor, which measures the factor's productive power, is equal to the factor's share in total factor cost. Having commanded only a tiny cost share of about 5 percent so far, energy is often neglected altogether. On the other hand, energy conversion in the machines of the capital stock has been the basis of industrial growth. How can the physically obvious economic importance of energy be reconciled with the conditions for economic equilibrium, which result from the maximization of profit or overall welfare? We show that these equilibrium conditions no longer yield the equality of cost shares and output elasticities, if the optimization calculus takes technological constraints on the combinations of capital, labor, and energy into account. New econometric analyses of economic growth in Germany, Japan, and the USA yield output elasticities that are for energy much larger and for labor much smaller than their cost shares. Social consequences are discussed.
Power loss in open cavity diodes and a modified Child-Langmuir law
Biswas, Debabrata; Kumar, Raghwendra; Puri, R.R.
2005-09-15
Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.
NASA Astrophysics Data System (ADS)
Mehedi Faruk, Mir; Sazzad Hossain, Md.; Muktadir Rahman, Md.
2016-02-01
The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U=\\sumi=1dci\\vert xi/ai\\vertni are studied carefully. Detailed calculation of Kim et al. (J. Phys. Condens. Matter 11 (1999) 10269) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume CV are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.
Inverse free steering law for small satellite attitude control and power tracking with VSCMGs
NASA Astrophysics Data System (ADS)
Malik, M. S. I.; Asghar, Sajjad
2014-01-01
Recent developments in integrated power and attitude control systems (IPACSs) for small satellite, has opened a new dimension to more complex and demanding space missions. This paper presents a new inverse free steering approach for integrated power and attitude control systems using variable-speed single gimbal control moment gyroscope. The proposed inverse free steering law computes the VSCMG steering commands (gimbal rates and wheel accelerations) such that error signal (difference in command and output) in feedback loop is driven to zero. H∞ norm optimization approach is employed to synthesize the static matrix elements of steering law for a static state of VSCMG. Later these matrix elements are suitably made dynamic in order for the adaptation. In order to improve the performance of proposed steering law while passing through a singular state of CMG cluster (no torque output), the matrix element of steering law is suitably modified. Therefore, this steering law is capable of escaping internal singularities and using the full momentum capacity of CMG cluster. Finally, two numerical examples for a satellite in a low earth orbit are simulated to test the proposed steering law.
NASA Astrophysics Data System (ADS)
Afzal, Noor
2006-11-01
An alternate two layers theory, based on four new scalings for transitional wall roughness variables, is presented for large appropriate roughness Reynolds numbers. For velocity profile the matching of inner and outer layers in the overlap region, by Izakson-Millikan-Kolmogorov hypothesis (Afzal, N. 2005 Proc. Royal Society A: PME 461, 1889-1910) leads to functional solutions that are universal log laws, as well as universal power laws, that explicitly independent of transitional wall roughness, having same constants as in smooth wall case. The universal log or power laws velocity profile and skin friction, if expressed in terms of traditional Reynolds numbers also yield log law and power laws that depend on surface roughness. The skin friction, in traditional variables, is predicted by a single relation for inflectional type of Nikuradse roughness for sand grain type roughness data and Colebrook commercial monotonic roughness. The extensive experimental data for various types of wall transitional roughness provide very good support to present theory of universal log laws as well as new predictions in traditional log laws . The experimental data from various sources (Osaka and Mochizuki, Kameda et al, Antonia and Krogstad, Smalley et al, Schultz and Flack and Leonardi et al for boundary layers and Nikuradse, Shockling and Bakken for pipes/Channels) provide strong support to the new scaling for log and power laws. Moody type diagram for inflectional roughness for boundary layer and pipe flows are presented.
Power-law statistics and universal scaling in the absence of criticality.
Touboul, Jonathan; Destexhe, Alain
2017-01-01
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
AC losses in superconductors with a power-law constitutive relation
NASA Astrophysics Data System (ADS)
Agassi, Y. D.
2015-10-01
The observed constitutive relation between the electrical field and current density in cuprates high temperature superconductors is a power-law of the current. This functional dependence is presumably related to the giant flux-creep domain. It is shown that this constitutive relation reflects the statistical spread of the pinning potential associated with creep motion of vortex bundles. The AC losses emanating from a power-law constitutive relation are calculated in an approach focused on the superconductor's electric field. For a slab geometry in the presence of a parallel AC magnetic field or transport current, the calculated AC-loss scaling laws are consistent with BSCCO data and the critical state model. Extensions of the approach are briefly discussed.
Power-law statistics and universal scaling in the absence of criticality
NASA Astrophysics Data System (ADS)
Touboul, Jonathan; Destexhe, Alain
2017-01-01
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
Adjustment to Subtle Time Constraints and Power Law Learning in Rapid Serial Visual Presentation.
Shin, Jacqueline C; Chang, Seah; Cho, Yang Seok
2015-01-01
We investigated whether attention could be modulated through the implicit learning of temporal information in a rapid serial visual presentation (RSVP) task. Participants identified two target letters among numeral distractors. The stimulus-onset asynchrony immediately following the first target (SOA1) varied at three levels (70, 98, and 126 ms) randomly between trials or fixed within blocks of trials. Practice over 3 consecutive days resulted in a continuous improvement in the identification rate for both targets and attenuation of the attentional blink (AB), a decrement in target (T2) identification when presented 200-400 ms after another target (T1). Blocked SOA1s led to a faster rate of improvement in RSVP performance and more target order reversals relative to random SOA1s, suggesting that the implicit learning of SOA1 positively affected performance. The results also reveal "power law" learning curves for individual target identification as well as the reduction in the AB decrement. These learning curves reflect the spontaneous emergence of skill through subtle attentional modulations rather than general attentional distribution. Together, the results indicate that implicit temporal learning could improve high level and rapid cognitive processing and highlights the sensitivity and adaptability of the attentional system to subtle constraints in stimulus timing.
Frequency variations of solar radio zebras and their power-law spectra
NASA Astrophysics Data System (ADS)
Karlický, M.
2014-01-01
Context. During solar flares several types of radio bursts are observed. The fine striped structures of the type IV solar radio bursts are called zebras. Analyzing them provides important information about the plasma parameters of their radio sources. We present a new analysis of zebras. Aims: Power spectra of the frequency variations of zebras are computed to estimate the spectra of the plasma density variations in radio zebra sources. Methods: Frequency variations of zebra lines and the high-frequency boundary of the whole radio burst were determined with and without the frequency fitting. The computed time dependencies of these variations were analyzed with the Fourier method. Results: First, we computed the variation spectrum of the high-frequency boundary of the whole radio burst, which is composed of several zebra patterns. This power spectrum has a power-law form with a power-law index -1.65. Then, we selected three well-defined zebra-lines in three different zebra patterns and computed the spectra of their frequency variations. The power-law indices in these cases are found to be in the interval between -1.61 and -1.75. Finally, assuming that the zebra-line frequency is generated on the upper-hybrid frequency and that the plasma frequency ωpe is much higher than the electron-cyclotron frequency ωce, the Fourier power spectra are interpreted to be those of the electron plasma density in zebra radio sources.
THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.
Jiang, H; Liu, F; Meerschaert, M M; McGough, R J
2013-01-01
Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.
Branching random walk with step size coming from a power law
NASA Astrophysics Data System (ADS)
Bhattacharya, Ayan; Subhra Hazra, Rajat; Roy, Parthanil
2015-09-01
In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.
Does Stevens's Power Law for Brightness Extend to Perceptual Brightness Averaging?
ERIC Educational Resources Information Center
Bauer, Ben
2009-01-01
Stevens's power law ([Psi][infinity][Phi][beta]) captures the relationship between physical ([Phi]) and perceived ([Psi]) magnitude for many stimulus continua (e.g., luminance and brightness, weight and heaviness, area and size). The exponent ([beta]) indicates whether perceptual magnitude grows more slowly than physical magnitude ([beta] less…
Power-law cosmic expansion in f(R) gravity models
Goheer, Naureen; Larena, Julien; Dunsby, Peter K. S.
2009-09-15
We show that within the class of f(R) gravity theories, Friedmann-Lemaitre-Robertson-Walker power-law perfect fluid solutions only exist for R{sup n} gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard general relativity.
NASA Astrophysics Data System (ADS)
Carrano, Charles S.; Rino, Charles L.
2016-06-01
We extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two-component inverse power law spectrum. The two-component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two-dimensional field-aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self-similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large- and small-scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.
Graph Structure in Three National Academic Webs: Power Laws with Anomalies.
ERIC Educational Resources Information Center
Thelwall, Mike; Wilkinson, David
2003-01-01
Explains how the Web can be modeled as a mathematical graph and analyzes the graph structures of three national university publicly indexable Web sites from Australia, New Zealand, and the United Kingdom. Topics include commercial search engines and academic Web link research; method-analysis environment and data sets; and power laws. (LRW)
Realization of power law inflation & variants via variation of the strong coupling constant
AlHallak, M.; Chamoun, N.
2016-09-05
We present a model of power law inflation generated by variation of the strong coupling constant. We then extend the model to two varying coupling constants which leads to a potential consisting of a linear combination of exponential terms. Some variants of the latter may be self-consistent and can accommodate the experimental data of the Planck 2015 and other recent experiments.
Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method
NASA Astrophysics Data System (ADS)
Abbasi Souraki, B.; Tondro, H.; Ghavami, M.
2014-10-01
In this study, unsteady one-dimensional mass transfer during osmotic dehydration of apple was modeled using an approximate mathematical model. The mathematical model has been developed based on a power law profile approximation for moisture and solute concentrations in the spatial direction. The proposed model was validated by the experimental water loss and solute gain data, obtained from osmotic dehydration of infinite slab and cylindrical shape samples of apple in sucrose solutions (30, 40 and 50 % w/w), at different temperatures (30, 40 and 50 °C). The proposed model's predictions were also compared with the exact analytical and also a parabolic approximation model's predictions. The values of mean relative errors respect to the experimental data were estimated between 4.5 and 8.1 %, 6.5 and 10.2 %, and 15.0 and 19.1 %, for exact analytical, power law and parabolic approximation methods, respectively. Although the parabolic approximation leads to simpler relations, the power law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time. Considering both simplicity and precision of the mathematical models, the power law model for short dehydration times and the simplified exact analytical model for long dehydration times could be used for explanation of the variations of the average water loss and solute gain in the whole domain of dimensionless times.
Power law for the duration of recession and prosperity in Latin American countries
NASA Astrophysics Data System (ADS)
Redelico, Francisco O.; Proto, Araceli N.; Ausloos, Marcel
2008-11-01
Ormerod and Mounfield [P. Ormerod, C. Mounfield, Power law distribution of duration and magnitude of recessions in capitalist economies: Breakdown of scaling, Physica A 293 (2001) 573] and Ausloos et al. [M. Ausloos, J. Mikiewicz, M. Sanglier, The durations of recession and prosperity: Does their distribution follow a power or an exponential law? Physica A 339 (2004) 548] have independently analyzed the duration of recessions for developed countries through the evolution of the GDP in different time windows. It was found that there is a power law governing the duration distribution. We have analyzed data collected from 19 Latin American countries in order to observe whether such results are valid or not for developing countries. The case of prosperity years is also discussed. We observe that the power law of recession time intervals, see Ref. [1], is valid for Latin American countries as well. Thus an interesting point is discovered: the same scaling time is found in the case of recessions for the three data sets (ca. 1 year), and this could represent a universal feature. Other time scale parameters differ significantly from each other.
THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN
Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.
2013-01-01
Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian. PMID:26425384
Exponential and power-law contact distributions represent different atmospheric conditions.
Reynolds, A M
2011-12-01
It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions.
The effect of a power-law mantle viscosity on trench retreat rate
NASA Astrophysics Data System (ADS)
Holt, Adam F.; Becker, Thorsten W.
2017-01-01
The subduction of lithospheric plates is partitioned between subducting plate motion and lateral slab migration (i.e. trench retreat and advance). We use 3-D, dynamic models of subduction to address the role of a power-law mantle viscosity on subduction dynamics and, in particular, rates of trench retreat. For all numerical models tested, we find that a power-law rheology results in reduced rates of trench retreat, and elevated slab dip angles, relative to the equivalent isoviscous mantle model. We analyse the asthenospheric pressure distribution and the style of mantle flow, which exhibits only limited variability as a function of mantle rheology, in order to compute estimates of the mantle forces associated with subduction. The inclusion of a power-law rheology reduces the mantle shear force (which resists subducting plate motion) to a greater degree than it reduces the dynamic pressure gradient across the slab (which resists trench retreat). Therefore, the inclusion of a power-law mantle rheology favours a shift towards a subduction mode with a reduced trench retreat component, typically a relative reduction of order 25 per cent in our 3-D models. We suggest that this mechanism may be of importance for reducing the high trench retreat rates observed in many previous models to levels more in line with the average subduction partitioning observed on Earth at present (i.e. trench velocity ≤ plate velocity), for most absolute plate motion reference frames.
Apparent power-law behavior of conductance in disordered quasi-one-dimensional systems.
Rodin, A S; Fogler, M M
2010-09-03
The dependence of hopping conductance on temperature and voltage for an ensemble of modestly long one-dimensional wires is studied numerically using the shortest-path algorithm. In a wide range of parameters this dependence can be approximated by a power law rather than the usual stretched-exponential form. The relation to recent experiments and prior analytical theory is discussed.
DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM
Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K.
2016-04-10
A double power law or a power law with exponential rollover at a few to tens of MeV nucleon{sup −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{sup −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.
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
Bose-Einstein condensation with a finite number of particles in a power-law trap
NASA Astrophysics Data System (ADS)
Jaouadi, A.; Telmini, M.; Charron, E.
2011-02-01
Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number N of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation temperature Tc in terms of a power series in x0=ɛ0/kBTc, where ɛ0 denotes the zero-point energy of the trapping potential. This expression, which applies in Cartesian, cylindrical, and spherical power-law traps, is given analytically at infinite order. It is also given numerically for specific potential shapes as an expansion in powers of x0 up to the second order. We show that, for a harmonic trap, the well-known first-order shift of the critical temperature ΔTc/Tc∝N-1/3 is inaccurate when N⩽105, the next order (proportional to N-1/2) being significant. We also show that finite-size effects on the condensation temperature cancel out in a cubic trapping potential, e.g., V(r)∝r3. Finally, we show that in a generic power-law potential of higher order, e.g., V(r)∝rα with α>3, the shift of the critical temperature becomes positive. This effect provides a large increase of Tc for relatively small atom numbers. For instance, an increase of about +40% is expected with 104 atoms in a V(r)∝r12 trapping potential.
Phase diagram of softly repulsive systems: the Gaussian and inverse-power-law potentials.
Prestipino, Santi; Saija, Franz; Giaquinta, Paolo V
2005-10-08
We redraw, using state-of-the-art methods for free-energy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inverse-power-law repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the body-centered-cubic (bcc) and face-centered-cubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussian-core model, just above the triple point. We also trace the bcc-fcc coexistence line of the inverse-power-law model as a function of the power exponent n and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.
Taylor's power law and fluctuation scaling explained by a central-limit-like convergence
NASA Astrophysics Data System (ADS)
Kendal, Wayne S.; Jørgensen, Bent
2011-06-01
A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock
NASA Astrophysics Data System (ADS)
Fareo, A. G.; Mason, D. P.
2016-06-01
Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.
Fertility heterogeneity as a mechanism for power law distributions of recurrence times
NASA Astrophysics Data System (ADS)
Saichev, A.; Sornette, D.
2013-02-01
We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future events. Specifically, we analyze the impact of the power law distribution of fertilities with exponent α, where the fertility of an event is the number of triggered events of first generation, on the probability distribution function (PDF) f(τ) of the recurrence times τ between successive events. The other input of the model is an exponential law quantifying the PDF of waiting times between an event and its first generation triggered events, whose characteristic time scale is taken as our time unit. At short-time scales, we discover two intermediate power law asymptotics, f(τ)˜τ-(2-α) for τ≪τc and f(τ)˜τ-α for τc≪τ≪1, where τc is associated with the self-excited cascades of triggered events. For 1≪τ≪1/ν, we find a constant plateau f(τ)≃const, while at long times, 1/ν≲τ, f(τ)≃e-ντ has an exponential tail controlled by the arrival rate ν of exogenous events. These results demonstrate a novel mechanism for the generation of power laws in the distribution of recurrence times, which results from a power law distribution of fertilities in the presence of self-excitation and cascades of triggering.
Simple power law for transport ratio with bimodal distributions of coarse sediments under waves
NASA Astrophysics Data System (ADS)
Calantoni, Joseph; Thaxton, Christopher S.
2008-03-01
Morphodynamic models of coastal evolution require relatively simple parameterizations of sediment transport for application over larger scales. Here we present a transport parameterization for bimodal distributions of coarse quartz grains using simulations from a discrete particle model for sheet flow and near sheet flow conditions. The discrete particle model simulates the simplest one-dimensional fluid using a turbulent eddy viscosity determined from a mixing length coupled to particle motions. The motions of individual sand grains are simulated using spherical elements. Newton's second law in translational and rotational forms is solved for every particle in the domain as determined by both grain-grain and grain-fluid interactions. The forcing from idealized monochromatic waves is accomplished by specifying a spatially constant, time varying horizontal pressure gradient acting on the simulation domain. Consequently, the time series of the free-stream fluid acceleration and velocity are also fixed. Simulations cover a range of wave forcing, diameter ratios for the large and small grains in the bimodal size distribution, and mass ratios of large to small grains in the simulation domain, for a total of 243 unique simulation conditions. The simulation results are successfully parameterized with a simple power law that allows for the prediction of the transport rates of each size fraction in the bimodal distribution. The simple power law determined from simulations provides favorable predictions of transport rates for each size fraction when applied to available laboratory data for sheet flow with bimodal size distributions. It is important to note that rapid vertical kinematic sorting of grains by size is explicitly simulated with the model and thus implicitly captured by the power law. Discussion focuses on practical application of the power law.
NASA Astrophysics Data System (ADS)
Brook, Martin; Hebblewhite, Bruce; Mitra, Rudrajit
2016-04-01
The size-scaling of rock fractures is a well-studied problem in geology, especially for permeability quantification. The intensity of fractures may control the economic exploitation of fractured reservoirs because fracture intensity describes the abundance of fractures potentially available for fluid flow. Moreover, in geotechnical engineering, fractures are important for parameterisation of stress models and excavation design. As fracture data is often collected from widely-spaced boreholes where core recovery is often incomplete, accurate interpretation and representation of fracture aperture-frequency relationships from sparse datasets is important. Fracture intensity is the number of fractures encountered per unit length along a sample scanline oriented perpendicular to the fractures in a set. Cumulative frequency of fractures (F) is commonly related to fracture aperture (A) in the form of a power-law (F = aA-b), with variations in the size of the a coefficient between sites interpreted to equate to fracture frequency for a given aperture (A). However, a common flaw in this approach is that even a small change in b can have a large effect on the response of the fracture frequency (F) parameter. We compare fracture data from the Late Permian Rangal Coal Measures from Australia's Bowen Basin, with fracture data from Jurassic carbonates from the Sierra Madre Oriental, northeastern Mexico. Both power-law coefficient a and exponent b control the fracture aperture-frequency relationship in conjunction with each other; that is, power-laws with relatively low a coefficients have relatively high b exponents and vice versa. Hence, any comparison of different power-laws must take both a and b into consideration. The corollary is that different sedimentary beds in the Sierra Madre carbonates do not show ˜8× the fracture frequency for a given fracture aperture, as based solely on the comparison of coefficient a. Rather, power-law "sensitivity factors" developed from both
High-index asymptotics of spherical Bessel products averaged with modulated Gaussian power laws
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
2014-12-01
Bessel integrals of type are investigated, where the kernel g( k) is a modulated Gaussian power-law distribution , and the jl ( m) are multiple derivatives of spherical Bessel functions. These integrals define the multipole moments of Gaussian random fields on the unit sphere, arising in multipole fits of temperature and polarization power spectra of the cosmic microwave background. Two methods allowing efficient numerical calculation of these integrals are presented, covering Bessel indices l in the currently accessible multipole range 0 ≤ l ≤ 104 and beyond. The first method is based on a representation of spherical Bessel functions by Lommel polynomials. Gaussian power-law averages can then be calculated in closed form as finite Hankel series of parabolic cylinder functions, which allow high-precision evaluation. The second method is asymptotic, covering the high- l regime, and is applicable to general distribution functions g( k) in the integrand; it is based on the uniform Nicholson approximation of the Bessel derivatives in conjunction with an integral representation of squared Airy functions. A numerical comparison of these two methods is performed, employing Gaussian power laws and Kummer distributions to average the Bessel products.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Pacific Northwest Electric Power Planning and Conservation Act, with Index (Public Law 96-501).
