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.

Benford's law gives better scaling exponents in phase transitions of quantum XY models.

PubMed

Rane, Ameya Deepak; Mishra, Utkarsh; Biswas, Anindya; Sen De, Aditi; Sen, Ujjwal

2014-08-01

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.

Origin of the scaling laws of sediment transport

NASA Astrophysics Data System (ADS)

Ali, Sk Zeeshan; Dey, Subhasish

2017-01-01

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the `(1 + σ)/4' scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a `(1 + σ)/6' scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the `3/2' and `(1 + σ)/4' scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the `-Z ' scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the `4/(3 - σ)', `-4/(3 - σ)' and `-(1 + σ)/(3 - σ)' scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

The evolution of scaling laws in the sea ice floe size distribution

NASA Astrophysics Data System (ADS)

Horvat, Christopher; Tziperman, Eli

2017-09-01

The sub-gridscale floe size and thickness distribution (FSTD) is an emerging climate variable, playing a leading-order role in the coupling between sea ice, the ocean, and the atmosphere. The FSTD, however, is difficult to measure given the vast range of horizontal scales of individual floes, leading to the common use of power-law scaling to describe it. The evolution of a coupled mixed-layer-FSTD model of a typical marginal ice zone is explicitly simulated here, to develop a deeper understanding of how processes active at the floe scale may or may not lead to scaling laws in the floe size distribution. The time evolution of mean quantities obtained from the FSTD (sea ice concentration, mean thickness, volume) is complex even in simple scenarios, suggesting that these quantities, which affect climate feedbacks, should be carefully calculated in climate models. The emergence of FSTDs with multiple separate power-law regimes, as seen in observations, is found to be due to the combination of multiple scale-selective processes. Limitations in assuming a power-law FSTD are carefully analyzed, applying methods used in observations to FSTD model output. Two important sources of error are identified that may lead to model biases: one when observing an insufficiently small range of floe sizes, and one from the fact that floe-scale processes often do not produce power-law behavior. These two sources of error may easily lead to biases in mean quantities derived from the FSTD of greater than 100%, and therefore biases in modeled sea ice evolution.

Scaling laws and bulk-boundary decoupling in heat flow.

PubMed

del Pozo, Jesús J; Garrido, Pedro L; Hurtado, Pablo I

2015-03-01

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows one to measure the marginal anomaly of the heat conductivity predicted for hard disks.

Scaling laws of Rydberg excitons

NASA Astrophysics Data System (ADS)

Heckötter, J.; Freitag, M.; Fröhlich, D.; Aßmann, M.; Bayer, M.; Semina, M. A.; Glazov, M. M.

2017-09-01

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number n for features such as the magnetic field for level crossing or the electric field of dissociation. Recently, the observation of excitons in highly excited states has allowed studying Rydberg physics in cuprous oxide crystals. Fundamentally different insights may be expected for Rydberg excitons, as the crystal environment and associated symmetry reduction compared to vacuum give not only optical access to many more states within an exciton multiplet but also extend the Hamiltonian for describing the exciton beyond the hydrogen model. Here we study experimentally and theoretically the scaling of several parameters of Rydberg excitons with n , for some of which we indeed find laws different from those of atoms. For others we find identical scaling laws with n , even though their origin may be distinctly different from the atomic case. At zero field the energy splitting of a particular multiplet n scales as n-3 due to crystal-specific terms in the Hamiltonian, e.g., from the valence band structure. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a Br∝n-4 dependence of the resonance field strength, Br, due to the dominant paramagnetic term unlike for atoms for which the diamagnetic contribution is decisive, resulting in a Br∝n-6 dependence. By contrast, the resonance electric field strength shows a scaling as Er∝n-5 as for Rydberg atoms. Also similar to atoms with the exception of hydrogen we observe anticrossings between states belonging to multiplets with different principal quantum numbers at these resonances. The energy splittings at the avoided crossings scale roughly as n-4, again due to crystal specific features in the exciton Hamiltonian. The data also allow us to

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

Outbreak statistics and scaling laws for externally driven epidemics.

PubMed

Singh, Sarabjeet; Myers, Christopher R

2014-04-01

Power-law scalings are ubiquitous to physical phenomena undergoing a continuous phase transition. The classic susceptible-infectious-recovered (SIR) model of epidemics is one such example where the scaling behavior near a critical point has been studied extensively. In this system the distribution of outbreak sizes scales as P(n)∼n-3/2 at the critical point as the system size N becomes infinite. The finite-size scaling laws for the outbreak size and duration are also well understood and characterized. In this work, we report scaling laws for a model with SIR structure coupled with a constant force of infection per susceptible, akin to a "reservoir forcing". We find that the statistics of outbreaks in this system fundamentally differ from those in a simple SIR model. Instead of fixed exponents, all scaling laws exhibit tunable exponents parameterized by the dimensionless rate of external forcing. As the external driving rate approaches a critical value, the scale of the average outbreak size converges to that of the maximal size, and above the critical point, the scaling laws bifurcate into two regimes. Whereas a simple SIR process can only exhibit outbreaks of size O(N1/3) and O(N) depending on whether the system is at or above the epidemic threshold, a driven SIR process can exhibit a richer spectrum of outbreak sizes that scale as O(Nξ), where ξ∈(0,1]∖{2/3} and O((N/lnN)2/3) at the multicritical point.

Fluctuation Scaling, Taylor’s Law, and Crime

PubMed Central

Hanley, Quentin S.; Khatun, Suniya; Yosef, Amal; Dyer, Rachel-May

2014-01-01

Fluctuation scaling relationships have been observed in a wide range of processes ranging from internet router traffic to measles cases. Taylor’s law is one such scaling relationship and has been widely applied in ecology to understand communities including trees, birds, human populations, and insects. We show that monthly crime reports in the UK show complex fluctuation scaling which can be approximated by Taylor’s law relationships corresponding to local policing neighborhoods and larger regional and countrywide scales. Regression models applied to local scale data from Derbyshire and Nottinghamshire found that different categories of crime exhibited different scaling exponents with no significant difference between the two regions. On this scale, violence reports were close to a Poisson distribution (α = 1.057±0.026) while burglary exhibited a greater exponent (α = 1.292±0.029) indicative of temporal clustering. These two regions exhibited significantly different pre-exponential factors for the categories of anti-social behavior and burglary indicating that local variations in crime reports can be assessed using fluctuation scaling methods. At regional and countrywide scales, all categories exhibited scaling behavior indicative of temporal clustering evidenced by Taylor’s law exponents from 1.43±0.12 (Drugs) to 2.094±0081 (Other Crimes). Investigating crime behavior via fluctuation scaling gives insight beyond that of raw numbers and is unique in reporting on all processes contributing to the observed variance and is either robust to or exhibits signs of many types of data manipulation. PMID:25271781

Origin of Noncubic Scaling Law in Disordered Granular Packing.

PubMed

Xia, Chengjie; Li, Jindong; Kou, Binquan; Cao, Yixin; Li, Zhifeng; Xiao, Xianghui; Fu, Yanan; Xiao, Tiqiao; Hong, Liang; Zhang, Jie; Kob, Walter; Wang, Yujie

2017-06-09

Recent diffraction experiments on metallic glasses have unveiled an unexpected noncubic scaling law between density and average interatomic distance, which led to the speculation of the presence of fractal glass order. Using x-ray tomography we identify here a similar noncubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within the first nearest neighbor shell, and, therefore, is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with a contact number around 6, and we argue that the exponent should not be universal.

Rime-, mixed- and glaze-ice evaluations of three scaling laws

NASA Technical Reports Server (NTRS)

Anderson, David N.

1994-01-01

This report presents the results of tests at NASA Lewis to evaluate three icing scaling relationships or 'laws' for an unheated model. The laws were LWC x time = constant, one proposed by a Swedish-Russian group and one used at ONERA in France. Icing tests were performed in the NASA Lewis Icing Research Tunnel (IRT) with cylinders ranging from 2.5- to 15.2-cm diameter. Reference conditions were chosen to provide rime, mixed and glaze ice. Scaled conditions were tested for several scenarios of size and velocity scaling, and the resulting ice shapes compared. For rime-ice conditions, all three of the scaling laws provided scaled ice shapes which closely matched reference ice shapes. For mixed ice and for glaze ice none of the scaling laws produced consistently good simulation of the reference ice shapes. Explanations for the observed results are proposed, and scaling issues requiring further study are identified.

Scaling laws of passive-scalar diffusion in the interstellar medium

NASA Astrophysics Data System (ADS)

Colbrook, Matthew J.; Ma, Xiangcheng; Hopkins, Philip F.; Squire, Jonathan

2017-05-01

Passive-scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant 'effective diffusivity' as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian 'patches' remain coherent (poorly mixed) and simply advect for a large number of turbulent flow-crossing times.

Origin of Noncubic Scaling Law in Disordered Granular Packing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Chengjie; Li, Jindong; Kou, Binquan

Recent diffraction experiments on metallic glasses have unveiled an unexpected non-cubic scaling law between density and average interatomic distance, which lead to the speculations on the presence of fractal glass order. Using X-ray tomography we identify here a similar non-cubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within first nearest neighbor shell, and therefore is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with contact number around 6, and we argue that themore » exponent should not be universal.« less

Temperature Scaling Law for Quantum Annealing Optimizers.

PubMed

Albash, Tameem; Martin-Mayor, Victor; Hen, Itay

2017-09-15

Physical implementations of quantum annealing unavoidably operate at finite temperatures. We point to a fundamental limitation of fixed finite temperature quantum annealers that prevents them from functioning as competitive scalable optimizers and show that to serve as optimizers annealer temperatures must be appropriately scaled down with problem size. We derive a temperature scaling law dictating that temperature must drop at the very least in a logarithmic manner but also possibly as a power law with problem size. We corroborate our results by experiment and simulations and discuss the implications of these to practical annealers.

Looking for scaling laws, or physics with nuts and shells

NASA Astrophysics Data System (ADS)

Sheets, H. David; Lauffenburger, James C.

1999-09-01

Scaling laws relating the volume of a class of objects to a characteristic dimension of the object appear commonly in physics, chemistry, and biology. In this laboratory exercise for an introductory physics course scaling laws are derived for machine nuts and clam shells. In addition to covering a standard problem in physics, determining volume of the object by measuring the buoyant force on it, the biologically interesting idea of scaling laws are incorporated into the same lab.

Band gap scaling laws in group IV nanotubes.

PubMed

Wang, Chongze; Fu, Xiaonan; Guo, Yangyang; Guo, Zhengxiao; Xia, Congxin; Jia, Yu

2017-03-17

By using the first-principles calculations, the band gap properties of nanotubes formed by group IV elements have been investigated systemically. Our results reveal that for armchair nanotubes, the energy gaps at K points in the Brillouin zone decrease as 1/r scaling law with the radii (r) increasing, while they are scaled by -1/r 2  + C at Γ points, here, C is a constant. Further studies show that such scaling law of K points is independent of both the chiral vector and the type of elements. Therefore, the band gaps of nanotubes for a given radius can be determined by these scaling laws easily. Interestingly, we also predict the existence of indirect band gap for both germanium and tin nanotubes. Our new findings provide an efficient way to determine the band gaps of group IV element nanotubes by knowing the radii, as well as to facilitate the design of functional nanodevices.

Scaling laws from geomagnetic time series

USGS Publications Warehouse

Voros, Z.; Kovacs, P.; Juhasz, A.; Kormendi, A.; Green, A.W.

1998-01-01

The notion of extended self-similarity (ESS) is applied here for the X - component time series of geomagnetic field fluctuations. Plotting nth order structure functions against the fourth order structure function we show that low-frequency geomagnetic fluctuations up to the order n = 10 follow the same scaling laws as MHD fluctuations in solar wind, however, for higher frequencies (f > l/5[h]) a clear departure from the expected universality is observed for n > 6. ESS does not allow to make an unambiguous statement about the non triviality of scaling laws in "geomagnetic" turbulence. However, we suggest to use higher order moments as promising diagnostic tools for mapping the contributions of various remote magnetospheric sources to local observatory data. Copyright 1998 by the American Geophysical Union.

Model selection for identifying power-law scaling.

PubMed

Ton, Robert; Daffertshofer, Andreas

2016-08-01

Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present. Copyright © 2016 Elsevier Inc. All rights reserved.

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

PubMed

Touboul, Jonathan; Destexhe, Alain

2010-02-11

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

Power-law scaling of plasma pressure on laser-ablated tin microdroplets

NASA Astrophysics Data System (ADS)

Kurilovich, Dmitry; Basko, Mikhail M.; Kim, Dmitrii A.; Torretti, Francesco; Schupp, Ruben; Visschers, Jim C.; Scheers, Joris; Hoekstra, Ronnie; Ubachs, Wim; Versolato, Oscar O.

2018-01-01

The measurement of the propulsion of metallic microdroplets exposed to nanosecond laser pulses provides an elegant method for probing the ablation pressure in a dense laser-produced plasma. We present the measurements of the propulsion velocity over three decades in the driving Nd:YAG laser pulse energy and observe a near-perfect power law dependence. Simulations performed with the RALEF-2D radiation-hydrodynamic code are shown to be in good agreement with the power law above a specific threshold energy. The simulations highlight the importance of radiative losses which significantly modify the power of the pressure scaling. Having found a good agreement between the experiment and the simulations, we investigate the analytic origins of the obtained power law and conclude that none of the available analytic theories is directly applicable for explaining our power exponent.

Family-specific scaling laws in bacterial genomes.

PubMed

De Lazzari, Eleonora; Grilli, Jacopo; Maslov, Sergei; Cosentino Lagomarsino, Marco

2017-07-27

Among several quantitative invariants found in evolutionary genomics, one of the most striking is the scaling of the overall abundance of proteins, or protein domains, sharing a specific functional annotation across genomes of given size. The size of these functional categories change, on average, as power-laws in the total number of protein-coding genes. Here, we show that such regularities are not restricted to the overall behavior of high-level functional categories, but also exist systematically at the level of single evolutionary families of protein domains. Specifically, the number of proteins within each family follows family-specific scaling laws with genome size. Functionally similar sets of families tend to follow similar scaling laws, but this is not always the case. To understand this systematically, we provide a comprehensive classification of families based on their scaling properties. Additionally, we develop a quantitative score for the heterogeneity of the scaling of families belonging to a given category or predefined group. Under the common reasonable assumption that selection is driven solely or mainly by biological function, these findings point to fine-tuned and interdependent functional roles of specific protein domains, beyond our current functional annotations. This analysis provides a deeper view on the links between evolutionary expansion of protein families and the functional constraints shaping the gene repertoire of bacterial genomes. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

A simple scaling law for the equation of state and the radial distribution functions calculated by density-functional theory molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.

2018-06-01

It is shown that the equation of state (EOS) and the radial distribution functions obtained by density-functional theory molecular dynamics (DFT-MD) obey a simple scaling law. At given temperature, the thermodynamic properties and the radial distribution functions given by a DFT-MD simulation remain unchanged if the mole fractions of nuclei of given charge and the average volume per atom remain unchanged. A practical interest of this scaling law is to obtain an EOS table for a fluid from that already obtained for another fluid if it has the right characteristics. Another practical interest of this result is that an asymmetric mixture made up of light and heavy atoms requiring very different time steps can be replaced by a mixture of atoms of equal mass, which facilitates the exploration of the configuration space in a DFT-MD simulation. The scaling law is illustrated by numerical results.

Universal scaling law in human behavioral organization.

PubMed

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R; Yamamoto, Yoshiharu

2007-09-28

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

Universal Scaling Law in Human Behavioral Organization

NASA Astrophysics Data System (ADS)

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R.; Yamamoto, Yoshiharu

2007-09-01

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

Universal scaling laws of diffusion in two-dimensional granular liquids.

PubMed

Wang, Chen-Hung; Yu, Szu-Hsuan; Chen, Peilong

2015-06-01

We find, in a two-dimensional air table granular system, that the reduced diffusion constant D* and excess entropy S(2) follow two distinct scaling laws: D*∼e(S(2)*) for dense liquids and D∼e(3S(2)*) for dilute ones. The scaling for dense liquids is very similar to that for three-dimensional liquids proposed previously [M. Dzugutov, Nature (London) 381, 137 (1996); A. Samanta et al., Phys. Rev. Lett. 92, 145901 (2004)]. In the dilute regime, a power law [Y. Rosenfeld, J. Phys.: Condens. Matter 11, 5415 (1999)] also fits our data reasonably well. In our system, particles experience low air drag dissipation and interact with each others through embedded magnets. These near-conservative many-body interactions are responsible for the measured Gaussian velocity distribution functions and the scaling laws. The dominance of cage relaxations in dense liquids leads to the different scaling laws for dense and dilute regimes.

Two-threshold model for scaling laws of noninteracting snow avalanches

USGS Publications Warehouse

Faillettaz, J.; Louchet, F.; Grasso, J.-R.

2004-01-01

A two-threshold model was proposed for scaling laws of noninteracting snow avalanches. It was found that the sizes of the largest avalanches just preceding the lattice system were power-law distributed. The proposed model reproduced the range of power-law exponents observe for land, rock or snow avalanches, by tuning the maximum value of the ratio of the two failure thresholds. A two-threshold 2D cellular automation was introduced to study the scaling for gravity-driven systems.

Scaling laws for perturbations in the ocean-atmosphere system following large CO2 emissions

NASA Astrophysics Data System (ADS)

Towles, N.; Olson, P.; Gnanadesikan, A.

2015-01-01

Scaling relationships are derived for the perturbations to atmosphere and ocean variables from large transient CO2 emissions. Using the carbon cycle model LOSCAR (Zeebe et al., 2009; Zeebe, 2012b) we calculate perturbations to atmosphere temperature and total carbon, ocean temperature, total ocean carbon, pH, and alkalinity, marine sediment carbon, plus carbon-13 isotope anomalies in the ocean and atmosphere resulting from idealized CO2 emission events. The peak perturbations in the atmosphere and ocean variables are then fit to power law functions of the form γDαEbeta, where D is the event duration, E is its total carbon emission, and γ is a coefficient. Good power law fits are obtained for most system variables for E up to 50 000 PgC and D up to 100 kyr. However, these power laws deviate substantially from predictions based on simplified equilibrium considerations. For example, although all of the peak perturbations increase with emission rate E/D, we find no evidence of emission rate-only scaling α + β =0, a prediction of the long-term equilibrium between CO2 input by volcanism and CO2 removal by silicate weathering. Instead, our scaling yields α + β ≃ 1 for total ocean and atmosphere carbon and 0< α + β < 1 for most of the other system variables. The deviations in these scaling laws from equilibrium predictions are mainly due to the multitude and diversity of time scales that govern the exchange of carbon between marine sediments, the ocean, and the atmosphere.

Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

NASA Astrophysics Data System (ADS)

Cai, Qing; Xu, Hai-Chuan; Zhou, Wei-Xing

2016-08-01

Taylor’s law of temporal fluctuation scaling, variance ˜ a(mean)b, is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity of almost all stocks traded on the Shanghai Stock Exchange (SHSE) and the Shenzhen Stock Exchange (SZSE) during the period from 1999 to 2011. Taylor’s law holds for A-share markets (SZSE Main Board, SZSE Small & Mediate Enterprise Board, SZSE Second Board, and SHSE Main Board) and B-share markets (SZSE B-share and SHSE B-share). We find that the scaling exponent b is greater than 2 for the A-share markets and less than 2 for the B-share markets. We further unveil that Taylor’s law holds for stocks in 17 industry categories, in 28 industrial sectors and in 31 provinces and direct-controlled municipalities with the majority of scaling exponents b ∈ (2, 3). We also investigate the Δt-min illiquidity and find that the scaling exponent b(Δt) increases logarithmically for small Δt values and decreases fast to a stable level.

Obtaining patient test results from clinical laboratories: a survey of state law for pharmacists.

PubMed

Witry, Matthew J; Doucette, William R

2009-01-01

To identify states with laws that restrict to whom clinical laboratories may release copies of laboratory test results and to describe how these laws may affect pharmacists' ability to obtain patient laboratory test results. Researchers examined state statutes and administrative codes for all 50 states and the District of Columbia at the University of Iowa Law Library between June and July 2007. Researchers also consulted with lawyers, state Clinical Laboratory Improvement Amendments officers, and law librarians. Laws relating to the study objective were analyzed. 34 jurisdictions do not restrict the release of laboratory test results, while 17 states have laws that restrict to whom clinical laboratories can send copies of test results. In these states, pharmacists will have to use alternative sources, such as physician offices, to obtain test results. Pharmacists must consider state law before requesting copies of laboratory test results from clinical laboratories. This may be an issue that state pharmacy associations can address to increase pharmacist access to important patient information.

Lightning Scaling Laws Revisited

NASA Technical Reports Server (NTRS)

Boccippio, D. J.; Arnold, James E. (Technical Monitor)

2000-01-01

Scaling laws relating storm electrical generator power (and hence lightning flash rate) to charge transport velocity and storm geometry were originally posed by Vonnegut (1963). These laws were later simplified to yield simple parameterizations for lightning based upon cloud top height, with separate parameterizations derived over land and ocean. It is demonstrated that the most recent ocean parameterization: (1) yields predictions of storm updraft velocity which appear inconsistent with observation, and (2) is formally inconsistent with the theory from which it purports to derive. Revised formulations consistent with Vonnegut's original framework are presented. These demonstrate that Vonnegut's theory is, to first order, consistent with observation. The implications of assuming that flash rate is set by the electrical generator power, rather than the electrical generator current, are examined. The two approaches yield significantly different predictions about the dependence of charge transfer per flash on storm dimensions, which should be empirically testable. The two approaches also differ significantly in their explanation of regional variability in lightning observations.

Covariations in ecological scaling laws fostered by community dynamics.

PubMed

Zaoli, Silvia; Giometto, Andrea; Maritan, Amos; Rinaldo, Andrea

2017-10-03

Scaling laws in ecology, intended both as functional relationships among ecologically relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances, and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked has been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply, and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations.

Scaling in Ecosystems and the Linkage of Macroecological Laws

NASA Astrophysics Data System (ADS)

Rinaldo, A.

2007-12-01

Are there predictable linkages among macroecological laws regulating size and abundance of organisms that are ubiquitously supported by empirical observations and that ecologists treat traditionally as independent? Do fragmentation of habitats, or reduced supply of energy and matter, result in predictable changes on whole ecosystems as a function of their size? Using a coherent theoretical framework based on scaling theory, it is argued that the answer to both these questions is affirmative. The concern of the talk is with the comparatively simple situation of the steady state behavior of a fully developed ecosystem in which, over evolutionary time, resources are exploited in full, individual and collective metabolic needs are met and enough time has elapsed to produce a rough balance between speciation and extinction and ecological fluxes. While ecological patterns and processes often show great variation when viewed at different scales of space, time, organismic size and organizational complexity, there is also widespread evidence for the existence of scaling regularities as embedded in macroecological "laws" or rules. These laws have commanded considerable attention from the ecological community. Indeed they are central to ecological theory as they describe the features of complex adaptive systems shown by a number of biological systems, and perhaps for the investigation of the dynamic origin of scale invariance of natural forms in general. The species-area and relative species-abundance relations, the scaling of community and species' size spectra, the scaling of population densities with their mean body mass and the scaling of the largest organism with ecosystem size are examples of such laws. Borrowing heavily from earlier successes in physics, it will be shown how simple mathematical scaling arguments, following from dimensional and finite-size scaling analyses, provide theoretical predictions of the inter- relationships among the species abundance

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.

Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws

PubMed Central

Palva, J. Matias; Zhigalov, Alexander; Hirvonen, Jonni; Korhonen, Onerva; Linkenkaer-Hansen, Klaus; Palva, Satu

2013-01-01

Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form long-range temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit power-law size and lifetime distributions. However, it remains unknown whether these neuronal scaling laws are correlated with those characterizing behavioral performance or whether neuronal LRTCs and avalanches are related. Here, we show that the neuronal scaling laws are strongly correlated both with each other and with behavioral scaling laws. We used source reconstructed magneto- and electroencephalographic recordings to characterize the dynamics of ongoing cortical activity. We found robust power-law scaling in neuronal LRTCs and avalanches in resting-state data and during the performance of audiovisual threshold stimulus detection tasks. The LRTC scaling exponents of the behavioral performance fluctuations were correlated with those of concurrent neuronal avalanches and LRTCs in anatomically identified brain systems. The behavioral exponents also were correlated with neuronal scaling laws derived from a resting-state condition and with a similar anatomical topography. Finally, despite the difference in time scales, the scaling exponents of neuronal LRTCs and avalanches were strongly correlated during both rest and task performance. Thus, long and short time-scale neuronal dynamics are related and functionally significant at the behavioral level. These data suggest that the temporal structures of human cognitive fluctuations and behavioral variability stem from the scaling laws of individual and intrinsic brain dynamics. PMID:23401536

Scaling laws and model of words organization in spoken and written language

NASA Astrophysics Data System (ADS)

Bian, Chunhua; Lin, Ruokuang; Zhang, Xiaoyu; Ma, Qianli D. Y.; Ivanov, Plamen Ch.

2016-01-01

A broad range of complex physical and biological systems exhibits scaling laws. The human language is a complex system of words organization. Studies of written texts have revealed intriguing scaling laws that characterize the frequency of words occurrence, rank of words, and growth in the number of distinct words with text length. While studies have predominantly focused on the language system in its written form, such as books, little attention is given to the structure of spoken language. Here we investigate a database of spoken language transcripts and written texts, and we uncover that words organization in both spoken language and written texts exhibits scaling laws, although with different crossover regimes and scaling exponents. We propose a model that provides insight into words organization in spoken language and written texts, and successfully accounts for all scaling laws empirically observed in both language forms.

Scaling and saturation laws for the expansion of concrete exposed to sulfate attack.

PubMed

Monteiro, Paulo J M

2006-08-01

Reinforced concrete structures exposed to aggressive environments often require repair or retrofit even though they were designed to last >50 years. This statement is especially true for structures subjected to sulfate attack. It is critical that fundamental models of life prediction be developed for durability of concrete. Based on experimental results obtained over a 40-year period, scaling and saturation laws were formulated for concrete exposed to sulfate solution. These features have not been considered in current models used to predict life cycle of concrete exposed to aggressive environment. The mathematical analysis shows that porous concrete made with high and moderate water-to-cement ratios develops a definite scaling law after an initiation time. The scaling coefficient depends on the cement composition but does not depend on the original water-to-cement ratio. Dense concrete made with low water-to-cement ratios develops a cyclic saturation curve. An index for "potential of damage" is created to allow engineers to design concrete structures with better precision and cement chemists to develop portland cements with optimized composition.

Scaling law analysis of paraffin thin films on different surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dotto, M. E. R.; Camargo, S. S. Jr.

2010-01-15

The dynamics of paraffin deposit formation on different surfaces was analyzed based on scaling laws. Carbon-based films were deposited onto silicon (Si) and stainless steel substrates from methane (CH{sub 4}) gas using radio frequency plasma enhanced chemical vapor deposition. The different substrates were characterized with respect to their surface energy by contact angle measurements, surface roughness, and morphology. Paraffin thin films were obtained by the casting technique and were subsequently characterized by an atomic force microscope in noncontact mode. The results indicate that the morphology of paraffin deposits is strongly influenced by substrates used. Scaling laws analysis for coated substratesmore » present two distinct dynamics: a local roughness exponent ({alpha}{sub local}) associated to short-range surface correlations and a global roughness exponent ({alpha}{sub global}) associated to long-range surface correlations. The local dynamics is described by the Wolf-Villain model, and a global dynamics is described by the Kardar-Parisi-Zhang model. A local correlation length (L{sub local}) defines the transition between the local and global dynamics with L{sub local} approximately 700 nm in accordance with the spacing of planes measured from atomic force micrographs. For uncoated substrates, the growth dynamics is related to Edwards-Wilkinson model.« less

A New Scaling Law of Resonance in Total Scattering Cross Section in Gases

NASA Astrophysics Data System (ADS)

Raju, Gorur Govinda

2009-10-01

scaling of total cross section of gases at resonance energy and the electron energy at which resonance occurs. The meaning of resonance is briefly explained in the following section. Here, we use the term scaling to relate the two quantities mentioned, namely, the resonance energy and the total cross section at that energy. Consistent with the definition of scaling, if the law proposed holds, one of the two quantities mentioned above may be calculated if the other is known. Such a method is very useful in gas discharge modeling and calculation of breakdown voltages, as more fully explained in the later section of the paper. 2 DESCRIPTION OF RESONANCE: A brief description of resonance phenomena in several types of target particles, viz., atomic, poly atomic, polar, non-polar phenomena are presented. 3 PREVIOUS SCALING LAWS: A common representation of a given characteristic with as few adjustable parameters as possible is generally known as the scaling law. The Paschen curve for breakdown voltage is such a familiar scaling law. With reference to cross sections several attempts have been made to obtain a scaling law, with varying degree of success. If the cross section-energy curve is qualitatively similar without having sharp peaks and oscillations, moderately successful scaling laws may be devised. For example, the ionization cross section- energy curves for most gases follow a general pattern. Several published scaling laws are discussed. 4 A NEW SCALING LAW AND DISCUSSION: In this work the author has compiled the resonance details for more than 60 gasest hat include the range from simple atoms to complex molecules that are polyatomic, dipolar, electron-attaching and isomers. The target particles exhibit a number of distinct features, as far as their total cross section variation with electron energy is concerned as already explained.

Scaling laws for testing of high lift airfoils under heavy rainfall

NASA Technical Reports Server (NTRS)

Bilanin, A. J.

1985-01-01

The results of studies regarding the effect of rainfall about aircraft are briefly reviewed. It is found that performance penalties on airfoils have been identified in subscale tests. For this reason, it is of great importance that scaling laws be dveloped to aid in the extrapolation of these data to fullscale. The present investigation represents an attempt to develop scaling laws for testing subscale airfoils under heavy rain conditions. Attention is given to rain statistics, airfoil operation in heavy rain, scaling laws, thermodynamics of condensation and/or evaporation, rainfall and airfoil scaling, aspects of splash back, film thickness, rivulets, and flap slot blockage. It is concluded that the extrapolation of airfoil performance data taken at subscale under simulated heavy rain conditions to fullscale must be undertaken with caution.

Vortex clustering and universal scaling laws in two-dimensional quantum turbulence.

PubMed

Skaugen, Audun; Angheluta, Luiza

2016-03-01

We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal -5/3 scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The -5/3 scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a -5/3 exponent.

Polyelectrolyte scaling laws for microgel yielding near jamming.

PubMed

Bhattacharjee, Tapomoy; Kabb, Christopher P; O'Bryan, Christopher S; Urueña, Juan M; Sumerlin, Brent S; Sawyer, W Gregory; Angelini, Thomas E

2018-02-28

Micro-scale hydrogel particles, known as microgels, are used in industry to control the rheology of numerous different products, and are also used in experimental research to study the origins of jamming and glassy behavior in soft-sphere model systems. At the macro-scale, the rheological behaviour of densely packed microgels has been thoroughly characterized; at the particle-scale, careful investigations of jamming, yielding, and glassy-dynamics have been performed through experiment, theory, and simulation. However, at low packing fractions near jamming, the connection between microgel yielding phenomena and the physics of their constituent polymer chains has not been made. Here we investigate whether basic polymer physics scaling laws predict macroscopic yielding behaviours in packed microgels. We measure the yield stress and cross-over shear-rate in several different anionic microgel systems prepared at packing fractions just above the jamming transition, and show that our data can be predicted from classic polyelectrolyte physics scaling laws. We find that diffusive relaxations of microgel deformation during particle re-arrangements can predict the shear-rate at which microgels yield, and the elastic stress associated with these particle deformations predict the yield stress.

Natural Scale for Employee's Payment Based on the Entropy Law

NASA Astrophysics Data System (ADS)

Cosma, Ioan; Cosma, Adrian

2009-05-01

An econophysical modeling fated to establish an equitable scale of employees' salary in accordance with the importance and effectiveness of labor is considered. Our model, based on the concept and law of entropy, can designate all the parameters connected to the level of personal incomes and taxations, and also to the distribution of employees versus amount of salary in any remuneration system. Consistent with the laws of classical and statistical thermodynamics, this scale reveals that the personal incomes increased progressively in a natural logarithmic way, different compared with other scales arbitrary established by the governments of each country or by employing companies.

Scaling laws for impact fragmentation of spherical solids.

PubMed

Timár, G; Kun, F; Carmona, H A; Herrmann, H J

2012-07-01

We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v(0). The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.

Scaling laws and dynamics of bubble coalescence

NASA Astrophysics Data System (ADS)

Anthony, Christopher R.; Kamat, Pritish M.; Thete, Sumeet S.; Munro, James P.; Lister, John R.; Harris, Michael T.; Basaran, Osman A.

2017-08-01

The coalescence of bubbles and drops plays a central role in nature and industry. During coalescence, two bubbles or drops touch and merge into one as the neck connecting them grows from microscopic to macroscopic scales. The hydrodynamic singularity that arises when two bubbles or drops have just touched and the flows that ensue have been studied thoroughly when two drops coalesce in a dynamically passive outer fluid. In this paper, the coalescence of two identical and initially spherical bubbles, which are idealized as voids that are surrounded by an incompressible Newtonian liquid, is analyzed by numerical simulation. This problem has recently been studied (a) experimentally using high-speed imaging and (b) by asymptotic analysis in which the dynamics is analyzed by determining the growth of a hole in the thin liquid sheet separating the two bubbles. In the latter, advantage is taken of the fact that the flow in the thin sheet of nonconstant thickness is governed by a set of one-dimensional, radial extensional flow equations. While these studies agree on the power law scaling of the variation of the minimum neck radius with time, they disagree with respect to the numerical value of the prefactors in the scaling laws. In order to reconcile these differences and also provide insights into the dynamics that are difficult to probe by either of the aforementioned approaches, simulations are used to access both earlier times than has been possible in the experiments and also later times when asymptotic analysis is no longer applicable. Early times and extremely small length scales are attained in the new simulations through the use of a truncated domain approach. Furthermore, it is shown by direct numerical simulations in which the flow within the bubbles is also determined along with the flow exterior to them that idealizing the bubbles as passive voids has virtually no effect on the scaling laws relating minimum neck radius and time.

Fundamental Scaling Laws in Nanophotonics

PubMed Central

Liu, Ke; Sun, Shuai; Majumdar, Arka; Sorger, Volker J.

2016-01-01

The success of information technology has clearly demonstrated that miniaturization often leads to unprecedented performance, and unanticipated applications. This hypothesis of “smaller-is-better” has motivated optical engineers to build various nanophotonic devices, although an understanding leading to fundamental scaling behavior for this new class of devices is missing. Here we analyze scaling laws for optoelectronic devices operating at micro and nanometer length-scale. We show that optoelectronic device performance scales non-monotonically with device length due to the various device tradeoffs, and analyze how both optical and electrical constrains influence device power consumption and operating speed. Specifically, we investigate the direct influence of scaling on the performance of four classes of photonic devices, namely laser sources, electro-optic modulators, photodetectors, and all-optical switches based on three types of optical resonators; microring, Fabry-Perot cavity, and plasmonic metal nanoparticle. Results show that while microrings and Fabry-Perot cavities can outperform plasmonic cavities at larger length-scales, they stop working when the device length drops below 100 nanometers, due to insufficient functionality such as feedback (laser), index-modulation (modulator), absorption (detector) or field density (optical switch). Our results provide a detailed understanding of the limits of nanophotonics, towards establishing an opto-electronics roadmap, akin to the International Technology Roadmap for Semiconductors. PMID:27869159

Fundamental Scaling Laws in Nanophotonics.

PubMed

Liu, Ke; Sun, Shuai; Majumdar, Arka; Sorger, Volker J

2016-11-21

The success of information technology has clearly demonstrated that miniaturization often leads to unprecedented performance, and unanticipated applications. This hypothesis of "smaller-is-better" has motivated optical engineers to build various nanophotonic devices, although an understanding leading to fundamental scaling behavior for this new class of devices is missing. Here we analyze scaling laws for optoelectronic devices operating at micro and nanometer length-scale. We show that optoelectronic device performance scales non-monotonically with device length due to the various device tradeoffs, and analyze how both optical and electrical constrains influence device power consumption and operating speed. Specifically, we investigate the direct influence of scaling on the performance of four classes of photonic devices, namely laser sources, electro-optic modulators, photodetectors, and all-optical switches based on three types of optical resonators; microring, Fabry-Perot cavity, and plasmonic metal nanoparticle. Results show that while microrings and Fabry-Perot cavities can outperform plasmonic cavities at larger length-scales, they stop working when the device length drops below 100 nanometers, due to insufficient functionality such as feedback (laser), index-modulation (modulator), absorption (detector) or field density (optical switch). Our results provide a detailed understanding of the limits of nanophotonics, towards establishing an opto-electronics roadmap, akin to the International Technology Roadmap for Semiconductors.

Fundamental Scaling Laws in Nanophotonics

NASA Astrophysics Data System (ADS)

Liu, Ke; Sun, Shuai; Majumdar, Arka; Sorger, Volker J.

2016-11-01

The success of information technology has clearly demonstrated that miniaturization often leads to unprecedented performance, and unanticipated applications. This hypothesis of “smaller-is-better” has motivated optical engineers to build various nanophotonic devices, although an understanding leading to fundamental scaling behavior for this new class of devices is missing. Here we analyze scaling laws for optoelectronic devices operating at micro and nanometer length-scale. We show that optoelectronic device performance scales non-monotonically with device length due to the various device tradeoffs, and analyze how both optical and electrical constrains influence device power consumption and operating speed. Specifically, we investigate the direct influence of scaling on the performance of four classes of photonic devices, namely laser sources, electro-optic modulators, photodetectors, and all-optical switches based on three types of optical resonators; microring, Fabry-Perot cavity, and plasmonic metal nanoparticle. Results show that while microrings and Fabry-Perot cavities can outperform plasmonic cavities at larger length-scales, they stop working when the device length drops below 100 nanometers, due to insufficient functionality such as feedback (laser), index-modulation (modulator), absorption (detector) or field density (optical switch). Our results provide a detailed understanding of the limits of nanophotonics, towards establishing an opto-electronics roadmap, akin to the International Technology Roadmap for Semiconductors.

General Entanglement Scaling Laws from Time Evolution

NASA Astrophysics Data System (ADS)

Eisert, Jens; Osborne, Tobias J.

2006-10-01

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.

Developing the Attitude Scale for Islamic Law Lesson

ERIC Educational Resources Information Center

Ersoy, Mustafa; Izci, Eyüp

2017-01-01

This study was conducted for the purpose of developing an attitude scale in order to be able to measure the attitudes of students towards Islamic Law Lesson in a valid and reliable way. The sampling of the study consisted of 198 students who studied at 4th Grade at Cumhuriyet University, Faculty of Theology, and who answered the measurement scale.…

Testing Collisional Scaling Laws: Comparing with Observables

NASA Astrophysics Data System (ADS)

Davis, D. R.; Marzari, F.; Farinella, P.

1999-09-01

How large bodies break up in response to energetic collisions is a problem that has attracted considerable attention in recent years. Ever more sophisticated computation methods have also been developed; prominent among these are hydrocode simulations of collisional disruption by Benz and Asphaug (1999, Icarus, in press), Love and Ahrens (1996, LPSC XXVII, 777-778), and Melosh and Ryan (1997, Icarus 129, 562-564). Durda et al. (1998, Icarus 135, 431-440) used the observed asteroid size distribution to infer a scaling algorithm. The present situation is that there are several proposed scaling laws that differ by as much as two orders of magnitude at particular sizes. We have expanded upon the work of Davis et al. (1994, Goutelas Proceedings) and tested the suite of proposed scaling algorithms against observations of the main-belt asteroids. The effects of collisions among the asteroids produce the following observables: (a) the size distribution has been significantly shaped by collisions, (b) collisions have produced about 25 well recognized asteroid families, and (c) the basaltic crust of Vesta has been largely preserved in the face of about 4.5 Byr of impacts. We will present results from a numerical simulation of asteroid collisional evolution over the age of the solar system using proposed scaling laws and a range of hypothetical initial populations.

Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to

Scaling laws for ignition at the National Ignition Facility from first principles.

PubMed

Cheng, Baolian; Kwan, Thomas J T; Wang, Yi-Ming; Batha, Steven H

2013-10-01

We have developed an analytical physics model from fundamental physics principles and used the reduced one-dimensional model to derive a thermonuclear ignition criterion and implosion energy scaling laws applicable to inertial confinement fusion capsules. The scaling laws relate the fuel pressure and the minimum implosion energy required for ignition to the peak implosion velocity and the equation of state of the pusher and the hot fuel. When a specific low-entropy adiabat path is used for the cold fuel, our scaling laws recover the ignition threshold factor dependence on the implosion velocity, but when a high-entropy adiabat path is chosen, the model agrees with recent measurements.

Cardiovascular performance of adult breeding sows fails to obey allometric scaling laws.

PubMed

van Essen, G J; Vernooij, J C M; Heesterbeek, J A P; Anjema, D; Merkus, D; Duncker, D J

2011-02-01

In view of the remarkable decrease of the relative heart weight (HW) and the relative blood volume in growing pigs, we investigated whether HW, cardiac output (CO), and stroke volume (SV) of modern growing pigs are proportional to BW, as predicted by allometric scaling laws: HW (or CO or SV) = a·BW(b), in which a and b are constants, and constant b is a multiple of 0.25 (quarter-power scaling law). Specifically, we tested the hypothesis that both HW and CO scale with BW to the power of 0.75 (HW or CO = a·BW(0.75)) and SV scales with BW to the power of 1.00 (SV = a·BW(1.0)). For this purpose, 2 groups of pigs (group 1, consisting of 157 pigs of 50 ± 1 kg; group 2, consisting of 45 pigs of 268 ± 18 kg) were surgically instrumented with a flow probe or a thermodilution dilution catheter, under open-chest anesthetized conditions to measure CO and SV, after which HW was determined. The 95% confidence intervals of power-coefficient b for HW were 0.74 to 0.80, encompassing the predicted value of 0.75, suggesting that HW increased proportionally with BW, as predicted by the allometric scaling laws. In contrast, the 95% confidence intervals of power-coefficient b for CO and SV as measured with flow probes were 0.40 to 0.56 and 0.39 to 0.61, respectively, and values obtained with the thermodilution technique were 0.34 to 0.53 and 0.40 to 0.62, respectively. Thus, the 95% confidence limits failed to encompass the predicted values of b for CO and SV of 0.75 and 1.0, respectively. In conclusion, although adult breeding sows display normal heart growth, cardiac performance appears to be disproportionately low for BW. This raises concern regarding the health status of adult breeding sows.

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

PubMed

Tinker, Jesse; Velazquez, Jose Luis Perez

2014-01-01

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

Numerical determination of Paris law constants for carbon steel using a two-scale model

NASA Astrophysics Data System (ADS)

Mlikota, M.; Staib, S.; Schmauder, S.; Božić, Ž.

2017-05-01

For most engineering alloys, the long fatigue crack growth under a certain stress level can be described by the Paris law. The law provides a correlation between the fatigue crack growth rate (FCGR or da/dN), the range of stress intensity factor (ΔK), and the material constants C and m. A well-established test procedure is typically used to determine the Paris law constants C and m, considering standard specimens, notched and pre-cracked. Definition of all the details necessary to obtain feasible and comparable Paris law constants are covered by standards. However, these cost-expensive tests can be replaced by appropriate numerical calculations. In this respect, this paper deals with the numerical determination of Paris law constants for carbon steel using a two-scale model. A micro-model containing the microstructure of a material is generated using the Finite Element Method (FEM) to calculate the fatigue crack growth rate at a crack tip. The model is based on the Tanaka-Mura equation. On the other side, a macro-model serves for the calculation of the stress intensity factor. The analysis yields a relationship between the crack growth rates and the stress intensity factors for defined crack lengths which is then used to determine the Paris law constants.

Centrifugal fans: Similarity, scaling laws, and fan performance

NASA Astrophysics Data System (ADS)

Sardar, Asad Mohammad

Centrifugal fans are rotodynamic machines used for moving air continuously against moderate pressures through ventilation and air conditioning systems. There are five major topics presented in this thesis: (1) analysis of the fan scaling laws and consequences of dynamic similarity on modelling; (2) detailed flow visualization studies (in water) covering the flow path starting at the fan blade exit to the evaporator core of an actual HVAC fan scroll-diffuser module; (3) mean velocity and turbulence intensity measurements (flow field studies) at the inlet and outlet of large scale blower; (4) fan installation effects on overall fan performance and evaluation of fan testing methods; (5) two point coherence and spectral measurements conducted on an actual HVAC fan module for flow structure identification of possible aeroacoustic noise sources. A major objective of the study was to identity flow structures within the HVAC module that are responsible for noise and in particular "rumble noise" generation. Possible mechanisms for the generation of flow induced noise in the automotive HVAC fan module are also investigated. It is demonstrated that different modes of HVAC operation represent very different internal flow characteristics. This has implications on both fan HVAC airflow performance and noise characteristics. It is demonstrated from principles of complete dynamic similarity that fan scaling laws require that Reynolds, number matching is a necessary condition for developing scale model fans or fan test facilities. The physical basis for the fan scaling laws derived was established from both pure dimensional analysis and also from the fundamental equations of fluid motion. Fan performance was measured in a three times scale model (large scale blower) in air of an actual forward curved automotive HVAC blower. Different fan testing methods (based on AMCA fan test codes) were compared on the basis of static pressure measurements. Also, the flow through an actual HVAC

Allometric scaling law in a simple oxygen exchanging network: possible implications on the biological allometric scaling laws.

PubMed

Santillán, Moisés

2003-07-21

A simple model of an oxygen exchanging network is presented and studied. This network's task is to transfer a given oxygen rate from a source to an oxygen consuming system. It consists of a pipeline, that interconnects the oxygen consuming system and the reservoir and of a fluid, the active oxygen transporting element, moving through the pipeline. The network optimal design (total pipeline surface) and dynamics (volumetric flow of the oxygen transporting fluid), which minimize the energy rate expended in moving the fluid, are calculated in terms of the oxygen exchange rate, the pipeline length, and the pipeline cross-section. After the oxygen exchanging network is optimized, the energy converting system is shown to satisfy a 3/4-like allometric scaling law, based upon the assumption that its performance regime is scale invariant as well as on some feasible geometric scaling assumptions. Finally, the possible implications of this result on the allometric scaling properties observed elsewhere in living beings are discussed.

Scaling laws for perturbations in the ocean-atmosphere system following large CO2 emissions

NASA Astrophysics Data System (ADS)

Towles, N.; Olson, P.; Gnanadesikan, A.

2015-07-01

Scaling relationships are found for perturbations to atmosphere and ocean variables from large transient CO2 emissions. Using the Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir (LOSCAR) model (Zeebe et al., 2009; Zeebe, 2012b), we calculate perturbations to atmosphere temperature, total carbon, ocean temperature, total ocean carbon, pH, alkalinity, marine-sediment carbon, and carbon-13 isotope anomalies in the ocean and atmosphere resulting from idealized CO2 emission events. The peak perturbations in the atmosphere and ocean variables are then fit to power law functions of the form of γ DαEβ, where D is the event duration, E is its total carbon emission, and γ is a coefficient. Good power law fits are obtained for most system variables for E up to 50 000 PgC and D up to 100 kyr. Although all of the peak perturbations increase with emission rate E/D, we find no evidence of emission-rate-only scaling, α + β = 0. Instead, our scaling yields α + β ≃ 1 for total ocean and atmosphere carbon and 0 < α + β < 1 for most of the other system variables.

Identifying all moiety conservation laws in genome-scale metabolic networks.

PubMed

De Martino, Andrea; De Martino, Daniele; Mulet, Roberto; Pagnani, Andrea

2014-01-01

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Species survival and scaling laws in hostile and disordered environments

NASA Astrophysics Data System (ADS)

Rocha, Rodrigo P.; Figueiredo, Wagner; Suweis, Samir; Maritan, Amos

2016-10-01

In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.

A scaling law of radial gas distribution in disk galaxies

NASA Technical Reports Server (NTRS)

Wang, Zhong

1990-01-01

Based on the idea that local conditions within a galactic disk largely determine the region's evolution time scale, researchers built a theoretical model to take into account molecular cloud and star formations in the disk evolution process. Despite some variations that may be caused by spiral arms and central bulge masses, they found that many late-type galaxies show consistency with the model in their radial atomic and molecular gas profiles. In particular, researchers propose that a scaling law be used to generalize the gas distribution characteristics. This scaling law may be useful in helping to understand the observed gas contents in many galaxies. Their model assumes an exponential mass distribution with disk radius. Most of the mass are in atomic gas state at the beginning of the evolution. Molecular clouds form through a modified Schmidt Law which takes into account gravitational instabilities in a possible three-phase structure of diffuse interstellar medium (McKee and Ostriker, 1977; Balbus and Cowie, 1985); whereas star formation proceeds presumably unaffected by the environmental conditions outside of molecular clouds (Young, 1987). In such a model both atomic and molecular gas profiles in a typical galactic disk (as a result of the evolution) can be fitted simultaneously by adjusting the efficiency constants. Galaxies of different sizes and masses, on the other hand, can be compared with the model by simply scaling their characteristic length scales and shifting their radial ranges to match the assumed disk total mass profile sigma tot(r).

Plasma focus ion beam-scaling laws

NASA Astrophysics Data System (ADS)

Saw, S. H.

2014-08-01

Measurements on plasma focus ion beams include various advanced techniques producing a variety of data which has yet to produce benchmark numbers. Recent numerical experiments using an extended version of the Lee Code has produced reference numbers and scaling trends for number and energy fluence of deuteron beams as functions of stored energy E0. At the pinch exit the ion number fluence (ions m-2) and energy fluence (J m-2) computed as 2.4-7.8×1020 and 2.2-33×106 respectively were found to be independent of E0 from 0.4 - 486 kJ. This work was extended to the ion beams for various gases. The results show that, for a given plasma focus, the fluence, flux, ion number and ion current decrease from the lightest to the heaviest gas except for trend-breaking higher values for Ar fluence and flux. The energy fluence, energy flux, power flow and damage factors are relatively constant from H2 to N2 but increase for Ne, Ar, Kr and Xe due to radiative cooling and collapse effects. This paper reviews this work and in a concluding section attempts to put the accumulating large amounts of data into the form of a scaling law of beam energy Ebeam versus storage energy E0 taking the form for deuteron as: {Ebeam} = 18.2{E}01.23; where Ebeam is in J and E0 is in kJ. It is hoped that the establishment of such scaling laws places on a firm footing the reference quantitative ideas for plasma focus ion beams.

Library Anxiety of Law Students: A Study Utilizing the Multidimensional Library Anxiety Scale

ERIC Educational Resources Information Center

Bowers, Stacey L.

2010-01-01

The purpose of this study was to determine whether law students experienced library anxiety and, if so, which components contributed to that anxiety. The Multidimensional Library Anxiety Scale (MLAS) developed by Dr. Doris Van Kampen was used to assess library anxiety levels of law students. The MLAS is a 53 question Likert scale instrument that…

A psychometric appraisal of the Jefferson Scale of Empathy using law students.

PubMed

Williams, Brett; Sifris, Adiva; Lynch, Marty

2016-01-01

A growing body of literature indicates that empathic behaviors are positively linked, in several ways, with the professional performance and mental well-being of lawyers and law students. It is therefore important to assess empathy levels among law students using psychometrically sound tools that are suitable for this cohort. The 20-item Jefferson Scale of Empathy - Health Profession Students Version was adapted for a law context (eg, the word "health care" became "legal"), and the new Jefferson Scale of Empathy - Law Students (JSE-L-S) version was completed by 275 students at Monash University, Melbourne, Australia. Data were subjected to principal component analysis. Four factors emerged from the principal component analysis ("understanding the client's perspective", "responding to clients' experiences and emotions", "responding to clients' cues and behaviors", and "standing in clients' shoes"), which accounted for 46.7% of the total variance. The reliability of the factors varied, but the overall 18-item JSE-L-S yielded a Cronbach's alpha coefficient of 0.80. Several patterns among the item loadings were similar to those reported in studies using other versions of the Jefferson Scale of Empathy. The JSE-L-S appears to be a reliable measure of empathy among undergraduate law students, which could help provide insights into law student welfare and future performance as legal practitioners. Additional evaluation of the JSE-L-S is required to disambiguate some of the minor findings explored. Adjustments may improve the psychometric properties.

Dynamo Scaling Laws for Uranus and Neptune: The Role of Convective Shell Thickness on Dipolarity

NASA Astrophysics Data System (ADS)

Stanley, Sabine; Yunsheng Tian, Bob

2017-10-01

Previous dynamo scaling law studies (Christensen and Aubert, 2006) have demonstrated that the morphology of a planet’s magnetic field is determined by the local Rossby number (Ro_l): a non-dimensional diagnostic variable that quantifies the ratio of inertial forces to Coriolis forces on the average length scale of the flow. Dynamos with Ro_l <~ 0.1 produce dipolar dominated magnetic fields whereas dynamos with Ro_l >~ 0.1 produce multipolar magnetic fields. Scaling studies have also determined the dependence of the local Rossby number on non-dimensional parameters governing the system - specifically the Ekman, Prandtl, magnetic Prandtl and flux-based Rayleigh numbers (Olson and Christensen, 2006). When these scaling laws are applied to the planets, it appears that Uranus and Neptune should have dipole-dominated fields, contrary to observations. However, those scaling laws were derived using the specific convective shell thickness of the Earth’s core. Here we investigate the role of convective shell thickness on dynamo scaling laws. We find that the local Rossby number depends exponentially on the convective shell thickness. Including this new dependence on convective shell thickness, we find that the dynamo scaling laws now predict that Uranus and Neptune reside deeply in the multipolar regime, thereby resolving the previous contradiction with observations.

DOES A SCALING LAW EXIST BETWEEN SOLAR ENERGETIC PARTICLE EVENTS AND SOLAR FLARES?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kahler, S. W., E-mail: AFRL.RVB.PA@kirtland.af.mil

2013-05-20

Among many other natural processes, the size distributions of solar X-ray flares and solar energetic particle (SEP) events are scale-invariant power laws. The measured distributions of SEP events prove to be distinctly flatter, i.e., have smaller power-law slopes, than those of the flares. This has led to speculation that the two distributions are related through a scaling law, first suggested by Hudson, which implies a direct nonlinear physical connection between the processes producing the flares and those producing the SEP events. We present four arguments against this interpretation. First, a true scaling must relate SEP events to all flare X-raymore » events, and not to a small subset of the X-ray event population. We also show that the assumed scaling law is not mathematically valid and that although the flare X-ray and SEP event data are correlated, they are highly scattered and not necessarily related through an assumed scaling of the two phenomena. An interpretation of SEP events within the context of a recent model of fractal-diffusive self-organized criticality by Aschwanden provides a physical basis for why the SEP distributions should be flatter than those of solar flares. These arguments provide evidence against a close physical connection of flares with SEP production.« less

Maintaining Moore's law: enabling cost-friendly dimensional scaling

NASA Astrophysics Data System (ADS)

Mallik, Arindam; Ryckaert, Julien; Mercha, Abdelkarim; Verkest, Diederik; Ronse, Kurt; Thean, Aaron

2015-03-01

Moore's Law (Moore's Observation) has been driving the progress in semiconductor technology for the past 50 years. The semiconductor industry is at a juncture where significant increase in manufacturing cost is foreseen to sustain the past trend of dimensional scaling. At N10 and N7 technology nodes, the industry is struggling to find a cost-friendly solution. At a device level, technologists have come up with novel devices (finFET, Gate-All-Around), material innovations (SiGe, Ge) to boost performance and reduce power consumption. On the other hand, from the patterning side, the relative slow ramp-up of alternative lithography technologies like EUVL and DSA pushes the industry to adopt a severely multi-patterning-based solution. Both of these technological transformations have a big impact on die yield and eventually die cost. This paper is aimed to analyze the impact on manufacturing cost to keep the Moore's law alive. We have proposed and analyzed various patterning schemes that can enable cost-friendly scaling. We evaluated the impact of EUVL introduction on tackling the high cost of manufacturing. The primary objective of this paper is to maintain Moore's scaling from a patterning perspective and analyzing EUV lithography introduction at a die level.

Robust regression on noisy data for fusion scaling laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be; Laboratoire de Physique des Plasmas de l'ERM - Laboratorium voor Plasmafysica van de KMS

2014-11-15

We introduce the method of geodesic least squares (GLS) regression for estimating fusion scaling laws. Based on straightforward principles, the method is easily implemented, yet it clearly outperforms established regression techniques, particularly in cases of significant uncertainty on both the response and predictor variables. We apply GLS for estimating the scaling of the L-H power threshold, resulting in estimates for ITER that are somewhat higher than predicted earlier.

Diversity of individual mobility patterns and emergence of aggregated scaling laws

PubMed Central

Yan, Xiao-Yong; Han, Xiao-Pu; Wang, Bing-Hong; Zhou, Tao

2013-01-01

Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries of volunteers, we show the absence of scaling properties in the displacement distribution at the individual level,while the aggregated displacement distribution follows a power law with an exponential cutoff. Given the constraint on total travelling cost, this aggregated scaling law can be analytically predicted by the mixture nature of human travel under the principle of maximum entropy. A direct corollary of such theory is that the displacement distribution of a single mode of transportation should follow an exponential law, which also gets supportive evidences in known data. We thus conclude that the travelling cost shapes the displacement distribution at the aggregated level. PMID:24045416

Model of the Dynamic Construction Process of Texts and Scaling Laws of Words Organization in Language Systems

PubMed Central

Li, Shan; Lin, Ruokuang; Bian, Chunhua; Ma, Qianli D. Y.

2016-01-01

Scaling laws characterize diverse complex systems in a broad range of fields, including physics, biology, finance, and social science. The human language is another example of a complex system of words organization. Studies on written texts have shown that scaling laws characterize the occurrence frequency of words, words rank, and the growth of distinct words with increasing text length. However, these studies have mainly concentrated on the western linguistic systems, and the laws that govern the lexical organization, structure and dynamics of the Chinese language remain not well understood. Here we study a database of Chinese and English language books. We report that three distinct scaling laws characterize words organization in the Chinese language. We find that these scaling laws have different exponents and crossover behaviors compared to English texts, indicating different words organization and dynamics of words in the process of text growth. We propose a stochastic feedback model of words organization and text growth, which successfully accounts for the empirically observed scaling laws with their corresponding scaling exponents and characteristic crossover regimes. Further, by varying key model parameters, we reproduce differences in the organization and scaling laws of words between the Chinese and English language. We also identify functional relationships between model parameters and the empirically observed scaling exponents, thus providing new insights into the words organization and growth dynamics in the Chinese and English language. PMID:28006026

Model of the Dynamic Construction Process of Texts and Scaling Laws of Words Organization in Language Systems.

PubMed

Li, Shan; Lin, Ruokuang; Bian, Chunhua; Ma, Qianli D Y; Ivanov, Plamen Ch

2016-01-01

Scaling laws characterize diverse complex systems in a broad range of fields, including physics, biology, finance, and social science. The human language is another example of a complex system of words organization. Studies on written texts have shown that scaling laws characterize the occurrence frequency of words, words rank, and the growth of distinct words with increasing text length. However, these studies have mainly concentrated on the western linguistic systems, and the laws that govern the lexical organization, structure and dynamics of the Chinese language remain not well understood. Here we study a database of Chinese and English language books. We report that three distinct scaling laws characterize words organization in the Chinese language. We find that these scaling laws have different exponents and crossover behaviors compared to English texts, indicating different words organization and dynamics of words in the process of text growth. We propose a stochastic feedback model of words organization and text growth, which successfully accounts for the empirically observed scaling laws with their corresponding scaling exponents and characteristic crossover regimes. Further, by varying key model parameters, we reproduce differences in the organization and scaling laws of words between the Chinese and English language. We also identify functional relationships between model parameters and the empirically observed scaling exponents, thus providing new insights into the words organization and growth dynamics in the Chinese and English language.

General wave optics propagation scaling law.

PubMed

Shakir, Sami A; Dolash, Thomas M; Spencer, Mark; Berdine, Richard; Cargill, Daniel S; Carreras, Richard

2016-12-01

A general far-field wave propagation scaling law is developed. The formulation is simple but predicts diffraction peak irradiance accurately in the far field, regardless of the near-field beam type or geometry, including laser arrays. We also introduce the concept of the equivalent uniform circular beam that generates a far-field peak irradiance and power-in-the-bucket that are the same as an arbitrary laser source. Applications to clipped Gaussian beams with an obscuration, both as a single beam and as an array of beams, are shown.

A new scaling law for temperature variance profile in the mixing zone of turbulent Rayleigh-Bénard convection

NASA Astrophysics Data System (ADS)

Wang, Yin; Xu, Wei; He, Xiao-Zhou; Yik, Hiu-Fai; Wang, Xiao-Ping; Schumacher, Jorg; Tong, Penger

2017-11-01

We report a combined experimental and numerical study of the scaling properties of the temperature variance profile η(z) along the central z axis of turbulent Rayleigh-Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. In the mixing zone outside the thermal boundary layer region, the measured η(z) is found to scale with the cell height H in both cells and obey a power law, η(z) (z/H)ɛ, with the obtained values of ɛ being very close to -1. Based on the experimental and numerical findings, we derive a new equation for η(z) in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work thus provides a common framework for understanding the effect of boundary layer fluctuations on the scaling properties of the temperature variance profile in turbulent Rayleigh-Bénard convection. This work was supported in part by Hong Kong Research Grants Council.

A psychometric appraisal of the Jefferson Scale of Empathy using law students

PubMed Central

Williams, Brett; Sifris, Adiva; Lynch, Marty

2016-01-01

Background A growing body of literature indicates that empathic behaviors are positively linked, in several ways, with the professional performance and mental well-being of lawyers and law students. It is therefore important to assess empathy levels among law students using psychometrically sound tools that are suitable for this cohort. Participants and methods The 20-item Jefferson Scale of Empathy – Health Profession Students Version was adapted for a law context (eg, the word “health care” became “legal”), and the new Jefferson Scale of Empathy – Law Students (JSE-L-S) version was completed by 275 students at Monash University, Melbourne, Australia. Data were subjected to principal component analysis. Results Four factors emerged from the principal component analysis (“understanding the client’s perspective”, “responding to clients’ experiences and emotions”, “responding to clients’ cues and behaviors”, and “standing in clients’ shoes”), which accounted for 46.7% of the total variance. The reliability of the factors varied, but the overall 18-item JSE-L-S yielded a Cronbach’s alpha coefficient of 0.80. Several patterns among the item loadings were similar to those reported in studies using other versions of the Jefferson Scale of Empathy. Conclusion The JSE-L-S appears to be a reliable measure of empathy among undergraduate law students, which could help provide insights into law student welfare and future performance as legal practitioners. Additional evaluation of the JSE-L-S is required to disambiguate some of the minor findings explored. Adjustments may improve the psychometric properties. PMID:27524924

Fifth dimension of life and the 4/5 allometric scaling law for human brain.

PubMed

He, Ji-Huan; Zhang, Juan

2004-01-01

Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.

Coexistence of a well-determined kinetic law and a scale-invariant power law during the same physical process

NASA Astrophysics Data System (ADS)

Zreihan, Noam; Faran, Eilon; Vives, Eduard; Planes, Antoni; Shilo, Doron

2018-01-01

It is generally claimed that physical processes which display scale-invariant power-law distributions are subjected to a dynamic criticality that prohibits a well-defined kinetic law. In this paper, we demonstrate the coexistence of these two apparently contradicting behaviors during the same physical process—the motion of type-II twin boundaries in martensite Ni-Mn-Ga. The process is investigated by combined measurements of the temporal twin-boundary velocity and the acoustic emitted energy. Velocity values are extracted from high-resolution force measurements taken during displacement-driven mechanical tests, as well as from force-driven magnetic tests, and cover an overall range of six orders of magnitude. Acoustic emission (AE) is measured during mechanical tests. Velocity values follow a normal distribution whose characteristic value is determined by the material's kinetic relation, and its width scales with the average velocity. In addition, it is observed that velocity distributions are characterized by a heavy tail at the right (i.e., faster) end that exhibits a power law over more than one and a half orders of magnitude. At the same time, the AE signals follow a scale-invariant power-law distribution, which is not sensitive to the average twin-boundary velocity. The coexistence of these two different statistical behaviors reflects the complex nature of twin-boundary motion and suggests the possibility that the transformation proceeds through physical subprocesses that are close to criticality alongside other processes that are not.

Nonlinear Analysis and Scaling Laws for Noncircular Composite Structures Subjected to Combined Loads

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Rose, Cheryl A.; Starnes, James H., Jr.

2001-01-01

Results from an analytical study of the response of a built-up, multi-cell noncircular composite structure subjected to combined internal pressure and mechanical loads are presented. Nondimensional parameters and scaling laws based on a first-order shear-deformation plate theory are derived for this noncircular composite structure. The scaling laws are used to design sub-scale structural models for predicting the structural response of a full-scale structure representative of a portion of a blended-wing-body transport aircraft. Because of the complexity of the full-scale structure, some of the similitude conditions are relaxed for the sub-scale structural models. Results from a systematic parametric study are used to determine the effects of relaxing selected similitude conditions on the sensitivity of the effectiveness of using the sub-scale structural model response characteristics for predicting the full-scale structure response characteristics.

Scaling-law equilibria for calcium in canopy-type models of the solar chromosphere

NASA Technical Reports Server (NTRS)

Jones, H. P.

1982-01-01

Scaling laws for resonance line formation are used to obtain approximate excitation and ionization equilibria for a three-level model of singly ionized calcium. The method has been developed for and is applied to the study of magnetograph response in the 8542 A infrared triplet line to magnetostatic canopies which schematically model diffuse, nearly horizontal fields in the low solar chromosphere. For this application, the method is shown to be efficient and semi-quantitative, and the results indicate the type and range of effects on calcium-line radiation which result from reduced gas pressure inside the magnetic regions.

Structural Similitude and Scaling Laws for Plates and Shells: A Review

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Starnes, J. H., Jr.; Rezaeepazhand, J.

2000-01-01

This paper deals with the development and use of scaled-down models in order to predict the structural behavior of large prototypes. The concept is fully described and examples are presented which demonstrate its applicability to beam-plates, plates and cylindrical shells of laminated construction. The concept is based on the use of field equations, which govern the response behavior of both the small model as well as the large prototype. The conditions under which the experimental data of a small model can be used to predict the behavior of a large prototype are called scaling laws or similarity conditions and the term that best describes the process is structural similitude. Moreover, since the term scaling is used to describe the effect of size on strength characteristics of materials, a discussion is included which should clarify the difference between "scaling law" and "size effect". Finally, a historical review of all published work in the broad area of structural similitude is presented for completeness.

Scaling Laws for NanoFET Sensors

NASA Astrophysics Data System (ADS)

Wei, Qi-Huo; Zhou, Fu-Shan

2008-03-01

In this paper, we report our numerical studies of the scaling laws for nanoplate field-effect transistor (FET) sensors by simplifying the nanoplates as random resistor networks. Nanowire/tube FETs are included as the limiting cases where the device width goes small. Computer simulations show that the field effect strength exerted by the binding molecules has significant impact on the scaling behaviors. When the field effect strength is small, nanoFETs have little size and shape dependence. In contrast, when the field-effect strength becomes stronger, there exists a lower detection threshold for charge accumulation FETs and an upper detection threshold for charge depletion FET sensors. At these thresholds, the nanoFET devices undergo a transition between low and large sensitivities. These thresholds may set the detection limits of nanoFET sensors. We propose to eliminate these detection thresholds by employing devices with very short source-drain distance and large width.

A scaling law for the local CHF on the external bottom side of a fully submerged reactor vessel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheung, F.B.; Haddad, K.H.; Liu, Y.C.

1997-02-01

A scaling law for estimating the local critical heat flux on the outer surface of a heated hemispherical vessel that is fully submerged in water has been developed from the results of an advanced hydrodynamic CHF model for pool boiling on a downward facing curved heating surface. The scaling law accounts for the effects of the size of the vessel, the level of liquid subcooling, the intrinsic properties of the fluid, and the spatial variation of the local critical heat flux along the heating surface. It is found that for vessels with diameters considerably larger than the characteristic size ofmore » the vapor masses, the size effect on the local critical heat flux is limited almost entirely to the effect of subcooling associated with the local liquid head. When the subcooling effect is accounted for separately, the local CHF limit is nearly independent of the vessel size. Based upon the scaling law developed in this work, it is possible to merge, within the experimental uncertainties, all the available local CHF data obtained for various vessel sizes under both saturated and subcooled boiling conditions into a single curve. Applications of the scaling law to commercial-size vessels have been made for various system pressures and water levels above the heated vessel. Over the range of conditions explored in this study, the local CHF limit is found to increase by a factor of two or more from the bottom center to the upper edge of the vessel. Meanwhile, the critical heat flux at a given angular position of the heated vessel is also found to increase appreciably with the system pressure and the water level.« less

Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process

PubMed Central

Corral, Álvaro; Garcia-Millan, Rosalba; Font-Clos, Francesc

2016-01-01

The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary. PMID:27584596

Turbulent scaling laws as solutions of the multi-point correlation equation using statistical symmetries

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Rosteck, Andreas; Avsarkisov, Victor

2013-11-01

Text-book knowledge proclaims that Lie symmetries such as Galilean transformation lie at the heart of fluid dynamics. These important properties also carry over to the statistical description of turbulence, i.e. to the Reynolds stress transport equations and its generalization, the multi-point correlation equations (MPCE). Interesting enough, the MPCE admit a much larger set of symmetries, in fact infinite dimensional, subsequently named statistical symmetries. Most important, theses new symmetries have important consequences for our understanding of turbulent scaling laws. The symmetries form the essential foundation to construct exact solutions to the infinite set of MPCE, which in turn are identified as classical and new turbulent scaling laws. Examples on various classical and new shear flow scaling laws including higher order moments will be presented. Even new scaling have been forecasted from these symmetries and in turn validated by DNS. Turbulence modellers have implicitly recognized at least one of the statistical symmetries as this is the basis for the usual log-law which has been employed for calibrating essentially all engineering turbulence models. An obvious conclusion is to generally make turbulence models consistent with the new statistical symmetries.

Challenges in Upscaling Geomorphic Transport Laws: Scale-dependence of Local vs. Non-local Formalisms and Derivation of Closures (Invited)

NASA Astrophysics Data System (ADS)

Foufoula-Georgiou, E.; Ganti, V. K.; Passalacqua, P.

2010-12-01

Nonlinear geomorphic transport laws are often derived from mechanistic considerations at a point, and yet they are implemented on 90m or 30 m DEMs, presenting a mismatch in the scales of derivation and application of the flux laws. Since estimates of local slopes and curvatures are known to depend on the scale of the DEM used in their computation, two questions arise: (1) how to meaningfully compensate for the scale dependence, if any, of local transport laws? and (2) how to formally derive, via upscaling, constitutive laws that are applicable at larger scales? Recently, non-local geomorphic transport laws for sediment transport on hillslopes have been introduced using the concept of an integral flux that depends on topographic attributes in the vicinity of a point of interest. In this paper, we demonstrate the scale dependence of local nonlinear hillslope sediment transport laws and derive a closure term via upscaling (Reynolds averaging). We also show that the non-local hillslope transport laws are inherently scale independent owing to their non-local, scale-free nature. These concepts are demonstrated via an application to a small subbasin of the Oregon Coast Range using 2m LiDAR topographic data.

Preliminary scaling laws for plasma current, ion kinetic temperature, and plasma number density in the NASA Lewis bumpy torus plasma

NASA Technical Reports Server (NTRS)

Roth, J. R.

1976-01-01

Parametric variation of independent variables which may affect the characteristics of bumpy torus plasma have identified those which have a significant effect on the plasma current, ion kinetic temperature, and plasma number density, and those which do not. Empirical power law correlations of the plasma current, and the ion kinetic temperature and number density were obtained as functions of potential applied to the midplane electrode rings, the background neutral gas pressure, and the magnetic field strength. Additional parameters studied included the type of gas, the polarity of the midplane electrode rings, the mode of plasma operation, and the method of measuring the plasma number density. No significant departures from the scaling laws appear to occur at the highest ion kinetic temperatures or number densities obtained to date.

Scaling Law for Cross-stream Diffusion in Microchannels under Combined Electroosmotic and Pressure Driven Flow.

PubMed

Song, Hongjun; Wang, Yi; Pant, Kapil

2013-01-01

This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially-dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection-diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin Electric Double Layer (EDL). The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5% relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient (NPG) cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly-shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially-dependent diffusion layer thickness and scaling law across a wide range of the parameter space.

Scaling Law for Cross-stream Diffusion in Microchannels under Combined Electroosmotic and Pressure Driven Flow

PubMed Central

Song, Hongjun; Wang, Yi; Pant, Kapil

2012-01-01

This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially-dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection-diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin Electric Double Layer (EDL). The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5% relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient (NPG) cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly-shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially-dependent diffusion layer thickness and scaling law across a wide range of the parameter space. PMID:23554584

From coastal barriers to mountain belts - commonalities in fundamental geomorphic scaling laws

NASA Astrophysics Data System (ADS)

Lazarus, E.

2016-12-01

Overwash is a sediment-transport process essential to the form and resilience of coastal barrier landscapes. Driven by storm events, overwash leaves behind distinctive sedimentary features that, although intensively studied, have lacked unifying quantitative descriptions with which to compare their morphological attributes across documented examples or relate them to other morphodynamic phenomena. Geomorphic scaling laws quantify how measures of shape and size change with respect to another - information that helps to constrain predictions of future change and reconstructions of past environmental conditions. Here, a physical model of erosional and depositional overwash morphology yields intrinsic, allometric scaling laws involving length, width, area, volume, and alongshore spacing. Corroborative comparisons with natural washover morphology indicate scale invariance spanning several orders of magnitude. Several observers of the physical model remarked that the overwashed barrier resembled a dissected linear mountain front with an alluvial apron - an intriguing reimagining of the intended analog. Indeed, that resemblance is reflected quantitatively in these new scaling relationships, which align with canonical scaling laws for terrestrial and marine drainage basins and alluvial fans on Earth and Mars. This finding suggests disparate geomorphic systems that share common allometric properties may be related dynamically, perhaps by an influence more fundamental than characteristic erosion and deposition processes. Such an influence could come from emergent behavior at the intersection of advection and diffusion. Geomorphic behaviors at advection-diffusion transitions (and vice versa), specifically, could be the key to disentangling mechanistic causality from acausality in physical landscape patterns.

Spectral scaling laws of solar wind fluctuations at 1 AU: Part 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Podesta, John J.

2013-06-13

In-situ measurements of solar wind fluctuations at 1 AU show that the reduced energy spectrum, equal to the sum of the reduced kinetic plus magnetic energy spectra, is characterized by a power-law scaling k{sup -{alpha}} in the inertial range with an average spectral exponent {alpha} Asymptotically-Equal-To 3/2, a result confirmed by independent analyses using data from different spacecraft. Magnetic field and electron density spectra at kinetic scales {rho}{sup -1}{sub i} < k < {rho}{sup -1}{sub e} both have a spectral index of approximately 2.7. These and other recent observations of spectral scaling laws in the solar wind using single spacecraftmore » measurements are briefly reviewed. The first part of this review, Part 1, is contained in a separate paper in these proceedings.« less

Women's awareness of liberalization of abortion law and knowledge of place for obtaining services in Nepal.

PubMed

Thapa, Shyam; Sharma, Sharad K

2015-03-01

In Nepal, following the liberalization of the abortion law, expansion and scaling up of services proceeded in parallel with efforts to create awareness of the legalization status of abortion and provide women with information about where services are available. This article assesses the effectiveness of these programmatic interventions in the early years of the country's abortion program. Data from a 2006 national survey are analyzed with 2 outcome measures-awareness of the legal status of abortion and knowledge of places to obtain abortion services among women ages 15 to 44 years. The variations in the outcomes are analyzed by ecological-development subregion, residence, education, household wealth quintile, age, and number of living children. Bivariate and multivariate logistic regression techniques are used. Overall 32.3% (95% confidence interval = 31.4% to 33.2%) of the respondents were aware of the legal status of abortion and 56.5% (95% confidence interval = 55.5% to 57.4%) knew of a place where they could obtain an abortion. Both outcome measures showed considerable variations by the covariates. Women with secondary or higher level of education had the highest odds ratio of being aware of the law and having knowledge of a source for abortion services. Ecological-development subregions showed the second highest levels of odds ratios. Significant disparities among the population subgroups existed in the diffusion of awareness of the legal status of abortion and having knowledge of a place for abortion services in Nepal. The results point to which population subgroups to focus on and also serve as a baseline for assessing future progress in the diffusion process. © 2012 APJPH.