Not Available
1991-12-01
The Pacific Northwest Electric Power Planning and Conservation Act was enacted by the Senate and House of Representatives of the United States of America. It was enacted to assist the electrical consumers of the Pacific Northwest through use of the Federal columbia River Power System to achieve cost-effective energy conservation, to encourage the development of renewable energy resources, to establish a representative regional power planning process, to assure the region of an efficient and adequate power supply, and for other purposes. Contents of the Act are: short title and table of contents; purposes; definitions; regional planning and participation; sale of power; conservation and resource acquisition; rates; amendments to existing law; administrative provisions; savings provisions; effective date; and severability.
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
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 Entanglement Spectrum in Many-Body Localized Phases
NASA Astrophysics Data System (ADS)
Serbyn, Maksym; Michailidis, Alexios A.; Abanin, Dmitry A.; Papić, Z.
2016-10-01
The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
Power-Law Entanglement Spectrum in Many-Body Localized Phases.
Serbyn, Maksym; Michailidis, Alexios A; Abanin, Dmitry A; Papić, Z
2016-10-14
The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
Linking multiple relaxation, power-law attenuation, and fractional wave equations.
Näsholm, Sven Peter; Holm, Sverre
2011-11-01
The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.
Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
Holm, Sverre; Näsholm, Sven Peter
2014-04-01
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
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.
Segmentation of genomic DNA through entropic divergence: Power laws and scaling
NASA Astrophysics Data System (ADS)
Azad, Rajeev K.; Bernaola-Galván, Pedro; Ramaswamy, Ramakrishna; Rao, J. Subba
2002-05-01
Genomic DNA is fragmented into segments using the Jensen-Shannon divergence. Use of this criterion results in the fragments being entropically homogeneous to within a predefined level of statistical significance. Application of this procedure is made to complete genomes of organisms from archaebacteria, eubacteria, and eukaryotes. The distribution of fragment lengths in bacterial and primitive eukaryotic DNAs shows two distinct regimes of power-law scaling. The characteristic length separating these two regimes appears to be an intrinsic property of the sequence rather than a finite-size artifact, and is independent of the significance level used in segmenting a given genome. Fragment length distributions obtained in the segmentation of the genomes of more highly evolved eukaryotes do not have such distinct regimes of power-law behavior.
NASA Technical Reports Server (NTRS)
Raj, S. V.; Pharr, G. M.
1989-01-01
Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.
Deviations from uniform power-law scaling due to exposure to high altitude
NASA Astrophysics Data System (ADS)
Posiewnik, A.
2002-12-01
A major challenge in biological physics is the analysis of time series that are typically highly nonstationary. Viswanathan et al. (Phys. Rev. E 55 (1) (1997) 845-899) using techniques based on the Fano factor and the Allan factor functions, as well as on detrended fluctuation analysis showed that the scaling properties of the dynamics of healthy physiological systems in normal conditions are more stable than those of pathological systems-there is underlying loss of uniform power-law scaling in disease. Here we test, using the same techniques as Viswanathan et al. (1997), the hypothesis that deviations from uniform power-law scaling, similar to those seen in heart failure and deep apnea syndrome occur also for healthy subjects under pathological conditions (hypoxaemic stress during exposure to high altitude, over 6000 m).
Sliding friction in the hydrodynamic lubrication regime for a power-law fluid
NASA Astrophysics Data System (ADS)
Warren, P. B.
2017-02-01
A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning regime is mechanically unstable if the power-law index n < 1/2, where n is the exponent that relates the shear stress to the shear rate. Consequently the Stribeck (friction) curve should be discontinuous, with possible hysteresis. Further analysis suggests that normal stress and flow transience (stress overshoot) do not destroy this basic picture, although they may provide stabilising mechanisms at higher shear rates. Extensional viscosity is also expected to be insignificant unless the Trouton ratio is large. A possible application to shear thickening in non-Brownian particulate suspensions is indicated.
Finite sample properties of power-law cross-correlations estimators
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2015-02-01
We study finite sample properties of estimators of power-law cross-correlations-detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA)-with a special focus on short-term memory bias as well as power-law coherency. We present a broad Monte Carlo simulation study that focuses on different time series lengths, specific methods' parameter setting, and memory strength. We find that each method is best suited for different time series dynamics so that there is no clear winner between the three. The method selection should be then made based on observed dynamic properties of the analyzed series.
Speed-invariant encoding of looming object distance requires power law spike rate adaptation.
Clarke, Stephen E; Naud, Richard; Longtin, André; Maler, Leonard
2013-08-13
Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.
Market reaction to a bid-ask spread change: A power-law relaxation dynamics
NASA Astrophysics Data System (ADS)
Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N.
2009-07-01
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.
Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions
NASA Astrophysics Data System (ADS)
Kuo, Huan-Yu; Wu, Kuo-An
2015-12-01
We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α ≤1 is identical to that of the all-to-all coupling case. For α >1 , oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations.
Treeby, Bradley E; Cox, B T
2010-05-01
The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.
Market reaction to a bid-ask spread change: a power-law relaxation dynamics.
Ponzi, Adam; Lillo, Fabrizio; Mantegna, Rosario N
2009-07-01
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.
The origin of tablet boudinage: Results from experiments using power-law rock analogs
NASA Astrophysics Data System (ADS)
Zulauf, J.; Zulauf, G.; Kraus, R.; Gutiérrez-Alonso, G.; Zanella, F.
2011-10-01
We used power-law viscous plasticine ( n = ca. 7) as a rock analog to simulate boudinage of rocks undergoing dislocation creep and brittle fracture. A competent plasticine layer, oriented perpendicular to the main shortening direction, Z, underwent bulk pure flattening inside a less competent plasticine matrix. Computer tomographic analyses of the deformed samples revealed that boudinage results from an initial phase of viscous necking followed by tensile failure along the previously formed necks. The resulting boudins display a polygonal shape in plan-view and are referred to as 'tablet boudins' (in contrast to the square to rectangular shaped chocolate-tablet boudins). The ratio between the plan-view long and short axis, R, ranges from 1.2 to 2.6. The polygonal, non-isometric shape of the tablet boudins can be explained by the strong interaction of concentric and radial tensile fractures. With increasing layer thickness, Hi, the mean diameter of the boudin tablets, Wa, increases, while the number of boudins, N, decreases. Progressive finite strain results in a higher number of the boudins and a smaller mean diameter. The thickness of the boudins, Hf, is almost the same as the initial layer thickness, Hi, while the aspect ratio ( Wd = Wa / Hf) decreases with layer thickness and finite strain. The mean Wd values obtained from all experiments span from ca. 4 to ca. 11. Tablet boudins, described in the present paper, have yet not been described from natural outcrops. The reasons might be that pure flattening strain is not common in nature, and the characterization and evaluation of tablet boudins requires geometrical analysis in three dimensions, which is a difficult task when such structures occur in nature.
Caduff, Marloes; Huijbregts, Mark A J; Althaus, Hans-Joerg; Hendriks, A Jan
2011-01-15
To perform life-cycle assessment studies, data on the production and use of the products is required. However, often only few data or measurements are available. Estimation of properties can be performed by applying scaling relationships. In many disciplines, they are used to either predict data or to search for underlying patterns, but they have not been considered in the context of product assessments hitherto. The goal of this study was to explore size scaling for commonly used energy conversion equipment, that is, boilers, engines, and generators. The variables mass M, fuel consumption Q, and costs C were related to power P. The established power-law relationships were M = 10(0.73.. 1.89)P(0.64.. 1.23) (R(2) ≥ 0.94), Q = 10(0.06.. 0.68)P(0.82.. 1.02) (R(2) ≥ 0.98) and C = 10(2.46.. 2.86)P(0.83.. 0.85) (R(2) ≥ 0.83). Mass versus power and costs versus power showed that none of the equipment types scaled isometrically, that is, with a slope of 1. Fuel consumption versus power scaled approximately isometrically for steam boilers, the other equipments scaled significantly lower than 1. This nonlinear scaling behavior induces a significant size effect. The power laws we established can be applied to scale the mass, fuel consumption and costs of energy conversion equipments up or down. Our findings suggest that empirical scaling laws can be used to estimate properties, particularly relevant in studies focusing on early product development for which generally only little information is available.
Soloway, Alexander G; Dahl, Peter H; Odom, Robert I
2015-10-01
Experimental measurements of Scholte waves from underwater explosions collected off the coast of Virginia Beach, VA in shallow water are presented. It is shown here that the dispersion of these explosion-generated Scholte waves traveling in the sandy seabed can be modeled using a power-law dependent shear wave speed profile and an empirical source model that determines the pressure time-series at 1 m from the source as a function of TNT-equivalent charge weight.
Epitrochoid Power-Law Nozzle Rapid Prototype Build/Test Project (Briefing Charts)
2015-02-01
Production Approved for public release; distribution is unlimited. PA clearance # 15122. 4 Epitrochoid Power-Law Nozzle Build/Test Build on SpaceX ...Multiengine Approach SpaceX ) Approved for public release; distribution is unlimited. PA clearance # 15122. Engines: Merlin 1D on Falcon 9 v1.1 (Photo 5...to utilize features of high performance engines advances and the economies of scale of the multi-engine approach of SpaceX Falcon 9 – Rapid Prototype
A power-law distribution for tenure lengths of sports managers
NASA Astrophysics Data System (ADS)
Aidt, Toke S.; Leong, Bernard; Saslaw, William C.; Sgroi, Daniel
2006-10-01
We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.
Improved power-law estimates from multiple samples provided by millennium climate simulations
NASA Astrophysics Data System (ADS)
Henriksson, S. V.; Räisänen, P.; Silen, J.; Järvinen, H.; Laaksonen, A.
2015-02-01
Using the long annual mean temperature time series provided by millennium Earth System Model simulations and a method of discrete Fourier transform with varying starting point and length of time window together with averaging, we get good fits to power laws between two characteristic oscillatory timescales of the model climate: multidecadal (50-80 years) and El Nino (3-6 years) timescales. For global mean temperature, we fit β ˜ 0.35 in a relation S( f) ˜ f - β in a simulation without external climate forcing and β over 0.7 in a simulation with external forcing included. The power law is found both with and without external forcing despite the forcings, e.g. the volcanic forcing, not showing similar behaviour, indicating a nonlinear temperature response to time-varying forcing. We also fit a power law with β ˜ 8 to the narrow frequency range between El Nino frequencies (up to 1/(3.2 years)) and the Nyquist frequency (1/(2 years)). Also, monthly mean temperature time series are considered and a decent power-law fit for frequencies above 1/year is obtained. Regional variability in best-fit β is explored, and the impact of choosing the frequency range on the result is illustrated. When all resolved frequencies are used, land areas seem to have lower βs than ocean areas on average, but when fits are restricted to frequencies below 1/(6 years), this difference disappears, while regional differences still remain. Results compare well with measurements both for global mean temperature and for the central England temperature record.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows
NASA Astrophysics Data System (ADS)
Anbarlooei, H. R.; Cruz, D. O. A.; Ramos, F.; Silva Freire, A. P.
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
Huo, Yunlong; Choy, Jenny Susana; Wischgoll, Thomas; Luo, Tong; Teague, Shawn D.; Bhatt, Deepak L.; Kassab, Ghassan S.
2013-01-01
Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length–volume scaling power law ( where Lc and Vc are crown length and volume) were found for both the high-fat and control groups (R2 = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, KLV, decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow–length scaling power law, however, was nearly unaffected by the positive remodelling. The length–volume and flow–length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. KLV < 18 in the length–volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans. PMID:23365197
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W., Jr.
2003-01-01
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
Laboratory Constraints on Chameleon Dark Energy and Power-Law Fields
Steffen, J. H.; Baumbaugh, A.; Chou, A. S.; Mazur, P. O.; Tomlin, R.; Wester, W.; Upadhye, A.; Weltman, A.
2010-12-31
We report results from a search for chameleon particles created via photon-chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of unexplored chameleon power-law and dark energy models. These results exclude 5 orders of magnitude in the coupling of chameleons to photons covering a range of 4 orders of magnitude in chameleon effective mass and, for individual models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Werner, G. R.; Uzdensky, D. A.; Cerutti, B.; ...
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 lawmore » $${\\gamma }^{-\\alpha }$$, 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.« less
Comment on "Time needed to board an airplane: a power law and the structure behind it".
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the "back-to-front" strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-03-16
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.
Mobility of power-law and Carreau fluids through fibrous media.
Shahsavari, Setareh; McKinley, Gareth H
2015-12-01
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
NASA Astrophysics Data System (ADS)
Furey, Peter R.; Gupta, Vijay K.
2007-11-01
Observations from the Goodwin Creek experimental watershed (GCEW), Mississippi show that peak-discharge Q( A) and drainage area A are related, on average, by a power law or scaling relationship, Q( A) = αAθ, during single rainfall-runoff events. Observations also show that α and θ change between events, and, based on a recent analysis of 148 events, observations indicate that α and θ change because of corresponding changes in the depth, duration, and spatial variability of excess-rainfall. To improve our physical understanding of these observations, a 5-step framework for diagnosing observed power laws, or other space-time patterns in a basin, is articulated and applied to GCEW using a combination of analysis and numerical simulations. Diagnostic results indicate how the power laws are connected to physical conditions and processes. Derived expressions for α and θ show that if excess-rainfall depth is fixed then there is a decreasing concave relationship between α and excess-rainfall duration, and an increasing and slightly convex relationship between θ and excess rainfall duration. These trends are consistent with observations only when hillslope velocity vh is given a physically realistic value near 0.1 m/s. If vh ≫ 0.1 m/s, then the predicted trends deviate from observed trends. Results also suggest that trends in α and θ can be impacted by the dependence of vh and link velocity vl on excess-rainfall rate.
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.
Power-law scaling in daily rainfall patterns and consequences in urban stream discharges
NASA Astrophysics Data System (ADS)
Park, Jeryang; Krueger, Elisabeth H.; Kim, Dongkyun; Rao, Suresh C.
2016-04-01
Poissonian rainfall has been frequently used for modelling stream discharge in a catchment at the daily scale. Generally, it is assumed that the daily rainfall depth is described by memoryless exponential distribution which is transformed to stream discharge, resulting in an analytical pdf for discharge [Gamma distribution]. While it is true that catchment hydrological filtering processes (censored by constant rate ET losses, and first-order recession) increases "memory", reflected in 1/f noise in discharge time series. Here, we show that for urban watersheds in South Korea: (1) the observation of daily rainfall depths follow power-law pdfs, and spectral slopes range between 0.2 ~ 0.4; and (2) the stream discharge pdfs have power-law tails. These observation results suggest that multiple hydro-climatic factors (e.g., non-stationarity of rainfall patterns) and hydrologic filtering (increasing impervious area; more complex urban drainage networks) influence the catchment hydrologic responses. We test the role of such factors using a parsimonious model, using different types of daily rainfall patterns (e.g., power-law distributed rainfall depth with Poisson distribution in its frequency) and urban settings to reproduce patterns similar to those observed in empirical records. Our results indicate that fractality in temporally up-scaled rainfall, and the consequences of large extreme events are preserved as high discharge events in urbanizing catchments. Implications of these results to modeling urban hydrologic responses and impacts on receiving waters are discussed.
Kiflawi, Moshe; Mann, Ofri; Meekan, Mark G
2016-10-21
Taylor's Power Law for the temporal fluctuation in population size (TL) posits that the variance in abundance scales according to aM(b); where M is the mean abundance and a and b are the 'proportionality' and 'scaling' coefficients. As one of the few empirical rules in population ecology, TL has attracted substantial theoretical and empirical attention. Much of this attention focused on the scaling coefficient; particularly its ubiquitous deviation from the null value of 2. Here we present a line of reasoning that challenges the power-law interpretation of the empirical log-linear relationship between the mean and variance of population size. At the core of our reasoning is the proposition that populations vary not only with respect to M but also with respect to a; which leaves the log-linear relationship intact but forfeits its power-law interpretation. Using the stochastic logistic-growth model as an example, we show that ignoring among-population variation in a is akin to ignoring the variation in the intrinsic rate of growth (r). Accordingly, we show that the slope of the log-linear relationship (b) is a function of the among-population (co)variation in r and the carrying-capacity. We further demonstrate that local environmental stochasticity is sufficient to generate the full range of observed values of b, and that b can in fact be insensitive to substantial differences in the balance between variance-generating and stabilizing processes.
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-01-01
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns. PMID:25779306
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.
Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L
2011-10-01
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.
A stability analysis of the power-law steady state of marine size spectra.
Datta, Samik; Delius, Gustav W; Law, Richard; Plank, Michael J
2011-10-01
This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.
NASA Astrophysics Data System (ADS)
Huang, M.; Wada, R.; Chen, Z.; Keutgen, T.; Kowalski, S.; Hagel, K.; Barbui, M.; Bonasera, A.; Bottosso, C.; Materna, T.; Natowitz, J. B.; Qin, L.; Rodrigues, M. R. D.; Sahu, P. K.; Schmidt, K. J.; Wang, J.
2010-11-01
Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, asym/T, extracted in previous work and that of the pairing term, ap/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I=N-Z value, the corrected yields of isotopes relative to the yield of C12 show a power law distribution Y(N,Z)/Y(12C)~A-τ in the mass range 1⩽A⩽30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted τ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be τprim=2.4±0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.
Comment on ``Time needed to board an airplane: A power law and the structure behind it''
NASA Astrophysics Data System (ADS)
Bernstein, Noam
2012-08-01
Frette and Hemmer [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.011130 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the “back-to-front” strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.
Tippett, Michael K.; Cohen, Joel E.
2016-01-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from ‘outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954–2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210
NASA Astrophysics Data System (ADS)
Zhao, Kai; Musolesi, Mirco; Hui, Pan; Rao, Weixiong; Tarkoma, Sasu
2015-03-01
Human mobility has been empirically observed to exhibit Lévy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we propose to explain the Lévy walk behaviour observed in human mobility patterns by decomposing them into different classes according to the different transportation modes, such as Walk/Run, Bike, Train/Subway or Car/Taxi/Bus. Our analysis is based on two real-life GPS datasets containing approximately 10 and 20 million GPS samples with transportation mode information. We show that human mobility can be modelled as a mixture of different transportation modes, and that these single movement patterns can be approximated by a lognormal distribution rather than a power-law distribution. Then, we demonstrate that the mixture of the decomposed lognormal flight distributions associated with each modality is a power-law distribution, providing an explanation to the emergence of Lévy Walk patterns that characterize human mobility patterns.
Power graph compression reveals dominant relationships in genetic transcription networks.
Ahnert, Sebastian E
2013-11-01
We introduce a framework for the discovery of dominant relationship patterns in transcription networks, by compressing the network into a power graph with overlapping power nodes. Our application of this approach to the transcription networks of S. cerevisiae and E. coli, paired with GO term enrichment analysis, provides a highly informative overview of the most prominent relationships in the gene regulatory networks of these two organisms.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Salari, Erfan
2016-09-01
In the present study, thermo-electro-mechanical vibration characteristics of both sigmoid and power-law functionally graded piezoelectric (FGP) nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier-type solution for the first time. Three kinds of thermal loading, namely uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness according to power-law and sigmoid distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as various temperature distributions, external electric voltage, different material compositions, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams. The results should be relevant to the design and application of the piezoelectric nanodevices.
Fujiyama, Toshifumi; Matsui, Chihiro; Takemura, Akimichi
2016-01-01
We propose a power-law growth and decay model for posting data to social networking services before and after social events. We model the time series structure of deviations from the power-law growth and decay with a conditional Poisson autoregressive (AR) model. Online postings related to social events are described by five parameters in the power-law growth and decay model, each of which characterizes different aspects of interest in the event. We assess the validity of parameter estimates in terms of confidence intervals, and compare various submodels based on likelihoods and information criteria. PMID:27505155
On the interplay between short and long term memory in the power-law cross-correlations setting
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav
2015-03-01
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equal to an average of separate Hurst exponents of the analyzed processes. Strength of short term memory has no effect on these asymptotic properties. Implications of these findings for the power-law cross-correlations concept are further discussed.
Accurate and unbiased estimation of power-law exponents from single-emitter blinking data.