Scaling laws for first and second generation electrospray droplets

NASA Astrophysics Data System (ADS)

Basaran, Osman; Sambath, Krishnaraj; Anthony, Christopher; Collins, Robert; Wagoner, Brayden; Harris, Michael

2017-11-01

When uncharged liquid interfaces of pendant and free drops (hereafter referred to as parent drops) or liquid films are subject to a sufficiently strong electric field, they can emit thin fluid jets from conical tip structures that form at their surfaces. The disintegration of such jets into a spray consisting of charged droplets (hereafter referred to as daughter droplets) is common to electrospray ionization mass spectrometry, printing and coating processes, and raindrops in thunderclouds. We use simulation to determine the sizes and charges of these first-generation daughter droplets which are shown to be Coulombically stable and charged below the Rayleigh limit of stability. Once these daughter droplets shrink in size due to evaporation, they in turn reach their respective Rayleigh limits and explode by emitting yet even smaller second-generation daughter droplets from their conical tips. Once again, we use simulation and theory to deduce scaling laws for the sizes and charges of these second-generation droplets. A comparison is also provided for scaling laws pertaining to different generations of daughter droplets.

Unsteady loads due to propulsive lift configurations. Part A: Investigation of scaling laws

NASA Technical Reports Server (NTRS)

Morton, J. B.; Haviland, J. K.

1978-01-01

This study covered scaling laws, and pressure measurements made to determine details of the large scale jet structure and to verify scaling laws by direct comparison. The basis of comparison was a test facility at NASA Langley in which a JT-15D exhausted over a boilerplater airfoil surface to reproduce upper surface blowing conditions. A quarter scale model was built of this facility, using cold jets. A comparison between full scale and model pressure coefficient spectra, presented as functions of Strouhal numbers, showed fair agreement, however, a shift of spectral peaks was noted. This was not believed to be due to Mach number or Reynolds number effects, but did appear to be traceable to discrepancies in jet temperatures. A correction for jet temperature was then tried, similar to one used for far field noise prediction. This was found to correct the spectral peak discrepancy.

Scaling laws in decaying helical hydromagnetic turbulence

NASA Astrophysics Data System (ADS)

Christensson, M.; Hindmarsh, M.; Brandenburg, A.

2005-07-01

We study the evolution of growth and decay laws for the magnetic field coherence length ξ, energy E_M and magnetic helicity H in freely decaying 3D MHD turbulence. We show that with certain assumptions, self-similarity of the magnetic power spectrum alone implies that ξ σm t1/2. This in turn implies that magnetic helicity decays as Hσm t-2s, where s=(ξ_diff/ξH)2, in terms of ξ_diff, the diffusion length scale, and ξ_H, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as E_M σm t-1/2-2s. The parameter s is inversely proportional to the magnetic Reynolds number Re_M, which is constant in the self-similar regime.

Scaling laws and vortex profiles in two-dimensional decaying turbulence.

PubMed

Laval, J P; Chavanis, P H; Dubrulle, B; Sire, C

2001-06-01

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, like predicted in Carnevale et al., Phys. Rev. Lett. 66, 2735 (1991), and it is observed that viscous effects spoil this scaling regime. The exponent controlling the decay of the number of vortices shows some trends toward xi=1, in agreement with a recent theory based on the Kirchhoff model [C. Sire and P. H. Chavanis, Phys. Rev. E 61, 6644 (2000)]. In terms of scaled variables, the vortices have a similar profile with a functional form related to the Fermi-Dirac distribution.

CT-based Diagnosis of Diffuse Coronary Artery Disease on the Basis of Scaling Power Laws

PubMed Central

Huo, Yunlong; Wischgoll, Thomas; Choy, Jenny Susana; Sola, Srikanth; Navia, Jose L.; Teague, Shawn D.; Bhatt, Deepak L.

2013-01-01

Purpose: To provide proof of concept for a diagnostic method to assess diffuse coronary artery disease (CAD) on the basis of coronary computed tomography (CT) angiography. Materials and Methods: The study was approved by the Cleveland Clinic Institutional Review Board, and all subjects gave informed consent. Morphometric data from the epicardial coronary artery tree, determined with CT angiography in 120 subjects (89 patients with metabolic syndrome and 31 age- and sex-matched control subjects) were analyzed on the basis of the scaling power law. Results obtained in patients with metabolic syndrome and control subjects were compared statistically. Results: The mean lumen cross-sectional area (ie, lumen cross-sectional area averaged over each vessel of an epicardial coronary artery tree) and sum of intravascular volume in patients with metabolic syndrome (0.039 cm2 ± 0.015 [standard deviation] and 2.71 cm3 ± 1.75, respectively) were significantly less than those in control subjects (0.054 cm2± 0.015 and 3.29 cm3± 1.77, respectively; P < .05). The length-volume power law showed coefficients of 27.0 cm−4/3 ± 9.0 (R2 = 0.91 ± 0.08) for patients with metabolic syndrome and 19.9 cm−4/3 ± 4.3 (R2 = 0.92 ± 0.07) for control subjects (P < .05). The probability frequency shows that more than 65% of patients with metabolic syndrome had a coefficient of 23 or more for the length-volume scaling power law, whereas approximately 90% of the control subjects had a coefficient of less than 23. Conclusion: The retrospective scaling analysis provides a quantitative rationale for diagnosis of diffuse CAD. © RSNA, 2013 Supplemental material: http://radiology.rsna.org/lookup/suppl/doi:10.1148/radiol.13122181/-/DC1 PMID:23616633

Improved scaling laws for stage inert mass of space propulsion systems. Volume 1: Summary

NASA Technical Reports Server (NTRS)

1971-01-01

Summarized is a study which satisfies the need for improved scaling laws for stage inert mass of space propulsion systems. The resulting laws are applicable to current and future vehicle systems and designs for a comprehensive spectrum of anticipated planetary missions.

Scaling laws for nanoFET sensors

NASA Astrophysics Data System (ADS)

Zhou, Fu-Shan; Wei, Qi-Huo

2008-01-01

The sensitive conductance change of semiconductor nanowires and carbon nanotubes in response to the binding of charged molecules provides a novel sensing modality which is generally denoted as nanoFET sensors. In this paper, we study the scaling laws of nanoplate FET sensors by simplifying nanoplates as random resistor networks with molecular receptors sitting on lattice sites. Nanowire/tube FETs are included as the limiting cases where the device width goes small. Computer simulations show that the field effect strength exerted by the binding molecules has significant impact on the scaling behaviors. When the field effect strength is small, nanoFETs have little size and shape dependence. In contrast, when the field effect strength becomes stronger, there exists a lower detection threshold for charge accumulation FETs and an upper detection threshold for charge depletion FET sensors. At these thresholds, the nanoFET devices undergo a transition between low and large sensitivities. These thresholds may set the detection limits of nanoFET sensors, while they could be eliminated by designing devices with very short source-drain distance and large width.

Fractionaly Integrated Flux model and Scaling Laws in Weather and Climate

NASA Astrophysics Data System (ADS)

Schertzer, Daniel; Lovejoy, Shaun

2013-04-01

The Fractionaly Integrated Flux model (FIF) has been extensively used to model intermittent observables, like the velocity field, by defining them with the help of a fractional integration of a conservative (i.e. strictly scale invariant) flux, such as the turbulent energy flux. It indeed corresponds to a well-defined modelling that yields the observed scaling laws. Generalised Scale Invariance (GSI) enables FIF to deal with anisotropic fractional integrations and has been rather successful to define and model a unique regime of scaling anisotropic turbulence up to planetary scales. This turbulence has an effective dimension of 23/9=2.55... instead of the classical hypothesised 2D and 3D turbulent regimes, respectively for large and small spatial scales. It therefore theoretically eliminates a non plausible "dimension transition" between these two regimes and the resulting requirement of a turbulent energy "mesoscale gap", whose empirical evidence has been brought more and more into question. More recently, GSI-FIF was used to analyse climate, therefore at much larger time scales. Indeed, the 23/9-dimensional regime necessarily breaks up at the outer spatial scales. The corresponding transition range, which can be called "macroweather", seems to have many interesting properties, e.g. it rather corresponds to a fractional differentiation in time with a roughly flat frequency spectrum. Furthermore, this transition yields the possibility to have at much larger time scales scaling space-time climate fluctuations with a much stronger scaling anisotropy between time and space. Lovejoy, S. and D. Schertzer (2013). The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge Press (in press). Schertzer, D. et al. (1997). Fractals 5(3): 427-471. Schertzer, D. and S. Lovejoy (2011). International Journal of Bifurcation and Chaos 21(12): 3417-3456.

Scaling Law of Urban Ride Sharing.

PubMed

Tachet, R; Sagarra, O; Santi, P; Resta, G; Szell, M; Strogatz, S H; Ratti, C

2017-03-06

Sharing rides could drastically improve the efficiency of car and taxi transportation. Unleashing such potential, however, requires understanding how urban parameters affect the fraction of individual trips that can be shared, a quantity that we call shareability. Using data on millions of taxi trips in New York City, San Francisco, Singapore, and Vienna, we compute the shareability curves for each city, and find that a natural rescaling collapses them onto a single, universal curve. We explain this scaling law theoretically with a simple model that predicts the potential for ride sharing in any city, using a few basic urban quantities and no adjustable parameters. Accurate extrapolations of this type will help planners, transportation companies, and society at large to shape a sustainable path for urban growth.

Revisiting the generalized scaling law for adhesion: role of compliance and extension to progressive failure.

PubMed

Mojdehi, Ahmad R; Holmes, Douglas P; Dillard, David A

2017-10-25

A generalized scaling law, based on the classical fracture mechanics approach, is developed to predict the bond strength of adhesive systems. The proposed scaling relationship depends on the rate of change of debond area with compliance, rather than the ratio of area to compliance. This distinction can have a profound impact on the expected bond strength of systems, particularly when the failure mechanism changes or the compliance of the load train increases. Based on the classical fracture mechanics approach for rate-independent materials, the load train compliance should not affect the force capacity of the adhesive system, whereas when the area to compliance ratio is used as the scaling parameter, it directly influences the bond strength, making it necessary to distinguish compliance contributions. To verify the scaling relationship, single lap shear tests were performed for a given pressure sensitive adhesive (PSA) tape specimens with different bond areas, number of backing layers, and load train compliance. The shear lag model was used to derive closed-form relationships for the system compliance and its derivative with respect to the debond area. Digital image correlation (DIC) is implemented to verify the non-uniform shear stress distribution obtained from the shear lag model in a lap shear geometry. The results obtained from this approach could lead to a better understanding of the relationship between bond strength and the geometry and mechanical properties of adhesive systems.

Scaling Law of Impact Induced Shock Pressure in Planetary Mantle

NASA Astrophysics Data System (ADS)

Monteux, Julien; Arkani-Hamed, Jafar

2015-04-01

While hydrocode simulation of impact induced shock pressure inside planetary mantle is more accurate, it is not suitable for studying several hundreds of impacts occurring during the accretion of a planet. Not only simulation of each impact takes over two orders of magnitude longer computer time than that of a scaling law simulation [1], but also it is cumbersome to apply for growing proto-planets where size of a proto-planet and impact velocities of the accreting bodies increase significantly. This is compounded by the formation of the iron core during the accretion with increasing size. Major impacting bodies during accretion of a Mars type planet have very low velocities. We use iSale hydrocode simulations and adopt physical properties of dunite for the mantle to calculate shock pressure and particle velocity in a Mars type body for 11 impact velocities ranging from 4 to 60 km/s. Large impactors of 100 to 1000 km in diameter, comparable to those impacted on Mars and created giant impact basins, are examined. The results are in good agreement with those of Pierazzo et al. [2] which were calculated for impact velocities higher than 10 km/s and impactor of 0.2 to 10 km in diameter. The internal consistency of our models indicates that our scaling laws are also accurate for lower impact velocities. We found no distinct isobaric region, rather the peak shock pressure changes relatively slowly versus distance from the impact site in the near field zone, within ~ 3 times the impactor radius, compare to that in the far field zone as also suggested by Ahrens and O'Keefe [3]. Hence we propose two distinct scaling laws, the power law distribution of shock pressure P as a function of distance R from the impact site at the surface, one for the near field zone and the other for the far field zone: Log P = a + n Log (R/Rimp) With n = 1.72 - 2.44 Log(Vimp) for R < ~3 Rimp, and n = -0.84 -0.51 Log(Vimp) for R > ~3 Rimp where a is a constant, Rimp is the impactor radius, and Vimp

Assessing changes in extreme river flow regulation from non-stationarity in hydrological scaling laws

NASA Astrophysics Data System (ADS)

Rodríguez, Estiven; Salazar, Juan Fernando; Villegas, Juan Camilo; Mercado-Bettín, Daniel

2018-07-01

Extreme flows are key components of river flow regimes that affect manifold hydrological, geomorphological and ecological processes with societal relevance. One fundamental characteristic of extreme flows in river basins is that they exhibit scaling properties which can be identified through scaling (power) laws. Understanding the physical mechanisms behind such scaling laws is a continuing challenge in hydrology, with potential implications for the prediction of river flow regimes in a changing environment and ungauged basins. After highlighting that the scaling properties are sensitive to environmental change, we develop a physical interpretation of how temporal changes in scaling exponents relate to the capacity of river basins to regulate extreme river flows. Regulation is defined here as the basins' capacity to either dampen high flows or to enhance low flows. Further, we use this framework to infer temporal changes in the regulation capacity of five large basins in tropical South America. Our results indicate that, during the last few decades, the Amazon river basin has been reducing its capacity to enhance low flows, likely as a consequence of pronounced environmental change in its south and south-eastern sub-basins. The proposed framework is widely applicable to different basins, and provides foundations for using scaling laws as empirical tools for inferring temporal changes of hydrological regulation, particularly relevant for identifying and managing hydrological consequences of environmental change.

Preliminary scaling laws for plasma current, ion kinetic temperature, and plasma number density in the NASA Lewis Bumpy Torus plasma

NASA Technical Reports Server (NTRS)

Roth, J. R.

1976-01-01

Parametric variation of independent variables which may affect the characteristics of the NASA Lewis Bumpy Torus plasma have identified those which have a significant effect on the plasma current, ion kinetic temperature, and plasma number density, and those which do not. Empirical power-law correlations of the plasma current, and the ion kinetic temperature and number density were obtained as functions of the potential applied to the midplane electrode rings, the background neutral gas pressure, and the magnetic field strength. Additional parameters studied include the type of gas, the polarity of the midplane electrode rings (and hence the direction of the radial electric field), the mode of plasma operation, and the method of measuring the plasma number density. No significant departures from the scaling laws appear to occur at the highest ion kinetic temperatures or number densities obtained to date.

Scaling phenomena in fatigue and fracture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barenblatt, G.I.

2004-12-01

The general classification of scaling laws will be presented and the basic concepts of modern similarity analysis--intermediate asymptotics, complete and incomplete similarity--will be introduced and discussed. The examples of scaling laws corresponding to complete similarity will be given. The Paris scaling law in fatigue will be discussed as an instructive example of incomplete similarity. It will be emphasized that in the Paris law the powers are not the material constants. Therefore, the evaluation of the life-time of structures using the data obtained from standard fatigue tests requires some precautions.

The Development and Psychometric Properties of the Immigration Law Concerns Scale (ILCS) for HIV Testing.

PubMed

Lechuga, Julia; Galletly, Carol L; Broaddus, Michelle R; Dickson-Gomez, Julia B; Glasman, Laura R; McAuliffe, Timothy L; Vega, Miriam Y; LeGrand, Sarah; Mena, Carla A; Barlow, Morgan L; Valera, Erik; Montenegro, Judith I

2017-11-08

To develop, pilot test, and conduct psychometric analyses of an innovative scale measuring the influence of perceived immigration laws on Latino migrants' HIV-testing behavior. The Immigration Law Concerns Scale (ILCS) was developed in three phases: Phase 1 involved a review of law and literature, generation of scale items, consultation with project advisors, and subsequent revision of the scale. Phase 2 involved systematic translation- back translation and consensus-based editorial processes conducted by members of a bilingual and multi-national study team. In Phase 3, 339 sexually active, HIV-negative Spanish-speaking, non-citizen Latino migrant adults (both documented and undocumented) completed the scale via audio computer-assisted self-interview. The psychometric properties of the scale were tested with exploratory factor analysis and estimates of reliability coefficients were generated. Bivariate correlations were conducted to test the discriminant and predictive validity of identified factors. Exploratory factor analysis revealed a three-factor, 17-item scale. subscale reliability ranged from 0.72 to 0.79. There were significant associations between the ILCS and the HIV-testing behaviors of participants. Results of the pilot test and psychometric analysis of the ILCS are promising. The scale is reliable and significantly associated with the HIV-testing behaviors of participants. Subscales related to unwanted government attention and concerns about meeting moral character requirements should be refined.

Pinch-off Scaling Law of Soap Bubbles

NASA Astrophysics Data System (ADS)

Davidson, John; Ryu, Sangjin

2014-11-01

Three common interfacial phenomena that occur daily are liquid drops in gas, gas bubbles in liquid and thin-film bubbles. One aspect that has been studied for these phenomena is the formation or pinch-off of the drop/bubble from the liquid/gas threads. In contrast to the formation of liquid drops in gas and gas bubbles in liquid, thin-film bubble pinch-off has not been well documented. Having thin-film interfaces may alter the pinch-off process due to the limiting factor of the film thickness. We observed the pinch-off of one common thin-film bubble, soap bubbles, in order to characterize its pinch-off behavior. We achieved this by constructing an experimental model replicating the process of a human producing soap bubbles. Using high-speed videography and image processing, we determined that the minimal neck radius scaled with the time left till pinch-off, and that the scaling law exponent was 2/3, similar to that of liquid drops in gas.

Revised scaling laws for asteroid disruptions

NASA Astrophysics Data System (ADS)

Jutzi, M.

2014-07-01

Models for the evolution of small-body populations (e.g., the asteroid main belt) of the solar system compute the time-dependent size and velocity distributions of the objects as a result of both collisional and dynamical processes. A scaling parameter often used in such numerical models is the critical specific impact energy Q^*_D, which results in the escape of half of the target's mass in a collision. The parameter Q^*_D is called the catastrophic impact energy threshold. We present recent improvements of the Smooth Particle Hydrodynamics (SPH) technique (Benz and Asphaug 1995, Jutzi et al. 2008, Jutzi 2014) for the modeling of the disruption of small bodies. Using the improved models, we then systematically study the effects of various target properties (e.g., strength, porosity, and friction) on the outcome of disruptive collisions (Figure), and we compute the corresponding Q^*_D curves as a function of target size. For a given specific impact energy and impact angle, the outcome of a collision in terms of Q^*_D does not only depend on the properties of the bodies involved, but also on the impact velocity and the size ratio of target/impactor. Leinhardt and Stewardt (2012) proposed scaling laws to predict the outcome of collisions with a wide range of impact velocities (m/s to km/s), target sizes and target/impactor mass ratios. These scaling laws are based on a "principal disruption curve" defined for collisions between equal-sized bodies: Q^*_{RD,γ = 1} = c^* 4/5 π ρ G R_{C1}^2, where the parameter c^* is a measure of the dissipation of energy within the target, R_{C1} the radius of a body with the combined mass of target and projectile and a density ρ = 1000 kg/m^3, and γ is the mass ratio. The dissipation parameter c^* is proposed to be 5±2 for bodies with strength and 1.9±0.3 for hydrodynamic bodies (Leinhardt and Stewardt 2012). We will present values for c^* based on our SPH simulations using various target properties and impact conditions. We

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

NASA Technical Reports Server (NTRS)

Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye

1998-01-01

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

Study of the Anatomy of the X-Ray and Neutron Production Scaling Laws in the Plasma Focus.

DTIC Science & Technology

1980-05-15

plasma focus discharge in deuterium as an extension of our previous work on scaling laws of x-ray and neutron production. The structure of dense plasmoids which emit MeV ions has been recorded by ion imaging with pinhole camera and contact print techniques. The plasmoids are generated in the same region in which particle beams, neutron and x-ray emission reach a maximum of intensity. Sharply defined boundaries of the ion-beam source and of plasmoids have been obtained by ion track etching on plastic material

Optimal Control Modification Adaptive Law for Time-Scale Separated Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

SIMILARITY PROPERTIES AND SCALING LAWS OF RADIATION HYDRODYNAMIC FLOWS IN LABORATORY ASTROPHYSICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Falize, E.; Bouquet, S.; Michaut, C., E-mail: emeric.falize@cea.fr

The spectacular recent development of modern high-energy density laboratory facilities which concentrate more and more energy in millimetric volumes allows the astrophysical community to reproduce and to explore, in millimeter-scale targets and during very short times, astrophysical phenomena where radiation and matter are strongly coupled. The astrophysical relevance of these experiments can be checked from the similarity properties and especially scaling law establishment, which constitutes the keystone of laboratory astrophysics. From the radiating optically thin regime to the so-called optically thick radiative pressure regime, we present in this paper, for the first time, a complete analysis of the main radiatingmore » regimes that we encountered in laboratory astrophysics with the same formalism based on Lie group theory. The use of the Lie group method appears to be a systematic method which allows us to construct easily and systematically the scaling laws of a given problem. This powerful tool permits us to unify the recent major advances on scaling laws and to identify new similarity concepts that we discuss in this paper, and suggests important applications for present and future laboratory astrophysics experiments. All these results enable us to demonstrate theoretically that astrophysical phenomena in such radiating regimes can be explored experimentally thanks to powerful facilities. Consequently, the results presented here are a fundamental tool for the high-energy density laboratory astrophysics community in order to quantify the astrophysics relevance and justify laser experiments. Moreover, relying on Lie group theory, this paper constitutes the starting point of any analysis of the self-similar dynamics of radiating fluids.« less

Analysis of a Compressed Thin Film Bonded to a Compliant Substrate: The Energy Scaling Law

NASA Astrophysics Data System (ADS)

Kohn, Robert V.; Nguyen, Hoai-Minh

2013-06-01

We consider the deformation of a thin elastic film bonded to a thick compliant substrate, when the (compressive) misfit is far beyond critical. We take a variational viewpoint—focusing on the total elastic energy, i.e. the membrane and bending energy of the film plus the elastic energy of the substrate—viewing the buckling of the film as a problem of energy-driven pattern formation. We identify the scaling law of the minimum energy with respect to the physical parameters of the problem, and we prove that a herringbone pattern achieves the optimal scaling. These results complement previous numerical studies, which have shown that an optimized herringbone pattern has lower energy than a number of other patterns. Our results are different, because (i) we make the scaling law achieved by the herringbone pattern explicit, and (ii) we give an elementary, ansatz-free proof that no pattern can achieve a better law.

Straight scaling FFAG beam line

NASA Astrophysics Data System (ADS)

Lagrange, J.-B.; Planche, T.; Yamakawa, E.; Uesugi, T.; Ishi, Y.; Kuriyama, Y.; Qin, B.; Okabe, K.; Mori, Y.

2012-11-01

Fixed field alternating gradient (FFAG) accelerators are recently subject to a strong revival. They are usually designed in a circular shape; however, it would be an asset to guide particles with no overall bend in this type of accelerator. An analytical development of a straight FFAG cell which keeps zero-chromaticity is presented here. A magnetic field law is thus obtained, called "straight scaling law", and an experiment has been conducted to confirm this zero-chromatic law. A straight scaling FFAG prototype has been designed and manufactured, and horizontal phase advances of two different energies are measured. Results are analyzed to clarify the straight scaling law.

Jet Mixing Noise Scaling Laws SHJAR Data Vs. Predictions

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James

2008-01-01

High quality jet noise spectral data measured at the anechoic dome 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 as well as convergent-divergent axisymmetric nozzles. The spectral measurements are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of (0.01 10.0). Measurements are reported as lossless (i.e. atmospheric attenuation is added to as-measured data), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter arc. Following the work of Viswanathan [Ref. 1], velocity power laws are derived using a least square fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit is studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. On the application side, power laws are extremely useful in identifying components from various noise generation mechanisms. From this analysis, jet noise prediction tools can be developed with physics derived from the different spectral components.

Centrifuge impact cratering experiments: Scaling laws for non-porous targets

NASA Technical Reports Server (NTRS)

Schmidt, Robert M.

1987-01-01

A geotechnical centrifuge was used to investigate large body impacts onto planetary surfaces. At elevated gravity, it is possible to match various dimensionless similarity parameters which were shown to govern large scale impacts. Observations of crater growth and target flow fields have provided detailed and critical tests of a complete and unified scaling theory for impact cratering. Scaling estimates were determined for nonporous targets. Scaling estimates for large scale cratering in rock proposed previously by others have assumed that the crater radius is proportional to powers of the impactor energy and gravity, with no additional dependence on impact velocity. The size scaling laws determined from ongoing centrifuge experiments differ from earlier ones in three respects. First, a distinct dependence of impact velocity is recognized, even for constant impactor energy. Second, the present energy exponent for low porosity targets, like competent rock, is lower than earlier estimates. Third, the gravity exponent is recognized here as being related to both the energy and the velocity exponents.

Theoretical scaling law of coronal magnetic field and electron power-law index in solar microwave burst sources

NASA Astrophysics Data System (ADS)

Huang, Y.; Song, Q. W.; Tan, B. L.

2018-04-01

It is first proposed a theoretical scaling law respectively for the coronal magnetic field strength B and electron power-law index δ versus frequency and coronal height in solar microwave burst sources. Based on the non-thermal gyro-synchrotron radiation model (Ramaty in Astrophys. J. 158:753, 1969), B and δ are uniquely solved by the observable optically-thin spectral index and turnover (peak) frequency, the other parameters (plasma density, temperature, view angle, low and high energy cutoffs, etc.) are relatively insensitive to the calculations, thus taken as some typical values. Both of B and δ increase with increasing of radio frequency but with decreasing of coronal height above photosphere, and well satisfy a square or cubic logarithmic fitting.

The star-formation law at GMC scales in M33, the Triangulum Galaxy

NASA Astrophysics Data System (ADS)

Williams, Thomas G.; Gear, Walter K.; Smith, Matthew W. L.

2018-06-01

We present a high spatial resolution study, on scales of ˜100pc, of the relationship between star-formation rate (SFR) and gas content within Local Group galaxy M33. Combining deep SCUBA-2 observations with archival GALEX, SDSS, WISE, Spitzer and submillimetre Herschel data, we are able to model the entire SED from UV to sub-mm wavelengths. We calculate the SFR on a pixel-by-pixel basis using the total infrared luminosity, and find a total SFR of 0.17 ± 0.06 {M}_⊙/yr, somewhat lower than our other two measures of SFR - combined FUV and 24μ SFR (0.25^{+0.10}_{-0.07} {M}_⊙/yr) and SED-fitting tool MAGPHYS (0.33^{+0.05}_{-0.06} {M}_⊙/yr). We trace the total gas using a combination of the 21cm HI line for atomic hydrogen, and CO(J=2-1) data for molecular hydrogen. We have also traced the total gas using dust masses. We study the star-formation law in terms of molecular gas, total gas, and gas from dust. We perform an analysis of the star-formation law on a variety of pixel scales, from 25" to 500" (100pc to 2kpc). At kpc scales, we find that a linear Schmidt-type power law index is suitable for molecular gas, but the index appears to be much higher with total gas, and gas from dust. Whilst we find a strong scale dependence on the Schmidt index, the gas depletion timescale is invariant with pixel scale.

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

PubMed Central

Kang, Chang-kwon; Shyy, Wei

2013-01-01

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots. PMID:23760300

Scale-Dependent Friction and Damage Interface law: implications for effective earthquake rupture dynamics and radiation

NASA Astrophysics Data System (ADS)

Festa, Gaetano; Vilotte, Jean-Pierre; Raous, Michel; Henninger, Carole

2010-05-01

Propagation and radiation of an earthquake rupture is commonly considered as a friction dominated process on fault surfaces. Friction laws, such as the slip weakening and the rate-and-state laws are widely used in the modeling of the earthquake rupture process. These laws prescribe the traction evolution versus slip, slip rate and potentially other internal variables. They introduce a finite cohesive length scale over which the fracture energy is released. However faults are finite-width interfaces with complex internal structures, characterized by highly damaged zones embedding a very thin principal slip interface where most of the dynamic slip localizes. Even though the rupture process is generally investigated at wavelengths larger than the fault zone thickness, which should justify a formulation based upon surface energy, a consistent homogeneization, a very challenging problem, is still missing. Such homogeneization is however be required to derive the consistent form of an effective interface law, as well as the appropriate physical variables and length scales, to correctly describe the coarse-grained dissipation resulting from surface and volumetric contributions at the scale of the fault zone. In this study, we investigate a scale-dependent law, introduced by Raous et al. (1999) in the context of adhesive material interfaces, that takes into account the transition between a damage dominated and a friction dominated state. Such a phase-field formalism describes this transition through an order parameter. We first compare this law to standard slip weakening friction law in terms of the rupture nucleation. The problem is analyzed through the representation of the solution of the quasi-static elastic problem onto the Chebyshev polynomial basis, generalizing the Uenishi-Rice solution. The nucleation solutions, at the onset of instability, are then introduced as initial conditions for the study of the dynamic rupture propagation, in the case of in-plane rupture

MAGNETIC SCALING LAWS FOR THE ATMOSPHERES OF HOT GIANT EXOPLANETS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Menou, Kristen

2012-02-01

We present scaling laws for advection, radiation, magnetic drag, and ohmic dissipation in the atmospheres of hot giant exoplanets. In the limit of weak thermal ionization, ohmic dissipation increases with the planetary equilibrium temperature (T{sub eq} {approx}> 1000 K) faster than the insolation power does, eventually reaching values {approx}> 1% of the insolation power, which may be sufficient to inflate the radii of hot Jupiters. At higher T{sub eq} values still magnetic drag rapidly brakes the atmospheric winds, which reduces the associated ohmic dissipation power. For example, for a planetary field strength B = 10 G, the fiducial scaling lawsmore » indicate that ohmic dissipation exceeds 1% of the insolation power over the equilibrium temperature range T{sub eq} {approx} 1300-2000 K, with a peak contribution at T{sub eq} {approx} 1600 K. Evidence for magnetically dragged winds at the planetary thermal photosphere could emerge in the form of reduced longitudinal offsets for the dayside infrared hotspot. This suggests the possibility of an anticorrelation between the amount of hotspot offset and the degree of radius inflation, linking the atmospheric and interior properties of hot giant exoplanets in an observationally testable way. While providing a useful framework to explore the magnetic scenario, the scaling laws also reveal strong parameter dependencies, in particular with respect to the unknown planetary magnetic field strength.« less

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

PubMed

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.

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

PubMed Central

Tippett, Michael K.; Cohen, Joel E.

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Tippett, Michael K.; Cohen, Joel E.

2016-02-01

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

A fresh look at crater scaling laws for normal and oblique hypervelocity impacts

NASA Technical Reports Server (NTRS)

Watts, A. J.; Atkinson, D. R.; Rieco, S. R.; Brandvold, J. B.; Lapin, S. L.; Coombs, C. R.

1993-01-01

With the concomitant increase in the amount of man-made debris and an ever increasing use of space satellites, the issue of accidental collisions with particles becomes more severe. While the natural micrometeoroid population is unavoidable and assumed constant, continued launches increase the debris population at a steady rate. Debris currently includes items ranging in size from microns to meters which originated from spent satellites and rocket cases. To understand and model these environments, impact damage in the form of craters and perforations must be analyzed. Returned spacecraft materials such as those from LDEF and Solar Max have provided such a testbed. From these space-aged samples various impact parameters (i.e., particle size, particle and target material, particle shape, relative impact speed, etc.) may be determined. These types of analyses require the use of generic analytic scaling laws which can adequately describe the impact effects. Currently, most existing analytic scaling laws are little more than curve-fits to limited data and are not based on physics, and thus are not generically applicable over a wide range of impact parameters. During this study, a series of physics-based scaling laws for normal and oblique crater and perforation formation has been generated into two types of materials: aluminum and Teflon.

CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.

2013-09-01

Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and stellar dynamos. This qualitative agreement fuels the idea that both numerical models and astrophysical objects may operate in the same asymptotic regime of dynamics. This can be tested by exploring the scaling behavior of the models. For convection-driven incompressible spherical shell dynamos with constant material properties, scaling laws had been established previously that relate flow velocity and magnetic field strength to the available power. Here we analyzemore » 273 direct numerical simulations using the anelastic approximation, involving also cases with radius-dependent magnetic, thermal, and viscous diffusivities. These better represent conditions in gas giant planets and low-mass stars compared to Boussinesq models. Our study provides strong support for the hypothesis that both mean velocity and mean magnetic field strength scale as a function of the power generated by buoyancy forces in the same way for a wide range of conditions.« less

Laser-ion accelerators: State-of-the-art and scaling laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borghesi, M.; Kar, S.; Margarone, D.

2013-07-26

A significant amount of experimental work has been devoted over the last decade to the development and optimization of proton acceleration based on the so-called Target Normal Sheath acceleration mechanism. Several studies have been dedicated to the determination of scaling laws for the maximum energy of the protons as a function of the parameters of the irradiating pulses, studies based on experimental results and on models of the acceleration process. We briefly summarize the state of the art in this area, and review some of the scaling studies presented in the literature. We also discuss some recent results, and projectedmore » scalings, related to a different acceleration mechanism for ions, based on the Radiation Pressure of an ultraintense laser pulse.« less

An animal-to-human scaling law for blast-induced traumatic brain injury risk assessment.

PubMed

Jean, Aurélie; Nyein, Michelle K; Zheng, James Q; Moore, David F; Joannopoulos, John D; Radovitzky, Raúl

2014-10-28

Despite recent efforts to understand blast effects on the human brain, there are still no widely accepted injury criteria for humans. Recent animal studies have resulted in important advances in the understanding of brain injury due to intense dynamic loads. However, the applicability of animal brain injury results to humans remains uncertain. Here, we use advanced computational models to derive a scaling law relating blast wave intensity to the mechanical response of brain tissue across species. Detailed simulations of blast effects on the brain are conducted for different mammals using image-based biofidelic models. The intensity of the stress waves computed for different external blast conditions is compared across species. It is found that mass scaling, which successfully estimates blast tolerance of the thorax, fails to capture the brain mechanical response to blast across mammals. Instead, we show that an appropriate scaling variable must account for the mass of protective tissues relative to the brain, as well as their acoustic impedance. Peak stresses transmitted to the brain tissue by the blast are then shown to be a power function of the scaling parameter for a range of blast conditions relevant to TBI. In particular, it is found that human brain vulnerability to blast is higher than for any other mammalian species, which is in distinct contrast to previously proposed scaling laws based on body or brain mass. An application of the scaling law to recent experiments on rabbits furnishes the first physics-based injury estimate for blast-induced TBI in humans.

Energy harvesting with stacked dielectric elastomer transducers: Nonlinear theory, optimization, and linearized scaling law

NASA Astrophysics Data System (ADS)

Tutcuoglu, A.; Majidi, C.

2014-12-01

Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.

Scaling Laws in Canopy Flows: A Wind-Tunnel Analysis

NASA Astrophysics Data System (ADS)

Segalini, Antonio; Fransson, Jens H. M.; Alfredsson, P. Henrik

2013-08-01

An analysis of velocity statistics and spectra measured above a wind-tunnel forest model is reported. Several measurement stations downstream of the forest edge have been investigated and it is observed that, while the mean velocity profile adjusts quickly to the new canopy boundary condition, the turbulence lags behind and shows a continuous penetration towards the free stream along the canopy model. The statistical profiles illustrate this growth and do not collapse when plotted as a function of the vertical coordinate. However, when the statistics are plotted as function of the local mean velocity (normalized with a characteristic velocity scale), they do collapse, independently of the streamwise position and freestream velocity. A new scaling for the spectra of all three velocity components is proposed based on the velocity variance and integral time scale. This normalization improves the collapse of the spectra compared to existing scalings adopted in atmospheric measurements, and allows the determination of a universal function that provides the velocity spectrum. Furthermore, a comparison of the proposed scaling laws for two different canopy densities is shown, demonstrating that the vertical velocity variance is the most sensible statistical quantity to the characteristics of the canopy roughness.

Scaling laws in the dynamics of crime growth rate

NASA Astrophysics Data System (ADS)

Alves, Luiz G. A.; Ribeiro, Haroldo V.; Mendes, Renio S.

2013-06-01

The increasing number of crimes in areas with large concentrations of people have made cities one of the main sources of violence. Understanding characteristics of how crime rate expands and its relations with the cities size goes beyond an academic question, being a central issue for contemporary society. Here, we characterize and analyze quantitative aspects of murders in the period from 1980 to 2009 in Brazilian cities. We find that the distribution of the annual, biannual and triannual logarithmic homicide growth rates exhibit the same functional form for distinct scales, that is, a scale invariant behavior. We also identify asymptotic power-law decay relations between the standard deviations of these three growth rates and the initial size. Further, we discuss similarities with complex organizations.

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.

Scaling laws for light-weight optics

NASA Technical Reports Server (NTRS)

Valente, Tina M.

1990-01-01

Scaling laws for light-weight optical systems are examined. A cubic relationship between mirror diameter and weight has been suggested and used by many designers of optical systems as the best description for all light-weight mirrors. A survey of existing light-weight systems in the open literature has been made to clarify this issue. Fifty existing optical systems were surveyed with all varieties of light-weight mirrors including glass and beryllium structured mirrors, contoured mirrors, and very thin solid mirrors. These mirrors were then categorized and weight to diameter ratio was plotted to find a best fit curve for each case. A best fitting curve program tests nineteen different equations and ranks a 'goodness of fit' for each of these equations. The resulting relationship found for each light-weight mirror category helps to quantify light-weight optical systems and methods of fabrication and provides comparisons between mirror types.

Network-State Modulation of Power-Law Frequency-Scaling in Visual Cortical Neurons

PubMed Central

Béhuret, Sébastien; Baudot, Pierre; Yger, Pierre; Bal, Thierry; Destexhe, Alain; Frégnac, Yves

2009-01-01

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

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

PubMed

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

Filament velocity scaling laws for warm ions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manz, P.; Max-Planck-Institut für Plasmaphysik, EURATOM Assoziation, Boltzmannstr. 2, 85748 Garching; Carralero, D.

2013-10-15

The dynamics of filaments or blobs in the scrape-off layer of magnetic fusion devices are studied by magnitude estimates of a comprehensive drift-interchange-Alfvén fluid model. The standard blob models are reproduced in the cold ion case. Even though usually neglected, in the scrape-off layer, the ion temperature can exceed the electron temperature by an order of magnitude. The ion pressure affects the dynamics of filaments amongst others by adding up to the interchange drive and the polarisation current. It is shown how both effects modify the scaling laws for filament velocity in dependence of its size. Simplifications for experimentally relevantmore » limit regimes are given. These are the sheath dissipation, collisional, and electromagnetic regime.« less

Computed tomography-based diagnosis of diffuse compensatory enlargement of coronary arteries using scaling power laws.

PubMed

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

2013-04-06

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

The Scaling Law of The Near-Field Coseismic Ionospheric Disturbances

NASA Astrophysics Data System (ADS)

Cahyadi, M.; Heki, K.

2013-12-01

percents relative to the background TEC. When we plot relative CID amplitudes as a function of seismic moment in the double logarithmic plot, data are distributed roughly around a line, suggesting that they obey a certain scaling law. The slope of the line shows that the CID amplitudes increase by two orders of magnitude as Mw increases by three. We speculate that this reflects the scaling law governing the maximum uplift in relatively large shallow-angle reverse faultings. This scaling law and its empirical factor-two uncertainty in CID amplitude imply that we can determine Mw with an uncertainty of ×0.45 by measuring CID amplitudes. This is useful for early warning in a region where tsunamis arrive at the coast later than acoustic waves arrive at the ionospheric F layer, and this is the case for the Pacific coast of NE Japan. There are two earthquakes deviating negatively beyond the factor 2 uncertainty. They are the 2012 North Sumatra earthquake (Mw8.6), the largest strike-slip earthquakes ever recorded, and its largest aftershock (Mw8.1). This negative deviation would possibly reflect the smaller vertical crustal movements in strike-slip earthquakes than dip-slip events.

Empirical scaling law connecting persistence and severity of global terrorism

NASA Astrophysics Data System (ADS)

Gao, Jianbo; Fang, Peng; Liu, Feiyan

2017-09-01

Terrorism and counterterrorism have both been evolving rapidly. From time to time, there have been debates on whether the new terrorism is evolutionary or revolutionary. Such debate often becomes more heated after major terrorist activities, such as the terrorist attacks on September 11, 2001 and the November 13, 2015 coordinated Paris terror attack. Using country-wide terrorism data since 1970, we show that there exist scaling laws governing the continuity and persistence of world-wide terrorism, with the long-term scaling parameter for each country closely related to its yearly global terrorism index. This suggests that the new terrorism is more accurately considered evolutionary. It is further shown that the imbalance in the seesaw of terrorism and counterterrorism is not only responsible for the scaling behavior found here, but also provides new means of quantifying the severity of the global terrorism.

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

Scaling laws in magnetized plasma turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boldyrev, Stanislav

2015-06-28

Interactions of plasma motion with magnetic fields occur in nature and in the laboratory in an impressively broad range of scales, from megaparsecs in astrophysical systems to centimeters in fusion devices. The fact that such an enormous array of phenomena can be effectively studied lies in the existence of fundamental scaling laws in plasma turbulence, which allow one to scale the results of analytic and numerical modeling to the sized of galaxies, velocities of supernovae explosions, or magnetic fields in fusion devices. Magnetohydrodynamics (MHD) provides the simplest framework for describing magnetic plasma turbulence. Recently, a number of new features ofmore » MHD turbulence have been discovered and an impressive array of thought-provoking phenomenological theories have been put forward. However, these theories have conflicting predictions, and the currently available numerical simulations are not able to resolve the contradictions. MHD turbulence exhibits a variety of regimes unusual in regular hydrodynamic turbulence. Depending on the strength of the guide magnetic field it can be dominated by weakly interacting Alfv\\'en waves or strongly interacting wave packets. At small scales such turbulence is locally anisotropic and imbalanced (cross-helical). In a stark contrast with hydrodynamic turbulence, which tends to ``forget'' global constrains and become uniform and isotropic at small scales, MHD turbulence becomes progressively more anisotropic and unbalanced at small scales. Magnetic field plays a fundamental role in turbulent dynamics. Even when such a field is not imposed by external sources, it is self-consistently generated by the magnetic dynamo action. This project aims at a comprehensive study of universal regimes of magnetic plasma turbulence, combining the modern analytic approaches with the state of the art numerical simulations. The proposed study focuses on the three topics: weak MHD turbulence, which is relevant for laboratory devices, the

On the Scaling Laws for Jet Noise in Subsonic and Supersonic Flow

NASA Technical Reports Server (NTRS)

Vu, Bruce; Kandula, Max

2003-01-01

The scaling laws for the simulation of noise from subsonic and ideally expanded supersonic jets are examined with regard to their applicability to deduce full scale conditions from small-scale model testing. Important parameters of scale model testing for the simulation of jet noise are identified, and the methods of estimating full-scale noise levels from simulated scale model data are addressed. The limitations of cold-jet data in estimating high-temperature supersonic jet noise levels are discussed. It is shown that the jet Mach number (jet exit velocity/sound speed at jet exit) is a more general and convenient parameter for noise scaling purposes than the ratio of jet exit velocity to ambient speed of sound. A similarity spectrum is also proposed, which accounts for jet Mach number, angle to the jet axis, and jet density ratio. The proposed spectrum reduces nearly to the well-known similarity spectra proposed by Tam for the large-scale and the fine-scale turbulence noise in the appropriate limit.

Empirical Scaling Laws of Rocket Exhaust Cratering

NASA Technical Reports Server (NTRS)

Donahue, Carly M.; Metzger, Philip T.; Immer, Christopher D.

2005-01-01

When launching or landing a space craft on the regolith of a terrestrial surface, special attention needs to be paid to the rocket exhaust cratering effects. If the effects are not controlled, the rocket cratering could damage the spacecraft or other surrounding hardware. The cratering effects of a rocket landing on a planet's surface are not understood well, especially for the lunar case with the plume expanding in vacuum. As a result, the blast effects cannot be estimated sufficiently using analytical theories. It is necessary to develop physics-based simulation tools in order to calculate mission-essential parameters. In this work we test out the scaling laws of the physics in regard to growth rate of the crater depth. This will provide the physical insight necessary to begin the physics-based modeling.

Experiments and scaling laws for catastrophic collisions. [of asteroids

NASA Technical Reports Server (NTRS)

Fujiwara, A.; Cerroni, P.; Davis, D.; Ryan, E.; Di Martino, M.

1989-01-01

The existing data on shattering impacts are reviewed using natural silicate, ice, and cement-mortar targets. A comprehensive data base containing the most important parameters describing these experiments was prepared. The collisional energy needed to shatter consolidated homogeneous targets and the ensuing fragment size distributions have been well studied experimentally. However, major gaps exist in the data on fragment velocity and rotational distributions, as well as collisional energy partitioning for these targets. Current scaling laws lead to predicted outcomes of asteroid collisions that are inconsistent with interpretations of astronomical data.

Scaling laws and deformation mechanisms of nanoporous copper under adiabatic uniaxial strain compression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, Fuping, E-mail: fpyuan@lnm.imech.ac.cn; Wu, Xiaolei, E-mail: xlwu@imech.ac.cn

2014-12-15

A series of large-scale molecular dynamics simulations were conducted to investigate the scaling laws and the related atomistic deformation mechanisms of Cu monocrystal samples containing randomly placed nanovoids under adiabatic uniaxial strain compression. At onset of yielding, plastic deformation is accommodated by dislocations emitted from void surfaces as shear loops. The collapse of voids are observed by continuous emissions of dislocations from void surfaces and their interactions with further plastic deformation. The simulation results also suggest that the effect modulus, the yield stress and the energy aborption density of samples under uniaxial strain are linearly proportional to the relative densitymore » ρ. Moreover, the yield stress, the average flow stress and the energy aborption density of samples with the same relative density show a strong dependence on the void diameter d, expressed by exponential relations with decay coefficients much higher than -1/2. The corresponding atomistic mechanisms for scaling laws of the relative density and the void diameter were also presented. The present results should provide insights for understanding deformation mechanisms of nanoporous metals under extreme conditions.« less

Wide range scaling laws for radiation driven shock speed, wall albedo and ablation parameters for high-Z materials

NASA Astrophysics Data System (ADS)

Mishra, Gaurav; Ghosh, Karabi; Ray, Aditi; Gupta, N. K.

2018-06-01

Radiation hydrodynamic (RHD) simulations for four different potential high-Z hohlraum materials, namely Tungsten (W), Gold (Au), Lead (Pb), and Uranium (U) are performed in order to investigate their performance with respect to x-ray absorption, re-emission and ablation properties, when irradiated by constant temperature drives. A universal functional form is derived for estimating time dependent wall albedo for high-Z materials. Among the high-Z materials studied, it is observed that for a fixed simulation time the albedo is maximum for Au below 250 eV, whereas it is maximum for U above 250 eV. New scaling laws for shock speed vs drive temperature, applicable over a wide temperature range of 100 eV to 500 eV, are proposed based on the physics of x-ray driven stationary ablation. The resulting scaling relation for a reference material Aluminium (Al), shows good agreement with that of Kauffman's power law for temperatures ranging from 100 eV to 275 eV. New scaling relations are also obtained for temperature dependent mass ablation rate and ablation pressure, through RHD simulation. Finally, our study reveals that for temperatures above 250 eV, U serves as a better hohlraum material since it offers maximum re-emission for x-rays along with comparable mass ablation rate. Nevertheless, traditional choice, Au works well for temperatures below 250 eV. Besides inertial confinement fusion (ICF), the new scaling relations may find its application in view-factor codes, which generally ignore atomic physics calculations of opacities and emissivities, details of laser-plasma interaction and hydrodynamic motions.

Phase boundaries of power-law Anderson and Kondo models: A poor man's scaling study

NASA Astrophysics Data System (ADS)

Cheng, Mengxing; Chowdhury, Tathagata; Mohammed, Aaron; Ingersent, Kevin

2017-07-01

We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states ρ (ɛ ) ∝|ɛ| r , either vanishing (for r >0 ) or diverging (for r <0 ) at the Fermi energy ɛ =0 , that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., r >0 ), we find the phase boundary for (a) 0 1 , where the phases are separated by first-order quantum phase transitions that are accessible only for broken p-h symmetry. For the p-h-symmetric Kondo model with easy-axis or easy-plane anisotropy of the impurity-band spin exchange, the phase boundary and scaling trajectories are obtained for both r >0 and r <0 . Throughout the regime of weak-to-moderate impurity-band coupling in which poor man's scaling is expected to be valid, the approach predicts phase boundaries in excellent qualitative and good quantitative agreement with the nonperturbative numerical renormalization group, while also establishing the functional relations between model parameters along these boundaries.

Trajectory and Mixing Scaling Laws for Confined and Unconfined Transverse Jets

DTIC Science & Technology

2012-05-01

engines , issues of confinement, very large density ratio, and super/transcritical effects complicate the utility of the ...opposite wall at a streamwise position that is one -half pipe diameter downstream of the injection location (termed moderate impaction). This...BD, and Eq. 10 scaling laws are 0.97 and 0.90, respectively. One of the primary effects of the confinement is that the

A study of flame spread in engineered cardboard fuelbeds: Part II: Scaling law approach

Treesearch

Brittany A. Adam; Nelson K. Akafuah; Mark Finney; Jason Forthofer; Kozo Saito

2013-01-01

In this second part of a two part exploration of dynamic behavior observed in wildland fires, time scales differentiating convective and radiative heat transfer is further explored. Scaling laws for the two different types of heat transfer considered: Radiation-driven fire spread, and convection-driven fire spread, which can both occur during wildland fires. A new...

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes.

PubMed

Hernandez-Perez, Ruth; García-Cordero, José L; Escobar, Juan V

2017-12-01

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

Simple scaling laws for the evaporation of droplets pinned on pillars: Transfer-rate- and diffusion-limited regimes

NASA Astrophysics Data System (ADS)

Hernandez-Perez, Ruth; García-Cordero, José L.; Escobar, Juan V.

2017-12-01

The evaporation of droplets can give rise to a wide range of interesting phenomena in which the dynamics of the evaporation are crucial. In this work, we find simple scaling laws for the evaporation dynamics of axisymmetric droplets pinned on millimeter-sized pillars. Different laws are found depending on whether evaporation is limited by the diffusion of vapor molecules or by the transfer rate across the liquid-vapor interface. For the diffusion-limited regime, we find that a mass-loss rate equal to 3/7 of that of a free-standing evaporating droplet brings a good balance between simplicity and physical correctness. We also find a scaling law for the evaporation of multicomponent solutions. The scaling laws found are validated against experiments of the evaporation of droplets of (1) water, (2) blood plasma, and (3) a mixture of water and polyethylene glycol, pinned on acrylic pillars of different diameters. These results shed light on the macroscopic dynamics of evaporation on pillars as a first step towards the understanding of other complex phenomena that may be taking place during the evaporation process, such as particle transport and chemical reactions.

Scaling Laws of Microactuators and Potential Applications of Electroactive Polymers in MEMS

NASA Technical Reports Server (NTRS)

Liu, Chang; Bar-Cohen, Y.

1999-01-01

Besides the scale factor that distinguishes the various species, fundamentally biological muscles changes little between species, indicating a highly optimized system. Electroactive polymer actuators offer the closest resemblance to biological muscles, however besides the large actuation displacement these materials are falling short with regards to the actuation force. As improved materials are emerging it is becoming necessary to address key issues such as the need for effective electromechanical modeling and guiding parameters in scaling the actuators. In this paper, we will review the scaling laws for three major actuation mechanisms that are of relevance to micro electromechanical systems: electrostatic actuation, magnetic actuation, thermal bimetallic actuation, and piezoelectric actuation.

On the Scaling Law for Broadband Shock Noise Intensity in Supersonic Jets

NASA Technical Reports Server (NTRS)

Kanudula, Max

2009-01-01

A theoretical model for the scaling of broadband shock noise intensity in supersonic jets was formulated on the basis of linear shock-shear wave interaction. An hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process rather than the noise generation contribution from off-peak incident angles. The proposed theory satisfactorily explains the well-known scaling law for the broadband shock -associated noise in supersonic jets.

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Anomalous scaling law of strength and toughness of cellulose nanopaper

PubMed Central

Zhu, Hongli; Zhu, Shuze; Jia, Zheng; Parvinian, Sepideh; Li, Yuanyuan; Vaaland, Oeyvind; Hu, Liangbing; Li, Teng

2015-01-01

The quest for both strength and toughness is perpetual in advanced material design; unfortunately, these two mechanical properties are generally mutually exclusive. So far there exists only limited success of attaining both strength and toughness, which often needs material-specific, complicated, or expensive synthesis processes and thus can hardly be applicable to other materials. A general mechanism to address the conflict between strength and toughness still remains elusive. Here we report a first-of-its-kind study of the dependence of strength and toughness of cellulose nanopaper on the size of the constituent cellulose fibers. Surprisingly, we find that both the strength and toughness of cellulose nanopaper increase simultaneously (40 and 130 times, respectively) as the size of the constituent cellulose fibers decreases (from a mean diameter of 27 μm to 11 nm), revealing an anomalous but highly desirable scaling law of the mechanical properties of cellulose nanopaper: the smaller, the stronger and the tougher. Further fundamental mechanistic studies reveal that reduced intrinsic defect size and facile (re)formation of strong hydrogen bonding among cellulose molecular chains is the underlying key to this new scaling law of mechanical properties. These mechanistic findings are generally applicable to other material building blocks, and therefore open up abundant opportunities to use the fundamental bottom-up strategy to design a new class of functional materials that are both strong and tough. PMID:26150482

From Single-Cell Dynamics to Scaling Laws in Oncology

NASA Astrophysics Data System (ADS)

Chignola, Roberto; Sega, Michela; Stella, Sabrina; Vyshemirsky, Vladislav; Milotti, Edoardo

We are developing a biophysical model of tumor biology. We follow a strictly quantitative approach where each step of model development is validated by comparing simulation outputs with experimental data. While this strategy may slow down our advancements, at the same time it provides an invaluable reward: we can trust simulation outputs and use the model to explore territories of cancer biology where current experimental techniques fail. Here, we review our multi-scale biophysical modeling approach and show how a description of cancer at the cellular level has led us to general laws obeyed by both in vitro and in vivo tumors.

Scaling laws describe memories of host-pathogen riposte in the HIV population.

PubMed

Barton, John P; Kardar, Mehran; Chakraborty, Arup K

2015-02-17

The enormous genetic diversity and mutability of HIV has prevented effective control of this virus by natural immune responses or vaccination. Evolution of the circulating HIV population has thus occurred in response to diverse, ultimately ineffective, immune selection pressures that randomly change from host to host. We show that the interplay between the diversity of human immune responses and the ways that HIV mutates to evade them results in distinct sets of sequences defined by similar collectively coupled mutations. Scaling laws that relate these sets of sequences resemble those observed in linguistics and other branches of inquiry, and dynamics reminiscent of neural networks are observed. Like neural networks that store memories of past stimulation, the circulating HIV population stores memories of host-pathogen combat won by the virus. We describe an exactly solvable model that captures the main qualitative features of the sets of sequences and a simple mechanistic model for the origin of the observed scaling laws. Our results define collective mutational pathways used by HIV to evade human immune responses, which could guide vaccine design.

The interstellar redding law in the ultraviolet deduced from filter photometry obtained by the OAO-2 satellite

NASA Technical Reports Server (NTRS)

Laget, M.

1972-01-01

Filter photometry has been obtained of 16 BO stars at ten effective wavelengths in the range 4250-1430 A. The wavelength dependence of the interstellar reddening law, deduced from a least squares fit of the observed values to the reddening line at each band, is found in satisfactory agreement with that derived by Bless and Savage (1972). Toward the shorter wavelengths the increase of the computed probable error of the slope of the mean reddening line suggests that large fluctuations in the law may occur from star to star. Similar computations, separating main-sequence stars and supergiants, indicate that the large fluctuations of the law appear to be well related to the luminosity of the stars; the supergiants show systematically less extinction, this deficiency becoming large toward the far UV. The small number in the sample however, does not allow a general conclusion to be drawn.

Applicability of Macroscopic Wear and Friction Laws on the Atomic Length Scale.

PubMed

Eder, S J; Feldbauer, G; Bianchi, D; Cihak-Bayr, U; Betz, G; Vernes, A

2015-07-10

Using molecular dynamics, we simulate the abrasion process of an atomically rough Fe surface with multiple hard abrasive particles. By quantifying the nanoscopic wear depth in a time-resolved fashion, we show that Barwell's macroscopic wear law can be applied at the atomic scale. We find that in this multiasperity contact system, the Bowden-Tabor term, which describes the friction force as a function of the real nanoscopic contact area, can predict the kinetic friction even when wear is involved. From this the Derjaguin-Amontons-Coulomb friction law can be recovered, since we observe a linear dependence of the contact area on the applied load in accordance with Greenwood-Williamson contact mechanics.

Universal scaling laws of top jet drop size and speed in bubble bursting

NASA Astrophysics Data System (ADS)

Ganan-Calvo, Alfonso

2017-11-01

The collapse of a bubble of radius Ro at the surface of a liquid generating a liquid jet and a subsequent first drop of radius R follows a universal flow pattern that can be universally scaled using the difference between the parent bubble radius and a critical radius R* =Oh*-2μ2 /(ρσ) below which no droplet is ejected for a given Newtonian liquid. Here, Oh* = 0.037 is the critical Ohnesorge number, where Oh = μ /(ρσRo) 1 / 2 ; ρ, σ and μ are the liquid density, surface tension and viscosity. Based on a flow singularity occurring for Ro =R* , a scaling analysis of the complex flow structure at the onset of jet ejection for Ro >R* leads to the diameter of the first emitted droplet and the initial ejection velocity: D =kd(Ro -R*) 5 / 4R* - 1 / 4 and V =kv σμ-1(Ro -R*) 3 / 4R* - 3 / 4 , respectively. A remarkable collapse of data taken from available literature since 1954 to 2017 furnishes the universal constants kd = 0.1 and kv = 1.6 , for negligible gravity effects.The role of gravity is subdominant and can be reflected by the exponential dependence of the scaling laws obtained on the Bond number. This work was supported by the Ministerio de Economy Competitividad, Plan Estatal 2013-2016 Retos, project DPI2016-78887-C3-1-R.

A scaling law for accretion zone sizes

NASA Technical Reports Server (NTRS)

Greenzweig, Yuval; Lissauer, Jack J.

1987-01-01

Current theories of runaway planetary accretion require small random velocities of the accreted particles. Two body gravitational accretion cross sections which ignore tidal perturbations of the Sun are not valid for the slow encounters which occur at low relative velocities. Wetherill and Cox have studied accretion cross sections for rocky protoplanets orbiting at 1 AU. Using analytic methods based on Hill's lunar theory, one can scale these results for protoplanets that occupy the same fraction of their Hill sphere as does a rocky body at 1 AU. Generalization to bodies of different sizes is achieved here by numerical integrations of the three-body problem. Starting at initial positions far from the accreting body, test particles are allowed to encounter the body once, and the cross section is computed. A power law is found relating the cross section to the radius of the accreting body (of fixed mass).

Joint scaling laws in functional and evolutionary categories in prokaryotic genomes

PubMed Central

Grilli, J.; Bassetti, B.; Maslov, S.; Cosentino Lagomarsino, M.

2012-01-01

We propose and study a class-expansion/innovation/loss model of genome evolution taking into account biological roles of genes and their constituent domains. In our model, numbers of genes in different functional categories are coupled to each other. For example, an increase in the number of metabolic enzymes in a genome is usually accompanied by addition of new transcription factors regulating these enzymes. Such coupling can be thought of as a proportional ‘recipe’ for genome composition of the type ‘a spoonful of sugar for each egg yolk’. The model jointly reproduces two known empirical laws: the distribution of family sizes and the non-linear scaling of the number of genes in certain functional categories (e.g. transcription factors) with genome size. In addition, it allows us to derive a novel relation between the exponents characterizing these two scaling laws, establishing a direct quantitative connection between evolutionary and functional categories. It predicts that functional categories that grow faster-than-linearly with genome size to be characterized by flatter-than-average family size distributions. This relation is confirmed by our bioinformatics analysis of prokaryotic genomes. This proves that the joint quantitative trends of functional and evolutionary classes can be understood in terms of evolutionary growth with proportional recipes. PMID:21937509

Universal scaling laws for the disintegration of electrified drops

PubMed Central

Collins, Robert T.; Sambath, Krishnaraj; Harris, Michael T.; Basaran, Osman A.

2013-01-01

Drops subjected to strong electric fields emit charged jets from their pointed tips. The disintegration of such jets into a spray consisting of charged droplets is common to electrospray ionization mass spectrometry, printing and coating processes, and raindrops in thunderclouds. Currently, there exist conflicting theories and measurements on the size and charge of these small electrospray droplets. We use theory and simulation to show that conductivity can be tuned to yield three scaling regimes for droplet radius and charge, a finding missed by previous studies. The amount of charge that electrospray droplets carry determines whether they are coulombically stable and charged below the Rayleigh limit of stability or are unstable and hence prone to further explosions once they are formed. Previous experiments reported droplet charge values ranging from 10% to in excess of . Simulations unequivocally show that electrospray droplets are coulombically stable at the instant they are created and that there exists a universal scaling law for droplet charge, . PMID:23487744

On the critical or geometrical nature of the observed scaling laws associated with the fracture and faulting processes

NASA Astrophysics Data System (ADS)

Potirakis, Stelios M.; Kopanas, John; Antonopoulos, George; Nomicos, Constantinos; Eftaxias, Konstantinos

2015-04-01

One of the largest controversial issues of the materials science community is the interpretation of scaling laws associated with the fracture and faulting processes. Especially, an important open question is whether the spatial and temporal complexity of earthquakes and fault structures, above all the interpretation of the observed scaling laws, emerge from geometrical and material built-in heterogeneities or from the critical behavior inherent to the nonlinear equations governing the earthquake dynamics. Crack propagation is the basic mechanism of material's failure. A number of laboratory studies carried out on a wide range of materials have revealed the existence of EMEs during fracture experiments, while these emissions are ranging in a wide frequency spectrum, i.e., from the kHz to the MHz bands. A crucial feature observed on the laboratory scale is that the MHz EME systematically precedes the corresponding kHz one. The aforementioned crucial feature is observed in geophysical scale, as well. The remarkable asynchronous appearance of these two EMEs both on the laboratory and the geophysical scale implies that they refer to different final stages of faulting process. Accumulated laboratory, theoretical and numerical evidence supports the hypothesis that the MHz EME is emitted during the fracture of process of heterogeneous medium surrounding the family of strong entities (asperities) distributed along the fault sustaining the system. The kHz EME is attributed to the family of asperities themselves. We argue in terms of the fracture induced pre-seismic MHz-kHz EMEs that the scaling laws associated with the fracture of heterogeneous materials emerge from the critical behavior inherent to the nonlinear equations governing their dynamics (second-order phase transition), while the scaling laws associated with the fracture of family of asperities have geometric nature, namely, are rooted in the fractal nature of the population of asperities.

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.

Evaluation of Large-scale Data to Detect Irregularity in Payment for Medical Services. An Extended Use of Benford's Law.

PubMed

Park, Junghyun A; Kim, Minki; Yoon, Seokjoon

2016-05-17

Sophisticated anti-fraud systems for the healthcare sector have been built based on several statistical methods. Although existing methods have been developed to detect fraud in the healthcare sector, these algorithms consume considerable time and cost, and lack a theoretical basis to handle large-scale data. Based on mathematical theory, this study proposes a new approach to using Benford's Law in that we closely examined the individual-level data to identify specific fees for in-depth analysis. We extended the mathematical theory to demonstrate the manner in which large-scale data conform to Benford's Law. Then, we empirically tested its applicability using actual large-scale healthcare data from Korea's Health Insurance Review and Assessment (HIRA) National Patient Sample (NPS). For Benford's Law, we considered the mean absolute deviation (MAD) formula to test the large-scale data. We conducted our study on 32 diseases, comprising 25 representative diseases and 7 DRG-regulated diseases. We performed an empirical test on 25 diseases, showing the applicability of Benford's Law to large-scale data in the healthcare industry. For the seven DRG-regulated diseases, we examined the individual-level data to identify specific fees to carry out an in-depth analysis. Among the eight categories of medical costs, we considered the strength of certain irregularities based on the details of each DRG-regulated disease. Using the degree of abnormality, we propose priority action to be taken by government health departments and private insurance institutions to bring unnecessary medical expenses under control. However, when we detect deviations from Benford's Law, relatively high contamination ratios are required at conventional significance levels.

Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries.

PubMed

Alecu, I M; Zheng, Jingjing; Zhao, Yan; Truhlar, Donald G

2010-09-14

Optimized scale factors for calculating vibrational harmonic and fundamental frequencies and zero-point energies have been determined for 145 electronic model chemistries, including 119 based on approximate functionals depending on occupied orbitals, 19 based on single-level wave function theory, three based on the neglect-of-diatomic-differential-overlap, two based on doubly hybrid density functional theory, and two based on multicoefficient correlation methods. Forty of the scale factors are obtained from large databases, which are also used to derive two universal scale factor ratios that can be used to interconvert between scale factors optimized for various properties, enabling the derivation of three key scale factors at the effort of optimizing only one of them. A reduced scale factor optimization model is formulated in order to further reduce the cost of optimizing scale factors, and the reduced model is illustrated by using it to obtain 105 additional scale factors. Using root-mean-square errors from the values in the large databases, we find that scaling reduces errors in zero-point energies by a factor of 2.3 and errors in fundamental vibrational frequencies by a factor of 3.0, but it reduces errors in harmonic vibrational frequencies by only a factor of 1.3. It is shown that, upon scaling, the balanced multicoefficient correlation method based on coupled cluster theory with single and double excitations (BMC-CCSD) can lead to very accurate predictions of vibrational frequencies. With a polarized, minimally augmented basis set, the density functionals with zero-point energy scale factors closest to unity are MPWLYP1M (1.009), τHCTHhyb (0.989), BB95 (1.012), BLYP (1.013), BP86 (1.014), B3LYP (0.986), MPW3LYP (0.986), and VSXC (0.986).

Cubic law with aperture-length correlation: implications for network scale fluid flow

NASA Astrophysics Data System (ADS)

Klimczak, Christian; Schultz, Richard A.; Parashar, Rishi; Reeves, Donald M.

2010-06-01

Previous studies have computed and modeled fluid flow through fractured rock with the parallel plate approach where the volumetric flow per unit width normal to the direction of flow is proportional to the cubed aperture between the plates, referred to as the traditional cubic law. When combined with the square root relationship of displacement to length scaling of opening-mode fractures, total flow rates through natural opening-mode fractures are found to be proportional to apertures to the fifth power. This new relationship was explored by examining a suite of flow simulations through fracture networks using the discrete fracture network model (DFN). Flow was modeled through fracture networks with the same spatial distribution of fractures for both correlated and uncorrelated fracture length-to-aperture relationships. Results indicate that flow rates are significantly higher for correlated DFNs. Furthermore, the length-to-aperture relations lead to power-law distributions of network hydraulic conductivity which greatly influence equivalent permeability tensor values. These results confirm the importance of the correlated square root relationship of displacement to length scaling for total flow through natural opening-mode fractures and, hence, emphasize the role of these correlations for flow modeling.

Impact of laws restricting the sale of tobacco to minors on adolescent smoking and perceived obtainability of cigarettes: an intervention-control pre-post study of 19 European Union countries.

PubMed

Kuipers, Mirte A G; Brandhof, Stephanie D; Monshouwer, Karin; Stronks, Karien; Kunst, Anton E

2017-02-01

To estimate the impact of introducing sales restriction laws in Europe by measuring changes in adolescent smoking prevalence and perceived obtainability of cigarettes over time in countries that have recently introduced sales restriction laws (intervention countries). These countries were compared with countries where such laws were already in force (control countries). The secondary aim was to test whether these trends differed between adolescents of higher and lower socio-economic position (SEP). Repeated cross-sectional data were used in a quasi-experimental pre-post design. Intervention countries raised tobacco sales restrictions to 18 years in 2007, 2008 or 2009. Control countries have had sales restrictions of 18 years since at least 2004. Nineteen European Union (EU) countries in 2007 and 2011. Data of 97 245 15- and 16-year-old adolescents from the 2007 and 2011 European Survey Project on Alcohol and other Drugs (ESPAD) surveys. Dependent variables were smoking status (weekly smoking versus non-smoking or less than weekly smoking) and perceived obtainability of tobacco (easy versus difficult). Key independent variables were time (2007 or 2011), intervention exposure (intervention or control country) and their interaction (time × intervention). Covariates included sex, SEP, the tobacco control scale (TCS), gross domestic product (GDP) and adult smoking prevalence. We did not find a difference in the change in smoking prevalence between intervention and control countries [odds ratio (OR) = 1.00, 95% confidence interval (CI) = 0.93-1.07]. However, sales restrictions were associated with a significantly greater decrease in perceived ease of cigarette obtainability in intervention countries (OR = 0.75, 95% CI = 0.70-0.80). No significant differential effects between high and low SEP adolescents were found (OR = 1.01, 95% CI = 0.81-1.25). Laws prohibiting the sales of tobacco to minors in Europe do not appear to be associated with a reduction

Magnetic properties of α' martensite in austenitic stainless steel studied by a minor-loop scaling law

NASA Astrophysics Data System (ADS)

Kobayashi, Satoru; Kikuchi, Nobuhiro; Takahashi, Seiki; Kamada, Yasuhiro; Kikuchi, Hiroaki

2010-08-01

We study the scaling behavior of magnetic minor hysteresis loops in strain-induced ferromagnetic α' martensites in an austenitic 316-type stainless steel. A scaling relationship between the hysteresis loss and the remanence, with a power law exponent of approximately 1.35, was found irrespective of the volume fraction of the α' martensites as well as temperature. The coefficient of the power law largely decreases with volume fraction, whereas it increases with a decrease in temperature and exhibits a kink at around 40 K, close to the Néel temperature of an austenitic γ' phase. The behavior of the coefficient was interpreted from the viewpoint of the morphology and exchange interaction of α' martensites.

Existence of k⁻¹ power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg's eddy viscosity.

PubMed

Katul, Gabriel G; Porporato, Amilcare; Nikora, Vladimir

2012-12-01

The existence of a "-1" power-law scaling at low wavenumbers in the longitudinal velocity spectrum of wall-bounded turbulence was explained by multiple mechanisms; however, experimental support has not been uniform across laboratory studies. This letter shows that Heisenberg's eddy viscosity approach can provide a theoretical framework that bridges these multiple mechanisms and explains the elusiveness of the "-1" power law in some experiments. Novel theoretical outcomes are conjectured about the role of intermittency and very-large scale motions in modifying the k⁻¹ scaling.

The Physical Origin of Galaxy Morphologies and Scaling Laws

NASA Technical Reports Server (NTRS)

Steinmetz, Matthias; Navarro, Julio F.

2002-01-01

We propose a numerical study designed to interpret the origin and evolution of galaxy properties revealed by space- and ground-based imaging and spectroscopical surveys. Our aim is to unravel the physical processes responsible for the development of different galaxy morphologies and for the establishment of scaling laws such as the Tully-Fisher relation for spirals and the Fundamental Plane of ellipticals. In particular, we plan to address the following major topics: (1) The morphology and observability of protogalaxies, and in particular the relationship between primordial galaxies and the z approximately 3 'Ly-break' systems identified in the Hubble Deep Field and in ground-based searches; (2) The origin of the disk and spheroidal components in galaxies, the timing and mode of their assembly, the corresponding evolution in galaxy morphologies and its sensitivity to cosmological parameters; (3) The origin and redshift evolution of the scaling laws that link the mass, luminosity size, stellar content, and metal abundances of galaxies of different morphological types. This investigation will use state-of-the-art N-body/gasdynamical codes to provide a spatially resolved description of the galaxy formation process in hierarchically clustering universes. Coupled with population synthesis techniques. our models can be used to provide synthetic 'observations' that can be compared directly with observations of galaxies both nearby and at cosmologically significant distances. This study will thus provide insight into the nature of protogalaxies and into the formation process of galaxies like our own Milky Way. It will also help us to assess the cosmological significance of these observations within the context of hierarchical theories of galaxy formation and will supply a theoretical context within which current and future observations can be interpreted.

Factor Structure of the Korean Version of Wong and Law's Emotional Intelligence Scale

ERIC Educational Resources Information Center

Fukuda, Eriko; Saklofske, Donald H.; Tamaoka, Katsuo; Lim, Hyunjung

2012-01-01

This study reports the factor structure of a Korean version of the 16-item Wong and Law Emotional Intelligence Scale (WLEIS) for a sample of 161 Korean university students. Confirmatory factor analysis supported the four-factor model of the WLEIS: (1) self-emotional appraisal, (2) others' emotional appraisal, (3) use of emotion, and (4) regulation…

A Unified Scaling Law in Spiral Galaxies.

PubMed

Koda; Sofue; Wada

2000-03-01

We investigate the origin of a unified scaling relation in spiral galaxies. Observed spiral galaxies are spread on a plane in the three-dimensional logarithmic space of luminosity L, radius R, and rotation velocity V. The plane is expressed as L~&parl0;VR&parr0;alpha in the I passband, where alpha is a constant. On the plane, observed galaxies are distributed in an elongated region which looks like the shape of a surfboard. The well-known scaling relations L-V (Tully-Fisher [TF] relation), V-R (also the TF relation), and R-L (Freeman's law) can be understood as oblique projections of the surfboard-like plane into two-dimensional spaces. This unified interpretation of the known scaling relations should be a clue to understand the physical origin of all the relations consistently. Furthermore, this interpretation can also explain why previous studies could not find any correlation between TF residuals and radius. In order to clarify the origin of this plane, we simulate formation and evolution of spiral galaxies with the N-body/smoothed particle hydrodynamics method, including cooling, star formation, and stellar feedback. Initial conditions are set to 14 isolated spheres with two free parameters, such as mass and angular momentum. The cold dark matter (h=0.5, Omega0=1) cosmology is considered as a test case. The simulations provide the following two conclusions: (1) The slope of the plane is well reproduced but the zero point is not. This zero-point discrepancy could be solved in a low-density (Omega0<1) and high-expansion (h>0.5) cosmology. (2) The surfboard-shaped plane can be explained by the control of galactic mass and angular momentum.

Reproducing the scaling laws for Slow and Fast ruptures

NASA Astrophysics Data System (ADS)

Romanet, Pierre; Bhat, Harsha; Madariaga, Raúl

2017-04-01

Modelling long term behaviour of large, natural fault systems, that are geometrically complex, is a challenging problem. This is why most of the research so far has concentrated on modelling the long term response of single planar fault system. To overcome this limitation, we appeal to a novel algorithm called the Fast Multipole Method which was developed in the context of modelling gravitational N-body problems. This method allows us to decrease the computational complexity of the calculation from O(N2) to O(N log N), N being the number of discretised elements on the fault. We then adapted this method to model the long term quasi-dynamic response of two faults, with step-over like geometry, that are governed by rate and state friction laws. We assume the faults have spatially uniform rate weakening friction. The results show that when stress interaction between faults is accounted, a complex spectrum of slip (including slow-slip events, dynamic ruptures and partial ruptures) emerges naturally. The simulated slow-slip and dynamic events follow the scaling law inferred by Ide et al. 2007 i. e. M ∝ T for slow-slip events and M ∝ T2 (in 2D) for dynamic events.

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.

Knowing the dense plasma focus - The coming of age (of the PF) with broad-ranging scaling laws

NASA Astrophysics Data System (ADS)

Saw, S. H.; Lee, S.

2017-03-01

The dense plasma focus is blessed not only with copious multi-radiations ranging from electron and ion beams, x-rays both soft and hard, fusion neutrons D-D and D-T but also with the property of enhanced compression from radiative collapse leading to HED (high energy density) states. The Lee code has been used in extensive systematic numerical experiments tied to reality through fitting with measured current waveforms and verified through comparison of measured and computed yields and measurements of multi-radiation. The studies have led to establishment of scaling laws with respect to storage energy, discharge current and pinch currents for fusion neutrons, characteristic soft x-rays, all-line radiation and ion beams. These are summarized here together with a first-time presentation of a scaling law of radiatively enhanced compression as a function of atomic number of operational gas. This paper emphasizes that such a broad range of scaling laws signals the coming of age of the DPF and presents a reference platform for planning the many potential applications such as in advanced SXR lithography, materials synthesizing and testing, medical isotopes, imaging and energy and high energy density (HED).

On the Scaling Laws and Similarity Spectra for Jet Noise in Subsonic and Supersonic Flow

NASA Technical Reports Server (NTRS)

Kandula, Max

2008-01-01

The scaling laws for the simulation of noise from subsonic and ideally expanded supersonic jets are reviewed with regard to their applicability to deduce full-scale conditions from small-scale model testing. Important parameters of scale model testing for the simulation of jet noise are identified, and the methods of estimating full- scale noise levels from simulated scale model data are addressed. The limitations of cold-jet data in estimating high-temperature supersonic jet noise levels are discussed. New results are presented showing the dependence of overall sound power level on the jet temperature ratio at various jet Mach numbers. A generalized similarity spectrum is also proposed, which accounts for convective Mach number and angle to the jet axis.