Hoogenboom, Jacob P; den Otter, Wouter K; Offerhaus, Herman L
2006-11-28
Single emitter blinking with a power-law distribution for the on and off times has been observed on a variety of systems including semiconductor nanocrystals, conjugated polymers, fluorescent proteins, and organic fluorophores. The origin of this behavior is still under debate. Reliable estimation of power exponents from experimental data is crucial in validating the various models under consideration. We derive a maximum likelihood estimator for power-law distributed data and analyze its accuracy as a function of data set size and power exponent both analytically and numerically. Results are compared to least-squares fitting of the double logarithmically transformed probability density. We demonstrate that least-squares fitting introduces a severe bias in the estimation result and that the maximum likelihood procedure is superior in retrieving the correct exponent and reducing the statistical error. For a data set as small as 50 data points, the error margins of the maximum likelihood estimator are already below 7%, giving the possibility to quantify blinking behavior when data set size is limited, e.g., due to photobleaching.
Emergence of power-law in a market with mixed models
NASA Astrophysics Data System (ADS)
Ali Saif, M.; Gade, Prashant M.
2007-10-01
We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.
Phase scintillations due to equatorial F region irregularities with two-component power law spectrum
NASA Astrophysics Data System (ADS)
Bhattacharyya, A.; Rastogi, R. G.
1986-10-01
Power spectra of weak phase scintillations on a 140-MHz signal, transmitted from the geostationary satellite ATS 6 and observed during premidnight and postmidnight periods at an equatorial station Ootacamund (magnetic dip 6 N), show that the nighttime equatorial F region irregularities in the wavelength range of about hundred meters to a few kilometers exhibit a two-component power law spectrum. The long- and short-wavelength spectral indices and the break scale at which the transition from a shallow to a steep slope occurs are determined self-consistently using both the phase and amplitude scintillation data. As the power spectra of phase scintillations do not exhibit the effect of Fresnel filtering, they provide fairly accurate estimates of the spectral indices and the break scale. These estimated parameters are utilized in a model calculation of the dependence of the S4 index on signal frequency based on weak scattering theory.
Pettersen, Klas H; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T
2014-11-01
Power laws, that is, power spectral densities (PSDs) exhibiting 1/f(α) behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency 1/f(α) power laws with power-law exponents analytically identified as α∞(I) = 1/2 for the soma membrane current, α∞(p) = 3/2 for the current-dipole moment, and α∞(V) = 2 for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink (1/f) noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how 1/f(α) power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.
Pettersen, Klas H.; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T.
2014-01-01
Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation. PMID:25393030
NASA Technical Reports Server (NTRS)
Murphy, Patrick C.; Davidson, John B.
1998-01-01
A multi-input, multi-output control law design methodology, named "CRAFT", is presented. CRAFT stands for the design objectives addressed, namely, Control power, Robustness, Agility, and Flying Qualities Tradeoffs. The methodology makes use of control law design metrics from each of the four design objective areas. It combines eigenspace assignment, which allows for direct specification of eigenvalues and eigenvectors, with a graphical approach for representing the metrics that captures numerous design goals in one composite illustration. Sensitivity of the metrics to eigenspace choice is clearly displayed, enabling the designer to assess the cost of design tradeoffs. This approach enhances the designer's ability to make informed design tradeoffs and to reach effective final designs. An example of the CRAFT methodology applied to an advanced experimental fighter and discussion of associated design issues are provided.
Code of Federal Regulations, 2013 CFR
2013-07-01
... consolidated or severed prior to issuance of administrative law judge decisions; (9) To approve stipulations, including stipulations of facts that waive a hearing and provide for a decision by the administrative law judge. Alternatively, the parties may agree to waive a hearing and decision by an administrative...
Code of Federal Regulations, 2014 CFR
2014-07-01
... consolidated or severed prior to issuance of administrative law judge decisions; (9) To approve stipulations, including stipulations of facts that waive a hearing and provide for a decision by the administrative law judge. Alternatively, the parties may agree to waive a hearing and decision by an administrative...
Code of Federal Regulations, 2010 CFR
2010-07-01
... consolidated or severed prior to issuance of administrative law judge decisions; (9) To approve stipulations, including stipulations of facts that waive a hearing and provide for a decision by the administrative law judge. Alternatively, the parties may agree to waive a hearing and decision by an administrative...
Code of Federal Regulations, 2011 CFR
2011-07-01
... consolidated or severed prior to issuance of administrative law judge decisions; (9) To approve stipulations, including stipulations of facts that waive a hearing and provide for a decision by the administrative law judge. Alternatively, the parties may agree to waive a hearing and decision by an administrative...
Code of Federal Regulations, 2012 CFR
2012-07-01
... consolidated or severed prior to issuance of administrative law judge decisions; (9) To approve stipulations, including stipulations of facts that waive a hearing and provide for a decision by the administrative law judge. Alternatively, the parties may agree to waive a hearing and decision by an administrative...
NASA Astrophysics Data System (ADS)
Liu, Hsing; Chen, Ying-Hsing; Lih, Jiann-Shing
2015-05-01
Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution.
Froese, M. W.; Blaum, K.; Fellenberger, F.; Grieser, M.; Lange, M.; Laux, F.; Menk, S.; Orlov, D. A.; Repnow, R.; Sieber, T.; Hahn, R. von; Wolf, A.; Toker, Y.
2011-02-15
The decay of excited aluminum-cluster anions (Al{sub n}{sup -}, n=4 and 5) has been investigated in a cryogenic linear ion-beam trap. A power-law is found to accurately reproduce the time dependence of the observed decay rates at early storage times, although the exponents are significantly larger than the typically observed 1/t decay. It is shown that the power-law exponent is, at most, weakly dependent on the cluster electron affinity and heat capacity. A previous power-law exponent model for small clusters is also shown to be in disagreement with both investigated species. The attribution of a drop in the decay rate at later times to radiative cooling as observed in larger molecules also does not appear justified in our case. A strong dependence of the power-law exponent on the ambient temperature was observed.
Ceronio, A D; Haarhoff, J
2005-01-01
In potable water treatment, the use of the power law to describe particle size distributions (PSDs) in particle counting practice is common. The power law is popular because it allows the reduction of numerous data bits to two meaningful parameters that completely describe the size distribution characteristics of a particle suspension. The model is however flawed. This paper presents the further development of an improved model (the variable-beta model) first proposed by Lawler (1997). Both the power law model and variable-beta model are used to describe the PSDs of a large number of potable water treatment samples taken from full-scale plants and the resulting correlations are compared. The findings from the comparison of data reduction methodologies support the argument that the variable-beta model is fundamentally more correct than the power law model and consequently describes the PSDs better.
NASA Astrophysics Data System (ADS)
Jiao, Chengru; Zheng, Liancun; Ma, Lianxi
2015-08-01
This paper studies the magnetohydrodynamic (MHD) thermosolutal Marangoni convection heat and mass transfer of power-law fluids driven by a power law temperature and a power law concentration which is assumed that the surface tension varies linearly with both the temperature and concentration. Heat and mass transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection-diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient and the mass diffusion depends non-linearly on both the concentration and the concentration gradient with modified Fourier heat conduction for power law fluid. The governing equations are reduced to nonlinear ordinary differential equations by using suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM). The transport characteristics of velocity, temperature and concentration fields are analyzed in detail.
Effect of phase morphology on bulk strength for power-law materials
NASA Astrophysics Data System (ADS)
Gerbi, Christopher; Johnson, Scott E.; Cook, Alden; Vel, Senthil S.
2015-01-01
The strength of a polyphase aggregate comprising power-law materials is a function of the constitutive laws of the phases present, the arrangement of those phases and environmental conditions such as temperature. Primarily for geological applications, we consider the degree to which the arrangement of the phases has a significant influence on bulk strength. Calculations based on current single-mineral experimental data indicate that the absolute and relative strength differences between the upper and lower theoretical bounds vary widely with mineral pair, environmental conditions and strain rate. For example, at 850 °C, some pairs, such as plagioclase-clinopyroxene, are highly sensitive to phase morphology, whereas others, such as quartz-plagioclase, are not. Using a finite-element implementation of asymptotic expansion homogenization, we have calculated the bulk strength of natural and synthetic microstructures across macroscale strain gradients. We find that phase morphology does not change sufficiently in most cases to be the dominant factor in bulk strength variation. Thus on its own, phase morphology in an aggregate of power-law materials does not appear to be a major control on bulk strength under typical viscous geological conditions. However, phase morphology does affect microscale stress and strain rate patterns, which in turn can induce microscale variations in constitutive laws and diffusional pathways. These factors, including reactions and changing deformation mechanisms, are strongly influenced by phase morphology and do cause strength variation in rocks. As a result, any parametrization of rock strength needs to account for evolving modal mineralogy and deformation mechanisms in addition to morphological changes alone.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
Power-Law Type Solutions of Fourth-Order Gravity for Multidimensional Bianchi i Universes
NASA Astrophysics Data System (ADS)
Caprasse, H.; Demaret, J.; Gatermann, K.; Melenk, H.
This paper is devoted to the application of computer algebra to the study of solutions of the field equations derived from a non-linear Lagrangian, as suggested by recently proposed unified theories. More precisely, we restrict ourselves to the most general quadratic Lagrangian, i.e. containing quadratic contributions in the different curvature tensors exclusively. The corresponding field equations are then fourth-order in the metric tensor components. The cosmological models studied are the simplest ones in the class of spatially homogeneous but anisotropic models, i.e. Bianchi I models. For these models, we consider only power-law type solutions of the field equations. All the solutions of the associated system of algebraic equations are found, using computer algebra, from a search of its Groebner bases. While, in space dimension d=3, the Einsteinian-Kasner metric is still the most general power-law type solution, for d>3, no solution, other than the Minkowski space-time, is common to the three systems of equations corresponding to the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution to the Lagrangian (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the d-dimensional space into a (d-3)-dimensional internal space and a physical 3-dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when d=9).
Power Law and Scaling in the Energy of Tropical Cyclones (Invited)
NASA Astrophysics Data System (ADS)
Corral, A.; Osso, A.; Llebot, J.
2010-12-01
The influence of climate variability and global warming on the occurrence of tropical cyclones is a controversial issue. Existing historical databases on the subject are not fully reliable, but a more fundamental hindrance is the lack of basic understanding regarding the intrinsic nature of tropical-cyclone genesis and evolution. It is known that tropical cyclones involve more than a passive response to changing external forcing, but it is not clear which dynamic behavior best describes them. We present an approach based on the application of the power dissipation index, which constitutes an estimation of released energy, to individual tropical cyclones. A robust law emerges for the statistics of power dissipation index, valid in four different ocean basins and over long time periods. In addition to suggesting a description of the physics of tropical cyclones in terms of critical phenomena, the scaling law enables us to quantify their response to changing climatic conditions, with an increase in the largest power dissipation index values with sea surface temperature or the presence of El Niño phenomena, depending on the basin under consideration. In this way, we demonstrate that the recent upswing in North Atlantic hurricane activity does not involve tropical cyclones that are quantitatively different from those in other sustained high-activity periods before 1970. A. Corral, A. Osso, and J.E. Llebot, Nature Phys. 2010.
Origins of Taylor's power law for fluctuation scaling in complex systems
NASA Astrophysics Data System (ADS)
Fronczak, Agata; Fronczak, Piotr
2010-06-01
Taylor’s fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here, we give a reliable explanation for the origins and abundance of Taylor’s FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and nonequilibrium) we prove that Taylor’s law results from the well-defined number of states of a system characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).
Growth and branching of charged wormlike micelles as revealed by dilution laws.
In, Martin; Bendjeriou, Baroudi; Noirez, Laurence; Grillo, Isabelle
2010-07-06
The successive transitions of morphology in aqueous solutions of interacting micelles are directly evidenced by the position q* of the correlation peak of the small angle neutron scattering profiles. As the volume fraction Phi increases, q* successively fits to the dilution laws expected for spheres and cylinders, and eventually gets close to the one expected for sheets when the micelles get branched. Data in between the swelling laws are quantitatively analyzed in terms of aggregation number and junction density. Varying the temperature in the dilute regime yields the end-cap energy which varies with molecular structure and scales as Phi(-1/2). In the semidilute regime, the junction density scales as nu(j) approximately Phi(1.8), close but slightly faster than theoretically expected. The boosting effect of intermicellar repulsion on growth and branching is pointed out by the present results which directly show that both condensation processes keep the micelles further apart.
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.
An Evaluation of Power Law Breakdown in Metals, Alloys, Dispersion Hardened Materials and Compounds
Lesuer, D.R.; Syn, C.K.; Sherby, O.D.
1999-10-20
Creep at high stresses often produces strain rates that exceed those that would be predicted by a power law relationship. In this paper, we examine available high stress creep data for pure metals, solid solution alloys, dispersion strengthened powder metallurgy materials and compounds for power law breakdown (PLB). The results show that, if PLB is observed, then the onset of PLB is generally observed at about {epsilon}/D{sub eff} = 10{sup 13} m{sup -2}, where D{sub eff} is the effective diffusion coefficient incorporating lattice and dislocation pipe diffusion. The common origins of PLB for the various systems studied can be found in the production of excess vacancies by plastic deformation. Anomalous behavior in two pure metals (nickel and tungsten) and a solid solution alloy (Fe-25Cr and Fe-26Cr-1Mo) has been analyzed and provides insight into this excess vacancy mechanism. In metal systems, the onset of PLB is related to a change in the nature of the subgrain structure developed. In the PLB region, subgrains become imperfect containing dislocation tangles adjacent to the sub-boundary, and dislocation cells are evident. The dislocation tangles and cells are the source of excess vacancies and increase the creep rate above that predicted from power law creep. If subgrains do not form then PLB is not observed. In solid solution alloys, in which the dominant deformation resistance results from the interaction of solute atoms with moving dislocations, excess vacancies influence the diffusion of these solute atoms. PLB is not observed in many systems. This is attributed either to the presence of a high equilibrium vacancy concentration (because of a low activation energy for vacancy formation) or to the inability to form subgrains.
Air-chemistry "turbulence": power-law scaling and statistical regularity
NASA Astrophysics Data System (ADS)
Hsu, H.-M.; Lin, C.-Y.; Guenther, A.; Tribbia, J. J.; Liu, S. C.
2011-03-01
With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, and plain/hill locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, intermediate (20 ~ 30 days) and intraseasonal (30 ~ 100 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of -5/3 and -1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, -3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are intriguingly interesting, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.
Air-chemistry "turbulence": power-law scaling and statistical regularity
NASA Astrophysics Data System (ADS)
Hsu, H.-M.; Lin, C.-Y.; Guenther, A.; Tribbia, J. J.; Liu, S. C.
2011-08-01
With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, plain/hill, and industrial/agricultural locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, and intermediate (20 ~ 30 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of -5/3 and -1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. These exponents are mostly independent of the averages and standard deviations of time series measured at various geographic settings, i.e., the spatial inhomogeneities. In other words, they possess dominant universal structures. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, -3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are important structural information, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.
Saichev, A; Sornette, D
2010-01-01
Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law approximately 1/t(alpha) with 0
Effects of diversity and procrastination in priority queuing theory: The different power law regimes
NASA Astrophysics Data System (ADS)
Saichev, A.; Sornette, D.
2010-01-01
Empirical analyses show that after the update of a browser, or the publication of the vulnerability of a software, or the discovery of a cyber worm, the fraction of computers still using the older browser or software version, or not yet patched, or exhibiting worm activity decays as a power law ˜1/tα with 0<α≤1 over a time scale of years. We present a simple model for this persistence phenomenon, framed within the standard priority queuing theory, of a target task which has the lowest priority compared to all other tasks that flow on the computer of an individual. We identify a “time deficit” control parameter β and a bifurcation to a regime where there is a nonzero probability for the target task to never be completed. The distribution of waiting time T until the completion of the target task has the power law tail ˜1/t1/2 , resulting from a first-passage solution of an equivalent Wiener process. Taking into account a diversity of time deficit parameters in a population of individuals, the power law tail is changed into 1/tα , with αɛ(0.5,∞) , including the well-known case 1/t . We also study the effect of “procrastination,” defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks. This regime provides an explanation for even slower apparent decay and longer persistence.
NASA Astrophysics Data System (ADS)
Wang, Q.; Yang, M.; Song, X. L.; Jia, J.; Xiang, Z. D.
2016-07-01
The conventional power law creep equation (Norton equation) relating the minimum creep rate to creep stress and temperature cannot be used to predict the long-term creep strengths of creep-resistant steels if its parameters are determined only from short-term measurements. This is because the stress exponent and activation energy of creep determined on the basis of this equation depend on creep temperature and stress and these dependences cannot be predicted using this equation. In this work, it is shown that these problems associated with the conventional power law creep equation can be resolved if the new power law equation is used to rationalize the creep data. The new power law creep equation takes a form similar to the conventional power law creep equation but has a radically different capability not only in rationalizing creep data but also in predicting the long-term creep strengths from short-term test data. These capabilities of the new power law creep equation are demonstrated using the tensile strength and creep test data measured for both pipe and tube grades of the creep-resistant steel 9Cr-1.8W-0.5Mo-V-Nb-B (P92 and T92).
On the power-law distributions of X-ray fluxes from solar flares observed with GOES
NASA Astrophysics Data System (ADS)
Li, You-Ping; Feng, Li; Zhang, Ping; Liu, Si-Ming; Gan, Wei-Qun
2016-10-01
The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality (SOC). In this paper, we first show that, so long as the shape of the normalized light curve is not correlated with the peak flux, the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the power-law frequency distribution of the peak flux, which may partially explain why power-law distributions are ubiquitous in the Universe. We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different: the higher energy channel has a harder distribution than the lower energy channel, which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites. The temperature (T) distribution, on the other hand, approaches a power-law distribution with an index of 2 for high values of T. Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.
NASA Astrophysics Data System (ADS)
Langlois, Dominic; Cousineau, Denis; Thivierge, J. P.
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Howard, Robert W
2014-09-01
The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development.
Langlois, Dominic; Cousineau, Denis; Thivierge, J P
2014-01-01
The coordination of activity amongst populations of neurons in the brain is critical to cognition and behavior. One form of coordinated activity that has been widely studied in recent years is the so-called neuronal avalanche, whereby ongoing bursts of activity follow a power-law distribution. Avalanches that follow a power law are not unique to neuroscience, but arise in a broad range of natural systems, including earthquakes, magnetic fields, biological extinctions, fluid dynamics, and superconductors. Here, we show that common techniques that estimate this distribution fail to take into account important characteristics of the data and may lead to a sizable misestimation of the slope of power laws. We develop an alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data. Using numerical simulations, we show that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches. Next, we apply these estimators to recordings of in vitro rat neocortical activity. We show that different estimators lead to marked discrepancies in the evaluation of power-law distributions. These results call into question a broad range of findings that may misestimate the slope of power laws by failing to take into account key aspects of the observed data.
Laboratory constraints on chameleon dark energy and power-law fields
Steffen, Jason H.; Upadhye, Amol; Baumbaugh, Al; Chou, Aaron S.; Mazur, Peter O.; Tomlin, Ray; Weltman, Amanda; Wester, William; /Fermilab
2010-10-01
We report results from the GammeV Chameleon Afterglow Search - a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.
Anomalous wave function statistics on a one-dimensional lattice with power-law disorder.
Titov, M; Schomerus, H
2003-10-24
Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.
Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids
Maloney, C. E.; Robbins, M. O.
2009-06-05
The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.
On global minimizers of repulsive–attractive power-law interaction energies
Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong
2014-01-01
We consider the minimization of the repulsive–attractive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations. PMID:25288810
Forces acting on a stationary sphere in power-law fluid flow near the wall
NASA Astrophysics Data System (ADS)
Bocharov, O. B.; Kushnir, D. Yu.
2016-01-01
The analysis and evaluation of the forces acting on the particle in a linear shear flow of power-law fluid (PLF) in the presence of the wall were performed. Using the results of a series of computations for a model problem with a spherical particle near a flat wall in the Reynolds number range of 0-200 and the distance to the wall from 0 to 20 particle diameters, the correlation formulas for calculating the coefficients of drag force and lift force were obtained. Special attention was paid to the behavior of the forces acting on the particle approaching the wall.