Fully determined scaling laws for volumetrically heated convective systems, a tool for assessing habitability of exoplanets

NASA Astrophysics Data System (ADS)

Vilella, Kenny; Kaminski, Edouard

2017-05-01

The long-term habitability of a planet rises from its ability to generate and maintain an atmosphere through partial melting and volcanism. This question has been mainly addressed in the framework of plate tectonics, which may be too specific to apply to the wide range of internal dynamics expected for exoplanets, and even to the thermal evolution of the early Earth. Here we propose a more general theoretical approach of convection to build a regime diagram giving the conditions for partial melting to occur, in planetary bodies, as a function of key parameters that can be estimated for exoplanets, their size and internal heating rate. To that aim, we introduce a refined view of the Thermal Boundary Layer (TBL) in a convective system heated from within, that focuses on the temperature and thickness of the TBL at the top of the hottest temperature profiles, along which partial melting shall first occur. This ;Hottest Thermal Boundary Layer; (HotTBL) is first characterized using fully theoretical scaling laws based on the dynamics of thermal boundary layers. These laws are the first ones proposed in the literature that do not rely on empirical determinations of dimensionless constants and that apply to both low Rayleigh and high Rayleigh convective regimes. We show that the scaling laws can be successfully applied to planetary bodies by comparing their predictions to full numerical simulations of the Moon. We then use the scaling laws to build a regime diagram for exoplanets. Combined with estimates of internal heating in exoplanets, the regime diagram predicts that in the habitable zone partial melting occurs in planets younger than the Earth.

Fully Determined Scaling Laws for Volumetrically Heated Convective Systems, a Tool for Assessing Habitability of Exoplanets.

NASA Astrophysics Data System (ADS)

Vilella, K.; Kaminski, E. C.

2016-12-01

The long-term habitability of a planet rises from its ability to generate and maintain an atmosphere through partial melting and volcanism. This question has been mainly addressed in the framework of plate tectonics, which may be too specific to apply to the wide range of internal dynamics expected for exoplanets, and even to the thermal evolution of the early Earth. Here we propose a more general theoretical approach of convection to build a regime diagram giving the conditions for partial melting to occur in planetary bodies, as a function of key parameters that can be estimated for exoplanets, their size and internal heating rate. To that aim, we introduce a refined view of the Thermal Boundary layer (TBL) in a convective system heated from within, that focuses on the temperature and thickness of the TBL at the top of the hottest temperature profiles, along which partial melting shall first occur. This "Hottest Thermal Boundary Layer" (HotTBL) is first characterized using fully theoretical scaling laws based on the dynamics of thermal boundary layers. These laws are the first ones proposed in the literature that do not rely on empirical determinations of dimensionless constants and that apply to both low Rayleigh and high Rayleigh convective regimes. We show that the scaling laws can be successfully applied to planetary bodies by comparing their predictions to full numerical simulations of the Moon. We then use the scaling laws to build a regime diagram for exoplanets. Combined with estimates of internal heating in exoplanets, the regime diagram predicts that in the habitable zone partial melting occurs in planets younger than the Earth.

Theoretical analysis for scaling law of thermal blooming based on optical phase deference

NASA Astrophysics Data System (ADS)

Sun, Yunqiang; Huang, Zhilong; Ren, Zebin; Chen, Zhiqiang; Guo, Longde; Xi, Fengjie

2016-10-01

In order to explore the laser propagation influence of thermal blooming effect of pipe flow and to analysis the influencing factors, scaling law theoretical analysis of the thermal blooming effects in pipe flow are carry out in detail based on the optical path difference caused by thermal blooming effects in pipe flow. Firstly, by solving the energy coupling equation of laser beam propagation, the temperature of the flow is obtained, and then the optical path difference caused by the thermal blooming is deduced. Through the analysis of the influence of pipe size, flow field and laser parameters on the optical path difference, energy scaling parameters Ne=nTαLPR2/(ρɛCpπR02) and geometric scaling parameters Nc=νR2/(ɛL) of thermal blooming for the pipe flow are derived. Secondly, for the direct solution method, the energy coupled equations have analytic solutions only for the straight tube with Gauss beam. Considering the limitation of directly solving the coupled equations, the dimensionless analysis method is adopted, the analysis is also based on the change of optical path difference, same scaling parameters for the pipe flow thermal blooming are derived, which makes energy scaling parameters Ne and geometric scaling parameters Nc have good universality. The research results indicate that when the laser power and the laser beam diameter are changed, thermal blooming effects of the pipeline axial flow caused by optical path difference will not change, as long as you keep energy scaling parameters constant. When diameter or length of the pipe changes, just keep the geometric scaling parameters constant, the pipeline axial flow gas thermal blooming effects caused by optical path difference distribution will not change. That is to say, when the pipe size and laser parameters change, if keeping two scaling parameters with constant, the pipeline axial flow thermal blooming effects caused by the optical path difference will not change. Therefore, the energy scaling

Scaling laws for positron production in laser-electron beam collisions

NASA Astrophysics Data System (ADS)

Blackburn, Tom; Ilderton, Anton; Murphy, Christopher; Marklund, Mattias

2017-10-01

Showers of gamma rays and positrons are produced when a multi-GeV electron beam collides with a super-intense laser pulse. All-optical realisation of this geometry, where the electron beam is generated by laser-wakefield acceleration, is currently attracting much experimental interest as a probe of radiation reaction and QED effects. These interactions may be modelled theoretically in the framework of strong-field QED or numerically by large-scale PIC simulation. To complement these, we present analytical scaling laws for the electron beam energy loss, gamma ray spectrum, and the positron yield and energy that are valid in the radiation-reaction-dominated regime. These indicate that by employing the collision of a 2 GeV electron beam with a laser pulse of intensity 5 ×1021Wcm-2 , it is possible to produce 10,000 positrons in a single shot at currently available laser facilities. The authors acknowledge support from the Knut and Alice Wallenberg Foundation.

Unusual scaling laws for plasmonic nanolasers beyond the diffraction limit.

PubMed

Wang, Suo; Wang, Xing-Yuan; Li, Bo; Chen, Hua-Zhou; Wang, Yi-Lun; Dai, Lun; Oulton, Rupert F; Ma, Ren-Min

2017-12-01

Plasmonic nanolasers are a new class of amplifiers that generate coherent light well below the diffraction barrier bringing fundamentally new capabilities to biochemical sensing, super-resolution imaging, and on-chip optical communication. However, a debate about whether metals can enhance the performance of lasers has persisted due to the unavoidable fact that metallic absorption intrinsically scales with field confinement. Here, we report plasmonic nanolasers with extremely low thresholds on the order of 10 kW cm -2 at room temperature, which are comparable to those found in modern laser diodes. More importantly, we find unusual scaling laws allowing plasmonic lasers to be more compact and faster with lower threshold and power consumption than photonic lasers when the cavity size approaches or surpasses the diffraction limit. This clarifies the long-standing debate over the viability of metal confinement and feedback strategies in laser technology and identifies situations where plasmonic lasers can have clear practical advantage.

Scale Invariance in Landscape Evolution Models Using Stream Power Laws

NASA Astrophysics Data System (ADS)

Kwang, J. S.; Parker, G.

2014-12-01

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

The generalized 20/80 law using probabilistic fractals applied to petroleum field size

USGS Publications Warehouse

Crovelli, R.A.

1995-01-01

Fractal properties of the Pareto probability distribution are used to generalize "the 20/80 law." The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The general p100/q100 law in probabilistic form is defined with q as a function of p, where p is the population proportion and q is the proportion of total value. Using the Pareto distribution, the p100/q100 law in fractal form is derived with the parameter q being a fractal, where q unexpectedly possesses the scale invariance property. The 20/80 law is a special case of the p100/q100 law in fractal form. The p100/q100 law in fractal form is applied to petroleum fieldsize data to obtain p and q such that p100% of the oil fields greater than any specified scale or size in a geologic play account for q100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractal q are extremely close to the empirical percentages from the data using the statistic q. Also, the empirical scale invariance property of the statistic q for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractal q. ?? 1995 Oxford University Press.

Modeling Aftershocks and Foreshocks by Time-Dependent Friction Laws

NASA Astrophysics Data System (ADS)

Lippiello, E.; Landes, F.

2017-12-01

The transition with depth from rate-weakening to rate-strengthening rheology represents a viable mechanism to explain both afterslip and the temporal and spatial organization of aftershocks(Avouac, Annu. Rev. Eart Planet Sci. 2015).On the other hand, elastic models for seismic faults, as the Burridge-Knopoff model, are able to reproduce the Gutenberg-Richter (GR) law (de Arcangelis et al., Phys. Rep. 2016). Here we show that the two approaches can be combined in a minimal model containing only a parameter controlling the heterogeneities of the friction force. The key ingredient is the presence of a time-dependent friction on a temporal scale intermediate between the instantaneous scale of fracture propagation and the very slow one of the driving rate. Several features of aftershocks as the GR law, the productivity law, the spatial clustering and the temporal decay of the aftershock number, appear universal properties independent of details of model parameters and friction law. Quantitative agreement with the Omori law constraints the friction law according to a velocity strengthening rheology. The model also provides agreement with recent experimental results on the statistical properties of foreshock occurrence (Lippiello et al. , Pageoph, 2017). We then obtain insights on the nucleation phase preceding mainshocks which we compare with existing models (Ohnaka, Tectonophysics 1992).

Swept shock/boundary-layer interactions: Scaling laws, flowfield structure, and experimental methods

NASA Technical Reports Server (NTRS)

Settles, Gary S.

1993-01-01

A general review is given of several decades of research on the scaling laws and flowfield structures of swept shock wave/turbulent boundary layer interactions. Attention is further restricted to the experimental study and physical understanding of the steady-state aspects of these flows. The interaction produced by a sharp, upright fin mounted on a flat plate is taken as an archetype. An overall framework of quasiconical symmetry describing such interactions is first developed. Boundary-layer separation, the interaction footprint, Mach number scaling, and Reynolds number scaling are then considered, followed by a discussion of the quasiconical similarity of interactions produced by geometrically-dissimilar shock generators. The detailed structure of these interaction flowfields is next reviewed, and is illustrated by both qualitative visualizations and quantitative flow images in the quasiconical framework. Finally, the experimental techniques used to investigate such flows are reviewed, with emphasis on modern non-intrusive optical flow diagnostics.

Does environmental policy affect scaling laws between population and pollution? Evidence from American metropolitan areas

PubMed Central

2017-01-01

Modern cities are engines of production, innovation, and growth. However, urbanization also increases both local and global pollution from household consumption and firms’ production. Do emissions change proportionately to city size or does pollution tend to outpace or lag urbanization? Do emissions scale differently with population versus economic growth or are emissions, population, and economic growth inextricably linked? How are the scaling relationships between emissions, population, and economic growth affected by environmental regulation? This paper examines the link between urbanization, economic growth and pollution using data from Metropolitan Statistical Areas (MSAs) in the United States between 1999 and 2011. We find that the emissions of local air pollution in these MSAs scale according to a ¾ power law with both population size and gross domestic product (GDP). However, the monetary damages from these local emissions scale linearly with both population and GDP. Counties that have previously been out of attainment with the local air quality standards set by the Clean Air Act show an entirely different relationship: local emissions scale according to the square root of population, while the monetary damages from local air pollution follow a 2/3rds power law with population. Counties out of attainment are subject to more stringent emission controls; we argue based on this that enforcement of the Clean Air Act induces sublinear scaling between emissions, damages, and city size. In contrast, we find that metropolitan GDP scales super-linearly with population in all MSAs regardless of attainment status. Summarizing, our findings suggest that environmental policy limits the adverse effects of urbanization without interfering with the productivity benefits that manifest in cities. PMID:28792949

Does environmental policy affect scaling laws between population and pollution? Evidence from American metropolitan areas.

PubMed

Muller, Nicholas Z; Jha, Akshaya

2017-01-01

Modern cities are engines of production, innovation, and growth. However, urbanization also increases both local and global pollution from household consumption and firms' production. Do emissions change proportionately to city size or does pollution tend to outpace or lag urbanization? Do emissions scale differently with population versus economic growth or are emissions, population, and economic growth inextricably linked? How are the scaling relationships between emissions, population, and economic growth affected by environmental regulation? This paper examines the link between urbanization, economic growth and pollution using data from Metropolitan Statistical Areas (MSAs) in the United States between 1999 and 2011. We find that the emissions of local air pollution in these MSAs scale according to a ¾ power law with both population size and gross domestic product (GDP). However, the monetary damages from these local emissions scale linearly with both population and GDP. Counties that have previously been out of attainment with the local air quality standards set by the Clean Air Act show an entirely different relationship: local emissions scale according to the square root of population, while the monetary damages from local air pollution follow a 2/3rds power law with population. Counties out of attainment are subject to more stringent emission controls; we argue based on this that enforcement of the Clean Air Act induces sublinear scaling between emissions, damages, and city size. In contrast, we find that metropolitan GDP scales super-linearly with population in all MSAs regardless of attainment status. Summarizing, our findings suggest that environmental policy limits the adverse effects of urbanization without interfering with the productivity benefits that manifest in cities.

Re-examining the effect of low and intermediate mode number perturbations on Ignition Metrics Scaling Laws

NASA Astrophysics Data System (ADS)

Malka, Elad; Shvarts, Dov

2017-10-01

We re-examine the way 2/3D effects on scaling laws for ignition metrics, such as the generalized Lawson Criterion (GLC) and the Ignition Threshold Factor (ITF). These scaling laws were derived for 1D symmetrical case and 2/3D perturbations [Hann et al. PoP 2010; Lindl et al., PoP 2014; Betti et al., PoP 2010]. The main cause for the difference between the 1D and the 2/3D scaling laws in those works, is heat conduction losses from the hot-spot bubbles to the cold shell [Kishony and Shvarts, PoP 2001]. This ``dry out'' of the bubbles is the dominant mechanism for intermediate mode number perturbations (6

BPS Z{sub N} string tensions, sine law and Casimir scaling, and integrable field theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kneipp, Marco A. C.; International Centre for Theoretical Physics

We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of the gauge group G{yields}U(1){sup r}{yields}C{sub G}, with C{sub G} being the center of G. We study two vacua solutions of the theory which produce this symmetry breaking. We show that for one of these vacua, the theory in the Coulomb phase has the mass spectrum of particles and monopoles which is exactly the same as the mass spectrum of particles and solitons of two-dimensional affine Toda field theory, for suitable coupling constants. That result holds also for N=4 super Yang-Mills theories. On the other hand, in the Higgs phase, wemore » show that for each of the two vacua the ratio of the tensions of the BPS Z{sub N} strings satisfy either the Casimir scaling or the sine law scaling for G=SU(N). These results are extended to other gauge groups: for the Casimir scaling, the ratios of the tensions are equal to the ratios of the quadratic Casimir constant of specific representations; for the sine law scaling, the tensions are proportional to the components of the left Perron-Frobenius eigenvector of Cartan matrix K{sub ij} and the ratios of tensions are equal to the ratios of the soliton masses of affine Toda field theories.« less

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.

49 CFR 350.343 - How may a State obtain a new exemption for State laws and regulations for a specific industry...

Code of Federal Regulations, 2011 CFR

2011-10-01

... SAFETY ASSISTANCE PROGRAM Funding § 350.343 How may a State obtain a new exemption for State laws and... circumstances under which they were granted. (h) Justification for the exemption. (i) Identifiable effects on...

49 CFR 350.343 - How may a State obtain a new exemption for State laws and regulations for a specific industry...

Code of Federal Regulations, 2010 CFR

2010-10-01

... SAFETY ASSISTANCE PROGRAM Funding § 350.343 How may a State obtain a new exemption for State laws and... circumstances under which they were granted. (h) Justification for the exemption. (i) Identifiable effects on...

COLLISIONS BETWEEN GRAVITY-DOMINATED BODIES. I. OUTCOME REGIMES AND SCALING LAWS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leinhardt, Zoee M.; Stewart, Sarah T., E-mail: Zoe.Leinhardt@bristol.ac.uk, E-mail: sstewart@eps.harvard.edu

2012-01-20

Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate mapsmore » of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation. Collision outcomes are described in terms of the impact conditions and the catastrophic disruption criteria, Q*{sub RD}-the specific energy required to disperse half the total colliding mass. All planet formation and collisional evolution studies have assumed that catastrophic disruption follows pure energy scaling; however, we find that catastrophic disruption follows nearly pure momentum scaling. As a result, Q*{sub RD} is strongly dependent on the impact velocity and projectile-to-target mass ratio in addition to the total mass and impact angle. To account for the impact angle, we derive the interacting mass fraction of the projectile; the outcome of a collision is dependent on the kinetic energy of the interacting mass rather than the kinetic energy of the total mass. We also introduce a new material parameter, c*, that defines the catastrophic disruption criteria between equal-mass bodies in units of the specific gravitational binding energy. For a diverse range of planetesimal compositions and internal structures, c* has a value of 5 {+-} 2

Earthquake scaling laws for rupture geometry and slip heterogeneity

NASA Astrophysics Data System (ADS)

Thingbaijam, Kiran K. S.; Mai, P. Martin; Goda, Katsuichiro

2016-04-01

We analyze an extensive compilation of finite-fault rupture models to investigate earthquake scaling of source geometry and slip heterogeneity to derive new relationships for seismic and tsunami hazard assessment. Our dataset comprises 158 earthquakes with a total of 316 rupture models selected from the SRCMOD database (http://equake-rc.info/srcmod). We find that fault-length does not saturate with earthquake magnitude, while fault-width reveals inhibited growth due to the finite seismogenic thickness. For strike-slip earthquakes, fault-length grows more rapidly with increasing magnitude compared to events of other faulting types. Interestingly, our derived relationship falls between the L-model and W-model end-members. In contrast, both reverse and normal dip-slip events are more consistent with self-similar scaling of fault-length. However, fault-width scaling relationships for large strike-slip and normal dip-slip events, occurring on steeply dipping faults (δ~90° for strike-slip faults, and δ~60° for normal faults), deviate from self-similarity. Although reverse dip-slip events in general show self-similar scaling, the restricted growth of down-dip fault extent (with upper limit of ~200 km) can be seen for mega-thrust subduction events (M~9.0). Despite this fact, for a given earthquake magnitude, subduction reverse dip-slip events occupy relatively larger rupture area, compared to shallow crustal events. In addition, we characterize slip heterogeneity in terms of its probability distribution and spatial correlation structure to develop a complete stochastic random-field characterization of earthquake slip. We find that truncated exponential law best describes the probability distribution of slip, with observable scale parameters determined by the average and maximum slip. Applying Box-Cox transformation to slip distributions (to create quasi-normal distributed data) supports cube-root transformation, which also implies distinctive non-Gaussian slip

Evaluating the assumption of power-law late time scaling of breakthrough curves in highly heterogeneous media

NASA Astrophysics Data System (ADS)

Pedretti, Daniele

2017-04-01

Power-law (PL) distributions are widely adopted to define the late-time scaling of solute breakthrough curves (BTCs) during transport experiments in highly heterogeneous media. However, from a statistical perspective, distinguishing between a PL distribution and another tailed distribution is difficult, particularly when a qualitative assessment based on visual analysis of double-logarithmic plotting is used. This presentation aims to discuss the results from a recent analysis where a suite of statistical tools was applied to evaluate rigorously the scaling of BTCs from experiments that generate tailed distributions typically described as PL at late time. To this end, a set of BTCs from numerical simulations in highly heterogeneous media were generated using a transition probability approach (T-PROGS) coupled to a finite different numerical solver of the flow equation (MODFLOW) and a random walk particle tracking approach for Lagrangian transport (RW3D). The T-PROGS fields assumed randomly distributed hydraulic heterogeneities with long correlation scales creating solute channeling and anomalous transport. For simplicity, transport was simulated as purely advective. This combination of tools generates strongly non-symmetric BTCs visually resembling PL distributions at late time when plotted in double log scales. Unlike other combination of modeling parameters and boundary conditions (e.g. matrix diffusion in fractures), at late time no direct link exists between the mathematical functions describing scaling of these curves and physical parameters controlling transport. The results suggest that the statistical tests fail to describe the majority of curves as PL distributed. Moreover, they suggest that PL or lognormal distributions have the same likelihood to represent parametrically the shape of the tails. It is noticeable that forcing a model to reproduce the tail as PL functions results in a distribution of PL slopes comprised between 1.2 and 4, which are the

Scaling laws of strategic behavior and size heterogeneity in agent dynamics

NASA Astrophysics Data System (ADS)

Vaglica, Gabriella; Lillo, Fabrizio; Moro, Esteban; Mantegna, Rosario N.

2008-03-01

We consider the financial market as a model system and study empirically how agents strategically adjust the properties of large orders in order to meet their preference and minimize their impact. We quantify this strategic behavior by detecting scaling relations between the variables characterizing the trading activity of different institutions. We also observe power-law distributions in the investment time horizon, in the number of transactions needed to execute a large order, and in the traded value exchanged by large institutions, and we show that heterogeneity of agents is a key ingredient for the emergence of some aggregate properties characterizing this complex system.

Flow Instability and Flow Control Scaling Laws

NASA Astrophysics Data System (ADS)

van Ness, Daniel; Corke, Thomas; Morris, Scott

2006-11-01

A flow instability that is receptive to perturbations is present in the tip clearance leakage flow over the tip of a turbine blade. This instability was investigated through the introduction of active flow control in the viscous flow field. Control was implemented in the form of a dielectric barrier discharge created by a weakly-ionized plasma actuation arrangement. The experimental setup consisted of a low-speed linear turbine cascade made up of an array of nine Pratt & Whitney ``PakB'' turbine blades. This idealized cascade configuration was used to examine the tip clearance leakage flow that exists within the low pressure turbine stage of a gas-turbine engine. The center blade of the cascade array had a variable tip clearance up to five percent chord. Reynolds numbers based on axial blade chord varied from 10^4 to 10^5. Multi-port pressure probe measurements, as well as Stereo Particle Image Velocimetry were used to document the dependence of the instability on the frequency and amplitude of flow control perturbations. Scaling laws based on the variation of blade tip clearance height and inflow conditions were investigated. These results permitted an improved understanding of the mechanism of flow instability.

Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

NASA Astrophysics Data System (ADS)

Elsas, José Hugo; Szalay, Alexander S.; Meneveau, Charles

2018-04-01

Motivated by interest in the geometry of high intensity events of turbulent flows, we examine the spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analysed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation and velocity gradient invariants Q and R and their joint spatial distributions, using data from a direct numerical simulation of isotropic turbulence at Reλ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus, a geometric characterisation in terms of these sets' correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behaviour. Nevertheless, the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow.

Evolution of scaling emergence in large-scale spatial epidemic spreading.

PubMed

Wang, Lin; Li, Xiang; Zhang, Yi-Qing; Zhang, Yan; Zhang, Kan

2011-01-01

Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified. In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.

Crossover from antipersistent to persistent behavior in time series possessing the generalyzed dynamic scaling law

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Morales Matamoros, Oswaldo; Gálvez M., Ernesto; Pérez A., Alfonso

2004-03-01

The behavior of crude oil price volatility is analyzed within a conceptual framework of kinetic roughening of growing interfaces. We find that the persistent long-horizon volatilities satisfy the Family-Viscek dynamic scaling ansatz, whereas the mean-reverting in time short horizon volatilities obey the generalized scaling law with continuously varying scaling exponents. Furthermore we find that the crossover from antipersistent to persistent behavior is accompanied by a change in the type of volatility distribution. These phenomena are attributed to the complex avalanche dynamics of crude oil markets and so a similar behavior may be observed in a wide variety of physical systems governed by avalanche dynamics.

A Scale-Invariant Model of Statistical Mechanics and Modified Forms of the First and the Second Laws of Thermodynamics

NASA Technical Reports Server (NTRS)

Sohrab, Siavash H.; Pitch, Nancy (Technical Monitor)

1999-01-01

A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).

Evolution of Scaling Emergence in Large-Scale Spatial Epidemic Spreading

PubMed Central

Wang, Lin; Li, Xiang; Zhang, Yi-Qing; Zhang, Yan; Zhang, Kan

2011-01-01

Background Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified. Methodology/Principal Findings In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. Conclusions/Significance The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease. PMID:21747932

Temperature and heat flux scaling laws for isoviscous, infinite Prandtl number mixed heating convection

NASA Astrophysics Data System (ADS)

Vilella, Kenny; Deschamps, Frédéric

2018-07-01

Thermal evolution of terrestrial planets is controlled by heat transfer through their silicate mantles. A suitable framework for modelling this heat transport is a system including bottom heating (from the core) and internal heating, for example, generated by secular cooling or by the decay of radioactive isotopes. The mechanism of heat transfer depends on the physical properties of the system. In systems where convection is able to operate, two different regimes are possible depending on the relative amount of bottom and internal heating. For moderate internal heating rates, the system is composed of active hot upwellings and cold downwellings. For large internal heating rates, the bottom heat flux becomes negative and the system is only composed of active cold downwellings. Here, we build theoretical scaling laws for both convective regimes following the approach of Vilella & Kaminski (2017), which links the surface heat flux and the temperature jump across both the top and the bottom thermal boundary layer (TBL) to the Rayleigh number and the dimensionless internal heating rate. Theoretical predictions are then verified against numerical simulations performed in 2-D and 3-D Cartesiangeometry, and covering a large range of the parameter space. Our theoretical scaling laws are more successful in predicting the thermal structure of systems with large internal heating rates than that of systems with no or moderate internal heating. The differences between moderate and large internal heating rates are interpreted as differences in the mechanisms generating thermal instabilities. We identified three mechanisms: conductive growth of the TBL, instability impacting, and TBL erosion, the last two being present only for moderate internal heating rates, in which hot plumes are generated at the bottom of the system and are able to reach the surface. Finally, we apply our scaling laws to the evolution of the early Earth, proposing a new model for the cooling of the primordial

Temperature and heat flux scaling laws for isoviscous, infinite Prandtl number mixed heating convection.

NASA Astrophysics Data System (ADS)

Vilella, Kenny; Deschamps, Frederic

2018-04-01

Thermal evolution of terrestrial planets is controlled by heat transfer through their silicate mantles. A suitable framework for modelling this heat transport is a system including bottom heating (from the core) and internal heating, e.g., generated by secular cooling or by the decay of radioactive isotopes. The mechanism of heat transfer depends on the physical properties of the system. In systems where convection is able to operate, two different regimes are possible depending on the relative amount of bottom and internal heating. For moderate internal heating rates, the system is composed of active hot upwellings and cold downwellings. For large internal heating rates, the bottom heat flux becomes negative and the system is only composed of active cold downwellings. Here, we build theoretical scaling laws for both convective regimes following the approach of Vilella & Kaminski (2017), which links the surface heat flux and the temperature jump across both the top and bottom thermal boundary layer (TBL) to the Rayleigh number and the dimensionless internal heating rate. Theoretical predictions are then verified against numerical simulations performed in 2D and 3D-Cartesian geometry, and covering a large range of the parameter space. Our theoretical scaling laws are more successful in predicting the thermal structure of systems with large internal heating rates than that of systems with no or moderate internal heating. The differences between moderate and large internal heating rates are interpreted as differences in the mechanisms generating thermal instabilities. We identified three mechanisms: conductive growth of the TBL, instability impacting, and TBL erosion, the last two being present only for moderate internal heating rates, in which hot plumes are generated at the bottom of the system and are able to reach the surface. Finally, we apply our scaling laws to the evolution of the early Earth, proposing a new model for the cooling of the primordial magma ocean

Universal Scaling Laws for Dense Particle Suspensions in Turbulent Wall-Bounded Flows.

PubMed

Costa, Pedro; Picano, Francesco; Brandt, Luca; Breugem, Wim-Paul

2016-09-23

The macroscopic behavior of dense suspensions of neutrally buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum limit in which its dynamics is well described by an effective suspension viscosity. This deviation is caused by the formation of a particle layer close to the wall with significant slip velocity. By assuming two distinct transport mechanisms in the near-wall layer and the turbulence in the bulk, we define an effective wall location such that the flow in the bulk can still be accurately described by an effective suspension viscosity. We thus propose scaling laws for the mean velocity profile of the suspension flow, together with a master equation able to predict the increase in drag as a function of the particle size and volume fraction.

Unification of small and large time scales for biological evolution: deviations from power law.

PubMed

Chowdhury, Debashish; Stauffer, Dietrich; Kunwar, Ambarish

2003-02-14

We develop a unified model that describes both "micro" and "macro" evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the "microevolution" over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the "macroevolution" over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.

Rapid inundation estimates at harbor scale using tsunami wave heights offshore simulation and coastal amplification laws

NASA Astrophysics Data System (ADS)

Gailler, A.; Loevenbruck, A.; Hebert, H.

2013-12-01

Numerical tsunami propagation and inundation models are well developed and have now reached an impressive level of accuracy, especially in locations such as harbors where the tsunami waves are mostly amplified. In the framework of tsunami warning under real-time operational conditions, the main obstacle for the routine use of such numerical simulations remains the slowness of the numerical computation, which is strengthened when detailed grids are required for the precise modeling of the coastline response of an individual harbor. Thus only tsunami offshore propagation modeling tools using a single sparse bathymetric computation grid are presently included within the French Tsunami Warning Center (CENALT), providing rapid estimation of tsunami warning at western Mediterranean and NE Atlantic basins scale. We present here a preliminary work that performs quick estimates of the inundation at individual harbors from these high sea forecasting tsunami simulations. The method involves an empirical correction based on theoretical amplification laws (either Green's or Synolakis laws). The main limitation is that its application to a given coastal area would require a large database of previous observations, in order to define the empirical parameters of the correction equation. As no such data (i.e., historical tide gage records of significant tsunamis) are available for the western Mediterranean and NE Atlantic basins, we use a set of synthetic mareograms, calculated for both fake and well-known historical tsunamigenic earthquakes in the area. This synthetic dataset is obtained through accurate numerical tsunami propagation and inundation modeling by using several nested bathymetric grids of increasingly fine resolution close to the shores (down to a grid cell size of 3m in some Mediterranean harbors). Non linear shallow water tsunami modeling performed on a single 2' coarse bathymetric grid are compared to the values given by time-consuming nested grids simulations (and

Scaling laws and universality for the strength of genetic interactions in yeast

NASA Astrophysics Data System (ADS)

Velenich, Andrea; Dai, Mingjie; Gore, Jeff

2012-02-01

Genetic interactions provide a window to the organization of the thousands of biochemical reactions in living cells. If two mutations affect unrelated cellular functions, the fitness effects of their combination can be easily predicted from the two separate fitness effects. However, because of interactions, for some pairs of mutations their combined fitness effect deviates from the naive prediction. We study genetic interactions in yeast cells by analyzing a publicly available database containing experimental growth rates of 5 million double mutants. We show that the characteristic strength of genetic interactions has a simple power law dependence on the fitness effects of the two interacting mutations and that the probability distribution of genetic interactions is a universal function. We further argue that the strength of genetic interactions depends only on the fitness effects of the interacting mutations and not on their biological origin in terms of single point mutations, entire gene knockouts or even more complicated physiological perturbations. Finally, we discuss the implications of the power law scaling of genetic interactions on the ruggedness of fitness landscapes and the consequent evolutionary dynamics.

On the universality of power laws for tokamak plasma predictions

NASA Astrophysics Data System (ADS)

Garcia, J.; Cambon, D.; Contributors, JET

2018-02-01

Significant deviations from well established power laws for the thermal energy confinement time, obtained from extensive databases analysis as the IPB98(y,2), have been recently reported in dedicated power scans. In order to illuminate the adequacy, validity and universality of power laws as tools for predicting plasma performance, a simplified analysis has been carried out in the framework of a minimal modeling for heat transport which is, however, able to account for the interplay between turbulence and collinear effects with the input power known to play a role in experiments with significant deviations from such power laws. Whereas at low powers, the usual scaling laws are recovered with little influence of other plasma parameters, resulting in a robust power low exponent, at high power it is shown how the exponents obtained are extremely sensitive to the heating deposition, the q-profile or even the sampling or the number of points considered due to highly non-linear behavior of the heat transport. In particular circumstances, even a minimum of the thermal energy confinement time with the input power can be obtained, which means that the approach of the energy confinement time as a power law might be intrinsically invalid. Therefore plasma predictions with a power law approximation with a constant exponent obtained from a regression of a broad range of powers and other plasma parameters which can non-linearly affect and suppress heat transport, can lead to misleading results suggesting that this approach should be taken cautiously and its results continuously compared with modeling which can properly capture the underline physics, as gyrokinetic simulations.

Applicability of scaling behavior and power laws in the analysis of the magnetocaloric effect in second-order phase transition materials

NASA Astrophysics Data System (ADS)

Romero-Muñiz, Carlos; Tamura, Ryo; Tanaka, Shu; Franco, Victorino

2016-10-01

In recent years, universal scaling has gained renewed attention in the study of magnetocaloric materials. It has been applied to a wide variety of pure elements and compounds, ranging from rare-earth-based materials to transition metal alloys, from bulk crystalline samples to nanoparticles. It is therefore necessary to quantify the limits within which the scaling laws would remain applicable for magnetocaloric research. For this purpose, a threefold approach has been followed: (a) the magnetocaloric responses of a set of materials with Curie temperatures ranging from 46 to 336 K have been modeled with a mean-field Brillouin model, (b) experimental data for Gd has been analyzed, and (c) a 3D-Ising model—which is beyond the mean-field approximation—has been studied. In this way, we can demonstrate that the conclusions extracted in this work are model-independent. It is found that universal scaling remains applicable up to applied fields, which provide a magnetic energy to the system up to 8% of the thermal energy at the Curie temperature. In this range, the predicted deviations from scaling laws remain below the experimental error margin of carefully performed experiments. Therefore, for materials whose Curie temperature is close to room temperature, scaling laws at the Curie temperature would be applicable for the magnetic field range available at conventional magnetism laboratories (˜10 T), well above the fields which are usually available for magnetocaloric devices.

Pore scale simulations for the extension of the Darcy-Forchheimer law to shear thinning fluids

NASA Astrophysics Data System (ADS)

Tosco, Tiziana; Marchisio, Daniele; Lince, Federica; Boccardo, Gianluca; Sethi, Rajandrea

2014-05-01

Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food as well as petroleum and groundwater engineering and in many other industrial applications (1 - 2). In particular, the use of shear thinning polymeric solutions has been recently proposed to improve colloidal stability of micro- and nanoscale zerovalent iron particles (MZVI and NZVI) for groundwater remediation. In all abovementioned applications, it is of paramount importance to correctly predict the pressure drop resulting from non-Newtonian fluid flow through the porous medium. For small Reynolds numbers, usually up to 1, typical of laboratory column tests, the extended Darcy law is known to be applicable also to non Newtonian fluids, provided that all non-Newtonian effects are lumped together into a proper viscosity parameter (1,3). For higher Reynolds numbers (eg. close to the injection wells) non linearities between pressure drop and flow rate arise, and the Darcy-Forchheimer law holds for Newtonian fluids, while for non-Newtonian fluids, it has been demonstrated that, at least for simple rheological models (eg. power law fluids) a generalized Forchheimer law can be applied, even if the determination of the flow parameters (permeability K, inertial coefficient β, and equivalent viscosity) is not straightforward. This work (co-funded by European Union project AQUAREHAB FP7 - Grant Agreement Nr. 226565) aims at proposing an extended formulation of the Darcy-Forchheimer law also for shear-thinning fluids, and validating it against results of pore-scale simulations via computational fluid dynamics (4). Flow simulations were performed using Fluent 12.0 on four different 2D porous domains for Newtonian and non-Newtonian fluids (Cross, Ellis and Carreau models). The micro-scale flow simulation results are analyzed in terms of 'macroscale' pressure drop between inlet and outlet of the model domain as a function of flow rate. The

Unified Scaling Law for flux pinning in practical superconductors: II. Parameter testing, scaling constants, and the Extrapolative Scaling Expression

NASA Astrophysics Data System (ADS)

Ekin, Jack W.; Cheggour, Najib; Goodrich, Loren; Splett, Jolene; Bordini, Bernardo; Richter, David

2016-12-01

A scaling study of several thousand Nb3Sn critical-current (I c) measurements is used to derive the Extrapolative Scaling Expression (ESE), a relation that can quickly and accurately extrapolate limited datasets to obtain full three-dimensional dependences of I c on magnetic field (B), temperature (T), and mechanical strain (ɛ). The relation has the advantage of being easy to implement, and offers significant savings in sample characterization time and a useful tool for magnet design. Thorough data-based analysis of the general parameterization of the Unified Scaling Law (USL) shows the existence of three universal scaling constants for practical Nb3Sn conductors. The study also identifies the scaling parameters that are conductor specific and need to be fitted to each conductor. This investigation includes two new, rare, and very large I c(B,T,ɛ) datasets (each with nearly a thousand I c measurements spanning magnetic fields from 1 to 16 T, temperatures from ˜2.26 to 14 K, and intrinsic strains from -1.1% to +0.3%). The results are summarized in terms of the general USL parameters given in table 3 of Part 1 (Ekin J W 2010 Supercond. Sci. Technol. 23 083001) of this series of articles. The scaling constants determined for practical Nb3Sn conductors are: the upper-critical-field temperature parameter v = 1.50 ± 0.04 the cross-link parameter w = 3.0 ± 0.3 and the strain curvature parameter u = 1.7 ± 0.1 (from equation (29) for b c2(ɛ) in Part 1). These constants and required fitting parameters result in the ESE relation, given by I c ( B , T , ɛ ) B = C [ b c 2 ( ɛ ) ] s ( 1 - t 1.5 ) η - μ ( 1 - t 2 ) μ b p ( 1 - b ) q with reduced magnetic field b ≡ B/B c2*(T,ɛ) and reduced temperature t ≡ T/T c*(ɛ), where: B c 2 * ( T , ɛ ) = B c 2 * ( 0 , 0 ) ( 1 - t 1.5 ) b c 2 ( ɛ ) T c * ( ɛ ) = T c * ( 0 ) [ b c 2 ( ɛ ) ] 1/3 and fitting parameters: C, B c2*(0,0), T c*(0), s, either η or μ (but not both), plus the parameters in the strain function b c2

Quantum phase transition from mixed atom-molecule phase to pure molecule phase: Characteristic scaling laws and Berry-curvature signature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Shengchang; Graduate School, China Academy of Engineering Physics, Beijing 100088; Fu Libin

2011-08-15

We investigate the quantum phase transition in an ultracold atom-molecule conversion system. It is found that the system undergoes a phase transition from a mixed atom-molecule phase to a pure molecule phase when the energy bias exceeds a critical value. By constructing a coherent state as variational state, we get a good approximation of the quantum ground state of the system. Using this variational state, we deduce the critical point analytically. We then discuss the scaling laws characterizing the transition and obtain the corresponding critical exponents. Furthermore, the Berry curvature signature of the transition is studied. In particular, we findmore » that the derivatives of the Berry curvature with respect to total particle number intersect at the critical point. The underlying mechanism of this finding is discussed as well.« less

Improved scaling laws for stage inert mass of space propulsion systems. Volume 2: System modeling and weight data

NASA Technical Reports Server (NTRS)

1971-01-01

Technical models and analytical approaches used to develop the weight data for vehicle system concepts using advanced technology are reported. Weight data are supplied for the following major system elements: engine, pressurization, propellant containers, structural shells and secondary structure, and environmental protection shields for the meteoroid and thermal design requirements. Scaling laws, improved and a simplified set, are developed from the system weight data. The laws consider the implications of the major design parameters and mission requirements on the stage inert mass.

Laboratory study of sonic booms and their scaling laws. [ballistic range simulation

NASA Technical Reports Server (NTRS)

Toong, T. Y.

1974-01-01

This program undertook to seek a basic understanding of non-linear effects associated with caustics, through laboratory simulation experiments of sonic booms in a ballistic range and a coordinated theoretical study of scaling laws. Two cases of superbooms or enhanced sonic booms at caustics have been studied. The first case, referred to as acceleration superbooms, is related to the enhanced sonic booms generated during the acceleration maneuvers of supersonic aircrafts. The second case, referred to as refraction superbooms, involves the superbooms that are generated as a result of atmospheric refraction. Important theoretical and experimental results are briefly reported.

A general scaling law reveals why the largest animals are not the fastest.

PubMed

Hirt, Myriam R; Jetz, Walter; Rall, Björn C; Brose, Ulrich

2017-08-01

Speed is the fundamental constraint on animal movement, yet there is no general consensus on the determinants of maximum speed itself. Here, we provide a general scaling model of maximum speed with body mass, which holds across locomotion modes, ecosystem types and taxonomic groups. In contrast to traditional power-law scaling, we predict a hump-shaped relationship resulting from a finite acceleration time for animals, which explains why the largest animals are not the fastest. This model is strongly supported by extensive empirical data (474 species, with body masses ranging from 30 μg to 100 tonnes) from terrestrial as well as aquatic ecosystems. Our approach unravels a fundamental constraint on the upper limit of animal movement, thus enabling a better understanding of realized movement patterns in nature and their multifold ecological consequences.

Engagement in the electoral processes: scaling laws and the role of political positions.

PubMed

Mantovani, M C; Ribeiro, H V; Lenzi, E K; Picoli, S; Mendes, R S

2013-08-01

We report on a statistical analysis of the engagement in the electoral processes of all Brazilian cities by considering the number of party memberships and the number of candidates for mayor and councillor. By investigating the relationships between the number of party members and the population of voters, we have found that the functional forms of these relationships are well described by sublinear power laws (allometric scaling) surrounded by a multiplicative log-normal noise. We have observed that this pattern is quite similar to those we previously reported for the relationships between the number of candidates (mayor and councillor) and population of voters [Europhys. Lett. 96, 48001 (2011)], suggesting that similar universal laws may be ruling the engagement in the electoral processes. We also note that the power-law exponents display a clear hierarchy, where the more influential is the political position the smaller is the value of the exponent. We have also investigated the probability distributions of the number of candidates (mayor and councillor), party memberships, and voters. The results indicate that the most influential positions are characterized by distributions with very short tails, while less influential positions display an intermediate power-law decay before showing an exponential-like cutoff. We discuss the possibility that, in addition to the political power of the position, limitations in the number of available seats can also be connected with this changing of behavior. We further believe that our empirical findings point out to an under-representation effect, where the larger the city is, the larger are the obstacles for more individuals to become directly engaged in the electoral process.

Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities.

PubMed

Zhang, Qun; Zhang, Qunzhi; Sornette, Didier

2016-01-01

We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the "S&P 500 1987" bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs.

Scaling laws for van der Waals interactions in nanostructured materials.

PubMed

Gobre, Vivekanand V; Tkatchenko, Alexandre

2013-01-01

Van der Waals interactions have a fundamental role in biology, physics and chemistry, in particular in the self-assembly and the ensuing function of nanostructured materials. Here we utilize an efficient microscopic method to demonstrate that van der Waals interactions in nanomaterials act at distances greater than typically assumed, and can be characterized by different scaling laws depending on the dimensionality and size of the system. Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons. As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture. We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.

Universal Scaling Laws in the Dynamics of a Homogeneous Unitary Bose Gas

NASA Astrophysics Data System (ADS)

Eigen, Christoph; Glidden, Jake A. P.; Lopes, Raphael; Navon, Nir; Hadzibabic, Zoran; Smith, Robert P.

2017-12-01

We study the dynamics of an initially degenerate homogeneous Bose gas after an interaction quench to the unitary regime at a magnetic Feshbach resonance. As the cloud decays and heats, it exhibits a crossover from degenerate- to thermal-gas behavior, both of which are characterized by universal scaling laws linking the particle-loss rate to the total atom number N . In the degenerate and thermal regimes, the per-particle loss rate is ∝N2 /3 and N26 /9, respectively. The crossover occurs at a universal kinetic energy per particle and at a universal time after the quench, in units of energy and time set by the gas density. By slowly sweeping the magnetic field away from the resonance and creating a mixture of atoms and molecules, we also map out the dynamics of correlations in the unitary gas, which display a universal temporal scaling with the gas density, and reach a steady state while the gas is still degenerate.

Universal Scaling Laws in the Dynamics of a Homogeneous Unitary Bose Gas.

PubMed

Eigen, Christoph; Glidden, Jake A P; Lopes, Raphael; Navon, Nir; Hadzibabic, Zoran; Smith, Robert P

2017-12-22

We study the dynamics of an initially degenerate homogeneous Bose gas after an interaction quench to the unitary regime at a magnetic Feshbach resonance. As the cloud decays and heats, it exhibits a crossover from degenerate- to thermal-gas behavior, both of which are characterized by universal scaling laws linking the particle-loss rate to the total atom number N. In the degenerate and thermal regimes, the per-particle loss rate is ∝N^{2/3} and N^{26/9}, respectively. The crossover occurs at a universal kinetic energy per particle and at a universal time after the quench, in units of energy and time set by the gas density. By slowly sweeping the magnetic field away from the resonance and creating a mixture of atoms and molecules, we also map out the dynamics of correlations in the unitary gas, which display a universal temporal scaling with the gas density, and reach a steady state while the gas is still degenerate.

Dependence of exponents on text length versus finite-size scaling for word-frequency distributions

NASA Astrophysics Data System (ADS)

Corral, Álvaro; Font-Clos, Francesc

2017-08-01

Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of this scaling law, using both careful statistical tests and analytical arguments based on the generalized central-limit theorem applied to the moments of the distribution (and obtaining a novel derivation of Heaps' law as a by-product). We also find that the picture of word-frequency distributions with power-law exponents that decrease with text length [X. Yan and P. Minnhagen, Physica A 444, 828 (2016), 10.1016/j.physa.2015.10.082] does not stand with rigorous statistical analysis. Instead, we show that the distributions are perfectly described by power-law tails with stable exponents, whose values are close to 2, in agreement with the classical Zipf's law. Some misconceptions about scaling are also clarified.

Cope's Rule and the Universal Scaling Law of Ornament Complexity.

PubMed

Raia, Pasquale; Passaro, Federico; Carotenuto, Francesco; Maiorino, Leonardo; Piras, Paolo; Teresi, Luciano; Meiri, Shai; Itescu, Yuval; Novosolov, Maria; Baiano, Mattia Antonio; Martínez, Ricard; Fortelius, Mikael

2015-08-01

Luxuriant, bushy antlers, bizarre crests, and huge, twisting horns and tusks are conventionally understood as products of sexual selection. This view stems from both direct observation and from the empirical finding that the size of these structures grows faster than body size (i.e., ornament size shows positive allometry). We contend that the familiar evolutionary increase in the complexity of ornaments over time in many animal clades is decoupled from ornament size evolution. Increased body size comes with extended growth. Since growth scales to the quarter power of body size, we predicted that ornament complexity should scale according to the quarter power law as well, irrespective of the role of sexual selection in the evolution and function of the ornament. To test this hypothesis, we selected three clades (ammonites, deer, and ceratopsian dinosaurs) whose species bore ornaments that differ in terms of the importance of sexual selection to their evolution. We found that the exponent of the regression of ornament complexity to body size is the same for the three groups and is statistically indistinguishable from 0.25. We suggest that the evolution of ornament complexity is a by-product of Cope's rule. We argue that although sexual selection may control size in most ornaments, it does not influence their shape.

Solving large scale unit dilemma in electricity system by applying commutative law

NASA Astrophysics Data System (ADS)

Legino, Supriadi; Arianto, Rakhmat

2018-03-01

The conventional system, pooling resources with large centralized power plant interconnected as a network. provides a lot of advantages compare to the isolated one include optimizing efficiency and reliability. However, such a large plant need a huge capital. In addition, more problems emerged to hinder the construction of big power plant as well as its associated transmission lines. By applying commutative law of math, ab = ba, for all a,b €-R, the problem associated with conventional system as depicted above, can be reduced. The idea of having small unit but many power plants, namely “Listrik Kerakyatan,” abbreviated as LK provides both social and environmental benefit that could be capitalized by using proper assumption. This study compares the cost and benefit of LK to those of conventional system, using simulation method to prove that LK offers alternative solution to answer many problems associated with the large system. Commutative Law of Algebra can be used as a simple mathematical model to analyze whether the LK system as an eco-friendly distributed generation can be applied to solve various problems associated with a large scale conventional system. The result of simulation shows that LK provides more value if its plants operate in less than 11 hours as peaker power plant or load follower power plant to improve load curve balance of the power system. The result of simulation indicates that the investment cost of LK plant should be optimized in order to minimize the plant investment cost. This study indicates that the benefit of economies of scale principle does not always apply to every condition, particularly if the portion of intangible cost and benefit is relatively high.

A Theoretical Basis for the Scaling Law of Broadband Shock Noise Intensity in Supersonic Jets

NASA Technical Reports Server (NTRS)

Kandula, Max

2011-01-01

A theoretical basis for the scaling of broadband shock noise intensity In supersonic jets was formulated considering linear shock-shear wave interaction. Modeling of broadband shock noise with the aid of shock-turbulence interaction with special reference to linear theories is briefly reviewed. An hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process with the noise generation contribution from off-peak incident angles being relatively unimportant. The proposed hypothesis satisfactorily explains the well-known scaling law for the broadband shock-associated noise in supersonic jets.

The scaling law of human travel - A message from George

NASA Astrophysics Data System (ADS)

Brockmann, Dirk; Hufnagel, Lars

The dispersal of individuals of a species is the key driving force of various spatiotemporal phenomena which occur on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools.1-3 The geographic spread of human infectious diseases such as influenza, measles and the recent severe acute respiratory syndrome (SARS) is essentially promoted by human travel which occurs on many length scales and is sustained by a variety of means of trans-portation4-8. In the light of increasing international trade, intensified human traffic, and an imminent influenza A pandemic the knowledge of dynamical and statistical properties of human dispersal is of fundamental importance and acute. 7,9,10 A quantitative statistical theory for human travel and concomitant reliable forecasts would substantially improve and extend existing prevention strategies. Despite its crucial role, a quantitative assessment of human dispersal remains elusive and the opinion that humans disperse diffusively still prevails in many models. 11 In this chapter we will report on a recently developed technique which permits a solid and quantitative assessment of human dispersal on geographical scales.12 The key idea is to infer the statistical properties of human travel by analysing the geographic circulation of individual bank notes for which comprehensive datasets are collected at online bill-tracking websites. The analysis shows that the distribution of traveling distances decays as a power law, indicating that the movement of bank notes is reminiscent of superdiffusive, scale free random walks known as Lévy flights.13 Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by heavy tails which attenuate superdiffusive dispersal. We will show that the dispersal of bank notes can be described on many spatiotemporal scales by a two parameter continuous time random walk (CTRW) model to a surprising accuracy. We

Localized Enzymatic Degradation of Polymers: Physics and Scaling Laws

NASA Astrophysics Data System (ADS)

Lalitha Sridhar, Shankar; Vernerey, Franck

2018-03-01

Biodegradable polymers are naturally abundant in living matter and have led to great advances in controlling environmental pollution due to synthetic polymer products, harnessing renewable energy from biofuels, and in the field of biomedicine. One of the most prevalent mechanisms of biodegradation involves enzyme-catalyzed depolymerization by biological agents. Despite numerous studies dedicated to understanding polymer biodegradation in different environments, a simple model that predicts the macroscopic behavior (mass and structural loss) in terms of microphysical processes (enzyme transport and reaction) is lacking. An interesting phenomenon occurs when an enzyme source (released by a biological agent) attacks a tight polymer mesh that restricts free diffusion. A fuzzy interface separating the intact and fully degraded polymer propagates away from the source and into the polymer as the enzymes diffuse and react in time. Understanding the characteristics of this interface will provide crucial insight into the biodegradation process and potential ways to precisely control it. In this work, we present a centrosymmetric model of biodegradation by characterizing the moving fuzzy interface in terms of its speed and width. The model predicts that the characteristics of this interface are governed by two time scales, namely the polymer degradation and enzyme transport times, which in turn depend on four main polymer and enzyme properties. A key finding of this work is simple scaling laws that can be used to guide biodegradation of polymers in different applications.

Scaling Law of High Harmonic Generation in the Framework of Photon Channels

NASA Astrophysics Data System (ADS)

Li, Liang; Lan, Pengfei; He, Lixin; Zhu, Xiaosong; Chen, Jing; Lu, Peixiang

2018-06-01

A photon channel perspective on high harmonic generation (HHG) is proposed by quantizing both the driving laser and high harmonics. It is shown that the HHG yield can be expressed as a sum of the contribution of all the photon channels. From this perspective, the contribution of a specific photon channel follows a simple scaling law and the competition between the channels is well interpreted. Our prediction is shown to be in good agreement with the simulations by solving the time-dependent Schrödinger equation. It also can explain well the experimental results of the HHG in the noncollinear two-color field and bicicular laser field.

Scaling Law of High Harmonic Generation in the Framework of Photon Channels.

PubMed

Li, Liang; Lan, Pengfei; He, Lixin; Zhu, Xiaosong; Chen, Jing; Lu, Peixiang

2018-06-01

A photon channel perspective on high harmonic generation (HHG) is proposed by quantizing both the driving laser and high harmonics. It is shown that the HHG yield can be expressed as a sum of the contribution of all the photon channels. From this perspective, the contribution of a specific photon channel follows a simple scaling law and the competition between the channels is well interpreted. Our prediction is shown to be in good agreement with the simulations by solving the time-dependent Schrödinger equation. It also can explain well the experimental results of the HHG in the noncollinear two-color field and bicicular laser field.

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

NASA Astrophysics Data System (ADS)

Boeck, Thomas; Thess, André

2001-08-01

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

A model of urban scaling laws based on distance dependent interactions

NASA Astrophysics Data System (ADS)

Ribeiro, Fabiano L.; Meirelles, Joao; Ferreira, Fernando F.; Neto, Camilo Rodrigues

2017-03-01

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log-log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

A model of urban scaling laws based on distance dependent interactions

PubMed Central

Ribeiro, Fabiano L.; Meirelles, Joao; Ferreira, Fernando F.

2017-01-01

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log–log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences. PMID:28405381

A model of urban scaling laws based on distance dependent interactions.

PubMed

Ribeiro, Fabiano L; Meirelles, Joao; Ferreira, Fernando F; Neto, Camilo Rodrigues

2017-03-01

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log-log plot, the so-called superlinear scaling . Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

Scaling Laws in Turbulence: Their Manifestation and Utility.

NASA Astrophysics Data System (ADS)

Juneja, Anurag

1995-01-01

It has long been hypothesized that small-scale features in turbulence possess some form of scale-invariance leading to several interesting predictions about related flow quantities. In the present work, we examine the scaling features and scaling exponents of various quantities in turbulence and the relationship they bear to Kolmogorov and multifractal scaling theories. A related goal (which is the inverse problem) is to synthesize stochastic fields which faithfully reproduce the observed scaling features of velocity fluctuations in high-Reynolds-number turbulence. First, we obtain, for structure functions of arbitrary order, an expression which is uniformly valid for the inertial and dissipation range. This enables a more definitive determination of scaling exponents than has been possible in the past. Next, we examine the scaling properties of circulation around contours of various sizes, as it is suggested that a better way to study the small-scale features might be to focus on the vortical component of the velocity field. We then utilize a quantity called the cancellation exponent to characterize the singular nature of vorticity fluctuations, whose trace exhibits an oscillation in sign on arbitrary fine scales. We note that the inter-relationships which can be established among the aforementioned scaling exponents for velocity structure functions, circulation and vorticity provide support for the multifractal formalism of turbulence. Next, we examine the fractal structure of self -affine time series data in turbulent flows. It is shown that the fractal dimension of velocity and temperature signals in atmospheric turbulence is 1.65 +/- 0.05 implying that the dimension of iso-velocity or iso-temperature surfaces in fully developed turbulence is about 2.65 +/- 0.05 in agreement with previous theoretical predictions. The Reynolds number dependence of the measured dimensions is also explored by examining laboratory data at moderate Reynolds numbers. Using simple

Inertial-range dynamics and scaling laws of two-dimensional magnetohydrodynamic turbulence in the weak-field regime.

PubMed

Blackbourn, Luke A K; Tran, Chuong V

2014-08-01

We study inertial-range dynamics and scaling laws in unforced two-dimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetic-to-kinetic-energy ratio r(0), with an emphasis on the latter. The regime of small r(0) corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the three-dimensional context). This conversion is an inertial-range phenomenon and, upon becoming quasisaturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic-energy spectrum E(b)(k) in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertial-range scaling depend strongly on r(0). In particular, for fully developed turbulence with r(0) in the range [1/4,1/4096], E(b)(k) is found to scale as k(α), where α≳-1, including α>0. The extent of such a shallow spectrum is limited, becoming broader as r(0) is decreased. The slope α increases as r(0) is decreased, appearing to tend to +1 in the limit of small r(0). This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling k(-1) of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic-energy spectrum is relatively steep, followed by a much shallower tail due to strong antidynamo excitation. This gives rise to a total

A method for obtaining reduced-order control laws for high-order systems using optimization techniques

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Newsom, J. R.; Abel, I.

1981-01-01

A method of synthesizing reduced-order optimal feedback control laws for a high-order system is developed. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean-square steady-state responses and control inputs. An analogy with the linear quadractic Gaussian solution is utilized to select a set of design variables and their initial values. To improve the stability margins of the system, an input-noise adjustment procedure is used in the design algorithm. The method is applied to the synthesis of an active flutter-suppression control law for a wind tunnel model of an aeroelastic wing. The reduced-order controller is compared with the corresponding full-order controller and found to provide nearly optimal performance. The performance of the present method appeared to be superior to that of two other control law order-reduction methods. It is concluded that by using the present algorithm, nearly optimal low-order control laws with good stability margins can be synthesized.

Health and Safety Management for Small-scale Methane Fermentation Facilities

NASA Astrophysics Data System (ADS)

Yamaoka, Masaru; Yuyama, Yoshito; Nakamura, Masato; Oritate, Fumiko

In this study, we considered health and safety management for small-scale methane fermentation facilities that treat 2-5 ton of biomass daily based on several years operation experience with an approximate capacity of 5 t·d-1. We also took account of existing knowledge, related laws and regulations. There are no qualifications or licenses required for management and operation of small-scale methane fermentation facilities, even though rural sewerage facilities with a relative similar function are required to obtain a legitimate license. Therefore, there are wide variations in health and safety consciousness of the operators of small-scale methane fermentation facilities. The industrial safety and health laws are not applied to the operation of small-scale methane fermentation facilities. However, in order to safely operate a small-scale methane fermentation facility, the occupational safety and health management system that the law recommends should be applied. The aims of this paper are to clarify the risk factors in small-scale methane fermentation facilities and encourage planning, design and operation of facilities based on health and safety management.

A variational approach to behavioral and neuroelectrical laws.

PubMed

Noventa, Stefano; Vidotto, Giulio

2012-09-01

Variational methods play a fundamental and unifying role in several fields of physics, chemistry, engineering, economics, and biology, as they allow one to derive the behavior of a system as a consequence of an optimality principle. A possible application of these methods to a model of perception is given by considering a psychophysical law as the solution of an Euler-Lagrange equation. A general class of Lagrangians is identified by requiring the measurability of prothetic continua on interval scales. The associated Hamiltonian (the energy of the process) is tentatively connected with neurophysiological aspects. As an example of the suggested approach a particular choice of the Lagrangian, that is a sufficient condition to obtain classical psychophysical laws, while accounting for psychophysical adaptation and the stationarity of neuronal activity, is used to explore a possible relation between a behavioral law and a neuroelectrical ,response based on the Naka-Rushton model.

Steady state and a general scale law of deformation

NASA Astrophysics Data System (ADS)

Huang, Yan

2017-07-01

Steady state deformation has been characterized based on the experimental results for dilute single-phase aluminium alloys. It was found that although characteristic properties such as flow stress and grain size remained constant with time, a continuous loss of grain boundaries occurred as an essential feature at steady state. A physical model, which takes into account the activity of grain boundary dislocations, was developed to describe the kinetics of steady state deformation. According to this model, the steady state as a function of strain rate and temperature defines the limit of the conventional grain size and strength relationship, i.e., the Hall-Petch relation holds when the grain size is larger than that at the steady state, and an inverse Hall-Petch relation takes over if grain size is smaller than the steady state value. The transition between the two relationships relating grain size and strength is a phenomenon that depends on deformation conditions, rather than an intrinsic property as generally perceived. A general scale law of deformation is established accordingly.

Multiscale entropy analysis of biological signals: a fundamental bi-scaling law

PubMed Central

Gao, Jianbo; Hu, Jing; Liu, Feiyan; Cao, Yinhe

2015-01-01

Since introduced in early 2000, multiscale entropy (MSE) has found many applications in biosignal analysis, and been extended to multivariate MSE. So far, however, no analytic results for MSE or multivariate MSE have been reported. This has severely limited our basic understanding of MSE. For example, it has not been studied whether MSE estimated using default parameter values and short data set is meaningful or not. Nor is it known whether MSE has any relation with other complexity measures, such as the Hurst parameter, which characterizes the correlation structure of the data. To overcome this limitation, and more importantly, to guide more fruitful applications of MSE in various areas of life sciences, we derive a fundamental bi-scaling law for fractal time series, one for the scale in phase space, the other for the block size used for smoothing. We illustrate the usefulness of the approach by examining two types of physiological data. One is heart rate variability (HRV) data, for the purpose of distinguishing healthy subjects from patients with congestive heart failure, a life-threatening condition. The other is electroencephalogram (EEG) data, for the purpose of distinguishing epileptic seizure EEG from normal healthy EEG. PMID:26082711

Modified circular velocity law

NASA Astrophysics Data System (ADS)

Djeghloul, Nazim

2018-05-01

A modified circular velocity law is presented for a test body orbiting around a spherically symmetric mass. This law exhibits a distance scale parameter and allows to recover both usual Newtonian behaviour for lower distances and a constant velocity limit at large scale. Application to the Galaxy predicts the known behaviour and also leads to a galactic mass in accordance with the measured visible stellar mass so that additional dark matter inside the Galaxy can be avoided. It is also shown that this circular velocity law can be embedded in a geometrical description of spacetime within the standard general relativity framework upon relaxing the usual asymptotic flatness condition. This formulation allows to redefine the introduced Newtonian scale limit in term of the central mass exclusively. Moreover, a satisfactory answer to the galactic escape speed problem can be provided indicating the possibility that one can also get rid of dark matter halo outside the Galaxy.

Fractal scaling laws of black carbon aerosol and their influence on spectral radiative properties

NASA Astrophysics Data System (ADS)

Tiwari, S.; Chakrabarty, R. K.; Heinson, W.

2016-12-01

Current estimates of the direct radiative forcing for Black Carbon (BC) aerosol span over a poorly constrained range between 0.2 and 1 W.m-2. To improve this large uncertainty, tighter constraints need to be placed on BC's key wavelength-dependent optical properties, namely, the absorption (MAC) and scattering (MSC) cross sections per unit mass and hemispherical upscatter fraction (β; a dimensionless scattering directionality parameter). These parameters are very sensitive to changes in particle morphology and complex refractive index nindex. Their interplay determines the magnitude of net positive or negative radiative forcing efficiencies. The current approach among climate modelers for estimating MAC and MSC values of BC is from their optical cross-sections calculated assuming spherical particle morphology with homogeneous, constant-valued refractive index in the visible solar spectrum. The β values are typically assumed to be a constant across this spectrum. This approach, while being computationally inexpensive and convenient, ignores the inherent fractal morphology of BC and its scaling behaviors, and resulting optical properties. In this talk, I will present recent results from my laboratory on determination of the fractal scaling laws of BC aggregate packing density and its complex refractive index for size spanning across three orders of magnitude, and their effects on spectral (Visible-infrared wavelength) scaling of MAC, MSC, and β values. Our experiments synergistically combined novel BC generation techniques, aggregation models, contact-free multi-wavelength optical measurements, and electron microscopy analysis. The scale dependence of nindex on aggregate size followed power-law exponents of -1.4 and -0.5 for sub- and super-micron size aggregates, respectively. The spherical Rayleigh-optics approximation limits, used by climate models for spectral extrapolation of BC optical cross-sections and deconvolution of multi-species mixing ratios, are

Obtaining lutein-rich extract from microalgal biomass at preparative scale.

PubMed

Fernández-Sevilla, José M; Fernández, F Gabriel Acién; Grima, Emilio Molina

2012-01-01

Lutein extracts are in increasing demand due to their alleged role in the prevention of degenerative disorders such as age-related macular degeneration (AMD). Lutein extracts are currently obtained from plant sources, but microalgae have been demonstrated to be a competitive source likely to become an alternative. The extraction of lutein from microalgae posesses specific problems that arise from the different structure and composition of the source biomass. Here is presented a method for the recovery of lutein-rich carotenoid extracts from microalgal biomass in the kilogram scale.

X-ray emission scaling law from a plasma focus with different anode tip materials (Cu, Mo, and W)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharif, M.; Ahmad, S.; Zakaullah, M.

X-ray emission from a 2.3-5.3 kJ Mather-type plasma focus [Phys. Fluids 7, 5 (1964)] employing copper, molybdenum, and tungsten anode tip is studied. Argon is used as a working gas. Characteristic Cu K{alpha} and Mo K-series emission and their ratio to the continuous x-rays are determined. From the variation of the x-ray yield data with filling pressure at different charging voltages, scaling laws are obtained. X-ray pinhole images demonstrate that a significant amount of x-ray emission is from the anode tip. The comparison of the ratio of characteristic to continuum radiation for copper anode with typical x-ray tube data revealsmore » that the contribution of very high energy electron beam from the focus region for x-ray generation through thick target bremsstrahlung mechanism is not significant. Rather, electrons with energy of the order of, or even less than, the charging voltage are responsible for bulk of the x-ray emission.« less

Structural similitude and design of scaled down laminated models

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Rezaeepazhand, J.

1993-01-01

The excellent mechanical properties of laminated composite structures make them prime candidates for wide variety of applications in aerospace, mechanical and other branches of engineering. The enormous design flexibility of advanced composites is obtained at the cost of large number of design parameters. Due to complexity of the systems and lack of complete design based informations, designers tend to be conservative in their design. Furthermore, any new design is extensively evaluated experimentally until it achieves the necessary reliability, performance and safety. However, the experimental evaluation of composite structures are costly and time consuming. Consequently, it is extremely useful if a full-scale structure can be replaced by a similar scaled-down model which is much easier to work with. Furthermore, a dramatic reduction in cost and time can be achieved, if available experimental data of a specific structure can be used to predict the behavior of a group of similar systems. This study investigates problems associated with the design of scaled models. Such study is important since it provides the necessary scaling laws, and the factors which affect the accuracy of the scale models. Similitude theory is employed to develop the necessary similarity conditions (scaling laws). Scaling laws provide relationship between a full-scale structure and its scale model, and can be used to extrapolate the experimental data of a small, inexpensive, and testable model into design information for a large prototype. Due to large number of design parameters, the identification of the principal scaling laws by conventional method (dimensional analysis) is tedious. Similitude theory based on governing equations of the structural system is more direct and simpler in execution. The difficulty of making completely similar scale models often leads to accept certain type of distortion from exact duplication of the prototype (partial similarity). Both complete and partial

Improved scaling laws for stage inert mass space Propulsion systems. Volume 3: Propulsion synthesis program users and programmers manual

NASA Technical Reports Server (NTRS)

1971-01-01

The analytical models developed for the Space Propulsion Automated Synthesis Modeling (SPASM) program are presented. Weight scaling laws developed during this study are incorporated into the program's scaling data bank. A detail listing, logic diagram and input/output formats are supplied for the SPASM program. Two test examples for one to four-stage vehicles performing different types of missions are shown to demonstrate the program's capability and versatility.

A wavelet analysis of scaling laws and long-memory in stock market volatility

NASA Astrophysics Data System (ADS)

Vuorenmaa, Tommi A.

2005-05-01

This paper studies the time-varying behavior of scaling laws and long-memory. This is motivated by the earlier finding that in the FX markets a single scaling factor might not always be sufficient across all relevant timescales: a different region may exist for intradaily time-scales and for larger time-scales. In specific, this paper investigates (i) if different scaling regions appear in stock market as well, (ii) if the scaling factor systematically differs from the Brownian, (iii) if the scaling factor is constant in time, and (iv) if the behavior can be explained by the heterogenuity of the players in the market and/or by intraday volatility periodicity. Wavelet method is used because it delivers a multiresolution decomposition and has excellent local adaptiviness properties. As a consequence, a wavelet-based OLS method allows for consistent estimation of long-memory. Thus issues (i)-(iv) shed light on the magnitude and behavior of a long-memory parameter, as well. The data are the 5-minute volatility series of Nokia Oyj at the Helsinki Stock Exchange around the burst of the IT-bubble. Period one represents the era of "irrational exuberance" and another the time after it. The results show that different scaling regions (i.e. multiscaling) may appear in the stock markets and not only in the FX markets, the scaling factor and the long-memory parameter are systematically different from the Brownian and they do not have to be constant in time, and that the behavior can be explained for a significant part by an intraday volatility periodicity called the New York effect. This effect was magnified by the frenzy trading of short-term speculators in the bubble period. The found stronger long-memory is also attributable to irrational exuberance.

Obtaining Public Records: Reporter Guide

ERIC Educational Resources Information Center

Hammond, Betsy

2013-01-01

Obtaining public records is essential to covering public education. Fortunately, the law is on the side of reporters: Public agencies generally must disclose their records to the public and to the media--with important exceptions. Public agencies are often reluctant to hand over records, however, even when the law clearly says they should.…

Power-laws in art

NASA Astrophysics Data System (ADS)

Etro, Federico; Stepanova, Elena

2018-09-01

We provide evidence of a cubic law of art prices that hints to a general pattern for the distribution of artistic talent. The persistence across heterogeneous markets from historical ones to contemporary art auctions of a power law in the distribution of the average price per artist suggests the possibility of a universal law for talent distribution. We explore scale-free networks of teacher-students to investigate the diffusion of talent over time.

Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities

PubMed Central

Zhang, Qun; Zhang, Qunzhi; Sornette, Didier

2016-01-01

We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the “S&P 500 1987” bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs. PMID:27806093

Dissipative particle dynamics simulations of polymer chains: scaling laws and shearing response compared to DNA experiments.

PubMed

Symeonidis, Vasileios; Em Karniadakis, George; Caswell, Bruce

2005-08-12

Dissipative particle dynamics simulations of several bead-spring representations of polymer chains in dilute solution are used to demonstrate the correct static scaling laws for the radius of gyration. Shear flow results for the wormlike chain simulating single DNA molecules compare well with average extensions from experiments, irrespective of the number of beads. However, coarse graining with more than a few beads degrades the agreement of the autocorrelation of the extension.

The Statistics of Urban Scaling and Their Connection to Zipf’s Law

PubMed Central

Gomez-Lievano, Andres; Youn, HyeJin; Bettencourt, Luís M. A.

2012-01-01

Urban scaling relations characterizing how diverse properties of cities vary on average with their population size have recently been shown to be a general quantitative property of many urban systems around the world. However, in previous studies the statistics of urban indicators were not analyzed in detail, raising important questions about the full characterization of urban properties and how scaling relations may emerge in these larger contexts. Here, we build a self-consistent statistical framework that characterizes the joint probability distributions of urban indicators and city population sizes across an urban system. To develop this framework empirically we use one of the most granular and stochastic urban indicators available, specifically measuring homicides in cities of Brazil, Colombia and Mexico, three nations with high and fast changing rates of violent crime. We use these data to derive the conditional probability of the number of homicides per year given the population size of a city. To do this we use Bayes’ rule together with the estimated conditional probability of city size given their number of homicides and the distribution of total homicides. We then show that scaling laws emerge as expectation values of these conditional statistics. Knowledge of these distributions implies, in turn, a relationship between scaling and population size distribution exponents that can be used to predict Zipf’s exponent from urban indicator statistics. Our results also suggest how a general statistical theory of urban indicators may be constructed from the stochastic dynamics of social interaction processes in cities. PMID:22815745

Heterogeneous population dynamics and scaling laws near epidemic outbreaks.

PubMed

Widder, Andreas; Kuehn, Christian

2016-10-01

In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical reformulation of the basic reproduction number, the homogeneous system and the heterogeneous system exhibit a completely analogous global behaviour. Then we consider noise terms to incorporate the fluctuation effects and the random import of the disease into the population and analyse the influence of heterogeneity on warning signs for critical transitions (or tipping points). This theory shows that one may be able to anticipate whether a bifurcation point is close before it happens. We use numerical simulations of a stochastic fast-slow heterogeneous population SIS model and show various aspects of heterogeneity have crucial influences on the scaling laws that are used as early-warning signs for the homogeneous system. Thus, although the basic structural qualitative dynamical properties are the same for both systems, the quantitative features for epidemic prediction are expected to change and care has to be taken to interpret potential warning signs for disease outbreaks correctly.

Titius-Bode laws in the solar system. 2: Build your own law from disk models

NASA Astrophysics Data System (ADS)

Dubrulle, B.; Graner, F.

1994-02-01

Simply respecting both scale and rotational invariance, it is easy to construct an endless collection of theoretical models predicting a Titius-Bode law, irrespective to their physical content. Due to the numerous ways to get the law and its intrinsic arbitrariness, it is not a useful constraint on theories of solar system formation. To illustrate the simple elegance of scale-invariant methods, we explicitly cook up one of the simplest examples, an infinitely thin cold gaseous disk rotating around a central object. In that academic case, the Titius-Bode law holds during the linear stage of the gravitational instability. The time scale of the instability is of the order of a self-gravitating time scale, (G rhod)-1/2, where rhod is the disk density. This model links the separation between different density maxima with the ratio MD/MC of the masses of the disk and the central object; for instance, MD/MC of the order of 0.18 roughly leads to the observed separation between the planets. We discuss the boundary conditions and the limit of the Wentzel-Kramer-Brillouin (WKB) approximation.

Structural Similitude and Scaling Laws

NASA Technical Reports Server (NTRS)

Simitses, George J.

1998-01-01

Aircraft and spacecraft comprise the class of aerospace structures that require efficiency and wisdom in design, sophistication and accuracy in analysis and numerous and careful experimental evaluations of components and prototype, in order to achieve the necessary system reliability, performance and safety. Preliminary and/or concept design entails the assemblage of system mission requirements, system expected performance and identification of components and their connections as well as of manufacturing and system assembly techniques. This is accomplished through experience based on previous similar designs, and through the possible use of models to simulate the entire system characteristics. Detail design is heavily dependent on information and concepts derived from the previous steps. This information identifies critical design areas which need sophisticated analyses, and design and redesign procedures to achieve the expected component performance. This step may require several independent analysis models, which, in many instances, require component testing. The last step in the design process, before going to production, is the verification of the design. This step necessitates the production of large components and prototypes in order to test component and system analytical predictions and verify strength and performance requirements under the worst loading conditions that the system is expected to encounter in service. Clearly then, full-scale testing is in many cases necessary and always very expensive. In the aircraft industry, in addition to full-scale tests, certification and safety necessitate large component static and dynamic testing. Such tests are extremely difficult, time consuming and definitely absolutely necessary. Clearly, one should not expect that prototype testing will be totally eliminated in the aircraft industry. It is hoped, though, that we can reduce full-scale testing to a minimum. Full-scale large component testing is necessary in

Fluorescence correlation spectroscopy diffusion laws to probe the submicron cell membrane organization.

PubMed

Wawrezinieck, Laure; Rigneault, Hervé; Marguet, Didier; Lenne, Pierre-François

2005-12-01

To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.

Role of defects in laser-induced modifications of silica coatings and fused silica using picosecond pulses at 1053 nm: II Scaling laws and the density of precursors

DOE PAGES

Laurence, T. A.; Negres, R. A.; Ly, S.; ...

2017-06-22

Here, we investigate the role of defects in laser-induced damage of fused silica and of silica coatings produced by e-beam and PIAD processes which are used in damage resistant, multi-layer dielectric, reflective optics. We perform experiments using 1053 nm, 1–60 ps laser pulses with varying beam size, number of shots, and pulse widths in order to understand the characteristics of defects leading to laser-induced damage. This pulse width range spans a transition in mechanisms from intrinsic material ablation for short pulses to defect-dominated damage for longer pulses. We show that for pulse widths as short as 10 ps, laser-induced damagemore » properties of fused silica and silica films are dominated by isolated absorbers. The density of these precursors and their fluence dependence of damage initiation suggest a single photon process for initial energy absorption in these precursors. Higher density precursors that initiate close to the ablation threshold at shorter pulse widths are also observed in fused silica, whose fluence and pulse width scaling suggest a multiphoton initiation process. We also show that these initiated damage sites grow with subsequent laser pulses. We show that scaling laws obtained in more conventional ways depend on the beam size and on the definition of damage for ps pulses. For this reason, coupling scaling laws with the density of precursors are critical to understanding the damage limitations of optics in the ps regime.« less

Role of defects in laser-induced modifications of silica coatings and fused silica using picosecond pulses at 1053 nm: II Scaling laws and the density of precursors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laurence, T. A.; Negres, R. A.; Ly, S.