Apparent Power Law Scaling of Variable Range Hopping Conduction in Carbonized Polymer Nanofibers
Kim, Kyung Ho; Lara-Avila, Samuel; Kang, Hojin; He, Hans; Eklӧf, Johnas; Hong, Sung Ju; Park, Min; Moth-Poulsen, Kasper; Matsushita, Satoshi; Akagi, Kazuo; Kubatkin, Sergey; Park, Yung Woo
2016-01-01
We induce dramatic changes in the structure of conducting polymer nanofibers by carbonization at 800 °C and compare charge transport properties between carbonized and pristine nanofibers. Despite the profound structural differences, both types of systems display power law dependence of current with voltage and temperature, and all measurements can be scaled into a single universal curve. We analyze our experimental data in the framework of variable range hopping and argue that this mechanism can explain transport properties of pristine polymer nanofibers as well. PMID:27886233
Apparent Power Law Scaling of Variable Range Hopping Conduction in Carbonized Polymer Nanofibers
NASA Astrophysics Data System (ADS)
Kim, Kyung Ho; Lara-Avila, Samuel; Kang, Hojin; He, Hans; Eklӧf, Johnas; Hong, Sung Ju; Park, Min; Moth-Poulsen, Kasper; Matsushita, Satoshi; Akagi, Kazuo; Kubatkin, Sergey; Park, Yung Woo
2016-11-01
We induce dramatic changes in the structure of conducting polymer nanofibers by carbonization at 800 °C and compare charge transport properties between carbonized and pristine nanofibers. Despite the profound structural differences, both types of systems display power law dependence of current with voltage and temperature, and all measurements can be scaled into a single universal curve. We analyze our experimental data in the framework of variable range hopping and argue that this mechanism can explain transport properties of pristine polymer nanofibers as well.
An explanation for the universal 3.5 power-law observed in currency markets
NASA Astrophysics Data System (ADS)
Johnson, Nicholas A.; Johnson, Neil F.
We present a mathematical theory to explain a recent empirical finding in the Physics literature (Zhao et al., 2013) in which the distributions of waiting-times between discrete events were found to exhibit power-law tails with an apparent universal exponent: α ∼ 3.5 . This new theory provides the first ever qualitative and quantitative explanation of Zhao et al.'s surprising finding. It also provides a mechanistic description of the origin of the observed universality, assigning its cause to the emergence of dynamical feedback processes between evolving clusters of like-minded agents.
Power-law tail of the velocity distribution in granular gases
NASA Astrophysics Data System (ADS)
Kang, Wenfeng; Ben-Naim, Eli; Machta, Jon
2007-03-01
We use a two-dimensional event-driven molecular dynamics simulation to study the velocity distribution of a granular gas. We implement the high energy injection mechanism described in Ref. [1]. At a small rate γ we boost randomly chosen particles to a high energy. The resulting driven steady state is found to have a power-law high-energy tail in the velocity distribution, f(v) ˜ v ^- σ. The simulation results for the exponent σ are in good agreement with the theoretical predictions of Ref. [1]. [1] E. Ben-Naim and J. Machta, Phys. Rev. Lett. 94, 138001 (2005).
Jell-O Optics: Edibly Exploring Snell's Law and Optical Power
NASA Astrophysics Data System (ADS)
Hendryx, Jennifer; Reynolds, Mathias
2012-03-01
This presentation details a laboratory exercise and/or demonstration of refraction with an inexpensive, simple set-up: a pan of Jell-O, protractors, and laser pointers. This activity is presented from the perspective of an optical sciences graduate student who has spent the school year team-teaching high school math and physics (through Academic Decathlon). The goal is to present some of the fundamentals of optics with an enjoyable and affordable approach. The concepts include Snell's law, index of refraction, and optical power/focal length as they relate to the curvature of a lens.
Spin-coating process evolution and reproducibility for power-law fluids.
Jardim, P L G; Michels, A F; Horowitz, F
2014-03-20
A distinct development of an exact analytical solution for power-law fluids during the spin-coating process is presented for temporal and spatial thickness evolution, after steady state conditions are attained. This solution leads to the definition of a characteristic time, related to the memory of the initial thickness profile. Previously obtained experimental data, for several rotation speeds and carboxymetilcellulose concentrations in water, are quantitatively analyzed through the evaluation of their characteristic times and compared with theoretical predictions, thus allowing better understanding of thickness profile evolution and of process reproducibility.
Additivity property and emergence of power laws in nonequilibrium steady states.
Das, Arghya; Chatterjee, Sayani; Pradhan, Punyabrata; Mohanty, P K
2015-11-01
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.
Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information
NASA Technical Reports Server (NTRS)
Howell, L. W.
2002-01-01
A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from
The time-domain behavior of power-law noises. [of many geophysical phenomena
NASA Technical Reports Server (NTRS)
Agnew, Duncan C.
1992-01-01
The power spectra of many geophysical phenomena are well approximated by a power-law dependence on frequency or wavenumber. A simple expression for the root-mean-square variability of a process with such a spectrum over an interval of time or space is derived. The resulting expression yields the powerlaw time dependence characteristic of fractal processes, but can be generalized to give the temporal variability for more general spectral behaviors. The method is applied to spectra of crustal strain (to show what size of strain events can be detected over periods of months to seconds) and of sea level (to show the difficulty of extracting long-term rates from short records).
Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses
NASA Astrophysics Data System (ADS)
Garcia, O. E.; Theodorsen, A.
2017-02-01
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For a constant pulse duration, this is shown to result in an exponential power spectral density for the stationary process. A random distribution of pulse durations modifies the frequency spectrum, and several examples are shown to result in power law spectra. The distribution of pulse durations does not influence the characteristic function and thus neither the moments nor the probability density function of the random variable. It is demonstrated that the fluctuations are intrinsically intermittent through a large excess kurtosis moment in the limit of weak pulse overlap. These results allow for estimation of the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.
Semiclassical trace formula for the two-dimensional radial power-law potentials.
Magner, A G; Vlasenko, A A; Arita, K
2013-06-01
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate up to a constant shift the radial dependence of the Woods-Saxon potential and its quantum spectra in a bound region, was derived by the improved stationary phase method. The specific analytical results are obtained for the powers α=4 and 6. The enhancement of periodic-orbit contribution to the level density near the bifurcations are found to be significant for the description of the fine shell structure. The semiclassical trace formulas for the shell corrections to the level density and the energy of many-fermion systems reproduce the quantum results with good accuracy through all the bifurcation (symmetry breaking) catastrophe points, where the standard stationary-phase method breaks down. Various limits (including the harmonic oscillator and the spherical billiard) are obtained from the same analytical trace formula.
NASA Astrophysics Data System (ADS)
Fan, Qingju; Wu, Yonghong
2015-08-01
In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.
Engines with ideal efficiency and nonzero power for sublinear transport laws
NASA Astrophysics Data System (ADS)
Koning, Jesper; Indekeu, Joseph O.
2016-11-01
It is known that an engine with ideal efficiency (η = 1 for a chemical engine and e = eCarnot for a thermal one) has zero power because a reversible cycle takes an infinite time. However, at least from a theoretical point of view, it is possible to conceive (irreversible) engines with nonzero power that can reach ideal efficiency. Here this is achieved by replacing the usual linear transport law by a sublinear one and taking the step-function limit for the particle current (chemical engine) or heat current (thermal engine) versus the applied force. It is shown that in taking this limit exact thermodynamic inequalities relating the currents to the entropy production are not violated.
Validation of a power-law noise model for simulating small-scale breast tissue
NASA Astrophysics Data System (ADS)
Reiser, I.; Edwards, A.; Nishikawa, R. M.
2013-09-01
We have validated a small-scale breast tissue model based on power-law noise. A set of 110 patient images served as truth. The statistical model parameters were determined by matching the radially averaged power-spectrum of the projected simulated tissue with that of the central tomosynthesis patient breast projections. Observer performance in a signal-known exactly detection task in simulated and actual breast backgrounds was compared. Observers included human readers, a pre-whitening observer model and a channelized Hotelling observer model. For all observers, good agreement between performance in the simulated and actual backgrounds was found, both in the tomosynthesis central projections and the reconstructed images. This tissue model can be used for breast x-ray imaging system optimization. The complete statistical description of the model is provided.
The Common Law Power of the Legislature: Insurer Conversions and Charitable Funds
Horwitz, Jill R; Fremont-Smith, Marion R
2005-01-01
New York's Empire Blue Cross and Blue Shield conversion from nonprofit to for-profit form has considerable legal significance. Three aspects of the conversion make the case unique: the role of the state legislature in directing the disposition of the conversion assets, the fact that it made itself the primary beneficiary of those assets, and the actions of the state attorney general defending the state rather than the public interest in the charitable assets. Drawing on several centuries of common law rejecting the legislative power to direct the disposition of charitable funds, this article argues that the legislature lacked power to control the conversion and direct the disposition of its proceeds and that its actions not only undermined the nonprofit form but also raised constitutional concerns. PMID:15960770
Phylogenies reveal predictive power of traditional medicine in bioprospecting.
Saslis-Lagoudakis, C Haris; Savolainen, Vincent; Williamson, Elizabeth M; Forest, Félix; Wagstaff, Steven J; Baral, Sushim R; Watson, Mark F; Pendry, Colin A; Hawkins, Julie A
2012-09-25
There is controversy about whether traditional medicine can guide drug discovery, and investment in bioprospecting informed by ethnobotanical data has fluctuated. One view is that traditionally used medicinal plants are not necessarily efficacious and there are no robust methods for distinguishing those which are most likely to be bioactive when selecting species for further testing. Here, we reconstruct a genus-level molecular phylogenetic tree representing the 20,000 species found in the floras of three disparate biodiversity hotspots: Nepal, New Zealand, and the Cape of South Africa. Borrowing phylogenetic methods from community ecology, we reveal significant clustering of the 1,500 traditionally used species, and provide a direct measure of the relatedness of the three medicinal floras. We demonstrate shared phylogenetic patterns across the floras: related plants from these regions are used to treat medical conditions in the same therapeutic areas. This finding strongly indicates independent discovery of plant efficacy, an interpretation corroborated by the presence of a significantly greater proportion of known bioactive species in these plant groups than in random samples. We conclude that phylogenetic cross-cultural comparisons can focus screening efforts on a subset of traditionally used plants that are richer in bioactive compounds, and could revitalize the use of traditional knowledge in bioprospecting.
A power-law approximation for fluvial incision by tools and bed coverage processes
NASA Astrophysics Data System (ADS)
Brandon, M. T.; Gasparini, N. M.
2005-12-01
The stream-power model is widely used to represent fluvial incision in bedrock channels. The model does not account for the amount of sediment in the channel, which can abrade the channel at low concentrations or armor the channel at high concentrations. Here we use a natural example (Clearwater River, Washington State, USA) and numerical experiments to explore how sediment flux influences bedrock incision at a drainage-wide scale. We have generated numerical landscapes with different uplift patterns using the CHILD numerical model and incision rules that include a tools-and-coverage formulation. We then use regression analysis to fit a power-law function I=K*Am*Sn*, where I is incision rate, S slope, and A drainage area, and K*, m*, and n* are fit parameters. We find that this formulation works very well for the Clearwater and all of our numerical experiments. The function has the same form as the stream-power model, but the parameters are empirically defined (as indicated by the asterisks) and can take on values quite different than those inferred from process-based arguments. The best-fit parameters appear to be constant at the scale of a single drainage, but they vary between drainages depending on the pattern of uplift, and whether or not the landscape has reached steady-state. In all cases, slope-area steepness analysis works well for estimating relative incision rates. Our analysis indicates that, in some cases, m* can be quite low, apparently due to the fact that bed coverage increases with increasing area. We conclude that the power-law formulation provides a good functional representation of fluvial incision, but that there are no universal values for m* and n*. These conclusions have important implications for the size of mountain belts and feedbacks between tectonic uplift and surface processes.
Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements
NASA Astrophysics Data System (ADS)
Mukherjee, Suvodip; Das, Santanu; Joy, Minu; Souradeep, Tarun
2015-01-01
Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass meff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation νt and change in spectral index for scalar perturbation νst to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of ns=0.96 by having a non-zero value of effective mass of the inflaton field m2eff/H2. The analysis with WP + Planck likelihood shows a non-zero detection of m2eff/H2 with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m2eff/H2 = -0.0237 ± 0.0135 which is consistent with zero.
Vortex Lattice Metastability and Power Law Dynamics in MgB2
NASA Astrophysics Data System (ADS)
Rastovski, Catherine; Kuhn, S. J.; Smith, K.; Eskildsen, M. R.; Debeer-Schmitt, L.; Dewhurst, C. D.; Gannon, W. J.; Zhigadlo, N. D.; Karpinski, J.
2014-03-01
Previous small-angle neutron scattering (SANS) studies of the vortex lattice (VL) of MgB2 with H ∥ c found a triangular VL which undergoes a field-driven 30° reorientation transition, forming three distinct ground state phases. A high degree of metastability exists between the VL phases of MgB2 that cannot be attributed to vortex pinning and may be a result of the jamming of VL domains [C. Rastovski et al., Phys. Rev. Lett. 111, 107002 (2013)]. To further investigate the effect of vortex motion on the metastable to ground state VL transition, we applied a small AC magnetic field parallel or perpendicular to the vortices to ``shake'' the lattice. The metastable VL volume fraction decreased with a two-step power law dependence on the number of applied AC cycles. The slow and then fast power law decay of the metastable state may indicate first nucleation and then growth of ground state VL domains. This work was supported by the Department of Energy, Basic Energy Sciences under Award No. DE-FG02-10ER46783.
Power law distribution in statistics of failures in operation of spacecraft onboard equipment
NASA Astrophysics Data System (ADS)
Karimova, L. M.; Kruglun, O. A.; Makarenko, N. G.; Romanova, N. V.
2011-10-01
The possibility of using the statistics of recurrence time for extreme events is studied in this paper having in mind the problems of control and prediction of failures in spacecraft operation. The information about failures onboard satellites of various types presented by the US National Geophysical Data Center was analyzed. It was found that the probability density of recurrence intervals followed a power law of the Pareto type with an index equal to 2.3. The obtained result is consistent both with the theory of normal catastrophes and with the principle of self-organization of criticality for metastable active heterogeneous environment. A practical consequence of the obtained result consists in the fact that predictions of these extreme events should not rely on traditional models with the second-order Pearson statistics. To make predictions, the models are necessary that take into account the power law distribution of recurrence intervals for failures on satellites. The failures should be considered in these models as extreme events connected with manifestation of the space environment factors.
Nonuniversal power law scaling in the probability distribution of scientific citations.
Peterson, George J; Pressé, Steve; Dill, Ken A
2010-09-14
We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ("classics") are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The "tipping point" at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975-1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.
2002-01-01
The method of Maximum Likelihood (ML) is used to estimate the spectral parameters of an assumed broken power law energy spectrum from simulated detector responses. This methodology, which requires the complete specificity of all cosmic-ray detector design parameters, is shown to provide approximately unbiased, minimum variance, and normally distributed spectra information for events detected by an instrument having a wide range of commonly used detector response functions. The ML procedure, coupled with the simulated performance of a proposed space-based detector and its planned life cycle, has proved to be of significant value in the design phase of a new science instrument. The procedure helped make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope. This ML methodology is then generalized to estimate broken power law spectral parameters from real cosmic-ray data sets.
NASA Astrophysics Data System (ADS)
Cota, Wesley; Ferreira, Silvio C.; Ódor, Géza
2016-03-01
We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space λ1<λ <λ2 , suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudothresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at λ2. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at λc=0 . Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.
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.
Ueno, Taro; Masuda, Naoki; Kume, Shoen; Kume, Kazuhiko
2012-01-01
We analyzed the effects of dopamine signaling on the temporal organization of rest and activity in Drosophila melanogaster. Locomotor behaviors were recorded using a video-monitoring system, and the amounts of movements were quantified by using an image processing program. We, first, confirmed that rest bout durations followed long-tailed (i.e., power-law) distributions, whereas activity bout durations did not with a strict method described by Clauset et al. We also studied the effects of circadian rhythm and ambient temperature on rest bouts and activity bouts. The fraction of activity significantly increased during subjective day and at high temperature, but the power-law exponent of the rest bout distribution was not affected. The reduction in rest was realized by reduction in long rest bouts. The distribution of activity bouts did not change drastically under the above mentioned conditions. We then assessed the effects of dopamine. The distribution of rest bouts became less long-tailed and the time spent in activity significantly increased after the augmentation of dopamine signaling. Administration of a dopamine biosynthesis inhibitor yielded the opposite effects. However, the distribution of activity bouts did not contribute to the changes. These results suggest that the modulation of locomotor behavior by dopamine is predominantly controlled by changing the duration of rest bouts, rather than the duration of activity bouts.
Observations of Suprathermal Power Law Tails with ACE, Ulysses, MESSENGER, and Voyager
NASA Astrophysics Data System (ADS)
Gloeckler, G.; Fisk, L. A.
2007-12-01
Observations of ubiquitous, suprathermal power law tails with the unique spectral index of -5 on the velocity distributions of solar wind and pickup ions raise important questions and have far reaching consequences. The question of how these tails are formed during quiet times, when no shocks are present, was previously addressed and is briefly reviewed here. One consequence of the existence of these tails during quiet times is that sufficiently energetic particles are always readily available for further acceleration by shocks. To study the evolution of suprathermal tails over a large range of heliocentric distances, we will use proton spectra measured with ACE, Ulysses and Voyager during quiet times as well as upstream and downstream of quasi-stationary and traveling shocks. To look for the first time at suprathermal tails at distances closer to the Sun than 1 AU, we will present our preliminary results from the FIPS instrument on the Mercury MESSENGER Mission. Applying thermodynamic constraints on non-adiabatic heating of upstream particles by a shock, we obtain the downstream -5 power law spectra that are observed and derive an expression for the tail pressure jump across the shock.
Universal correlations and power-law tails in financial covariance matrices
NASA Astrophysics Data System (ADS)
Akemann, G.; Fischmann, J.; Vivo, P.
2010-07-01
We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.
Keeping the edge: an accurate numerical method to solve the stream power law
NASA Astrophysics Data System (ADS)
Campforts, B.; Govers, G.
2015-12-01
Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.
Validity of a power law approach to model tablet strength as a function of compaction pressure.
Kloefer, Bastian; Henschel, Pascal; Kuentz, Martin
2010-03-01
Designing quality into dosage forms should not be only based on qualitative or purely heuristic relations. A knowledge space must be generated, in which at least some mechanistic understanding is included. This is of particular interest for critical dosage form parameters like the strength of tablets. In line with this consideration, the scope of the work is to explore the validity range of a theoretically derived power law for the tensile strength of tablets. Different grades of microcrystalline cellulose and lactose, as well as mixtures thereof, were used to compress model tablets. The power law was found to hold true in a low pressure range, which agreed with theoretical expectation. This low pressure range depended on the individual material characteristics, but as a rule of thumb, the tablets having a porosity of more than about 30% or being compressed below 100 MPa were generally well explained by the tensile strength relationship. Tablets at higher densities were less adequately described by the theory that is based on large-scale heterogeneity of the relevant contact points in the compact. Tablets close to the unity density therefore require other theoretical approaches. More research is needed to understand tablet strength in a wider range of compaction pressures.
Podesta, J. J.
2008-12-15
The relativistic plasma dispersion relation is derived for Langmuir waves in a spatially homogeneous unmagnetized plasma in which the electrons have an isotropic power-law distribution in momentum space. The theory is applied to the study of Langmuir waves in the quiescent solar wind near the orbit of the Earth assuming that the electron distribution function can be approximated as a power-law from thermal energies {approx}10 eV to relativistic energies < or approx. 100 keV. Numerical solutions of the dispersion relation show that in the regime of weak Landau damping the phase speeds of the waves match the velocities of the high-energy particles, known in the solar wind literature as the superhalo, which lie in the range 0.09
Finite and Infinite Width Stokes Layers in a Power-Law Fluid
NASA Astrophysics Data System (ADS)
Wilson, Stephen; Pritchard, David; McArdle, Catriona
2011-11-01
Self-similar solutions for the oscillatory boundary layer (the ``Stokes layer'') in a semi-infinite power-law fluid bounded by an oscillating wall (the so-called Stokes problem) are obtained and analysed. These semi-analytical solutions differ qualitatively from the classical solution for a Newtonian fluid, both in the non-sinusoidal form of the velocity oscillations and in the manner at which their amplitude decays with distance from the wall. In particular, for shear-thickening fluids the velocity reaches zero at a finite distance from the wall, and for shear-thinning fluids it decays algebraically with distance, in contrast to the exponential decay for a Newtonian fluid. We demonstrate numerically that these self-similar solutions provide a good approximation to the flow driven by a sinusoidally oscillating wall. Further details can be found in the recent paper by D. Pritchard, C. R. McArdle and S. K. Wilson entitled ``The Stokes boundary layer for a power-law fluid,'' in Journal of Non-Newtonian Fluid Mechanics 166, 745-753 (2011).
Nonuniversal power law scaling in the probability distribution of scientific citations
Peterson, George J.; Pressé, Steve; Dill, Ken A.
2010-01-01
We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations (“classics”) are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The “tipping point” at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975–1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited. PMID:20805513
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.
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.
Power-law decay exponents: A dynamical criterion for predicting thermalization
NASA Astrophysics Data System (ADS)
Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.
2017-01-01
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.
So You Think the Crab is Described by a Power-Law Spectrum
NASA Technical Reports Server (NTRS)
Weisskopf, Martin C.
2008-01-01
X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.
“Slimming” of power-law tails by increasing market returns
NASA Astrophysics Data System (ADS)
Sornette, D.
2002-06-01
We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r> rδ corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power-law exponent and thus the thinner is the tail of the distribution of price returns.
Underestimating extreme events in power-law behavior due to machine-dependent cutoffs
NASA Astrophysics Data System (ADS)
Radicchi, Filippo
2014-11-01
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law distributions. The task is usually performed through standard methods that map uniform random variates into the desired probability space. Whereas all these algorithms are theoretically solid, in this paper we show that they are subject to severe machine-dependent limitations. As a result, two dramatic consequences arise: (i) the sampling in the tail of the distribution is not random but deterministic; (ii) the moments of the sample distribution, which are theoretically expected to diverge as functions of the sample sizes, converge instead to finite values. We provide quantitative indications for the range of distribution parameters that can be safely handled by standard libraries used in computational analyses. Whereas our findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies, they also pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.
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.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
NASA Technical Reports Server (NTRS)
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology
NASA Astrophysics Data System (ADS)
Wu, Patrick; Wang, Hansheng
2008-10-01
Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology ( n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A ˜ 10 -35 Pa -3 s -1 for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.
Slater, Noa; Louzoun, Yoram; Gragert, Loren; Maiers, Martin; Chatterjee, Ansu; Albrecht, Mark
2015-04-01
Measures of allele and haplotype diversity, which are fundamental properties in population genetics, often follow heavy tailed distributions. These measures are of particular interest in the field of hematopoietic stem cell transplant (HSCT). Donor/Recipient suitability for HSCT is determined by Human Leukocyte Antigen (HLA) similarity. Match predictions rely upon a precise description of HLA diversity, yet classical estimates are inaccurate given the heavy-tailed nature of the distribution. This directly affects HSCT matching and diversity measures in broader fields such as species richness. We, therefore, have developed a power-law based estimator to measure allele and haplotype diversity that accommodates heavy tails using the concepts of regular variation and occupancy distributions. Application of our estimator to 6.59 million donors in the Be The Match Registry revealed that haplotypes follow a heavy tail distribution across all ethnicities: for example, 44.65% of the European American haplotypes are represented by only 1 individual. Indeed, our discovery rate of all U.S. European American haplotypes is estimated at 23.45% based upon sampling 3.97% of the population, leaving a large number of unobserved haplotypes. Population coverage, however, is much higher at 99.4% given that 90% of European Americans carry one of the 4.5% most frequent haplotypes. Alleles were found to be less diverse suggesting the current registry represents most alleles in the population. Thus, for HSCT registries, haplotype discovery will remain high with continued recruitment to a very deep level of sampling, but population coverage will not. Finally, we compared the convergence of our power-law versus classical diversity estimators such as Capture recapture, Chao, ACE and Jackknife methods. When fit to the haplotype data, our estimator displayed favorable properties in terms of convergence (with respect to sampling depth) and accuracy (with respect to diversity estimates). This
Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT
Vedantham, Srinivasan; Shi, Linxi; Glick, Stephen J.; Karellas, Andrew
2013-01-15
Purpose: To determine the x-ray photon energy dependence of the anatomic power spectrum of the breast when imaged with dedicated breast computed tomography (CT). Methods: A theoretical framework for scaling the empirically determined anatomic power spectrum at one x-ray photon energy to that at any given x-ray photon energy when imaged with dedicated breast CT was developed. Theory predicted that when the anatomic power spectrum is fitted with a power curve of the form k f{sup -{beta}}, where k and {beta} are fit coefficients and f is spatial frequency, the exponent {beta} would be independent of x-ray photon energy (E), and the amplitude k scales with the square of the difference in energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues. Twenty mastectomy specimens based numerical phantoms that were previously imaged with a benchtop flat-panel cone-beam CT system were converted to 3D distribution of glandular weight fraction (f{sub g}) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of f{sub g} and after converting to linear attenuation coefficients at monoenergetic x-ray photon energies of 20-80 keV in 5 keV intervals. The 1D power spectra along the axes were extracted and fitted with a power curve of the form k f{sup -{beta}}. The energy dependence of k and {beta} were analyzed. Results: For the 20 mastectomy specimen based numerical phantoms used in the study, the exponent {beta} was found to be in the range of 2.34-2.42, depending on the axis of measurement. Numerical simulations agreed with the theoretical predictions that for a power-law anatomic spectrum of the form k f{sup -{beta}}, {beta} was independent of E and k(E) =k{sub 1}[{mu}{sub g}(E) -{mu}{sub a}(E)]{sup 2}, where k{sub 1} is a constant, and {mu}{sub g}(E) and {mu}{sub a}(E) represent the energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues, respectively. Conclusions: Numerical
NASA Astrophysics Data System (ADS)
Saichev, A.; Helmstetter, A.; Sornette, D.
2005-06-01
We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (“fertility”), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities μ is characterized by a power law ~1/μ1+γ. For earthquakes we expect such a power-distribution of fertilities with γ=b/α based on the Gutenberg-Richter magnitude distribution ~ 10-bm and on the increase ~ 10-αm of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions pr(r) and pg(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime γ < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values α=0.8 1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother
Network-state modulation of power-law frequency-scaling in visual cortical neurons.
El Boustani, Sami; Marre, Olivier; Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves
2009-09-01
Various types of neural-based signals, such as EEG, local field potentials and intracellular synaptic potentials, integrate multiple sources of activity distributed across large assemblies. They have in common a power-law frequency-scaling structure at high frequencies, but it is still unclear whether this scaling property is dominated by intrinsic neuronal properties or by network activity. The latter case is particularly interesting because if frequency-scaling reflects the network state it could be used to characterize the functional impact of the connectivity. In intracellularly recorded neurons of cat primary visual cortex in vivo, the power spectral density of V(m) activity displays a power-law structure at high frequencies with a fractional scaling exponent. We show that this exponent is not constant, but depends on the visual statistics used to drive the network. To investigate the determinants of this frequency-scaling, we considered a generic recurrent model of cortex receiving a retinotopically organized external input. Similarly to the in vivo case, our in computo simulations show that the scaling exponent reflects the correlation level imposed in the input. This systematic dependence was also replicated at the single cell level, by controlling independently, in a parametric way, the strength and the temporal decay of the pairwise correlation between presynaptic inputs. This last model was implemented in vitro by imposing the correlation control in artificial presynaptic spike trains through dynamic-clamp techniques. These in vitro manipulations induced a modulation of the scaling exponent, similar to that observed in vivo and predicted in computo. We conclude that the frequency-scaling exponent of the V(m) reflects stimulus-driven correlations in the cortical network activity. Therefore, we propose that the scaling exponent could be used to read-out the "effective" connectivity responsible for the dynamical signature of the population signals measured
Listing triangles in expected linear time on a class of power law graphs.
Nordman, Daniel J.; Wilson, Alyson G.; Phillips, Cynthia Ann; Berry, Jonathan W.
2010-07-01
Enumerating triangles (3-cycles) in graphs is a kernel operation for social network analysis. For example, many community detection methods depend upon finding common neighbors of two related entities. We consider Cohen's simple and elegant solution for listing triangles: give each node a 'bucket.' Place each edge into the bucket of its endpoint of lowest degree, breaking ties consistently. Each node then checks each pair of edges in its bucket, testing for the adjacency that would complete that triangle. Cohen presents an informal argument that his algorithm should run well on real graphs. We formalize this argument by providing an analysis for the expected running time on a class of random graphs, including power law graphs. We consider a rigorously defined method for generating a random simple graph, the erased configuration model (ECM). In the ECM each node draws a degree independently from a marginal degree distribution, endpoints pair randomly, and we erase self loops and multiedges. If the marginal degree distribution has a finite second moment, it follows immediately that Cohen's algorithm runs in expected linear time. Furthermore, it can still run in expected linear time even when the degree distribution has such a heavy tail that the second moment is not finite. We prove that Cohen's algorithm runs in expected linear time when the marginal degree distribution has finite 4/3 moment and no vertex has degree larger than {radical}n. In fact we give the precise asymptotic value of the expected number of edge pairs per bucket. A finite 4/3 moment is required; if it is unbounded, then so is the number of pairs. The marginal degree distribution of a power law graph has bounded 4/3 moment when its exponent {alpha} is more than 7/3. Thus for this class of power law graphs, with degree at most {radical}n, Cohen's algorithm runs in expected linear time. This is precisely the value of {alpha} for which the clustering coefficient tends to zero asymptotically, and it is
From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies
NASA Astrophysics Data System (ADS)
Soesoo, Alvar; Bons, Paul D.
2015-07-01
Magma is generated by partial melting from micrometre-scale droplets at the source and may accumulate to form >100 km-scale plutons. Magma accumulation thus spans well over ten orders of magnitude in scale. Here we provide measurements of migmatitic leucosomes and granitic veins in drill cores from the Estonian Proterozoic basement and outcrops at Masku in SW Finland and Montemor-o-Novo, central Portugal. Despite the differences in size and number of measured leucosomes and magmatic veins, differences in host rock types and metamorphic grades, the cumulative width distribution of the studied magmatic leucosomes/veins follows a power law with exponents usually between 0.7 and 1.8. Published maps of the SE Australian Lachlan Fold Belt were used to investigate the distribution of granitoid pluton sizes. The granites occupy ca. 22 % of the 2.6 × 105 km2 area. The cumulative pluton area distributions show good power law distributions with exponents between 0.6 and 0.8 depending on pluton area group. Using the self-affine nature of pluton shapes, it is possible to estimate the total volume of magma that was expelled from the source in the 2.6 × 105 km2 map area, giving an estimated 0.8 km3 of magma per km2. It has been suggested in the literature that magma batches in the source merge to form ever-bigger batches in a self-organized way. This leads to a power law for the cumulative distribution of magma volumes, with an exponent m V between 1 for inefficient melt extraction, and 2/3 for maximum accumulation efficiency as most of the volume resides in the largest batches that can escape from the source. If m V ≥ 1, the mass of the magma is dominated by small batches; in case m = 2/3, about 50 % of all magma in the system is placed in a single largest batch. Our observations support the model that the crust develops a self-organized critical state during magma generation. In this state, magma batches accumulate in a non-continuous, step-wise manner to form ever
Zhao, Xiaofeng; McGough, Robert J
2016-05-01
The attenuation of ultrasound propagating in human tissue follows a power law with respect to frequency that is modeled by several different causal and noncausal fractional partial differential equations. To demonstrate some of the similarities and differences that are observed in three related time-fractional partial differential equations, time-domain Green's functions are calculated numerically for the power law wave equation, the Szabo wave equation, and for the Caputo wave equation. These Green's functions are evaluated for water with a power law exponent of y = 2, breast with a power law exponent of y = 1.5, and liver with a power law exponent of y = 1.139. Simulation results show that the noncausal features of the numerically calculated time-domain response are only evident very close to the source and that these causal and noncausal time-domain Green's functions converge to the same result away from the source. When noncausal time-domain Green's functions are convolved with a short pulse, no evidence of noncausal behavior remains in the time-domain, which suggests that these causal and noncausal time-fractional models are equally effective for these numerical calculations.
Wavelet-based analysis and power law classification of C/NOFS high-resolution electron density data
NASA Astrophysics Data System (ADS)
Rino, C. L.; Carrano, C. S.; Roddy, Patrick
2014-08-01
This paper applies new wavelet-based analysis procedures to low Earth-orbiting satellite measurements of equatorial ionospheric structure. The analysis was applied to high-resolution data from 285 Communications/Navigation Outage Forecasting System (C/NOFS) satellite orbits sampling the postsunset period at geomagnetic equatorial latitudes. The data were acquired during a period of progressively intensifying equatorial structure. The sampled altitude range varied from 400 to 800 km. The varying scan velocity remained within 20° of the cross-field direction. Time-to-space interpolation generated uniform samples at approximately 8 m. A maximum segmentation length that supports stochastic structure characterization was identified. A two-component inverse power law model was fit to scale spectra derived from each segment together with a goodness-of-fit measure. Inverse power law parameters derived from the scale spectra were used to classify the scale spectra by type. The largest category was characterized by a single inverse power law with a mean spectral index somewhat larger than 2. No systematic departure from the inverse power law was observed to scales greater than 100 km. A small subset of the most highly disturbed passes at the lowest sampled altitudes could be categorized by two-component power law spectra with a range of break scales from less than 100 m to several kilometers. The results are discussed within the context of other analyses of in situ data and spectral characteristics used for scintillation analyses.
Lee, S.R.; Irvine, T.F. Jr.; Greene, G.A.
1998-04-01
An implicit finite difference method was applied to analyze laminar natural convection in a vertical channel with a modified power law fluid. This fluid model was chosen because it describes the viscous properties of a pseudoplastic fluid over the entire shear rate range likely to be found in natural convection flows since it covers the shear rate range from Newtonian through transition to simple power law behavior. In addition, a dimensionless similarity parameter is identified which specifies in which of the three regions a particular system is operating. The results for the average channel velocity and average Nusselt number in the asymptotic Newtonian and power law regions are compared with numerical data in the literature. Also, graphical results are presented for the velocity and temperature fields and entrance lengths. The results of average channel velocity and Nusselt number are given in the three regions including developing and fully developed flows. As an example, a pseudoplastic fluid (carboxymethyl cellulose) was chosen to compare the different results of average channel velocity and Nusselt number between a modified power law fluid and the conventional power law model. The results show, depending upon the operating conditions, that if the correct model is not used, gross errors can result.
Random sampling of skewed distributions implies Taylor’s power law of fluctuation scaling
Cohen, Joel E.; Xu, Meng
2015-01-01
Taylor’s law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species’ population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)b, a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their uncertainty. In computer simulations and an empirical example using basal area densities of red oak trees from Black Rock Forest, our formulae agree with the estimates obtained by least-squares regression. Our results show that the correlated sampling variation of the mean and variance of skewed distributions is statistically sufficient to explain TL under random sampling, without the intervention of any biological or behavioral mechanisms. This finding connects TL with the underlying distribution of population density (or other nonnegative quantity) and provides a baseline against which more complex mechanisms of TL can be compared. PMID:25852144
Origins of power-law degree distribution in the heterogeneity of human activity in social networks
Muchnik, Lev; Pei, Sen; Parra, Lucas C.; Reis, Saulo D. S.; Andrade Jr, José S.; Havlin, Shlomo; Makse, Hernán A.
2013-01-01
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a “maximum entropy attachment” model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people. PMID:23648793
Observation of the 1/2 power law in Rayleigh-Bénard convection.
Roche, P E; Castaing, B; Chabaud, B; Hébral, B
2001-04-01
The 1/2 power law is reported in a Rayleigh-Bénard experiment: Nu approximately Ra(1/2), where Ra and Nu are the Rayleigh and Nusselt numbers. This observation is coherent with the predictions of the ultimate convection regime, characterized by fully turbulent heat transfers. Ordered rough boundaries are used to cancel the correction due to the thickness variation of the viscous sublayer, and the observation of the asymptotic regime is therefore possible. This result supports the interpretation of a laminar-turbulent boundary-layer transition to account for the observation of Chavanne et al. of a new regime [X. Chavanne et al., Phys. Rev. Lett. 79, 3648 (1997)].
Modified bosonic gas trapped in a generic 3-dim power law potential
NASA Astrophysics Data System (ADS)
Castellanos, E.; Laemmerzahl, C.
2014-04-01
We analyze the consequences caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the condensation temperature is shifted as a consequence of such deformation and show that this fact could be used to provide bounds on the deformation parameters. Additionally, we show that the shift in the condensation temperature, described as a non-trivial function of the number of particles and the trap parameters, could be used as a criterion to analyze the effects caused by a deformed dispersion relation in weakly interacting systems and also in finite size systems.
Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential
NASA Astrophysics Data System (ADS)
Koura, Katsuhisa; Matsumoto, Hiroaki
1991-10-01
The variable soft sphere (VSS) molecular model is introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse-power-law (IPL) or Lennard-Jones (LJ) potential. The VSS model has almost the same analytical and computational simplicity (computation time) as the variable hard sphere (VHS) model in the Monte Carlo simulation of rarefied gas flows. The null-collision Monte Carlo method is used to make comparative calculations for the molecular diffusion in a heat-bath gas and the normal shock wave structure in a simple gas. For the most severe test of the VSS model for the IPL potential, the softest practical model corresponding to the Maxwell molecule is chosen. The agreement in the molecular diffusion and shock wave structure between the VSS model and the IPL or LJ potential is remarkably good.
Power law classification scheme of time series correlations. On the example of G20 group
NASA Astrophysics Data System (ADS)
Miśkiewicz, Janusz
2013-05-01
A power law classification scheme (PLCS) of time series correlations is proposed. It is shown that PLCS provides the ability to classify nonlinear correlations and measure their stability. PLCS has been applied to gross domestic product (GDP) per capita of G20 members and their correlations analysed. It has been shown that the method does not only recognise linear correlations properly, but also allows to point out converging time series as well as to distinguish nonlinear correlations. PLCS is capable of crash recognition as it is shown in the Argentina example. Finally the strength of correlations and the stability of correlation matrices have been used to construct a minimum spanning tree (MST). The results were compared with those based on the ultrametric distance (UD). Comparing the structures of MST, UD and PLCS indicates that the latter one is more complicated, but better fits the expected economic relations within the G20.
Power law of shear viscosity in Einstein-Maxwell-Dilaton-Axion model
NASA Astrophysics Data System (ADS)
Ling, Yi; Xian, Zhuoyu; Zhou, Zhenhua
2017-02-01
We construct charged black hole solutions with hyperscaling violation in the infrared (IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is verified numerically at low temperature T, namely, η/s ∼ T κ , where the values of exponent κ coincide with the analytical results. We also find that the exponent κ is not affected by irrelevant current, but is reduced by the relevant current. Supported by National Natural Science Foundation of China (11275208, 11575195), Opening Project of Shanghai Key Laboratory of High Temperature Superconductors (14DZ2260700) and Jiangxi Young Scientists (JingGang Star) Program and 555 Talent Project of Jiangxi Province
NASA Astrophysics Data System (ADS)
Bianucci, M.
2016-01-01
This letter has two main goals. The first one is to give a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the El Ninõ-Southern Oscillation (ENSO) phenomenon. The second one is to obtain, from the theory, an analytical expression for the equilibrium density function of the anomaly sea surface temperature, an expression that fits the data from observations well, reproducing the asymmetry and the power law tail of the histograms of the NIÑO3 index. We succeed in these tasks exploiting some recent theoretical results of the author in the field of the dynamical origin of the stochastic processes. More precisely, we apply this approach to the celebrated recharge oscillator model (ROM), weakly interacting by a multiplicative term, with a general deterministic complex forcing (Madden-Julian Oscillations, westerly wind burst, etc.), and we obtain a Fokker-Planck equation that describes the statistical behavior of the ROM.
Scalar field probes of power-law space-time singularities
NASA Astrophysics Data System (ADS)
Blau, Matthias; Frank, Denis; Weiss, Sebastian
2006-08-01
We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading inverse square behaviour ~ x-2 in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in [1] for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x-2-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.
NASA Astrophysics Data System (ADS)
Liu, Chao; Li, Rong
2016-09-01
An evolutionary prisoner's dilemma game (PDG) with players located on Barabási-Albert scale-free networks is studied. The impact of players' heterogeneous temporal activity pattern on the evolution of cooperation is investigated. To this end, the normal procedure that players update their strategies immediately after a round of game is discarded. Instead, players update strategies according to their assigned reproduction time, which follows a power-law distribution. We find that the temporal heterogeneity of players' activities facilitates the prosperity of cooperation, indicating the important role of hubs in the maintenance of cooperation on scale-free networks. When the reproduction time is assigned to individuals negatively related to their degrees, a fluctuation of the cooperation level with the increase of the exponent β is observed.
NASA Technical Reports Server (NTRS)
Howell, Leonard W.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The maximum likelihood procedure is developed for estimating the three spectral parameters of an assumed broken power law energy spectrum from simulated detector responses and their statistical properties investigated. The estimation procedure is then generalized for application to real cosmic-ray data. To illustrate the procedure and its utility, analytical methods were developed in conjunction with a Monte Carlo simulation to explore the combination of the expected cosmic-ray environment with a generic space-based detector and its planned life cycle, allowing us to explore various detector features and their subsequent influence on estimating the spectral parameters. This study permits instrument developers to make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope.
NASA Technical Reports Server (NTRS)
Choi, Sung R.; Gyekenyesi, John P.
2002-01-01
The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.