Here, we investigate the role of defects in laser-induced damage of fused silica and of silica coatings produced by e-beam and PIAD processes which are used in damage resistant, multi-layer dielectric, reflective optics. We perform experiments using 1053 nm, 1–60 ps laser pulses with varying beam size, number of shots, and pulse widths in order to understand the characteristics of defects leading to laser-induced damage. This pulse width range spans a transition in mechanisms from intrinsic material ablation for short pulses to defect-dominated damage for longer pulses. We show that for pulse widths as short as 10 ps, laser-induced damagemore » properties of fused silica and silica films are dominated by isolated absorbers. The density of these precursors and their fluence dependence of damage initiation suggest a single photon process for initial energy absorption in these precursors. Higher density precursors that initiate close to the ablation threshold at shorter pulse widths are also observed in fused silica, whose fluence and pulse width scaling suggest a multiphoton initiation process. We also show that these initiated damage sites grow with subsequent laser pulses. We show that scaling laws obtained in more conventional ways depend on the beam size and on the definition of damage for ps pulses. For this reason, coupling scaling laws with the density of precursors are critical to understanding the damage limitations of optics in the ps regime.« less

Zipf law: an extreme perspective

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2016-04-01

Extreme value theory (EVT) asserts that the Fréchet law emerges universally from linearly scaled maxima of collections of independent and identically distributed random variables that are positive-valued. Observations of many real-world sizes, e.g. city-sizes, give rise to the Zipf law: if we rank the sizes decreasingly, and plot the log-sizes versus the log-ranks, then an affine line emerges. In this paper we present an EVT approach to the Zipf law. Specifically, we establish that whenever the Fréchet law emerges from the EVT setting, then the Zipf law follows. The EVT generation of the Zipf law, its universality, and its associated phase transition, are analyzed and described in detail.

On collisional disruption - Experimental results and scaling laws

NASA Technical Reports Server (NTRS)

Davis, Donald R.; Ryan, Eileen V.

1990-01-01

Both homogeneous and inhomogeneous targets have been addressed by the present experimental consideration of the impact strengths, fragment sizes, and fragment velocities generated by cement mortar targets whose crushing strengths vary by an order of magnitude, upon impact of projectiles in the velocity range of 50-5700 m/sec. When combined with additional published data, dynamic impact strength is found to correlate with quasi-static material strengths for materials ranging in character from basalt to ice; two materials not following this trend, however, are weak mortar and clay targets. Values consistent with experimental results are obtainable with a simple scaling algorithm based on impact energy, material properties, and collisional strain rate.

An exponential scaling law for the strain dependence of the Nb3Sn critical current density

NASA Astrophysics Data System (ADS)

Bordini, B.; Alknes, P.; Bottura, L.; Rossi, L.; Valentinis, D.

2013-07-01

The critical current density of the Nb3Sn superconductor is strongly dependent on the strain applied to the material. In order to investigate this dependence, it is a common practice to measure the critical current of Nb3Sn strands for different values of applied axial strain. In the literature, several models have been proposed to describe these experimental data in the reversible strain region. All these models are capable of fitting the measurement results in the strain region where data are collected, but tend to predict unphysical trends outside the range of data, and especially for large strain values. In this paper we present a model of a new strain function, together with the results obtained by applying the new scaling law on relevant datasets. The data analyzed consisted of the critical current measurements at 4.2 K that were carried out under applied axial strain at Durham University and the University of Geneva on different strand types. With respect to the previous models proposed, the new scaling function does not present problems at large strain values, has a lower number of fitting parameters (only two instead of three or four), and is very stable, so that, starting from few experimental points, it can estimate quite accurately the strand behavior in a strain region where there are no data. A relationship is shown between the proposed strain function and the elastic strain energy, and an analogy is drawn with the exponential form of the McMillan equation for the critical temperature.

Rapid inundation estimates at harbor scale using tsunami wave heights offshore simulation and Green's law approach

NASA Astrophysics Data System (ADS)

Gailler, Audrey; Hébert, Hélène; Loevenbruck, Anne

2013-04-01

Improvements in the availability of sea-level observations and advances in numerical modeling techniques are increasing the potential for tsunami warnings to be based on numerical model forecasts. Numerical tsunami propagation and inundation models are well developed and have now reached an impressive level of accuracy, especially in locations such as harbors where the tsunami waves are mostly amplified. In the framework of tsunami warning under real-time operational conditions, the main obstacle for the routine use of such numerical simulations remains the slowness of the numerical computation, which is strengthened when detailed grids are required for the precise modeling of the coastline response on the scale of an individual harbor. In fact, when facing the problem of the interaction of the tsunami wavefield with a shoreline, any numerical simulation must be performed over an increasingly fine grid, which in turn mandates a reduced time step, and the use of a fully non-linear code. Such calculations become then prohibitively time-consuming, which is clearly unacceptable in the framework of real-time warning. Thus only tsunami offshore propagation modeling tools using a single sparse bathymetric computation grid are presently included within the French Tsunami Warning Center (CENALT), providing rapid estimation of tsunami wave heights in high seas, and tsunami warning maps at western Mediterranean and NE Atlantic basins scale. We present here a preliminary work that performs quick estimates of the inundation at individual harbors from these deep wave heights simulations. The method involves an empirical correction relation derived from Green's law, expressing conservation of wave energy flux to extend the gridded wave field into the harbor with respect to the nearby deep-water grid node. The main limitation of this method is that its application to a given coastal area would require a large database of previous observations, in order to define the empirical

Gravity, turbulence and the scaling ``laws'' in molecular clouds

NASA Astrophysics Data System (ADS)

Ballesteros-Paredes, Javier

The so-called Larson (1981) scaling laws found empirically in molecular clouds have been generally interpreted as evidence that the clouds are turbulent and fractal. In the present contribution we discussed how recent observations and models of cloud formation suggest that: (a) these relations are the result of strong observational biases due to the cloud definition itself: since the filling factor of the dense structures is small, by thresholding the column density the computed mean density between clouds is nearly constant, and nearly the same as the threshold (Ballesteros-Paredes et al. 2012). (b) When accounting for column density variations, the velocity dispersion-size relation does not appears anymore. Instead, dense cores populate the upper-left corner of the δ v-R diagram (Ballesteros-Paredes et al. 2011a). (c) Instead of a δ v-R relation, a more appropriate relation seems to be δ v 2 / R = 2 GMΣ, which suggest that clouds are in collapse, rather than supported by turbulence (Ballesteros-Paredes et al. 2011a). (d) These results, along with the shapes of the star formation histories (Hartmann, Ballesteros-Paredes & Heitsch 2012), line profiles of collapsing clouds in numerical simulations (Heitsch, Ballesteros-Paredes & Hartmann 2009), core-to-core velocity dispersions (Heitsch, Ballesteros-Paredes & Hartmann 2009), time-evolution of the column density PDFs (Ballesteros-Paredes et al. 2011b), etc., strongly suggest that the actual source of the non-thermal motions is gravitational collapse of the clouds, so that the turbulent, chaotic component of the motions is only a by-product of the collapse, with no significant ``support" role for the clouds. This result calls into question if the scale-free nature of the motions has a turbulent, origin (Ballesteros-Paredes et al. 2011a; Ballesteros-Paredes et al. 2011b, Ballesteros-Paredes et al. 2012).

Comparison of RAGE Hydrocode Mars Impact Model Results to Scaling Law Predictions

NASA Astrophysics Data System (ADS)

Plesko, Catherine S.; Wohletz, K. H.; Coker, R. F.; Asphaug, E.; Gittings, M. L.

2007-10-01

Impact devolatilization has been proposed by Segura et al. (2002) and Carr (1996) as a mechanism for triggering sporadic, intense precipitation on Mars. We seek to examine this hypothesis, specifically to determine the lower bound on possible energy/size scales, and thus an upper bound on the frequency of such events. To do this, we employ various analytical and numerical modeling techniques including the RAGE hydrocode. RAGE (Baltrusaitis et al. 1996) is an Eulerian Hydrocode that runs in up to three dimensions and incorporates a variety of detailed equations of state including the temperature-based SESAME tables maintained by LANL. In order to validate RAGE hydrocode results at the scale of moderate to large asteroid impacts, we compare simplified models of vertical impacts of objects of diameter 10 -100 km into homogeneous basalt targets under Martian conditions to pressure scaling law predictions (Holsapple 1993, e.g. Tables 3-4) for the same scenario. Peak pressures are important to the volatile mobilization question (Stewart and Ahrens, 2005), thus it is of primary importance for planned future modeling efforts to confirm that pressures in RAGE are well behaved. Knowledge of the final crater geometry and the fate of ejecta are not required to understand our main question: to what depth and radius are subsurface volatiles are mobilized, for a given impact and target? This effort is supported by LANL/IGPP (CSP, RFC, KHW, MLG) and by NASA PG&G "Small Bodies and Planetary Collisions" (EA).

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

PubMed

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

2015-02-10

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

Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

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.

LAWS (Laser Atmospheric Wind Sounder) earth observing system

NASA Technical Reports Server (NTRS)

1988-01-01

Wind profiles can be measured from space using current technology. These wind profiles are essential for answering many of the interdisciplinary scientific questions to be addressed by EOS, the Earth Observing System. This report provides guidance for the development of a spaceborne wind sounder, the Laser Atmospheric Wind Sounder (LAWS), discussing the current state of the technology and reviewing the scientific rationale for the instrument. Whether obtained globally from the EOS polar platform or in the tropics and subtropics from the Space Station, wind profiles from space will provide essential information for advancing the skill of numerical weather prediction, furthering knowledge of large-scale atmospheric circulation and climate dynamics, and improving understanding of the global biogeochemical and hydrologic cycles. The LAWS Instrument Panel recommends that it be given high priority for new instrument development because of the pressing scientific need and the availability of the necessary technology. LAWS is to measure wind profiles with an accuracy of a few meters per second and to sample at intervals of 100 km horizontally for layers km thick.

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

NASA Astrophysics Data System (ADS)

Ormerod, Paul

2002-11-01

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

Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation

PubMed Central

Sáenz, P. J.; Wray, A. W.; Che, Z.; Matar, O. K.; Valluri, P.; Kim, J.; Sefiane, K.

2017-01-01

The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications. PMID:28294114

Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation.

PubMed

Sáenz, P J; Wray, A W; Che, Z; Matar, O K; Valluri, P; Kim, J; Sefiane, K

2017-03-15

The evaporation of a liquid drop on a solid substrate is a remarkably common phenomenon. Yet, the complexity of the underlying mechanisms has constrained previous studies to spherically symmetric configurations. Here we investigate well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a universal scaling law for the evaporation rate valid for any shape and demonstrate that more curved regions lead to preferential localized depositions in particle-laden drops. Furthermore, geometry induces well-defined flow structures within the drop that change according to the driving mechanism. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. Our results suggest that the drop geometry can be exploited to prescribe the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops, which may be of interest to a wide range of industrial and scientific applications.

Scaling laws for a compliant biomimetic swimmer

NASA Astrophysics Data System (ADS)

Gibouin, Florence; Raufaste, Christophe; Bouret, Yann; Argentina, Mederic

2017-11-01

Motivated by the seminal work of Lord Lighthill in the sixties, we study the motion of inertial aquatic swimmers that propels with undulatory gaits. In 2014, Gazzola et al. have uncovered the law linking the swimming velocity to the kinematics of the swimmer and the fluid properties. At high Reynolds numbers, the velocity appears to be equal to 0.4 Af /(2 π) , where A and f are respectively the amplitude and the frequency of the oscillating fin. We have constructed a compliant biomimetic swimmer, whose muscles have been modeled through a torque distribution thanks to a servomotor. A soft polymeric material mimics the flesh and provides the flexibility. By immersing our robot into a water tunnel, we find and characterize the operating point for which the propulsive force balances the drag. We bring the first experimental proof of the former law and probe large amplitude undulations which exhibits nonlinear effects. All data collapse perfectly onto a single master curve. We investigate the role of the fin flexibility by varying its length and its thickness and we figured out the existence of an efficient swimming regime. We thank the support of CNRS and Université Côte d'Azur.

Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey

NASA Astrophysics Data System (ADS)

Reynolds, A. M.

2008-07-01

The results of numerical simulations indicate that deterministic walks with inverse-square power-law scaling are a robust emergent property of predators that use chemotaxis to locate randomly and sparsely distributed stationary prey items. It is suggested that chemotactic destructive foraging accounts for the apparent Lévy flight movement patterns of Oxyrrhis marina microzooplankton in still water containing prey items. This challenges the view that these organisms are executing an innate optimal Lévy flight searching strategy. Crucial for the emergence of inverse-square power-law scaling is the tendency of chemotaxis to occasionally cause predators to miss the nearest prey item, an occurrence which would not arise if prey were located through the employment of a reliable cognitive map or if prey location were visually cued and perfect.

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

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1973-01-01

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

Utsu aftershock productivity law explained from geometric operations on the permanent static stress field of mainshocks

NASA Astrophysics Data System (ADS)

Mignan, Arnaud

2018-03-01

The aftershock productivity law is an exponential function of the form K ∝ exp(αM), with K being the number of aftershocks triggered by a given mainshock of magnitude M and α ≈ ln(10) being the productivity parameter. This law remains empirical in nature although it has also been retrieved in static stress simulations. Here, we parameterize this law using the solid seismicity postulate (SSP), the basis of a geometrical theory of seismicity where seismicity patterns are described by mathematical expressions obtained from geometric operations on a permanent static stress field. We first test the SSP that relates seismicity density to a static stress step function. We show that it yields a power exponent q = 1.96 ± 0.01 for the power-law spatial linear density distribution of aftershocks, once uniform noise is added to the static stress field, in agreement with observations. We then recover the exponential function of the productivity law with a break in scaling obtained between small and large M, with α = 1.5ln(10) and ln(10), respectively, in agreement with results from previous static stress simulations. Possible biases of aftershock selection, proven to exist in epidemic-type aftershock sequence (ETAS) simulations, may explain the lack of break in scaling observed in seismicity catalogues. The existence of the theoretical kink, however, remains to be proven. Finally, we describe how to estimate the solid seismicity parameters (activation density δ+, aftershock solid envelope r∗ and background stress amplitude range Δo∗) for large M values.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Scaling for hard-sphere colloidal glasses near jamming

NASA Astrophysics Data System (ADS)

Zargar, Rojman; DeGiuli, Eric; Bonn, Daniel

2016-12-01

Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the density of states, shear modulus, and mean-squared displacement (MSD) in a hard-sphere colloidal glass. Scaling the frequency with the boson-peak frequency, we find that the density of states at different volume fractions all collapse on a single master curve, which obeys a power law in terms of the scaled frequency. Below the boson peak, the exponent is consistent with theoretical results obtained by real-space and phase-space approaches to understanding amorphous solids. We find that the shear modulus and the MSD are nearly inversely proportional, and show a singular power-law dependence on the distance from random close packing. Our results are in very good agreement with the theoretical predictions.

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

PubMed

Schure, Mark R; Davis, Joe M

2011-12-30

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics. Copyright © 2011 Elsevier B.V. All rights reserved.

Charles' Law of Gases.

ERIC Educational Resources Information Center

Petty, John T.

1995-01-01

Describes an experiment that uses air to test Charles' law. Reinforces the student's intuitive feel for Charles' law with quantitative numbers they can see, introduces the idea of extrapolating experimental data to obtain a theoretical value, and gives a physical quantitative meaning to the concept of absolute zero. (JRH)

Frozen Fractals all Around: Solar flares, Ampere’s Law, and the Search for Units in Scale-Free Processes.

NASA Astrophysics Data System (ADS)

McAteer, R. T. James

2015-08-01

My soul is spiraling in frozen fractals all around, And one thought crystallizes like an icy blast, I'm never going back, the past is in the past.Elsa, from Disney’s Frozen, characterizes two fundamental aspects of scale-free processes in Nature: fractals are everywhere in space; fractals can be used to probe changes in time. Self-Organized Criticality provides a powerful set of tools to study scale-free processes. It connects spatial fractals (more generically, multifractals) to temporal evolution. The drawback is that this usually results in scale-free, unit-less, indices, which can be difficult to connect to everyday physics. Here, I show a novel method that connects one of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - to one of the most powerful equations in all of physics - Ampere’s law. In doing so I show how the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.Our physical understanding of the solar magnetic field structure, and hence our ability to predict solar activity, is limited by the type of data currently available. I show that the multifractal spectrum provides a powerful physical connection between the details of photospheric magnetic gradients of current data and the coronal magnetic structure. By decomposing Ampere’s law and comparing it to the wavelet transform modulus maximum method, I show how the scale-free Holder exponent provides a direct measure of current density across all relevant sizes. The prevalence of this current density across various scales is connected to its stability in time, and hence to the ability of the magnetic structure to store and then release energy. Hence (spatial) multifractals inform us of (future) solar activity.Finally I discuss how such an approach can be used in any study of scale-free processes, and highlight the necessary

Cross-scale morphology

USGS Publications Warehouse

Allen, Craig R.; Holling, Crawford S.; Garmestani, Ahjond S.; El-Shaarawi, Abdel H.; Piegorsch, Walter W.

2013-01-01

The scaling of physical, biological, ecological and social phenomena is a major focus of efforts to develop simple representations of complex systems. Much of the attention has been on discovering universal scaling laws that emerge from simple physical and geometric processes. However, there are regular patterns of departures both from those scaling laws and from continuous distributions of attributes of systems. Those departures often demonstrate the development of self-organized interactions between living systems and physical processes over narrower ranges of scale.

[A method for obtaining redshifts of quasars based on wavelet multi-scaling feature matching].

PubMed

Liu, Zhong-Tian; Li, Xiang-Ru; Wu, Fu-Chao; Zhao, Yong-Heng

2006-09-01

The LAMOST project, the world's largest sky survey project being implemented in China, is expected to obtain 10(5) quasar spectra. The main objective of the present article is to explore methods that can be used to estimate the redshifts of quasar spectra from LAMOST. Firstly, the features of the broad emission lines are extracted from the quasar spectra to overcome the disadvantage of low signal-to-noise ratio. Then the redshifts of quasar spectra can be estimated by using the multi-scaling feature matching. The experiment with the 15, 715 quasars from the SDSS DR2 shows that the correct rate of redshift estimated by the method is 95.13% within an error range of 0. 02. This method was designed to obtain the redshifts of quasar spectra with relative flux and a low signal-to-noise ratio, which is applicable to the LAMOST data and helps to study quasars and the large-scale structure of the universe etc.

On the Law of Intelligence

ERIC Educational Resources Information Center

Lichten, William

2004-01-01

The law of intelligence is presented in test independent form. Mental abilities, physical brain size, and infant motor capacity follow the same law of growth from birth to adolescence. Mental growth is independent of race, "SES" or the Flynn effect. The vitality of the mental age scale calls for a reexamination of Wechsler's deviation IQ. This…

Shock-driven transition to turbulence: Emergence of power-law scaling

DOE PAGES

Olmstead, D.; Wayne, P.; Simons, D.; ...

2017-05-25

Here, we consider two cases of interaction between a planar shock and a cylindrical density interface. In the first case (planar normal shock), the axis of the gas cylinder is parallel to the shock front and baroclinic vorticity deposited by the shock is predominantly two dimensional (directed along the axis of the cylinder). In the second case, the cylinder is tilted, resulting in an oblique shock interaction and a fully-three-dimensional shock-induced vorticity field. Furthermore, the statistical properties of the flow for both cases are analyzed based on images from two orthogonal visualization planes, using structure functions of the intensity mapsmore » of fluorescent tracer premixed with heavy gas. And at later times, these structure functions exhibit power-law-like behavior over a considerable range of scales. Manifestation of this behavior is remarkably consistent in terms of dimensionless time τ defined based on Richtmyer's linear theory within the range of Mach numbers from 1.1 to 2.0 and the range of gas cylinder tilt angles with respect to the plane of the shock front (0–30°).« less

A general derivation and quantification of the third law of thermodynamics.

PubMed

Masanes, Lluís; Oppenheim, Jonathan

2017-03-14

The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased.

Effect of helicity on the correlation time of large scales in turbulent flows

NASA Astrophysics Data System (ADS)

Cameron, Alexandre; Alexakis, Alexandros; Brachet, Marc-Étienne

2017-11-01

Solutions of the forced Navier-Stokes equation have been conjectured to thermalize at scales larger than the forcing scale, similar to an absolute equilibrium obtained for the spectrally truncated Euler equation. Using direct numeric simulations of Taylor-Green flows and general-periodic helical flows, we present results on the probability density function, energy spectrum, autocorrelation function, and correlation time that compare the two systems. In the case of highly helical flows, we derive an analytic expression describing the correlation time for the absolute equilibrium of helical flows that is different from the E-1 /2k-1 scaling law of weakly helical flows. This model predicts a new helicity-based scaling law for the correlation time as τ (k ) ˜H-1 /2k-1 /2 . This scaling law is verified in simulations of the truncated Euler equation. In simulations of the Navier-Stokes equations the large-scale modes of forced Taylor-Green symmetric flows (with zero total helicity and large separation of scales) follow the same properties as absolute equilibrium including a τ (k ) ˜E-1 /2k-1 scaling for the correlation time. General-periodic helical flows also show similarities between the two systems; however, the largest scales of the forced flows deviate from the absolute equilibrium solutions.

Law Education Lessons, Grade 4-8.

ERIC Educational Resources Information Center

Allen, Rodney F., Ed.; And Others

Teacher developed activities for elementary and junior high school students provide instruction in citizenship, civil governments, law in a free society, and the consequences for disobedience of the law. Part 1 contains 13 activities for lower elementary students. Games, questionnaires, discussions, checklists, and attitude scales reinforce…

Scaling laws in granular flow and pedestrian flow

NASA Astrophysics Data System (ADS)

Chen, Shumiao; Alonso-Marroquin, Fernando; Busch, Jonathan; Hidalgo, Raúl Cruz; Sathianandan, Charmila; Ramírez-Gómez, Álvaro; Mora, Peter

2013-06-01

We use particle-based simulations to examine the flow of particles through an exit. Simulations involve both gravity-driven particles (representing granular material) and velocity-driven particles (mimicking pedestrian dynamics). Contact forces between particles include elastic, viscous, and frictional forces; and simulations use bunker geometry. Power laws are observed in the relation between flow rate and exit width. Simulations of granular flow showed that the power law has little dependence on the coefficient of friction. Polydisperse granular systems produced higher flow rates than those produced by monodisperse ones. We extend the particle model to include the main features of pedestrian dynamics: thoracic shape, shoulder rotation, and desired velocity oriented towards the exit. Higher desired velocity resulted in higher flow rate. Granular simulations always give higher flow rate than pedestrian simulations, despite the values of aspect ratio of the particles. In terms of force distribution, pedestrians and granulates share similar properties with the non-democratic distribution of forces that poses high risks of injuries in a bottleneck situation.

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

PubMed Central

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

2015-01-01

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

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Perfectly monodisperse micro-bubble production by novel mechanical means. Scaling laws.

NASA Astrophysics Data System (ADS)

Ganan-Calvo, Alfonso M.; Gordillo, Jose M.; Ouarti, Nawel; Prevost, Thomas; Sampedro, Jose L.

2000-11-01

A continuous stream of controllable, perfectly homogeneous size micro-bubbles (of the order of some microns and larger) can be produced by a novel, extremely simple mechanical means that we call "Flow Focusing" (e.g. see Ganan-Calvo 1998, Phys. Rev. Lett. vol. 80, 285). Using this technique, a capillary gas micro-jet is formed ("focused") by a co-flowing stream of liquid forced through a sub-millimetric orifice. This gas micro-jet undergoes a rapid capillary breakup (e.g. Chandrasekhar 1961 "Hydrodynamic and Hydromagnetic Stability", p. 541) with a strong frequency "self-locking" effect. In this work we present a theoretical model which predicts the micro-bubble size as a function of the physical and geometrical parameters of the system. A complete experimental study is also provided, and the raw data are collapsed into a universal scaling law given by our theoretical model. This novel micro-fluidics phenomenon may have a wide variety of applications ranging from bio-medicine, pharmaceutical specialities, food industry, and even for the mesoscale micro-templating of micro-engineered materials (i.e. photonic crystals, smart materials, etc.).

The weather and Climate: emergent laws and multifractal cascades

NASA Astrophysics Data System (ADS)

Lovejoy, S.

2016-12-01

In the atmosphere, nonlinear terms are typically about a trillion times larger than linear ones; we anticipate the emergence of high level turbulence laws. The classical turbulence laws were restricted to homogeneous and isotropic systems; to apply them to the atmosphere they must be generalized to account for strong anisotropy (especially stratification) and variability (intermittency). Over the last 30 years, using scaling symmetry principles and multifractal cascades, this has been done. While hitherto they were believed applicable only up to ≈ 100 m, (generalized) turbulence laws now anisotropic and multifractal, they cover spatial scales up planetary in extent and in time well beyond weather scales to include the climate. These higher level laws are stochastic in nature and provide the theoretical basis both for stochastic parametrizations as well as stochastic forecasting. In the time domain the emergent laws for fluctuations DT (for example in temperature T) have means T > ≈ DtH i.e. they are scaling (power laws) in the time interval Dt. We find find exponents H>0 (fluctuations increase with scale) up to ≈ Dt ≈10 days (the lifetime of planetary scale structures, the analogous transition in the ocean is at Dt ≈ 1 year on Mars it is Dt ≈ 2 sols). At larger Dt, there is a transition to a new "macroweather" regime with H<0: successive fluctuations tend cancel each; at Dt >≈30 years (anthropocene; larger in the pre-industrial epoch), new climate processes begin to dominate, leading to H>0. "The climate is what you expect, the weather is what you get": the climate is thought to be a kind of "average weather". However this "expected" behavior is macroweather, not the climate. On the contrary, the climate is the new even lower frequency regime at scales Dt> 30 yrs and it has statistical properties very similar to the weather. At these scales, "macroweather is what you expect, the climate is what you get". The scaling in the macroweather regime implies

NMR permeability estimators in 'chalk' carbonate rocks obtained under different relaxation times and MICP size scalings

NASA Astrophysics Data System (ADS)

Rios, Edmilson Helton; Figueiredo, Irineu; Moss, Adam Keith; Pritchard, Timothy Neil; Glassborow, Brent Anthony; Guedes Domingues, Ana Beatriz; Bagueira de Vasconcellos Azeredo, Rodrigo

2016-07-01

The effect of the selection of different nuclear magnetic resonance (NMR) relaxation times for permeability estimation is investigated for a set of fully brine-saturated rocks acquired from Cretaceous carbonate reservoirs in the North Sea and Middle East. Estimators that are obtained from the relaxation times based on the Pythagorean means are compared with estimators that are obtained from the relaxation times based on the concept of a cumulative saturation cut-off. Select portions of the longitudinal (T1) and transverse (T2) relaxation-time distributions are systematically evaluated by applying various cut-offs, analogous to the Winland-Pittman approach for mercury injection capillary pressure (MICP) curves. Finally, different approaches to matching the NMR and MICP distributions using different mean-based scaling factors are validated based on the performance of the related size-scaled estimators. The good results that were obtained demonstrate possible alternatives to the commonly adopted logarithmic mean estimator and reinforce the importance of NMR-MICP integration to improving carbonate permeability estimates.

Measuring Black men's police-based discrimination experiences: Development and validation of the Police and Law Enforcement (PLE) Scale.

PubMed

English, Devin; Bowleg, Lisa; Del Río-González, Ana Maria; Tschann, Jeanne M; Agans, Robert P; Malebranche, David J

2017-04-01

Although social science research has examined police and law enforcement-perpetrated discrimination against Black men using policing statistics and implicit bias studies, there is little quantitative evidence detailing this phenomenon from the perspective of Black men. Consequently, there is a dearth of research detailing how Black men's perspectives on police and law enforcement-related stress predict negative physiological and psychological health outcomes. This study addresses these gaps with the qualitative development and quantitative test of the Police and Law Enforcement (PLE) Scale. In Study 1, we used thematic analysis on transcripts of individual qualitative interviews with 90 Black men to assess key themes and concepts and develop quantitative items. In Study 2, we used 2 focus groups comprised of 5 Black men each (n = 10), intensive cognitive interviewing with a separate sample of Black men (n = 15), and piloting with another sample of Black men (n = 13) to assess the ecological validity of the quantitative items. For Study 3, we analyzed data from a sample of 633 Black men between the ages of 18 and 65 to test the factor structure of the PLE, as we all as its concurrent validity and convergent/discriminant validity. Qualitative analyses and confirmatory factor analyses suggested that a 5-item, 1-factor measure appropriately represented respondents' experiences of police/law enforcement discrimination. As hypothesized, the PLE was positively associated with measures of racial discrimination and depressive symptoms. Preliminary evidence suggests that the PLE is a reliable and valid measure of Black men's experiences of discrimination with police/law enforcement. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws.

PubMed

Mininni, P D; Alexakis, A; Pouquet, A

2008-03-01

We analyze the data stemming from a forced incompressible hydrodynamic simulation on a grid of 2048(3) regularly spaced points, with a Taylor Reynolds number of R(lambda) ~ 1300. The forcing is given by the Taylor-Green vortex, which shares similarities with the von Kàrmàn flow used in several laboratory experiments; the computation is run for ten turnover times in the turbulent steady state. At this Reynolds number the anisotropic large scale flow pattern, the inertial range, the bottleneck, and the dissipative range are clearly visible, thus providing a good test case for the study of turbulence as it appears in nature. Triadic interactions, the locality of energy fluxes, and longitudinal structure functions of the velocity increments are computed. A comparison with runs at lower Reynolds numbers is performed and shows the emergence of scaling laws for the relative amplitude of local and nonlocal interactions in spectral space. Furthermore, the scaling of the Kolmogorov constant, and of skewness and flatness of velocity increments is consistent with previous experimental results. The accumulation of energy in the small scales associated with the bottleneck seems to occur on a span of wave numbers that is independent of the Reynolds number, possibly ruling out an inertial range explanation for it. Finally, intermittency exponents seem to depart from standard models at high R(lambda), leaving the interpretation of intermittency an open problem.

A general derivation and quantification of the third law of thermodynamics

PubMed Central

Masanes, Lluís; Oppenheim, Jonathan

2017-01-01

The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased. PMID:28290452

Ejecta velocity distribution of impact craters formed on quartz sand: Effect of projectile density on crater scaling law

NASA Astrophysics Data System (ADS)

Tsujido, Sayaka; Arakawa, Masahiko; Suzuki, Ayako I.; Yasui, Minami

2015-12-01

In order to clarify the effects of projectile density on ejecta velocity distributions for a granular target, impact cratering experiments on a quartz sand target were conducted by using eight types of projectiles with different densities ranging from 11 g cm-3 to 1.1 g cm-3, which were launched at about 200 m s-1 from a vertical gas gun at Kobe University. The scaling law of crater size, the ejection angle of ejecta grains, and the angle of the ejecta curtain were also investigated. The ejecta velocity distribution obtained from each projectile was well described by the π-scaling theory of v0/√{gR} =k2(x0/R)-1/μ , where v0, g, R and x0 are the ejection velocity, gravitational acceleration, crater radius and ejection position, respectively, and k2 and μ are constants mostly depending on target material properties (Housen, K.R., Holsapple, K.A. [2011]. Icarus 211, 856-875). The value of k2 was found to be almost constant at 0.7 for all projectiles except for the nylon projectile, while μ increased with the projectile density, from 0.43 for the low-density projectile to 0.6-0.7 for the high-density projectile. On the other hand, the π-scaling theory for crater size gave a μ value of 0.57, which was close to the average of the μ values obtained from ejecta velocity distributions. The ejection angle, θ, of each grain decreased slightly with distance, from higher than 45° near the impact point to 30-40° at 0.6 R. The ejecta curtain angle is controlled by the two elementary processes of ejecta velocity distribution and ejection angle; it gradually increased from 52° to 63° with the increase of the projectile density. The comparison of our experimental results with the theoretical model of the crater excavation flow known as the Z-model revealed that the relationship between μ and θ obtained by our experiments could not be described by the Z-model (Maxwell, D.E. [1977]. In: Roddy, D.J., Pepin, R.O., Merrill, R.B. (Eds.), Impact and Explosion Cratering

The onset of electrospray: the universal scaling laws of the first ejection

PubMed Central

Gañán-Calvo, A. M.; López-Herrera, J. M.; Rebollo-Muñoz, N.; Montanero, J. M.

2016-01-01

The disintegration of liquid drops with low electrical conductivity and subject to an electric field is investigated both theoretically and experimentally. This disintegration takes place through the development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling laws for the diameter and electric charge of the first issued droplet are proposed and validated both numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that differentiates the onset of electrospray, including the first droplet ejection, from the classical steady cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic phenomena come into play in electrospray, a subject of live controversy in the field. PMID:27581554

Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton's law

NASA Astrophysics Data System (ADS)

Gorshkov, A. V.; Prosviryakov, E. Yu.

2017-12-01

The paper considers the construction of analytical solutions to the Oberbeck-Boussinesq system. This system describes layered Bénard-Marangoni convective flows of an incompressible viscous fluid. The third-kind boundary condition, i. e. Newton's heat transfer law, is used on the boundaries of a fluid layer. The obtained solution is analyzed. It is demonstrated that there is a fluid layer thickness with tangential stresses vanishing simultaneously, this being equivalent to the existence of tensile and compressive stresses.

Scaling Phenomenology in Meson Photoproduction from CLAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biplab Dey, Curtis A. Meyer

2010-08-01

In the high energy limit, perturbative QCD predicts that hard scattering amplitudes should follow simple scaling laws. For hard scattering at 90°, we show that experiments support this prediction even in the “medium energy” regime of 2.3 GeV<=sqrt(s)<=2.84 GeV, as long as there are no s-channel resonances present. Our data consists of high statistics measurements for five different exclusive meson photoproduction channels (pomega, peta, peta[prime], K+Lambdaand K+[summation]0) recently obtained from CLAS at Jefferson Lab. The same power-law scaling also leads to “saturated” Regge trajectories at high energies. That is, at large -t and -u, Regge trajectories must approach constant negativemore » integers. We demonstrate the application of saturated Regge phenomenology by performing a partial wave analysis fit to the gammayp-->peta[prime]differential cross sections.« less

Measuring Black Men’s Police-Based Discrimination Experiences: Development and Validation of the Police and Law Enforcement (PLE) Scale

PubMed Central

English, Devin; Bowleg, Lisa; del Río-González, Ana Maria; Tschann, Jeanne M.; Agans, Robert; Malebranche, David J

2017-01-01

Objectives Although social science research has examined police and law enforcement-perpetrated discrimination against Black men using policing statistics and implicit bias studies, there is little quantitative evidence detailing this phenomenon from the perspective of Black men. Consequently, there is a dearth of research detailing how Black men’s perspectives on police and law enforcement-related stress predict negative physiological and psychological health outcomes. This study addresses these gaps with the qualitative development and quantitative test of the Police and Law Enforcement (PLE) scale. Methods In Study 1, we employed thematic analysis on transcripts of individual qualitative interviews with 90 Black men to assess key themes and concepts and develop quantitative items. In Study 2, we used 2 focus groups comprised of 5 Black men each (n=10), intensive cognitive interviewing with a separate sample of Black men (n=15), and piloting with another sample of Black men (n=13) to assess the ecological validity of the quantitative items. For study 3, we analyzed data from a sample of 633 Black men between the ages of 18 and 65 to test the factor structure of the PLE, as we all as its concurrent validity and convergent/discriminant validity. Results Qualitative analyses and confirmatory factor analyses suggested that a 5-item, 1-factor measure appropriately represented respondents’ experiences of police/law enforcement discrimination. As hypothesized, the PLE was positively associated with measures of racial discrimination and depressive symptoms. Conclusions Preliminary evidence suggests that the PLE is a reliable and valid measure of Black men’s experiences of discrimination with police/law enforcement. PMID:28080104

Scaling analysis for the direct reactor auxiliary cooling system for FHRs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lv, Q.; Kim, I. H.; Sun, X.

2015-04-01

The Direct Reactor Auxiliary Cooling System (DRACS) is a passive residual heat removal system proposed for the Fluoride-salt-cooled High-temperature Reactor (FHR) that combines the coated particle fuel and graphite moderator with a liquid fluoride salt as the coolant. The DRACS features three natural circulation/convection loops that rely on buoyancy as the driving force and are coupled via two heat exchangers, namely, the DRACS heat exchanger and the natural draft heat exchanger. A fluidic diode is employed to minimize the parasitic flow into the DRACS primary loop and correspondingly the heat loss to the DRACS during reactor normal operation, and tomore » activate the DRACS in accidents when the reactor is shut down. While the DRACS concept has been proposed, there are no actual prototypic DRACS systems for FHRs built or tested in the literature. In this paper, a detailed scaling analysis for the DRACS is performed, which will provide guidance for the design of scaled-down DRACS test facilities. Based on the Boussinesq assumption and one-dimensional flow formulation, the governing equations are non-dimensionalized by introducing appropriate dimensionless parameters. The key dimensionless numbers that characterize the DRACS system are obtained from the non-dimensional governing equations. Based on the dimensionless numbers and non-dimensional governing equations, similarity laws are proposed. In addition, a scaling methodology has been developed, which consists of a core scaling and a loop scaling. The consistency between the core and loop scaling is examined via the reference volume ratio, which can be obtained from both the core and loop scaling processes. The scaling methodology and similarity laws have been applied to obtain a scientific design of a scaled-down high-temperature DRACS test facility.« less

Determination of fractional flow reserve (FFR) based on scaling laws: a simulation study

NASA Astrophysics Data System (ADS)

Wong, Jerry T.; Molloi, Sabee

2008-07-01

Fractional flow reserve (FFR) provides an objective physiological evaluation of stenosis severity. A technique that can measure FFR using only angiographic images would be a valuable tool in the cardiac catheterization laboratory. To perform this, the diseased blood flow can be measured with a first pass distribution analysis and the theoretical normal blood flow can be estimated from the total coronary arterial volume based on scaling laws. A computer simulation of the coronary arterial network was used to gain a better understanding of how hemodynamic conditions and coronary artery disease can affect blood flow, arterial volume and FFR estimation. Changes in coronary arterial flow and volume due to coronary stenosis, aortic pressure and venous pressure were examined to evaluate the potential use of flow and volume for FFR determination. This study showed that FFR can be estimated using arterial volume and a scaling coefficient corrected for aortic pressure. However, variations in venous pressure were found to introduce some error in FFR estimation. A relative form of FFR was introduced and was found to cancel out the influence of pressure on coronary flow, arterial volume and FFR estimation. The use of coronary flow and arterial volume for FFR determination appears promising.