Slow synaptic dynamics in a network: From exponential to power-law forgetting
NASA Astrophysics Data System (ADS)
Luck, J. M.; Mehta, A.
2014-09-01
We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√t relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.
Collision-dependent power law scalings in two dimensional gyrokinetic turbulence
Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.
2014-08-15
Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.
Conductance statistics for the power-law banded random matrix model
Martinez-Mendoza, A. J.; Mendez-Bermudez, J. A.; Varga, Imre
2010-12-21
We study numerically the conductance statistics of the one-dimensional (1D) Anderson model with random long-range hoppings described by the Power-law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single-mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as w(lnT){proportional_to}T{sup M2/2}, for T<<
A comment on power-law inflation with a dark radiation component
NASA Astrophysics Data System (ADS)
Di Valentino, Eleonora; Bouchet, François R.
2016-10-01
Tram et al. 2016 recently pointed out in [1] that power-law inflation in presence of a dark radiation component may relieve the 3.3 σ tension which exists within standard ΛCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) [2] and the value derived from CMB anisotropy data [3] by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the σ8 tension between the Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from Planck HFI data [4] are included in the analysis, the H0 tension reappears and this scenario looses appeal.
Viscous-elastic dynamics of power-law fluids within an elastic cylinder
NASA Astrophysics Data System (ADS)
Gat, Amir; Boyko, Evgeniy; Bercovici, Moran
2016-11-01
We study the fluid-structure interaction dynamics of non-Newtonian flow through a slender linearly elastic cylinder at the creeping flow regime. Specifically, considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a non-homogeneous p-Laplacian equation governing the viscous-elastic dynamics. We obtain exact solutions for the pressure and deformation fields for various initial and boundary conditions, for both shear thinning and shear thickening fluids. In particular, impulse or a step in inlet pressure yield self-similar solutions, which exhibit a compactly supported propagation front solely for shear thinning fluids. Applying asymptotic expansions, we provide approximations for weakly non-Newtonian behavior showing good agreement with the exact solutions sufficiently far from the front.
Particle capture in axial magnetic filters with power law flow model
NASA Astrophysics Data System (ADS)
Abbasov, T.; Herdem, S.; Köksal, M.
1999-05-01
A theory of capture of magnetic particle carried by laminar flow of viscous non-Newtonian (power law) fluid in axially ordered filters is presented. The velocity profile of the fluid flow is determined by the Kuwabara-Happel cell model. For the trajectory of the particle, the capture area and the filter performance simple analytical expressions are obtained. These expressions are valid for particle capture processes from both Newtonian and non-Newtonian fluids. For this reason the obtained theoretical results make it possible to widen the application of high-gradient magnetic filtration (HGMF) to other industrial areas. For Newtonian fluids the theoretical results are shown to be in good agreement with the experimental ones reported in the literature.
Cohen, Joel E
2014-05-01
Taylor's power law of fluctuation scaling (TL) states that for population density, population abundance, biomass density, biomass abundance, cell mass, protein copy number, or any other nonnegative-valued random variable in which the mean and the variance are positive, variance=a(mean)(b),a>0, or equivalently log variance=loga+b×log mean. Many empirical examples and practical applications of TL are known, but understanding of TL's origins and interpretations remains incomplete. We show here that, as time becomes large, TL arises from multiplicative population growth in which successive random factors are chosen by a Markov chain. We give exact formulas for a and b in terms of the Markov transition matrix and the values of the successive multiplicative factors. In this model, the mean and variance asymptotically increase exponentially if and only if b>2 and asymptotically decrease exponentially if and only if b<2.
Origins of power-law degree distribution in the heterogeneity of human activity in social networks.
Muchnik, Lev; Pei, Sen; Parra, Lucas C; Reis, Saulo D S; Andrade, José S; Havlin, Shlomo; Makse, Hernán A
2013-01-01
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.
Mass transport in a thin layer of power-law mud under surface waves
NASA Astrophysics Data System (ADS)
Liu, Jie; Bai, Yuchuan; Xu, Dong
2017-02-01
The mass transport velocity in a two-layer system is studied theoretically. The wave motion is driven by a periodic pressure load on the free water surface, and mud in the lower layer is described by a power-law rheological model. Perturbation analysis is performed to the second order to find the mean Eulerian velocity. A numerical iteration method is employed to solve the non-linear governing equation at the leading order. The influence of rheological properties on fluid motion characteristics including the flow field, the surface displacement, the mass transport velocity, and the net discharge rates are investigated based on theoretical results. Theoretical analysis shows that under the action of interfacial shearing, a recirculation structure may appear near the interface in the upper water layer. A higher mass transport velocity at the interface does not necessarily mean a higher discharge rate for a pseudo-plastic fluid mud.
Architectures engender crises: The emergence of power laws in social networks
NASA Astrophysics Data System (ADS)
Tohmé, Fernando; Larrosa, Juan M. C.
2016-05-01
Recent financial crises posed a number of questions. The most salient were related to the cogency of derivatives and other sophisticated hedging instruments. One claim is that all those instruments rely heavily on the assumption that events in the world are guided by normal distributions while, instead, all the evidence shows that they actually follow fat-tailed power laws. Our conjecture is that it is the very financial architecture that engenders extreme events. Not on purpose but just because of its complexity. That is, the system has an internal connection structure that is able to propagate and enhance initially small disturbances. The final outcome ends up not being correlated with its triggering event. To support this claim, we appeal to the intuition drawn from the behavior of social networks. Most of the interesting cases constitute scale-free structures. In particular, we contend, those that arise from strategic decisions of the agents.
Vertical-channel free convection with a power-law fluid
Irvine, T.F. Jr.; Wu, K.C.; Schneider, W.J.
1982-01-01
A finite-difference solution is presented of the velocity and temperature fields for the flow of an Ostwald-de-Waele (power law) fluid between two vertical isothermal parallel plates under the influence of free convection. Two quantities are of particular interest: the total heat transferred from the plates and the average velocity between the plates. Although these quantities can be presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers, there is an important difference compared to the similar problem involving Newtonian fluids. In the present case, the generalized Prandtl number is not a fluid property but contains a geometric factor and thus the geometry of the system must be specified before the Prandtl number is fixed. The results and the manner in which they can be used are illustrated by a numerical example.
Efficiency and its bounds for thermal engines at maximum power using Newton's law of cooling
NASA Astrophysics Data System (ADS)
Yan, H.; Guo, Hao
2012-01-01
We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case, this model can simulate Otto, Joule-Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as that from Esposito [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.150603 105, 150603 (2010)] are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines.
Chaube, M. K.; Tripathi, D.; Bég, O. Anwar; Sharma, Shashi; Pandey, V. S.
2015-01-01
A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth. PMID:27057132
Efficiency and its bounds for thermal engines at maximum power using Newton's law of cooling.
Yan, H; Guo, Hao
2012-01-01
We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case, this model can simulate Otto, Joule-Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as that from Esposito et al. [Phys. Rev. Lett. 105, 150603 (2010)] are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines.
NASA Technical Reports Server (NTRS)
Beltrametti, M.
1980-01-01
The analytic solutions for radiatively driven winds are given for the case in which the winds are driven by absorption of line and continuum radiation. The wind solutions are analytically estimated for different parameters of the central source and for different power law spectra. For flat spectra, three sonic points can exist; it is shown, however, that only one of these sonic points is physically realistic. Parameters of the central source are given which generate winds of further interest for explaining the narrow and broad absorption lines in quasars. For the quasar model presented here, winds which could give rise to the narrow absorption lines are generated by central sources with parameters which are not realistic for quasars.
Supernova blast waves in wind-blown bubbles, turbulent, and power-law ambient media
NASA Astrophysics Data System (ADS)
Haid, S.; Walch, S.; Naab, T.; Seifried, D.; Mackey, J.; Gatto, A.
2016-08-01
Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media (densities of 0.1 ≥ n0 [cm- 3] ≥ 100) with uniform (and with stellar wind blown bubbles), power-law, and turbulent (Mach numbers M from 1to100) density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with n(r) ˜ r-2 (for n(r) > nfloor) the amount of momentum injection is solely regulated by the background density nfloor and compares to nuni = nfloor. However, in turbulent ambient media with lognormal density distributions the momentum input can increase by a factor of 2 (compared to the homogeneous case) for high Mach numbers. The average momentum boost can be approximated as p_{turb}/{p_{{0}}} =23.07 (n_{{0,turb}}/1 cm^{-3})^{-0.12} + 0.82 (ln (1+b2{M}2))^{1.49}(n_{{0,turb}}/1 cm^{-3})^{-1.6}. The velocity distributions are broad as gas can be accelerated to high velocities in low-density channels. The model values agree with results from recent, computationally expensive, three-dimensional simulations of SN explosions in turbulent media.
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.
Theory and evidence for using the economy-of-scale law in power plant economics
Phung, D.L.
1987-05-01
This report compiles theory and evidence for the use of the economy-of-scale law in energy economics, particularly in the estimation of capital costs for coal-fired and nuclear power plants. The economy-of-scale law is widely used in its simplest form: cost is directly proportional to capacity raised to an exponent. An additive constant is an important component that is not generally taken into account. Also, the economy of scale is perforce valid only over a limited size range. The majority of engineering studies have estimated an economy of scale exponent of 0.7 to 0.9 for coal-fired plants and an exponent of 0.4 to 0.6 for nuclear plants in the capacity ranges of 400 to 1000 MWe. However, the majority of econometric analyses found little or no economy of scale for coal-fired plants and only a slight economy of scale for nuclear plants. This disparity is explained by the fact that economists have included regulatory and time-related costs in addition to the direct and indirect costs used by the engineers. Regulatory and time-related costs have become an increasingly larger portion of total costs during the last decade. In addition, these costs appeared to have either a very small economy of scale or to be increasing as the size of the power plant increased. We conclude that gains in economy of scale can only be made by reducing regulatory and time-related costs through design standardization and regulatory stability, in combination with more favorable economic conditions. 59 refs.
Beets, I A M; Rösler, F; Fiehler, K
2010-09-01
Few studies have reported direct effects of motor learning on visual perception, especially when using novel movements for the motor system. Atypical motor behaviors that violate movement constraints provide an excellent opportunity to study action-to-perception transfer. In our study, we passively trained blindfolded participants on movements violating the 2/3 power law. Before and after motor training, participants performed a visual discrimination task in which they decided whether two consecutive movements were same or different. For motor training, we randomly assigned the participants to two motor training groups or a control group. The motor training group experienced either a weak or a strong elliptic velocity profile on a circular trajectory that matched one of the visual test stimuli. The control group was presented with linear trajectories unrelated to the viewed movements. After each training session, participants actively reproduced the movement to assess motor learning. The group trained on the strong elliptic velocity profile reproduced movements with increasing elliptic velocity profiles while circular geometry remained constant. Furthermore, both training groups improved in visual discrimination ability for the learned movement as well as for highly similar movements. Participants in the control group, however, did not show any improvements in the visual discrimination task nor did participants who did not acquire the trained movement. The present results provide evidence for a transfer from action to perception which generalizes to highly related movements and depends on the success of motor learning. Moreover, under specific conditions, it seems to be possible to acquire movements deviating from the 2/3 power law.
Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-01-01
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5–1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities. PMID:22355125
Undersampling power-law size distributions: effect on the assessment of extreme natural hazards
Geist, Eric L.; Parsons, Thomas E.
2014-01-01
The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and by attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historic data.
From the Cover: Musical rhythm spectra from Bach to Joplin obey a 1/f power law
NASA Astrophysics Data System (ADS)
Levitin, Daniel J.; Chordia, Parag; Menon, Vinod
2012-03-01
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5-1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.
A growth model for directed complex networks with power-law shape in the out-degree distribution
Esquivel-Gómez, J.; Stevens-Navarro, E.; Pineda-Rico, U.; Acosta-Elias, J.
2015-01-01
Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1. PMID:25567141
Prasad, N.E.; Malakondaiah, G.; Kutumbarao, V.V.
1997-09-01
Aluminium-lithium alloys, like many other aerospace structural alloys, exhibit bilinearity in power-law relationships between high strain, low cycle fatigue life (in terms of number of reversals to failure, 2N{sub f}) and plastic strain amplitude ({Delta}{epsilon}{sub p}/2) or average stress amplitude ({Delta}{sigma}/2) or average plastic strain energy per cycle ({Delta}W{sub p}). In the present paper the micromechanisms leading to bilinear fatigue power-law relationships, especially the Coffin-Manson (C-M) relationship, in aluminium-lithium alloys are compiled and discussed.
NASA Astrophysics Data System (ADS)
Zhou, Yanjun; Yin, Cangtao
2016-12-01
The Fokker-Planck equation (FPE) of the unimolecular reaction with Tsallis distribution is established by means of approximation to the master equation. The memory effect, taken into transition probability, is relevant and important for lots of anomalous phenomena. The Taylor expansion for large volume is applied to derive the power-law FPE. The steady-state solution of FPE and microscopic dynamics Ito-Langevin equation of concentration variables are therefore obtained and discussed. Two unimolecular reactions are taken as examples and the concentration distributions with different power-law parameters are analyzed, which may imply strong memory effect of hopping process.
A simple marriage model for the power-law behaviour in the frequency distributions of family names
NASA Astrophysics Data System (ADS)
Wu, Hao-Yun; Chou, Chung-I.; Tseng, Jie-Jun
2011-01-01
In many countries, the frequency distributions of family names are found to decay as a power law with an exponent ranging from 1.0 to 2.2. In this work, we propose a simple marriage model which can reproduce this power-law behaviour. Our model, based on the evolution of families, consists of the growth of big families and the formation of new families. Preliminary results from the model show that the name distributions are in good agreement with empirical data from Taiwan and Norway.
Viet, Dao Xuan; Kawamura, Hikaru
2010-08-27
We study the issue of the spin-chirality decoupling or coupling in the ordering of the Heisenberg spin glass by performing large-scale Monte Carlo simulations on a one-dimensional Heisenberg spin-glass model with a long-range power-law interaction up to large system sizes. We find that the spin-chirality decoupling occurs for an intermediate range of the power-law exponent. Implications to the corresponding d-dimensional short-range model are discussed.
Wave-speed dispersion associated with an attenuation obeying a frequency power law.
Buckingham, Michael J
2015-11-01
An attenuation scaling as a power of frequency, |ω|(β), over an infinite bandwidth is neither analytic nor square-integrable, thus calling into question the application of the Kramers-Krönig dispersion relations for determining the frequency dependence of the associated phase speed. In this paper, three different approaches are developed, all of which return the dispersion formula for the wavenumber, K(ω). The first analysis relies on the properties of generalized functions and the causality requirement that the impulse response, k(t), the inverse Fourier transform of -iK(ω), must vanish for t < 0. Second, a wave equation is introduced that yields the phase-speed dispersion associated with a frequency-power-law attenuation. Finally, it is shown that, with minor modification, the Kramers-Krönig dispersion relations with no subtractions (the Plemelj formulas) do in fact hold for an attenuation scaling as |ω|(β), yielding the same dispersion formula as the other two derivations. From this dispersion formula, admissible values of the exponent β are established. Physically, the inadmissible values of β, which include all the integers, correspond to attenuation-dispersion pairs whose Fourier components cannot combine in such a way as to make the impulse response, k(t), vanish for t < 0. There is no upper or lower limit on the value that β may take.
A Recommended Procedure for Estimating the Cosmic Ray Spectral Parameter of a Simple Power Law
NASA Technical Reports Server (NTRS)
Howell, Leonard W.; Rose, M. Franklin (Technical Monitor)
2000-01-01
A simple power law model consisting of a single spectral index a(f(sub i)) is believed to be an adequate description of the galactic cosmic ray (GQ proton flux at energies below 1013 eV. Two procedures for estimating a(f(sub i)), referred as (1) the method of moments, and (2) maximum likelihood, are developed and their statistical performance compared. I concluded that the maximum likelihood procedure attains the most desirable statistical properties and is hence the recommended statistic estimation procedure for estimating a1. The maximum likelihood procedure is then generalized for application to a set of real cosmic ray data and thereby makes this approach applicable to existing cosmic ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution, as well as inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic ray detector because they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose practical limits to the design envelope.
Highly optimized tolerance and power laws in dense and sparse resource regimes.
Manning, M; Carlson, J M; Doyle, J
2005-07-01
Power law cumulative frequency (P) versus event size (l) distributions P > or =l) approximately l(-alpha) are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete highly optimized tolerance (HOT) model, referred to as the probability, loss, resource (PLR) model, gives the exponent alpha=1/d as a function of the dimension d of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts alpha=1+1/d . In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.
Inertial migration of elastic particles in a pressure-driven power-law fluid
NASA Astrophysics Data System (ADS)
Bowie, Samuel; Alexeev, Alexander
2016-11-01
Using three-dimensional computer simulations, we study the cross-stream migration of deformable particles in a channel filled with a non-Newtonian fluid driven by a pressure gradient. Our numerical approach integrates lattice Boltzmann method and lattice spring method in order to model fluid structural interactions of the elastic particle and the surrounding power fluid in the channel. The particles are modeled as elastic shells filled with a viscous fluid that are initially spherical. We focus on the regimes where the inertial effects cannot be neglected and cause cross-stream drift of particles. We probe the flow with different power law indexes including both the shear thickening and thinning fluids. We also examine migration of particles of with different elasticity and relative size. To isolate the non-Newtonian effects on particle migration, we compare the results with the inertial migration results found in the case where the channel is filled with a simple Newtonian fluid. The results can be useful for applications requiring high throughput separation, sorting, and focusing of both synthetic particles and biological cells in microfluidic devices. Financial support provided by National Science Foundation (NSF) Grant No. CMMI1538161.
NASA Astrophysics Data System (ADS)
Kumar, S. S.; Roy, D. P.; Boschetti, L.; Kremens, R.
2011-10-01
Instantaneous estimates of the power released by fire (fire radiative power, FRP) are available with satellite active fire detection products. The temporal integral of FRP provides an estimate of the fire radiative energy (FRE) that is related linearly to the amount of biomass burned needed by the atmospheric emissions modeling community. The FRE, however, is sensitive to satellite temporal and spatial FRP undersampling due to infrequent satellite overpasses, cloud and smoke obscuration, and failure to detect cool and/or small fires. Satellite FRPs derived over individual burned areas and fires have been observed to exhibit power law distributions. This property is exploited to develop a new way to derive FRE, as the product of the fire duration and the expected FRP value derived from the FRP power law probability distribution function. The method is demonstrated and validated by the use of FRP data measured with a dual-band radiometer over prescribed fires in the United States and by the use of FRP data retrieved from moderate resolution imaging spectroradiometer (MODIS) active-fire detections over Brazilian deforestation and Australian savanna fires. The biomass burned derived using the conventional FRP temporal integration and power law FRE estimation methods is compared with biomass burned measurements (prescribed fires) and available fuel load information reported in the literature (Australian and Brazilian fires). The results indicate that the FRE power law derivation method may provide more reliable burned biomass estimates under sparse satellite FRP sampling conditions and correct for satellite active-fire detection omission errors if the FRP power law distribution parameters and the fire duration are known.
Papadopoulos, Anthony
2009-01-01
The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined. PMID:19333397
Debnath, P. K.; Chakrabarti, Barnali
2010-10-15
We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett. 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of (1-(A/A{sub cr})), A is the number of condensate atoms and A{sub cr} is the critical number near collapse. We observe that the power-law exponent becomes (1/6) in our calculation for the pure harmonic trap and it becomes (1/7), for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.
NASA Astrophysics Data System (ADS)
Debnath, P. K.; Chakrabarti, Barnali
2010-10-01
We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.80.1576 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of (1-(A)/(Acr)), A is the number of condensate atoms and Acr is the critical number near collapse. We observe that the power-law exponent becomes (1)/(6) in our calculation for the pure harmonic trap and it becomes (1)/(7), for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.
Rojas, Clara; Villalba, Victor M.
2007-03-15
The phase-integral approximation devised by Froeman and Froeman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform-approximation methods.
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.
Numakura, T.; Cho, T.; Kohagura, J.; Hirata, M.; Fukai, T.; Yoshida, M.; Minami, R.; Kiminami, S.; Sakamoto, K.; Imai, T.; Miyoshi, S.
2005-01-15
Scaling laws of potential formation and associated effects are theoretically and experimentally investigated in the GAMMA 10 tandem mirror. In GAMMA 10, the main tandem-mirror operations from 1979 to 2003 are characterized in terms of (i) a high-potential mode having kV-order plasma-confining potentials, and (ii) a hot-ion mode yielding fusion neutrons with 10-20 keV bulk-ion temperatures. In this paper, the externally controllable parameter scaling including electron cyclotron heating (ECH) powers for potential formation covering over these two representative operational modes is investigated; that is, the construction of 'the central-cell plasma-confining potentials' {phi}{sub c} formation scaling with plug ECH is studied on the basis of the electron energy-balance equation and Cohen's strong electron cyclotron heating (ECH) theory for investigating the formation physics of plasma confining potentials.It is found that our proposed scaling formulae are in good agreement with the experimental data in the two representative operational modes of the high-potential and hot-ion modes in the GAMMA 10 tandem mirror.This scaling shows a favorable increase in confining potentials with installing more powerful ECH sources by the use of ECH powers over the present 250 kW. On the basis of the scaling prediction, we also report the design of a newly developed 500 kW gyrotron for an application to investigate the validity of the above described {phi}{sub c} formation scaling with plug ECH aiming at achieving higher plasma parameters.
Thermodynamics of topological black holes in Brans-Dicke gravity with a power-law Maxwell field
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Dehghani, M. H.; Sheykhi, A.
2015-11-01
In this paper, we present a new class of higher-dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon.
Propagation of Gravity Currents of non-Newtonian Power-Law Fluids in Porous Media
NASA Astrophysics Data System (ADS)
Di Federico, V.; Longo, S.; Ciriello, V.; Chiapponi, L.
2014-12-01
A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by k; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, α; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters ω and β. Scalings for current length and thickness are derived in self similar form coupling the modified Darcy's law accounting for the fluid rheology with the mass balance equation. The length, thickness, and aspect ratio of the current are studied as functions of model parameters; several different critical values of α emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times.
NASA Astrophysics Data System (ADS)
Umansky, Moti; Weihs, Daphne
2012-08-01
In many physical and biophysical studies, single-particle tracking is utilized to reveal interactions, diffusion coefficients, active modes of driving motion, dynamic local structure, micromechanics, and microrheology. The basic analysis applied to those data is to determine the time-dependent mean-square displacement (MSD) of particle trajectories and perform time- and ensemble-averaging of similar motions. The motion of particles typically exhibits time-dependent power-law scaling, and only trajectories with qualitatively and quantitatively comparable MSD should be ensembled. Ensemble averaging trajectories that arise from different mechanisms, e.g., actively driven and diffusive, is incorrect and can result inaccurate correlations between structure, mechanics, and activity. We have developed an algorithm to automatically and accurately determine power-law scaling of experimentally measured single-particle MSD. Trajectories can then categorized and grouped according to user defined cutoffs of time, amplitudes, scaling exponent values, or combinations. Power-law fits are then provided for each trajectory alongside categorized groups of trajectories, histograms of power laws, and the ensemble-averaged MSD of each group. The codes are designed to be easily incorporated into existing user codes. We expect that this algorithm and program will be invaluable to anyone performing single-particle tracking, be it in physical or biophysical systems. Catalogue identifier: AEMD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 25 892 No. of bytes in distributed program, including test data, etc.: 5 572 780 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.11 (2010b) or higher, program
NASA Astrophysics Data System (ADS)
Jin, Fan; Guo, Xu; Gao, Huajian
2013-12-01
A cohesive zone model of axisymmetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the double-Hertz model of Greenwood and Johnson (1998). Closed-form solutions are obtained analytically for the surface stress, deformation fields and equilibrium relations among applied load, indentation depth, inner and outer radii of the cohesive zone, which include the corresponding solutions for homogeneous isotropic materials and the Gibson solid as special cases. These solutions provide a continuous transition between JKR and DMT type contact models through a generalized Tabor parameter μ. Our analysis reveals that the magnitude of the pull-off force ranges from (3+k)πRΔγ/2 to 2πRΔγ, where k, R and Δγ denote the gradient exponent of the elastic modulus for the half-space, the radius of the sphere and the work of adhesion, respectively. Interestingly, the pull-off force for the Gibson solid is found to be identically equal to 2πRΔγ, independent of the corresponding Tabor parameter. The obtained analytical solutions are validated with finite element simulations.
NASA Astrophysics Data System (ADS)
Burkhart, Blakesley; Stalpes, Kye; Collins, David C.
2017-01-01
We derive an analytic expression for the transitional column density value ({η }t) between the lognormal and power-law form of the probability distribution function (PDF) in star-forming molecular clouds. Our expression for {η }t depends on the mean column density, the variance of the lognormal portion of the PDF, and the slope of the power-law portion of the PDF. We show that {η }t can be related to physical quantities such as the sonic Mach number of the flow and the power-law index for a self-gravitating isothermal sphere. This implies that the transition point between the lognormal and power-law density/column density PDF represents the critical density where turbulent and thermal pressure balance, the so-called “post-shock density.” We test our analytic prediction for the transition column density using dust PDF observations reported in the literature, as well as numerical MHD simulations of self-gravitating supersonic turbulence with the Enzo code. We find excellent agreement between the analytic {η }t and the measured values from the numerical simulations and observations (to within 1.2 AV). We discuss the utility of our expression for determining the properties of the PDF from unresolved low-density material in dust observations, for estimating the post-shock density, and for determining the H i–H2 transition in clouds.
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.
Houel, Julien; Doan, Quang T; Cajgfinger, Thomas; Ledoux, Gilles; Amans, David; Aubret, Antoine; Dominjon, Agnès; Ferriol, Sylvain; Barbier, Rémi; Nasilowski, Michel; Lhuillier, Emmanuel; Dubertret, Benoît; Dujardin, Christophe; Kulzer, Florian
2015-01-27
We present an unbiased and robust analysis method for power-law blinking statistics in the photoluminescence of single nanoemitters, allowing us to extract both the bright- and dark-state power-law exponents from the emitters' intensity autocorrelation functions. As opposed to the widely used threshold method, our technique therefore does not require discriminating the emission levels of bright and dark states in the experimental intensity timetraces. We rely on the simultaneous recording of 450 emission timetraces of single CdSe/CdS core/shell quantum dots at a frame rate of 250 Hz with single photon sensitivity. Under these conditions, our approach can determine ON and OFF power-law exponents with a precision of 3% from a comparison to numerical simulations, even for shot-noise-dominated emission signals with an average intensity below 1 photon per frame and per quantum dot. These capabilities pave the way for the unbiased, threshold-free determination of blinking power-law exponents at the microsecond time scale.
Bernard, J.A. . Nuclear Reactor Lab.)
1989-09-01
This report describes both the theoretical development and the experimental evaluation of a novel, robust methodology for the time-optimal adjustment of a reactor's neutronic power under conditions of closed-loop digital control. Central to the approach are the MIT-SNL Period-Generated Minimum Time Control Laws' which determine the rate at which reactivity should be changed in order to cause a reactor's neutronic power to conform to a specified trajectory. Using these laws, reactor power can be safely raised by five to seven orders of magnitude in a few seconds. The MIT-SNL laws were developed to facilitate rapid increases of neutronic power on spacecraft reactors operating in an SDI environment. However, these laws are generic and have other applications including the rapid recovery of research and test reactors subsequent to an unanticipated shutdown, power increases following the achievement of criticality on commercial reactors, power adjustments on commercial reactors so as to minimize thermal stress, and automated startups. The work reported here was performed by the Massachusetts Institute of Technology under contract to the Sandia National Laboratories. Support was also provided by the US Department of Energy's Division of University and Industry Programs. The work described in this report is significant in that a novel solution to the problem of time-optimal control of neutronic power was identified, in that a rigorous description of a reactor's dynamics was derived in that the rate of change of reactivity was recognized as the proper control signal, and in that extensive experimental trials were conducted of these newly developed concepts on actual nuclear reactors. 43 refs., 118 figs., 11 tabs.
Emergence of power-law scalings in shock-driven mixing transition
NASA Astrophysics Data System (ADS)
Vorobieff, Peter; Wayne, Patrick; Olmstead, Dell; Simons, Dylan; Truman, C. Randall; Kumar, Sanjay
2016-11-01
We present an experimental study of transition to turbulence due to shock-driven instability evolving on an initially cylindrical, diffuse density interface between air and a mixture of sulfur hexafluoride (SF6) and acetone. The plane of the shock is at an initial angle θ with the axis of the heavy-gas cylinder. We present the cases of planar normal (θ = 0) and oblique (θ =20°) shock interaction with the initial conditions. Flow is visualized in two perpendicular planes with planar laser-induced fluorescence (PLIF) triggered in acetone with a pulsed ultraviolet laser. Statistics of the flow are characterized in terms of the second-order structure function of the PLIF intensity. As instabilities in the flow evolve, the structure functions begin to develop power-law scalings, at late times manifesting over a range of scales spanning more than two orders of magnitude. We discuss the effects of the initial conditions on the emergence of these scalings, comparing the fully three-dimensional case (oblique shock interaction) with the quasi-two-dimensional case (planar normal shock interaction). We also discuss the flow anisotropy apparent in statistical differences in data from the two visualization planes. This work is funded by NNSA Grant DE-NA0002913.
Temperature fluctuation in Rayleigh-Bénard convection: Logarithmic vs power-law
NASA Astrophysics Data System (ADS)
He, Yu-Hao; Xia, Ke-Qing
2016-11-01
We present an experimental measurement of the rms temperature (σT) profile in two regions inside a large aspect ratio (Γ = 4 . 2) rectangular Rayleigh-Bénard convection cell. The Rayleigh number (Ra) is from 3 . 2 ×107 to 1 . 9 ×108 at fixed Prandtl number (Pr = 4 . 34). It is found that, in one region, where the boundary layer is sheared by a large-scale wind, σT versus the distance (z) above the bottom plate, obeys power law over one decade, whereas in another region, where plumes concentrate and move upward (plume-ejection region), the profile of σT has a logarithmic dependence on z. When normalized by a typical temperature scale θ*, the profiles of σT at different Rayleigh numbers collapse onto a single curve, indicating a university of σT profile with respect to Ra . This work is supported by the Hong Kong Research Grant Council under Grant Number N_CUHK437/15.
Power-law scaling and fractal nature of medium-range order in metallic glasses.
Ma, D; Stoica, A D; Wang, X-L
2009-01-01
The atomic structure of metallic glasses has been a long-standing scientific problem. Unlike crystalline metals, where long-range ordering is established by periodic stacking of fundamental building blocks known as unit cells, a metallic glass has no long-range translational or orientational order, although some degrees of short- and medium-range order do exist. Previous studies have identified solute- (minority atom)-centred clusters as the fundamental building blocks or short-range order in metallic glasses. Idealized cluster packing schemes, such as efficient cluster packing on a cubic lattice and icosahedral packing as in a quasicrystal, have been proposed and provided first insights on the medium-range order in metallic glasses. However, these packing schemes break down beyond a length scale of a few clusters. Here, on the basis of neutron and X-ray diffraction experiments, we propose a new packing scheme-self-similar packing of atomic clusters. We show that the medium-range order has the characteristics of a fractal network with a dimension of 2.31, and is described by a power-law correlation function over the medium-range length scale. Our finding provides a new perspective of order in disordered materials and has broad implications for understanding their structure-property relationship, particularly those involving a change in length scales.
Observation of a power-law energy distribution in atom-ion hybrid system
NASA Astrophysics Data System (ADS)
Meir, Ziv; Akerman, Nitzan; Sikorsky, Tomas; Ben-Shlomi, Ruti; Dallal, Yehonatan; Ozeri, Roee
2016-05-01
Understanding atom-ion collision dynamics is at the heart of the growing field of ultra-cold atom-ion physics. The naive picture of a hot ion sympathetically-cooled by a cold atomic bath doesn't hold due to the time dependent potentials generated by the ion Paul trap. The energy scale of the atom-ion system is determined by a combination of the atomic bath temperature, the ion's excess micromotion (EMM) and the back action of the atom-ion attraction on the ion's position in the trap. However, it is the position dependent ion's inherent micromotion which acts as an amplifier for the ion's energy during random consecutive collisions. Due to this reason, the ion's energy distribution deviates from Maxwell-Boltzmann (MB) characterized by an exponential tail to one with power-law tail described by Tsallis q-exponential function. Here we report on the observation of a strong deviation from MB to Tsallis energy distribution of a trapped ion. In our experiment, a ground-state cooled 88 Sr+ ion is immersed in an ultra-cold cloud of 87 Rb atoms. The energy scale is determined by either EMM or solely due to the back action on the ion position during a collision with an atom in the trap. Energy distributions are obtained using narrow optical clock spectroscopy.
Power-law photoconductivity time decay in nanocrystalline TiO2 thin films
NASA Astrophysics Data System (ADS)
Comedi, D.; Heluani, S. P.; Villafuerte, M.; Arce, R. D.; Koropecki, R. R.
2007-12-01
The sub-band-gap excited photoconductivity (PC) time decay and the film structure of rf-sputter deposited nanocrystalline TiO2 thin films have been studied. Atomic force microscopy and x-ray diffraction measurements were used to assess roughness, crystalline structure and mean grain size of the films. Samples fabricated under different deposition conditions exhibit different microstructures and absolute PC, but similar persistent PC behaviour after switching off the light source. The very slow PC decay can be well represented by a function that is nearly constant for short times and decreases as a power law for times longer than about 100 s. This function is shown to be consistent with a rate equation characterized by a relaxation time that increases linearly with time. This behaviour, in turn, agrees with predictions of a previously reported model that assumes electron-hole recombination limited by carrier-density-dependent potential barriers associated with inhomogeneities. These results may have important implications on attempts to determine distributions of trap energies from PC decay curves in TiO2.
Contracting bubbles in Hele-Shaw cells with a power-law fluid
NASA Astrophysics Data System (ADS)
McCue, Scott W.; King, John R.
2011-02-01
The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalize the ellipses that characterize the Newtonian case being constructed by the Wiener-Hopf calculation.
Analysis of log-periodic power law singularity patterns in time series related to credit risk
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Sornette, Didier
2015-04-01
The log-periodic (super-exponential) power law singularity (LPPLS) has become a promising tool for predicting extreme behavior of self-organizing systems in natural sciences and finance. Some researchers have recently proposed to employ the LPPLS on credit risk markets. The review article at hand summarizes four papers in this field and shows how they are linked. After structuring the research questions, we collect the corresponding answers from the four articles. This eventually gives us an overall picture of the application of the LPPLS to credit risk data. Our literature review begins with grounding the view that credit default swap (CDS) spreads are hotbeds for LPPLS patterns and it ends up with drawing attention to the recently proposed alarm index for the prediction of institutional bank runs. By presenting a new field of application for the LPPLS, the reviewed strand of literature further substantiates the LPPLS hypothesis. Moreover, the results suggest that CDS spread trajectories belong to a different universality class than, for instance, stock prices.
Developing flow of a power-law liquid film on an inclined plane
NASA Astrophysics Data System (ADS)
Weinstein, Steven J.; Ruschak, Kenneth J.; Ng, Kam C.
2003-10-01
Developing flow of a liquid film along a stationary inclined wall is analyzed for a power-law constitutive equation. For films with appreciable inertia and therefore small interfacial slopes, the boundary-layer approximation may be used. The boundary-layer equations are solved numerically through the von Mises transformation that gives a partial differential equation over a semi-infinite strip and approximately by the method of von Kármán and Polhausen that gives an ordinary differential equation for the film thickness, called a film equation. Film equations derived from self-similar velocity profiles fail when the film thickens and the flow undergoes a supercritical to subcritical transition; a nonremovable singularity arises at the critical point, the location of the flow transition. A film equation is developed that accommodates this transition. Predictions exhibit a standing wave where hydrostatic pressure becomes important and opposes inertia. This thickening effect is accentuated for small angles of inclination at moderate Reynolds numbers. In the limit of small film thickness in which gravitational effects are negligible, the thickness profile is nonlinear in agreement with an independent and new similarity solution. This result contrasts with the established linear thickness profile for a Newtonian liquid. The circumstances in which the film equation gives results close to the full boundary layer equation are identified.
The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer
NASA Astrophysics Data System (ADS)
Castillo, Luciano; Hussain, Fazle
2017-02-01
Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ' + and the Reynolds shear stress, u'v'¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50 ≤y+≤170 ). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u' 2 ¯+ and v'θ'¯+ change little with the strength of acceleration, while v'+, w'+, and u'v'¯+ continue to decay in the flow direction. Furthermore, θ'+ and u'θ'¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for "transient growth" generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, "Coherent structure generation near-wall turbulence," J. Fluid Mech. 453, 57-108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.
Power Law Regression Analysis of Heat Flux Width in Type I ELMs
NASA Astrophysics Data System (ADS)
Stephens, C. D.; Makowski, M. A.; Leonard, A. W.; Osborne, T. H.
2014-10-01
In this project, a database of Type I ELM characteristics has been assembled and will be used to investigate possible dependencies of the heat flux width on physics and engineering parameters. At the edge near the divertor, high impulsive heat loads are imparted onto the surface. The impact of these ELMs can cause a reduction in divertor lifetime if the heat flux is great enough due to material erosion. A program will be used to analyze data, extract relevant, measurable quantities, and record the quantities in the table. Care is taken to accurately capture the complex space/time structure of the ELM. Then correlations between discharge and equilibrium parameters will be investigated. Power law regression analysis will be used to help determine the dependence of the heat flux width on these various measurable quantities and parameters. This will enable us to better understand the physics of heat flux at the edge. Work supported in part by the National Undergraduate Fellowship Program in Plasma Physics and Fusion Energy Sciences and the US DOE under DE-FG02-04ER54761, DE-AC52-07NA27344, DE-FC02-04ER54698.
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
Exact, E = 0, classical and quantum solutions for general power-law oscillators
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Daboul, Jamil
1995-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
The flow of power law fluids in elastic networks and porous media.
Sochi, Taha
2016-02-01
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
Cupid is Still Doomed: Overlapping Power Laws and the Stability of the Inner Uranian Satellites
NASA Astrophysics Data System (ADS)
French, Robert S.; Showalter, M. R.
2012-05-01
We have continued our exploration of the stability of the inner Uranian satellites (French & Showalter 2011, DDA abstract) using simulations based on recent observational data. We find that the moon subsets Cressida/Desdemona/Juliet and Cupid/Belinda/Perdita are unstable in isolation, crossing orbits in 106-107 years. The presence of the other inner moons reduces this time to 104-106 years. The stability of the inner moons is not changed by the presence of the five classical satellites but Perdita, a very small moon, has a surprisingly large effect on the stability of Cupid and Belinda. We extend the power law previously discovered by Duncan & Lissauer (1997, Icarus, 125, 1-12), in which the crossing time of a pair of moons can be predicted using multiple simulations with higher moon masses, to the case of two unstable moon pairs. We use this new formalism to predict the lifetimes of Cupid/Belinda and Cressida/Desdemona using a conservative density assumption, ρ=0.5 g/cm3. The inner satellites continue to exhibit instability with crossing times of 105-107 years in this case. Such short crossing times imply the continuing, rapid evolution of the Uranian satellites.
NASA Astrophysics Data System (ADS)
Wosnitza, Jan Henrik; Denz, Cornelia
2013-09-01
We employ the log-periodic power law (LPPL) to analyze the late-2000 financial crisis from the perspective of critical phenomena. The main purpose of this study is to examine whether LPPL structures in the development of credit default swap (CDS) spreads can be used for default classification. Based on the different triggers of Bear Stearns’ near bankruptcy during the late-2000 financial crisis and Ford’s insolvency in 2009, this study provides a quantitative description of the mechanism behind bank runs. We apply the Johansen-Ledoit-Sornette (JLS) positive feedback model to explain the rise of financial institutions’ CDS spreads during the global financial crisis 2007-2009. This investigation is based on CDS spreads of 40 major banks over the period from June 2007 to April 2009 which includes a significant CDS spread increase. The qualitative data analysis indicates that the CDS spread variations have followed LPPL patterns during the global financial crisis. Furthermore, the univariate classification performances of seven LPPL parameters as default indicators are measured by Mann-Whitney U tests. The present study supports the hypothesis that discrete scale-invariance governs the dynamics of financial markets and suggests the application of new and fast updateable default indicators to capture the buildup of long-range correlations between creditors.
Bond length estimates for oxide crystals with a molecular power law expression
NASA Astrophysics Data System (ADS)
Gibbs, G. V.; Ross, Nancy L.; Cox, David F.
2015-07-01
A molecular power law bond length regression expression, R(M-O) = 1.39( s/ r)-0.22, defined in terms of the quotient, s/ r, where s is the averaged Pauling bond strength for the bonded interaction comprising a given molecular coordination polyhedron and r is the periodic table row number for the M atom, serves to replicate the bulk of the 470 individual experimental M-O average bond lengths estimated with Shannon's (Acta Crystallogr A 32(5):751-767, 1976) crystal radii for oxides to within 0.10 Å. The success of the molecular expression is ascribed to a one-to-one deep-seated connection that obtains between the electron density accumulated between bonded pairs of atoms and the average Pauling bond strength. It also implies that the bonded interactions that constitute oxide crystals are governed in large part by local forces. Although the expression reproduces the bond lengths involving rare earth atoms typically to within ~0.05 Å, it does not reproduce the lanthanide ionic radius contraction. It also fails to reproduce the experimental bond lengths for selected transition cations like Cu1+, Ag1+ and VILSFe2+ and for cations like IVK+, VIBa2+ and IIU6+.
Interim Report on the Power Law Index of Interplanetary Suprathermal Ion Spectra
Hill, M. E.; Hamilton, D. C.
2010-12-30
There is a continuing debate about the applicability of the theory presented by Fisk and Gloeckler (FG) regarding the formation of suprathermal ion tails in phase space density vs. velocity spectra; in the solar wind frame the FG theory predicts a power law index of-5 (which is equivalent to a differential intensity vs. energy index of-1.5). There has also been uncertainty and perhaps misunderstanding regarding the extent to which such spectra are actually observed; i.e., is there really a significant preference for the -5 index? Here we report the results of an interim technique we use to analyze {approx}1-100 keV/nucleon interplanetary suprathermal H{sup +}, He{sup +}, and He{sup ++}, spectra measured at the Cassini spacecraft by the Charge Energy Mass Spectrometer (CHEMS) instrument of the Magnetospheric Imaging Instrument (MIMI) suite during the cruise to Saturn. We analyzed 18 active periods and report a mean index in the solar wind frame of 4.9{+-}0.4 for protons, 5.2{+-}0.5 for He{sup +}, and 4.7{+-}0.2 for alpha particles. MIMI/CHEMS offers much needed independent observations of heliospheric ions in the suprathermal energy range.
A unified econophysics explanation for the power-law exponents of stock market activity
NASA Astrophysics Data System (ADS)
Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, Eugene
2007-08-01
We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.
Wright, Christopher K
2010-07-01
Although habitat networks show promise for conservation planning at regional scales, their spatiotemporal dynamics have not been well studied, especially in climate-sensitive landscapes. Here I use satellite remote sensing to compile wetland habitat networks from the Prairie Pothole Region (PPR) of North America. An ensemble of networks assembled across a hydrologic gradient from deluge to drought and a range of representative dispersal distances exhibits power-law scaling of important topological parameters. Prairie wetland networks are "meso-worlds" with mean topological distance increasing faster with network size than small-world networks, but slower than a regular lattice (or "large world"). This scaling implies rapid dispersal through wetland networks without some of the risks associated with "small worlds" (e.g., extremely rapid propagation of disease or disturbance). Retrospective analysis of wetland networks establishes a climatic envelope for landscape connectivity in the PPR, where I show that a changing climate might severely impact metapopulation viability and restrict long-distance dispersal and range shifts. More generally, this study demonstrates an efficient approach to conservation planning at a level of abstraction addressing key drivers of the global biodiversity crisis: habitat fragmentation and climatic change.
Common origin of power-law tails in income distributions and relativistic gases
NASA Astrophysics Data System (ADS)
Modanese, G.
2016-01-01
Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms ("saving propensity") which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the macroscopic distribution for the income or respectively for the energy.
Success of a simulation approach for magnetic nanosystems: Power of physical laws
NASA Astrophysics Data System (ADS)
Liu, Z.-S.; Sechovský, V.; Diviš, M.
2014-05-01
The new quantum simulation model and the self-consistent algorithm (SCA) for magnetic nanosystems, that we proposed 2 years ago, were extended to study the magnetic properties of a nanowire consisting of 3d ions which are coupled ferromagnetically. To test the applicability of the algorithm, our simulations in the present work were started from a magnetic structure in which all spins in the whole nanosample were randomly oriented (defined as the random magnetic configuration for later use) as other authors have been doing with Monte Carlo or micromagnetism method, and such calculated results were all reasonable. Especially, the free energies evaluated at the chosen temperatures were found to attenuate spontaneously and quickly, as the program ran, towards the minima according to the principle of lowest free energy as expected. This suggests that the computational algorithm is able to lead the code to converge rapidly to the equilibrium state automatically without the need to minimize the total (free) energy of the system elaborately that must be done if the Monte Carlo or micromagnetism method is used, demonstrating the great power of natural laws.
Disorder-driven transition in a chain with power-law hopping
NASA Astrophysics Data System (ADS)
Gärttner, M.; Syzranov, S. V.; Rey, A. M.; Gurarie, V.; Radzihovsky, L.
2015-07-01
We study a one-dimensional (1D) system with a power-law quasiparticle dispersion ∝|k| αs g n k in the presence of a short-range-correlated random potential, and demonstrate that for α <1 /2 it exhibits a disorder-driven quantum phase transition with critical properties similar to those of the localization transition near the edge of the band of a semiconductor in high dimensions, as studied recently [Phys. Rev. Lett. 114, 166601 (2015), 10.1103/PhysRevLett.114.166601; Phys. Rev. B 91, 035133 (2015), 10.1103/PhysRevB.91.035133]. Despite the absence of localization in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of α . The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localization effects and has the potential for experimental realizations in chains of ultracold atoms in optical traps.
NASA Astrophysics Data System (ADS)
Ruiz, Michael J.
2006-02-01
The demonstration of Lenz's law by dropping a powerful magnet down a nonmagnetic metal pipe has become a classic lecture-hall demonstration.1,2 An inexpensive version is packaged as a professional magic trick3 called "Newton's Nightmare." Combining sleight-of-hand with a demonstration of Lenz's law is a surefire way to heighten student interest. The subsequent student discussion motivated by a desire to understand the magic trick can lead to a memorable physics lesson. This paper will discuss Lenz's law magic and review literature that reveals the subtlety of the physics.
Cioslowski, Jerzy; Albin, Joanna
2013-09-14
Energies E(N) of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials vary in a convoluted fashion with the particle totalities N. Accurate rigorous upper bounds to these energies, which are amenable to detailed mathematical analysis, are found to comprise terms with smooth, oscillatory, and fluctuating dependences on N. The smooth energy component is obtained as a power series in N(-2/3) with the first two terms corresponding to the bulk and Madelung energies. The oscillatory component possesses the large-N asymptotics given by a product of N(1/(λ + 1)), where λ is the power-law exponent, and a function periodic in N(1/3). The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy E(Th)(n) on n, also scales like N(1/(λ + 1)).
On the extent of size range and power law scaling for particles of natural carbonate fault cores
NASA Astrophysics Data System (ADS)
Billi, Andrea
2007-09-01
To determine the size range and both type and extent of the scaling laws for particles of loose natural carbonate fault rocks, six granular fault cores from Mesozoic carbonate strata of central Italy were sampled. Particle size distributions of twelve samples were determined by combining sieving and sedimentation methods. Results show that, regardless of the fault geometry, kinematics, and tectonic history, the size of fault rock particles respects a power law distribution across approximately four orders of magnitude. The fractal dimension ( D) of the particle size distribution in the analysed samples ranges between ˜2.0 and ˜3.5. A lower bound to the power law trend is evident in all samples except in those with the highest D-values; in these samples, the smallest analysed particles (˜0.0005 mm in diameter) were also included in the power law interval, meaning that the lower size limit of the power law distribution decreases for increasing D-values and that smallest particles start to be comminuted with increasing strain (i.e. increasing fault displacement and D-values). For increasing D-values, also the largest particles tends to decrease in number, but this evidence may be affected by a censoring bias connected with the sample size. Stick-slip behaviour is suggested for the studied faults on the basis of the inferred particle size evolutions. Although further analyses are necessary to make the results of this study more generalizable, the preliminary definition of the scaling rules for fault rock particles may serve as a tool for predicting a large scale of fault rock particles once a limited range is known. In particular, data from this study may result useful as input numbers in numerical models addressing the packing of fault rock particles for frictional and hydraulic purposes.
Power laws and self-organized criticality in theory and nature
NASA Astrophysics Data System (ADS)
Marković, Dimitrije; Gros, Claudius
2014-03-01
Power laws and distributions with heavy tails are common features of many complex systems. Examples are the distribution of earthquake magnitudes, solar flare intensities and the sizes of neuronal avalanches. Previously, researchers surmised that a single general concept may act as an underlying generative mechanism, with the theory of self organized criticality being a weighty contender. The power-law scaling observed in the primary statistical analysis is an important, but by far not the only feature characterizing experimental data. The scaling function, the distribution of energy fluctuations, the distribution of inter-event waiting times, and other higher order spatial and temporal correlations, have seen increased consideration over the last years. Leading to realization that basic models, like the original sandpile model, are often insufficient to adequately describe the complexity of real-world systems with power-law distribution. Consequently, a substantial amount of effort has gone into developing new and extended models and, hitherto, three classes of models have emerged. The first line of models is based on a separation between the time scales of an external drive and an internal dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of models is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of models proposes a non-critical self-organizing state, being guided by an optimization principle, such as the concept of highly optimized tolerance. We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real
Shalashilin, Dmitrii V; Beddard, Godfrey S; Paci, Emanuele; Glowacki, David R
2012-10-28
Molecular dynamics (MD) methods are increasingly widespread, but simulation of rare events in complex molecular systems remains a challenge. We recently introduced the boxed molecular dynamics (BXD) method, which accelerates rare events, and simultaneously provides both kinetic and thermodynamic information. We illustrate how the BXD method may be used to obtain high-resolution kinetic data from explicit MD simulations, spanning picoseconds to microseconds. The method is applied to investigate the loop formation dynamics and kinetics of cyclisation for a range of polypeptides, and recovers a power law dependence of the instantaneous rate coefficient over six orders of magnitude in time, in good agreement with experimental observations. Analysis of our BXD results shows that this power law behaviour arises when there is a broad and nearly uniform spectrum of reaction rate coefficients. For the systems investigated in this work, where the free energy surfaces have relatively small barriers, the kinetics is very sensitive to the initial conditions: strongly non-equilibrium conditions give rise to power law kinetics, while equilibrium initial conditions result in a rate coefficient with only a weak dependence on time. These results suggest that BXD may offer us a powerful and general algorithm for describing kinetics and thermodynamics in chemical and biochemical systems.
Parental Trigger Laws and the Power of Framing in Educational Politics
ERIC Educational Resources Information Center
Feuerstein, Abe
2015-01-01
This paper examines the discursive strategies employed by advocates of Parent Trigger laws in the United States which allow parents of children in "failing" schools, in some states, to call for interventions in the operation of the schools via petition. The paper reviews the genesis of Parent Trigger laws, the network of conservative…
PLNoise: a package for exact numerical simulation of power-law noises
NASA Astrophysics Data System (ADS)
Milotti, Edoardo
2006-08-01
Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1<β⩽1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v1_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B
The JKR-type adhesive contact problems for power-law shaped axisymmetric punches
NASA Astrophysics Data System (ADS)
Borodich, Feodor M.; Galanov, Boris A.; Suarez-Alvarez, Maria M.
2014-08-01
The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres, and between a flat-ended axisymmetric punch and an elastic half-space respectively. However, the shapes of contacting solids may be more general than spherical or flat ones. In addition, the derivation of the main formulae of these models is based on the assumption that the material points within the contact region can move along the punch surface without any friction. However, it is more natural to assume that a material point that came to contact with the punch sticks to its surface, i.e. to assume that the non-slipping boundary conditions are valid. It is shown that the frictionless JKR model may be generalized to arbitrary convex, blunt axisymmetric body, in particular to the case of the punch shape being described by monomial (power-law) punches of an arbitrary degree d≥1. The JKR and Boussinesq-Kendall models are particular cases of the problems for monomial punches, when the degree of the punch d is equal to two or it goes to infinity respectively. The generalized problems for monomial punches are studied under both frictionless and non-slipping (or no-slip) boundary conditions. It is shown that regardless of the boundary conditions, the solution to the problems is reduced to the same dimensionless relations among the actual force, displacements and contact radius. The explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. Connections of the results obtained for problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape and the shape function can be approximated by a monomial function of radius, are discussed.
Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.
Sardar, Tridip; Saha, Bapi
2017-03-06
In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R0). It is shown that if R0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic.
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
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions
NASA Astrophysics Data System (ADS)
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 γr-α . Such systems are useful in modeling melting transitions. The limit α→∞ corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (α>3) and repulsive (γ>0) interactions. The geometric theory solutions for given α>3 , γ>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b(ρT-3/α) , where ρ is the density; (2) all solutions are equivalent up to a single scaling constant for ρT-3/α , related to γ 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<α<3.7913 , the solution goes from the low to the expected high density limit smoothly; (6) for α>3.7913 a phase transition is required to go between these regimes; (7) for any α>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if α→∞ , the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.
NASA Astrophysics Data System (ADS)
Barlow, John; Rosser, Nick; Lime, Michael; Petley, David; Brain, Matthew; Sapsford, Melanie; Norman, Emma
2010-05-01
An increasing body of evidence suggests that rockfalls follow a negative power law scaling in their magnitude-frequency distribution of the form F = aM-b. Where F is the normalized frequency density, M is the event magnitude, and a / b are dimensionless scaling coefficients. Investigation using Terrestrial Laser Scanning (TLS) has produced an extremely high resolution inventory of rockfall magnitudes along the sea cliffs near Staithes, UK. Such data is ideal for erosion modelling. Once the scaling parameters have been estimated, the volume of eroded rock for events of magnitude x (Vx) is derived as Vx = ax-b+1. Therefore, the total volume (V t) of eroded rock between a minimum and maximum magnitude can be calculated by taking by integrating the above. An examination of monthly fluctuations in the scaling coefficients indicates greater variation within the winter months in response to higher deliveries of wave energy during these months. Initial results using geophone data indicate a relationship between the magnitude of the scaling coefficients and the amount of wave energy delivered to the cliff. Such linkages suggest the possibility of a predictive model for erosion based on wave climate, providing a predictive capability for the implications of environmental change. Model testing is to be accomplished using an innovative cliff recession model derived using cosmogenic isotope concentrations and paleoenvironmental data. Our cosmogenic dating model considers marine variables (tidal range, wave climate and inundation duration); Holocene relative sea level change; lateral cliff retreat, and the consequent changes in geometrical and marine shielding to establish the rate of retreat based on a continuum of Be10 concentrations.
Scocchia, Lisa; Bolognini, Nadia; Convento, Silvia; Stucchi, Natale
2015-11-16
Human movements conform to specific kinematic laws of motion. One of such laws, the "two-thirds power law", describes the systematic co-variation between curvature and velocity of body movements. Noticeably, the same law also influences the perception of moving stimuli: the velocity of a dot moving along a curvilinear trajectory is perceived as uniform when the dot kinematics complies with the two-thirds power law. Instead, if the dot moves at constant speed, its velocity is perceived as highly non-uniform. This dynamic visual illusion points to a strong coupling between action and perception; however, how this coupling is implemented in the brain remains elusive. In this study, we tested whether the premotor cortex (PM) and the primary visual cortex (V1) play a role in the illusion by means of transcranial Direct Current Stimulation (tDCS). All participants underwent three tDCS sessions during which they received active or sham cathodal tDCS (1.5mA) over PM or V1 of the left hemisphere. During tDCS, participants were required to adjust the velocity of a dot moving along an elliptical trajectory until it looked uniform across the whole trajectory. Results show that occipital tDCS decreases the illusion variability both within and across participants, as compared to sham tDCS. This means that V1 stimulation increases individual sensitivity to the illusory motion and also increases coherence across different observers. Conversely, the illusion seems resistant to tDCS in terms of its magnitude, with cathodal stimulation of V1 or PM not affecting the amount of the illusory effect. Our results provide evidence for strong visuo-motor coupling in visual perception: the velocity of a dot moving along an elliptical trajectory is perceived as uniform only when its kinematics closely complies to the same law of motion that constrains human movement production. Occipital stimulation by cathodal tDCS can stabilize such illusory percept.
Chen, W; Holm, S
2004-04-01
Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.
Brey, J Javier; Ruiz-Montero, M J
2015-01-01
The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power-law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power-law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored.
Freeman; Watkins; Riley
2000-12-01
We calculate the probability density functions P of burst energy e, duration T, and interburst interval tau for a known turbulent system in nature. Bursts in the Earth-Sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organized criticality (SOC). We find also a power-law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence.
NASA Astrophysics Data System (ADS)
Shin, Wae-Gyeong; Lee, Soo-Hong
Reliability of automotive parts has been one of the most interesting fields in the automotive industry. Especially small DC motor was issued because of the increasing adoption for passengers' safety and convenience. This study was performed to develop the accelerated life test method using Inverse power law model for small DC motors. The failure mode of small DC motor includes brush wear-out. Inverse power law model is applied effectively the electronic components to reduce the testing time and to achieve the accelerating test conditions. Accelerated life testing method was induced to bring on the brush wear-out as increasing voltage of motor. Life distribution of the small DC motor was supposed to follow Weibull distribution and life test time was calculated under the conditions of B10 life and 90% confidence level.
A MODEL FOR THE NON-UNIVERSAL POWER LAW OF THE SOLAR WIND SUB-ION-SCALE MAGNETIC SPECTRUM
Passot, T.; Sulem, P. L. E-mail: sulem@oca.eu
2015-10-20
A phenomenological turbulence model for kinetic Alfvén waves in a magnetized collisionless plasma that is able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere is presented. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition from large-scale weak turbulence to smaller scale strong turbulence is captured and nonlocal interactions, relevant in the case of steep spectra, are accounted for.
Hirose, H
1997-01-01
This paper proposes a new treatment for electrical insulation degradation. Some types of insulation which have been used under various circumstances are considered to degrade at various rates in accordance with their stress circumstances. The cross-linked polyethylene (XLPE) insulated cables inspected by major Japanese electric companies clearly indicate such phenomena. By assuming that the inspected specimen is sampled from one of the clustered groups, a mixed degradation model can be constructed. Since the degradation of the insulation under common circumstances is considered to follow a Weibull distribution, a mixture model and a Weibull power law can be combined. This is called The mixture Weibull power law model. By using the maximum likelihood estimation for the newly proposed model to Japanese 22 and 33 kV insulation class cables, they are clustered into a certain number of groups by using the AIC and the generalized likelihood ratio test method. The reliability of the cables at specified years are assessed.
Marshall, Najja; Timme, Nicholas M; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
Khamzin, A A; Popov, I I; Nigmatullin, R R
2014-03-01
Based on the supposition related to fractal nature of transport processes in ion-conducting materials, an expression for the low-frequency ac conductivity dependence was derived. This expression for the ac conductivity generalizes the power-law dependence and gives a possibility to take into account the influence of the electrode polarization effect. The ac conductivity expression obtained is in excellent agreement with experimental data for a wide frequency range.
Marshall, Najja; Timme, Nicholas M.; Bennett, Nicholas; Ripp, Monica; Lautzenhiser, Edward; Beggs, John M.
2016-01-01
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of “neural avalanches” (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods—power-law fitting, avalanche shape collapse, and neural complexity—have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox. PMID:27445842
NASA Astrophysics Data System (ADS)
Sazuka, Naoya; Inoue, Jun-Ichi
2007-03-01
A Weibull distribution with power-law tails is confirmed as a good candidate to describe the first passage time process of foreign currency exchange rates. The Lorentz curve and the corresponding Gini coefficient for a Weibull distribution are derived analytically. We show that the coefficient is in good agreement with the same quantity calculated from the empirical data. We also calculate the average waiting time which is an important measure to estimate the time for customers to wait until the next price change after they login to their computer systems. By assuming that the first passage time distribution might change its shape from the Weibull to the power-law at some critical time, we evaluate the averaged waiting time by means of the renewal-reward theorem. We find that our correction of tails of the distribution makes the averaged waiting time much closer to the value obtained from empirical data analysis. We also discuss the deviation from the estimated average waiting time by deriving the waiting time distribution directly. These results make us conclude that the first passage process of the foreign currency exchange rates is well described by a Weibull distribution with power-law tails.
What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?
NASA Astrophysics Data System (ADS)
Lange, Steffen; Bäcker, Arnd; Ketzmerick, Roland
2016-11-01
The statistics of Poincaré recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this power-law trapping is still unknown. We investigate trapped orbits of a generic 4D symplectic map in phase space and frequency space and find that, in contrast to 2D maps, the trapping is i) not due to a hierarchy in phase space. Instead, it occurs at the surface of the regular region, ii) outside of the Arnold web. The chaotic dynamics in this sticky region is iii) dominated by resonance channels which reach far into the chaotic region: We observe iii.a) clear signatures of some kind of partial transport barriers and conjecture iii.b) a stochastic process with an effective drift along resonance channels. These two processes lay the basis for a future understanding of the mechanism of power-law trapping in higher-dimensional systems.