Scaling laws between population and facility densities.

PubMed

Um, Jaegon; Son, Seung-Woo; Lee, Sung-Ik; Jeong, Hawoong; Kim, Beom Jun

2009-08-25

When a new facility like a grocery store, a school, or a fire station is planned, its location should ideally be determined by the necessities of people who live nearby. Empirically, it has been found that there exists a positive correlation between facility and population densities. In the present work, we investigate the ideal relation between the population and the facility densities within the framework of an economic mechanism governing microdynamics. In previous studies based on the global optimization of facility positions in minimizing the overall travel distance between people and facilities, it was shown that the density of facility D and that of population rho should follow a simple power law D approximately rho(2/3). In our empirical analysis, on the other hand, the power-law exponent alpha in D approximately rho(alpha) is not a fixed value but spreads in a broad range depending on facility types. To explain this discrepancy in alpha, we propose a model based on economic mechanisms that mimic the competitive balance between the profit of the facilities and the social opportunity cost for populations. Through our simple, microscopically driven model, we show that commercial facilities driven by the profit of the facilities have alpha = 1, whereas public facilities driven by the social opportunity cost have alpha = 2/3. We simulate this model to find the optimal positions of facilities on a real U.S. map and show that the results are consistent with the empirical data.

On the power law of passive scalars in turbulence

NASA Astrophysics Data System (ADS)

Gotoh, Toshiyuki; Watanabe, Takeshi

2015-11-01

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

How to choose a calving law

NASA Astrophysics Data System (ADS)

O'Leary, M.

2014-12-01

Any model of an ocean-terminating ice mass requires a frontal boundary condition, often referred to as a "calving law". The choice of this boundary condition can have complex and poorly-understood effects on the behaviour of the system. Despite this, calving laws are often chosen based on numerical convenience or fashions in the literature. This can often lead to predictions which have "hidden dependencies" on the particular choice of calving law. As an attempt to alleviate this problem, I will show results from a wide variety of calving laws, applied to tidewater glacier scenarios. I will demonstrate how the decadal-scale stability of a tidewater system can put constraints on possible calving laws, and how certain observational phenomena, such as the presence of "pinning points" are largely independent of the choice of calving law. These results can be used by practitioners to decide on appropriate calving laws for the specific problems at hand. They should also be useful to help direct research into new calving laws, and to guide our conception of what an ideal calving law should look like.

Similarity considerations and conservation laws for magneto-static atmospheres

NASA Technical Reports Server (NTRS)

Webb, G. M.

1986-01-01

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Coulomb-Gas scaling law for a superconducting Bi(2+y)Sr(2-x-y)La(x)CuO(6+delta) thin films in magnetic fields

PubMed

Zhang; Deltour; Zhao

2000-10-16

The electrical transport properties of epitaxial superconducting Bi(2+y)Sr(2-x-y)La(x)CuO(6+delta) thin films have been studied in magnetic fields. Using a modified Coulomb-gas scaling law, we can fit all the magnetic field dependent low resistance data with a universal scaling curve, which allows us to determine a relation between the activation energy of the thermally activated flux flow resistance and the characteristic temperature scaling parameters.

Development and analysis of a leak-based blast attenuator and scaling laws for primary blast peak overpressure for a large caliber muzzleloaded cannon

NASA Astrophysics Data System (ADS)

Carson, Robert Andrew

One of the primary aspects of the research and development work carried out at Benet Laboratories is the Soldier. Maintenance of their health in the field is the first priority while the second priority is the enhancement of their performance. Therefore, a new concept for a weapon system that targets these two priorities is highly desirable. This is the case with a new concept that can reduce the peak overpressure without the use of a muzzle device for a muzzle loaded cannon system. Such a novel concept was developed in this thesis through the application of propellant leak into the precursor region, i.e., when the projectile is still in the bore. A 3D hydrocode (ALE3D) was employed to predict the blast overpressure for the baseline and propellant leak configurations. However, a 3D hydrocode is computationally very expensive to predict peak overpressure in the far-field and an efficient method to predict peak overpressure in the far-field is of significance. Therefore, scaling laws for primary blast peak overpressure were also developed in this thesis. Initially, two propellant leak concepts were examined. A bulge leak method and a channel leak method, which were compared to the baseline configuration. The initial channel leak configuration (referred to as CLM-1) significantly reduced the exit pressure ratio during projectile ejection, and thereby, resulted in a weaker blast. This in-turn substantially attenuated the peak overpressure to the rear of the muzzle without the aid of a muzzle device while having a marginal loss in the projectile exit velocity. For CLM-1, at one monitored location with the largest peak overpressure, a reduction of about 38% in peak overpressure was observed as compared to the baseline case. In order to compare different leak configurations, a performance metric was defined by comparing the ratio of peak overpressure and projectile exit velocity for a leak configuration to that for the baseline configuration. This metric was referred to

Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants

NASA Astrophysics Data System (ADS)

Bitsch, Bertram; Morbidelli, Alessandro; Johansen, Anders; Lega, Elena; Lambrechts, Michiel; Crida, Aurélien

2018-04-01

The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τf < 0.005 can drift through the partial gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system.

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

NASA Astrophysics Data System (ADS)

Sharma, N. K.; Singh, J. K.

2014-12-01

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble's parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ϕ and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.

Evidence, temperature, and the laws of thermodynamics.

PubMed

Vieland, Veronica J

2014-01-01

A primary purpose of statistical analysis in genetics is the measurement of the strength of evidence for or against hypotheses. As with any type of measurement, a properly calibrated measurement scale is necessary if we want to be able to meaningfully compare degrees of evidence across genetic data sets, across different types of genetic studies and/or across distinct experimental modalities. In previous papers in this journal and elsewhere, my colleagues and I have argued that geneticists ought to care about the scale on which statistical evidence is measured, and we have proposed the Kelvin temperature scale as a template for a context-independent measurement scale for statistical evidence. Moreover, we have claimed that, mathematically speaking, evidence and temperature may be one and the same thing. On first blush, this might seem absurd. Temperature is a property of systems following certain laws of nature (in particular, the 1st and 2nd Law of Thermodynamics) involving very physical quantities (e.g., energy) and processes (e.g., mechanical work). But what do the laws of thermodynamics have to do with statistical systems? Here I address that question. © 2014 S. Karger AG, Basel.

Law machines: scale models, forensic materiality and the making of modern patent law.

PubMed

Pottage, Alain

2011-10-01

Early US patent law was machine made. Before the Patent Office took on the function of examining patent applications in 1836, questions of novelty and priority were determined in court, within the forum of the infringement action. And at all levels of litigation, from the circuit courts up to the Supreme Court, working models were the media through which doctrine, evidence and argument were made legible, communicated and interpreted. A model could be set on a table, pointed at, picked up, rotated or upended so as to display a point of interest to a particular audience within the courtroom, and, crucially, set in motion to reveal the 'mode of operation' of a machine. The immediate object of demonstration was to distinguish the intangible invention from its tangible embodiment, but models also'machined' patent law itself. Demonstrations of patent claims with models articulated and resolved a set of conceptual tensions that still make the definition and apprehension of the invention difficult, even today, but they resolved these tensions in the register of materiality, performativity and visibility, rather than the register of conceptuality. The story of models tells us something about how inventions emerge and subsist within the context of patent litigation and patent doctrine, and it offers a starting point for renewed reflection on the question of how technology becomes property.

Statistical scaling of pore-scale Lagrangian velocities in natural porous media.

PubMed

Siena, M; Guadagnini, A; Riva, M; Bijeljic, B; Pereira Nunes, J P; Blunt, M J

2014-08-01

We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

Machine learning to construct reduced-order models and scaling laws for reactive-transport applications

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Karra, S.; Vesselinov, V. V.

2017-12-01

The efficiency of many hydrogeological applications such as reactive-transport and contaminant remediation vastly depends on the macroscopic mixing occurring in the aquifer. In the case of remediation activities, it is fundamental to enhancement and control of the mixing through impact of the structure of flow field which is impacted by groundwater pumping/extraction, heterogeneity, and anisotropy of the flow medium. However, the relative importance of these hydrogeological parameters to understand mixing process is not well studied. This is partially because to understand and quantify mixing, one needs to perform multiple runs of high-fidelity numerical simulations for various subsurface model inputs. Typically, high-fidelity simulations of existing subsurface models take hours to complete on several thousands of processors. As a result, they may not be feasible to study the importance and impact of model inputs on mixing. Hence, there is a pressing need to develop computationally efficient models to accurately predict the desired QoIs for remediation and reactive-transport applications. An attractive way to construct computationally efficient models is through reduced-order modeling using machine learning. These approaches can substantially improve our capabilities to model and predict remediation process. Reduced-Order Models (ROMs) are similar to analytical solutions or lookup tables. However, the method in which ROMs are constructed is different. Here, we present a physics-informed ML framework to construct ROMs based on high-fidelity numerical simulations. First, random forests, F-test, and mutual information are used to evaluate the importance of model inputs. Second, SVMs are used to construct ROMs based on these inputs. These ROMs are then used to understand mixing under perturbed vortex flows. Finally, we construct scaling laws for certain important QoIs such as degree of mixing and product yield. Scaling law parameters dependence on model inputs are

Scaling law on formation and rupture of a dynamical liquid bridge

NASA Astrophysics Data System (ADS)

Zhang, Huang; Zhang, Zehao; Liu, Qianfeng; Li, Shuiqing; Department of Thermal Engineering, Tsinghua University Collaboration; Institute of Nuclear Energy; Technology, Tsinghua University Collaboration

2017-11-01

The formation and breakup of a pendular liquid bridge in dynamic state is investigated experimentally. The experimental setup arises from a system to measure the coefficient of restitution (COR) of a glass sphere impacting and bouncing on a wetted surface. We compare the effect of surface tension and gravity on the liquid bridge rupture by the capillary length κ-1. For water and liquid 1 (50% water mixed with 50% glycerol), the gravity is dominant on the liquid bridge breakup. And we find that the rupture distance is in good linear trend with the non-dimensional number G by the scaling law analysis. Further, for liquid 2 (25% water mixed with 75% glycerol) that is relatively high viscous, the linear changing of the rupture distance with the capillary number Ca is found. The relation of the rupture distance with G and Ca would be helpful in understanding the complex behavior of the dynamical liquid bridge. This work was funded by the Major State Basic Research Development Program of China (Grant No. 2016YFC0203705) and the China Postdoctoral Science Foundation (Grant No. 2016M601024).

A two-scale model for dynamic damage evolution

NASA Astrophysics Data System (ADS)

Keita, Oumar; Dascalu, Cristian; François, Bertrand

2014-03-01

This paper presents a new micro-mechanical damage model accounting for inertial effect. The two-scale damage model is fully deduced from small-scale descriptions of dynamic micro-crack propagation under tensile loading (mode I). An appropriate micro-mechanical energy analysis is combined with homogenization based on asymptotic developments in order to obtain the macroscopic evolution law for damage. Numerical simulations are presented in order to illustrate the ability of the model to describe known behaviors like size effects for the structural response, strain-rate sensitivity, brittle-ductile transition and wave dispersion.

Scaling law in free walking of mice in circular open fields of various diameters.

PubMed

Shoji, Hiroto

2016-03-01

Open-field tests are routinely used to study locomotor activity in rodents. I studied the effects of apparatus size on rodent locomotor activity, specifically with respect to how resting and walking periods are interwoven. I explored the open-field behavior of mice utilizing circular open fields of various diameters. When the diameter of the test apparatus was greater than 75 cm, the durations of the resting and moving periods of free walking behavior obeyed bounded power-law distribution functions. I found that the properties of the scaling exponents and model selection became similar for test apparatus diameters greater than 75 cm. These results can provide a guide for the selection of the size of the test apparatus for use in the study of the open-field behavior of rodents.

Chiral battery, scaling laws and magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anand, Sampurn; Bhatt, Jitesh R.; Pandey, Arun Kumar, E-mail: sampurn@prl.res.in, E-mail: jeet@prl.res.in, E-mail: arunp@prl.res.in

2017-07-01

We study the generation and evolution of magnetic field in the presence of chiral imbalance and gravitational anomaly which gives an additional contribution to the vortical current. The contribution due to gravitational anomaly is proportional to T {sup 2} which can generate seed magnetic field irrespective of plasma being chirally charged or neutral. We estimate the order of magnitude of the magnetic field to be 10{sup 30} G at T ∼ 10{sup 9} GeV, with a typical length scale of the order of 10{sup −18} cm, which is much smaller than the Hubble radius at that temperature (10{sup −8} cm).more » Moreover, such a system possess scaling symmetry. We show that the T {sup 2} term in the vorticity current along with scaling symmetry leads to more power transfer from lower to higher length scale as compared to only chiral anomaly without scaling symmetry.« less

Molecular Robots Obeying Asimov's Three Laws of Robotics.

PubMed

Kaminka, Gal A; Spokoini-Stern, Rachel; Amir, Yaniv; Agmon, Noa; Bachelet, Ido

2017-01-01

Asimov's three laws of robotics, which were shaped in the literary work of Isaac Asimov (1920-1992) and others, define a crucial code of behavior that fictional autonomous robots must obey as a condition for their integration into human society. While, general implementation of these laws in robots is widely considered impractical, limited-scope versions have been demonstrated and have proven useful in spurring scientific debate on aspects of safety and autonomy in robots and intelligent systems. In this work, we use Asimov's laws to examine these notions in molecular robots fabricated from DNA origami. We successfully programmed these robots to obey, by means of interactions between individual robots in a large population, an appropriately scoped variant of Asimov's laws, and even emulate the key scenario from Asimov's story "Runaround," in which a fictional robot gets into trouble despite adhering to the laws. Our findings show that abstract, complex notions can be encoded and implemented at the molecular scale, when we understand robots on this scale on the basis of their interactions.

Geomorphic Transport Laws and the Statistics of Topography and Stratigraphy

NASA Astrophysics Data System (ADS)

Schumer, R.; Taloni, A.; Furbish, D. J.

2016-12-01

Geomorphic transport laws take the form of partial differential equations in which sediment motion is a deterministic function of slope. The addition of a noise term, representing unmeasurable, or subgrid scale autogenic forcing, reproduces scaling properties similar to those observed in topography, landforms, and stratigraphy. Here we describe a transport law that generalizes previous equations by permitting transport that is local or non-local in addition to different types of noise. More importantly, we use this transport law to link the character of sediment transport to the statistics of topography and stratigraphy. In particular, we link the origin of the Sadler effect to the evolution of the earth surface via a transport law.

48 CFR 225.7402-4 - Law of war training.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 48 Federal Acquisition Regulations System 3 2014-10-01 2014-10-01 false Law of war training. 225... States 225.7402-4 Law of war training. (a) Basic training. Basic law of war training is required for all...=en-US. (b) Advanced law of war training. (1) The types of personnel that must obtain advanced law of...

48 CFR 225.7402-4 - Law of war training.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 48 Federal Acquisition Regulations System 3 2010-10-01 2010-10-01 false Law of war training. 225... States 225.7402-4 Law of war training. (a) Basic training. Basic law of war training is required for all...= en-US. (b) Advanced law of war training. (1) The types of personnel that must obtain advanced law of...

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.

Cosmological Ohm's law and dynamics of non-minimal electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hollenstein, Lukas; Jain, Rajeev Kumar; Urban, Federico R., E-mail: lukas.hollenstein@cea.fr, E-mail: jain@cp3.dias.sdu.dk, E-mail: furban@ulb.ac.be

2013-01-01

The origin of large-scale magnetic fields in cosmic structures and the intergalactic medium is still poorly understood. We explore the effects of non-minimal couplings of electromagnetism on the cosmological evolution of currents and magnetic fields. In this context, we revisit the mildly non-linear plasma dynamics around recombination that are known to generate weak magnetic fields. We use the covariant approach to obtain a fully general and non-linear evolution equation for the plasma currents and derive a generalised Ohm law valid on large scales as well as in the presence of non-minimal couplings to cosmological (pseudo-)scalar fields. Due to the sizeablemore » conductivity of the plasma and the stringent observational bounds on such couplings, we conclude that modifications of the standard (adiabatic) evolution of magnetic fields are severely limited in these scenarios. Even at scales well beyond a Mpc, any departure from flux freezing behaviour is inhibited.« less

Scaling laws for gas breakdown for nanoscale to microscale gaps at atmospheric pressure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loveless, Amanda M.; Garner, Allen L., E-mail: algarner@purdue.edu

2016-06-06

Electronics miniaturization motivates gas breakdown predictions for microscale and smaller gaps, since traditional breakdown theory fails when gap size, d, is smaller than ∼15 μm at atmospheric pressure, p{sub atm}. We perform a matched asymptotic analysis to derive analytic expressions for breakdown voltage, V{sub b}, at p{sub atm} for 1 nm ≤ d ≤ 35 μm. We obtain excellent agreement between numerical, analytic, and particle-in-cell simulations for argon, and show V{sub b} decreasing as d → 0, instead of increasing as predicted by Paschen's law. This work provides an analytic framework for determining V{sub b} at atmospheric pressure for various gap distances that may be extended tomore » other gases.« less

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.

The scaling law of climate change and its relevance to assessing (palaeo)biological responses

NASA Astrophysics Data System (ADS)

Kiessling, Wolfgang; Eichenseer, Kilian

2014-05-01

It is often argued that current rates of climate change are unprecedented in the geological past. At the same time, the magnitudes of change were often much greater in deep time than they are in history. The most severe global warming in the Phanerozoic, with dramatic consequences for life, probably occurred across the Permian-Triassic (P-T) boundary when an increase of tropical water temperatures of 15° C has been observed to occur over a timespan 0.8 myr (Sun et al. 2012), whereas global ocean warming over the last 50 years was 0.35° C (Burrows et al. 2011). When transforming these data into rates of change the P-T rate was roughly 370 times smaller than the current rate. We argue that the smaller rates of change inferred from geological proxy records are due to a scaling effect, that is, rates of climate change generally decrease with timespan of observation. We compiled from the published literature data on measured or inferred temperature changes and the timespans over which these changes were assessed. Our compilation currently comprises 120 values and covers timespans from 20 to 107 years. A log-log plot of timespan versus rate of temperature change depicts a highly significant correlation (r2 = 0.95) of a power-law relationship with an exponent of -0.87. Warming trends show a slightly lower exponent (-0.84) than cooling trends (-0.89) but the explained variance is better for the scaling of warming trends. Importantly, the scaled warming trend across the P-T boundary is higher than the current rates of warming. Similar scaling effects are well explored for sediment accumulation rates (Sadler 1981) and evolutionary rates (Gingerich 1993). These have been interpreted as being due to breaks in sedimentation and periods of stasis or transient reversals, respectively. In case of climate change, transient reversals in general trends are the most likely explanation for the scaling relationship. Even relatively rapid intervals of warming, such as the Pleistocene

Variability of three-dimensional sea breeze structure in southern France: observations and evaluation of empirical scaling laws

NASA Astrophysics Data System (ADS)

Drobinski, P.; Bastin, S.; Dabas, A.; Delville, P.; Reitebuch, O.

2006-08-01

Sea-breeze dynamics in southern France is investigated using an airborne Doppler lidar, a meteorological surface station network and radiosoundings, in the framework of the ESCOMPTE experiment conducted during summer 2001 in order to evaluate the role of thermal circulations on pollutant transport and ventilation. The airborne Doppler lidar WIND contributed to three-dimensional (3-D) mapping of the sea breeze circulation in an unprecedented way. The data allow access to the onshore and offshore sea breeze extents (xsb), and to the sea breeze depth (zsb) and intensity (usb). They also show that the return flow of the sea breeze circulation is very seldom seen in this area due to (i) the presence of a systematic non zero background wind, and (ii) the 3-D structure of the sea breeze caused by the complex coastline shape and topography. A thorough analysis is conducted on the impact of the two main valleys (Rhône and Durance valleys) affecting the sea breeze circulation in the area.

Finally, this dataset also allows an evaluation of the existing scaling laws used to derive the sea breeze intensity, depth and horizontal extent. The main results of this study are that (i) latitude, cumulative heating and surface friction are key parameters of the sea breeze dynamics; (ii) in presence of strong synoptic flow, all scaling laws fail in predicting the sea breeze characteristics (the sea breeze depth, however being the most accurately predicted); and (iii) the ratio zsb/usb is approximately constant in the sea breeze flow.

The weather and climate: emergent laws and multifractal cascades

NASA Astrophysics Data System (ADS)

Lovejoy, Shaun; Schertzer, Daniel

2013-04-01

Science in general and physics and geophysics in particular are hierarchies of interlocking theories and models with low level, fundamental laws such as quantum mechanics and statistical mechanics providing the underpinnings for the emergence of the qualitatively new, higher level laws of thermodynamics and continuum mechanics that provide the current bases for modelling the weather and climate. Yest it was the belief of generations of turbulence pioneers (notably Richardson, Kolmogorov, Obhukhov, Corrsin, Bolgiano) that at sufficiently high levels of nonlinearity (quantified by the Reynold's number, of the order 10**12 in the atmosphere) that new even higher level laws would emerge describing "fully developed turbulence". However for atmospheric applications, the pioneers' eponymous laws suffered from two basic restrictions - isotropy and homogeneity - that prevented them from being valid over wide ranges of scale. Over the last thirty years both of these restrictions have been overcome - the former with the generalization from isotropic to strongly anisotropic notions of scale (to account notably for stratification), and from homogeneity to strong heterogeneity (intermittency) via multifractal cascades. In this presentation we give an overview of recent developments and analyses covering huge ranges of space-time scales (including weather, macroweather and climate time scales). We show how the combination of strong anisotropy and strong intermittency commonly leads to the "phenomenological fallacy" in which morphology is confounded with mechanism. With the help of stochastic models, we show how processes with vastly different large and small scale morphologies can arise from a unique multifractal dynamical mechanisms [Lovejoy and Schertzer, 2013]. References: Lovejoy, S., and D. Schertzer (2013), The Weather and Climate: Emergent Laws and Multifractal Cascades, 480 pp., Cambridge University Press, Cambridge.

Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current

NASA Astrophysics Data System (ADS)

Buschauer, Robert

2013-12-01

The equation describing the magnetic field due to a single, nonrelativistic charged particle moving at constant velocity is often referred to as the "Biot-Savart law for a point charge." Introductory calculus-based physics books usually state this law without proof.2 Advanced texts often present it either without proof or as a special case of a complicated mathematical formalism.3 Either way, little or no physical insight is provided to the student regarding the underlying physics. This paper presents a novel, basic, and transparent derivation of the Biot-Savart law for a point charge based only on Maxwell's displacement current term in Ampere's law. This derivation can serve many pedagogical purposes. For example, it can be used as lecture material at any academic level to obtain the Biot-Savart law for a point charge from simple principles. It can also serve as a practical example of the important fact that a changing electric flux produces a magnetic field.

Fractality and the law of the wall

NASA Astrophysics Data System (ADS)

Xu, Haosen H. A.; Yang, X. I. A.

2018-05-01

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

The fourth law of black-hole thermodynamics

NASA Astrophysics Data System (ADS)

Lousto, C. O.

1993-12-01

We show that black holes fulfill the scaling laws arising in critical transitions. In particular, we find that in the transition from negative to positive values the heat capacities CJQ, CΩQ and CJΦ give rise to critical exponents satisfying the scaling laws. The three transitions have the same critical exponents as predicted by the universality hypothesis. We also briefly discuss the implications of this result with regards to the connections among gravitation, quantum mechanics and statistical physics. Permanent address: Instituto de Astronomía y Física del Espacio, Casilla de Correo 67-Sucursal 28, 1428 Buenos Aires, Argentina.

The Role of Convective Shell Thickness on Dynamo Scaling Laws for Magnetic Field Morphology: Implications for the Ice Giants and Future Earth

NASA Astrophysics Data System (ADS)

Stanley, S.; Tian, B. Y.

2016-12-01

Previous dynamo scaling law studies (Christensen and Aubert, 2006) have demonstrated that the morphology of a planet's magnetic field is determined by the local Rossby number (Rol): a non-dimensional diagnostic variable that quantifies the ratio of inertial forces to Coriolis forces on the average length scale of the flow. Dynamos with Rol < 0.1 produce dipolar dominated magnetic fields whereas dynamos with Rol > 0.1 produce multipolar magnetic fields. Scaling studies have also determined the dependence of the local Rossby number on non-dimensional parameters governing the system - specifically the Ekman, Prandtl, magnetic Prandtl and flux-based Rayleigh numbers (Olson and Christensen, 2006). However, those studies focused on the specific convective shell thickness of the Earth's core and hence could not determine the influence of convective shell thickness on the local Rossby number. Aubert et al. (2009) investigated the role of convective shell thickness on dynamo scaling laws in order to investigate the palaeo-evolution of the geodynamo. Due to the focus of that study, they varied the ratio of the inner to outer core radii (rio) from 0 to 0.35 and found Rol scales with (1+rio). Here we consider a larger range of convective shell thicknesses and find an exponential dependence of rio on the local Rossby number. Our results are consistent with Aubert et al. (2009) for their small rio values. With this new scaling dependence on convective shell thickness, we find that Uranus and Neptune reside deeply in the multipolar regime, whereas without the dependence on rio, they resided near Rol =0.1; i.e. on the boundary between dipolar and multipolar fields and close to where Earth resides in the parameter space. We also find that Earth will reside more deeply in the multipolar regime, and hence not produce a stable dipolar field once the inner core has grown such that rio = 0.4.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d-dimensional regular lattices.

PubMed

Dias, W S; Bertrand, D; Lyra, M L

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d -dimensional regular lattices

NASA Astrophysics Data System (ADS)

Dias, W. S.; Bertrand, D.; Lyra, M. L.

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d >4 .

A scaling law for the critical current of Nb3Sn stands based on strong-coupling theory of superconductivity

NASA Astrophysics Data System (ADS)

Oh, Sangjun; Kim, Keeman

2006-02-01

We study the transition temperature Tc, the thermodynamic critical field Bc, and the upper critical field Bc2 of Nb3Sn with Eliashberg theory of strongly coupled superconductors using the Einstein spectrum α2(ω)F(ω)=λ<ω2>1/2δ(ω-<ω2>1/2). The strain dependences of λ(ɛ) and <ω2>1/2(V) are introduced from the empirical strain dependence of Tc(V) for three model cases. It is found that the empirical relation Tc(V)/Tc(0)=[Bc2(4.2 K,V)/Bc2(4.2 K,0)]1/w (w~3) is mainly due to the low-energy-phonon mode softening. We derive analytic expressions for the strain and temperature dependences of Bc(T,V) and Bc2(T,V) and the Ginzburg-Landau parameter κ(T,V) from the numerical calculation results. The Summers refinement on the temperature dependence of κ(T) shows deviation from our calculation results. We propose a unified scaling law of flux pinning in Nb3Sn strands in the form of the Kramer model with the analytic expressions of Bc2(T,V) and κ(T,V) derived in this work. It is shown that the proposed scaling law gives a reasonable fit to the reported data with only eight fitting parameters.

Prediction of scaling physics laws for proton acceleration with extended parameter space of the NIF ARC

NASA Astrophysics Data System (ADS)

Bhutwala, Krish; Beg, Farhat; Mariscal, Derek; Wilks, Scott; Ma, Tammy

2017-10-01

The Advanced Radiographic Capability (ARC) laser at the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory is the world's most energetic short-pulse laser. It comprises four beamlets, each of substantial energy ( 1.5 kJ), extended short-pulse duration (10-30 ps), and large focal spot (>=50% of energy in 150 µm spot). This allows ARC to achieve proton and light ion acceleration via the Target Normal Sheath Acceleration (TNSA) mechanism, but it is yet unknown how proton beam characteristics scale with ARC-regime laser parameters. As theory has also not yet been validated for laser-generated protons at ARC-regime laser parameters, we attempt to formulate the scaling physics of proton beam characteristics as a function of laser energy, intensity, focal spot size, pulse length, target geometry, etc. through a review of relevant proton acceleration experiments from laser facilities across the world. These predicted scaling laws should then guide target design and future diagnostics for desired proton beam experiments on the NIF ARC. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LLNL LDRD program under tracking code 17-ERD-039.

Magnetization reversal mechanism for Co nanoparticles revealed by a magnetic hysteresis scaling technique

NASA Astrophysics Data System (ADS)

Kobayashi, Satoru; Sato, Takuma; Li, Zhang; Dong, Xing-Long; Murakami, Takeshi

2018-05-01

We report results of magnetic hysteresis scaling of minor loops for cobalt nanoparticles with variable mean particle size of 53 and 95 nm. A power-law scaling with an exponent of 1.40±0.05 was found to hold true between minor-loop remanence and hysteresis loss in the wide temperature range of 10 - 300 K, irrespective of particle size and cooling field. A coefficient deduced from the scaling law steeply increases with decreasing temperature and exhibits a cooling field dependence below T ˜ 150 K. The value obtained after field cooling at 5 T was lower than that after zero-field cooling, being opposite to a behavior of major-loop coercivity. These observations were explained from the viewpoint of the exchange coupling between ferromagnetic Co core and antiferromagnetic CoO shell, which becomes effective below T ˜ 150 K.

Morphological study of polymer surfaces exposed to non-thermal plasma based on contact angle and the use of scaling laws

NASA Astrophysics Data System (ADS)

Felix, T.; Cassini, F. A.; Benetoli, L. O. B.; Dotto, M. E. R.; Debacher, N. A.

2017-05-01

The experiments presented in this communication have the purpose to elaborate an explanation for the morphological evolution of the growth of polymeric surfaces provided by the treatment of non-thermal plasma. According to the roughness analysis and the model proposed by scaling laws it is possible relate to a predictable or merely random effect. Polyethylene terephthalate (PET) and poly(etherether)ketone (PEEK) samples were exposed to a non-thermal plasma discharge and the resulting surfaces roughness were analyzed based on the measurements from contact angle, scanning electron microscopy and atomic force microscopy coupled with scaling laws analysis which can help to describe and understand the dynamic of formation of a wide variety of rough surfaces. The roughness, RRMS (RMS- Root Mean Square) values for polymer surface range between 19.8 nm and 110.9 nm. The contact angle and the AFM (Atomic Force Microscopy) measurements as a function of the plasma exposure time were in agreement with both polar and dispersive components according to the surface roughness and also with the morphology evaluated described by Wolf-Villain model, with proximate values of α between 0.91(PET) and 0.88(PEEK), β = 0.25(PET) and z = 3,64(PET).

Scaling-laws of human broadcast communication enable distinction between human, corporate and robot Twitter users.

PubMed

Tavares, Gabriela; Faisal, Aldo

2013-01-01

Human behaviour is highly individual by nature, yet statistical structures are emerging which seem to govern the actions of human beings collectively. Here we search for universal statistical laws dictating the timing of human actions in communication decisions. We focus on the distribution of the time interval between messages in human broadcast communication, as documented in Twitter, and study a collection of over 160,000 tweets for three user categories: personal (controlled by one person), managed (typically PR agency controlled) and bot-controlled (automated system). To test our hypothesis, we investigate whether it is possible to differentiate between user types based on tweet timing behaviour, independently of the content in messages. For this purpose, we developed a system to process a large amount of tweets for reality mining and implemented two simple probabilistic inference algorithms: 1. a naive Bayes classifier, which distinguishes between two and three account categories with classification performance of 84.6% and 75.8%, respectively and 2. a prediction algorithm to estimate the time of a user's next tweet with an R(2) ≈ 0.7. Our results show that we can reliably distinguish between the three user categories as well as predict the distribution of a user's inter-message time with reasonable accuracy. More importantly, we identify a characteristic power-law decrease in the tail of inter-message time distribution by human users which is different from that obtained for managed and automated accounts. This result is evidence of a universal law that permeates the timing of human decisions in broadcast communication and extends the findings of several previous studies of peer-to-peer communication.

Scaling-Laws of Human Broadcast Communication Enable Distinction between Human, Corporate and Robot Twitter Users

PubMed Central

Tavares, Gabriela; Faisal, Aldo

2013-01-01

Human behaviour is highly individual by nature, yet statistical structures are emerging which seem to govern the actions of human beings collectively. Here we search for universal statistical laws dictating the timing of human actions in communication decisions. We focus on the distribution of the time interval between messages in human broadcast communication, as documented in Twitter, and study a collection of over 160,000 tweets for three user categories: personal (controlled by one person), managed (typically PR agency controlled) and bot-controlled (automated system). To test our hypothesis, we investigate whether it is possible to differentiate between user types based on tweet timing behaviour, independently of the content in messages. For this purpose, we developed a system to process a large amount of tweets for reality mining and implemented two simple probabilistic inference algorithms: 1. a naive Bayes classifier, which distinguishes between two and three account categories with classification performance of 84.6% and 75.8%, respectively and 2. a prediction algorithm to estimate the time of a user's next tweet with an . Our results show that we can reliably distinguish between the three user categories as well as predict the distribution of a user's inter-message time with reasonable accuracy. More importantly, we identify a characteristic power-law decrease in the tail of inter-message time distribution by human users which is different from that obtained for managed and automated accounts. This result is evidence of a universal law that permeates the timing of human decisions in broadcast communication and extends the findings of several previous studies of peer-to-peer communication. PMID:23843945

Growth laws for sub-delta crevasses in the Mississippi River Delta

NASA Astrophysics Data System (ADS)

Yocum, T. A.; Georgiou, I. Y.; Straub, K. M.

2017-12-01

River deltas are threatened by environmental change, including subsidence, global sea level rise, reduced sediment inputs and other local factors. In the Mississippi River Delta (MRD) these impacts are exemplified, and have led to proposed solutions to build land that include sediment diversions to reinitiate the delta cycle. Deltas were studied extensively using numerical models, theoretical and conceptual frameworks, empirical scaling relationships, laboratory models and field observations. But predicting the future of deltas relies on field observations where for most deltas data are still lacking. Moreover, empirical and theoretical scaling laws may be influenced by the data used to develop them, while laboratory deltas may be influenced by scaling issues. Anthropogenic crevasses in the MRD are large enough to overcome limitations of laboratory deltas, and small enough to allow for rapid channel and wetland development, providing an ideal setting to investigate delta development mechanics. Here we assessed growth laws of sub-delta crevasses (SDC) in the MRD, in two experimental laboratory deltas (LD - weakly and strongly cohesive) and compared them to river dominated deltas worldwide. Channel and delta geometry metrics for each system were obtained using geospatial tools, bathymetric datasets, sediment size, and hydrodynamic observations. Results show that SDC follow growth laws similar to large river dominated deltas, with the exception of some that exhibit anomalous behavior with respect to the frequency and distance to a bifurcation and the fraction of wetted delta shoreline (allometry metrics). Most SDC exhibit a systematic decrease of non-dimensional channel geometries with increased bifurcation order, indicating that channels are adjusting to decreased flow after bifurcations occur, and exhibit linear trends for land allometry and width-depth ratio, although geometries decrease more rapidly per bifurcation order. Measured distance to bifurcations in SDC

Scaling of wet granular flows in a rotating drum

NASA Astrophysics Data System (ADS)

Jarray, Ahmed; Magnanimo, Vanessa; Ramaioli, Marco; Luding, Stefan

2017-06-01

In this work, we investigate the effect of capillary forces and particle size on wet granular flows and we propose a scaling methodology that ensures the conservation of the bed flow. We validate the scaling law experimentally by using different size glass beads with tunable capillary forces. The latter is obtained using mixtures of ethanol-water as interstitial liquid and by increasing the hydrophobicity of glass beads with an ad-hoc silanization procedure. The scaling methodology in the flow regimes considered (slipping, slumping and rolling) yields similar bed flow for different particle sizes including the angle of repose that normally increases when decreasing the particle size.

Competing mechanisms and scaling laws for carbon nanotube scission by ultrasonication.

PubMed

Pagani, Guido; Green, Micah J; Poulin, Philippe; Pasquali, Matteo

2012-07-17

Dispersion of carbon nanotubes (CNTs) into liquids typically requires ultrasonication to exfoliate individuals CNTs from bundles. Experiments show that CNT length drops with sonication time (or energy) as a power law t(-m). Yet the breakage mechanism is not well understood, and the experimentally reported power law exponent m ranges from approximately 0.2 to 0.5. Here we simulate the motion of CNTs around cavitating bubbles by coupling brownian dynamics with the Rayleigh-Plesset equation. We observe that, during bubble growth, CNTs align tangentially to the bubble surface. Surprisingly, we find two dynamical regimes during the collapse: shorter CNTs align radially, longer ones buckle. We compute the phase diagram for CNT collapse dynamics as a function of CNT length, stiffness, and initial distance from the bubble nuclei and determine the transition from aligning to buckling. We conclude that, depending on their length, CNTs can break due to either buckling or stretching. These two mechanisms yield different power laws for the length decay (0.25 and 0.5, respectively), reconciling the apparent discrepancy in the experimental data.

Sharply curved turn around duct flow predictions using spectral partitioning of the turbulent kinetic energy and a pressure modified wall law

NASA Technical Reports Server (NTRS)

Santi, L. Michael

1986-01-01

Computational predictions of turbulent flow in sharply curved 180 degree turn around ducts are presented. The CNS2D computer code is used to solve the equations of motion for two-dimensional incompressible flows transformed to a nonorthogonal body-fitted coordinate system. This procedure incorporates the pressure velocity correction algorithm SIMPLE-C to iteratively solve a discretized form of the transformed equations. A multiple scale turbulence model based on simplified spectral partitioning is employed to obtain closure. Flow field predictions utilizing the multiple scale model are compared to features predicted by the traditional single scale k-epsilon model. Tuning parameter sensitivities of the multiple scale model applied to turn around duct flows are also determined. In addition, a wall function approach based on a wall law suitable for incompressible turbulent boundary layers under strong adverse pressure gradients is tested. Turn around duct flow characteristics utilizing this modified wall law are presented and compared to results based on a standard wall treatment.

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

PubMed

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

2015-06-21

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

The Role of Law-of-the-Wall and Roughness Scale in the Surface Stress Model for LES of the Rough-wall Boundary Layer

NASA Astrophysics Data System (ADS)

Brasseur, James; Paes, Paulo; Chamecki, Marcelo

2017-11-01

Large-eddy simulation (LES) of the high Reynolds number rough-wall boundary layer requires both a subfilter-scale model for the unresolved inertial term and a ``surface stress model'' (SSM) for space-time local surface momentum flux. Standard SSMs assume proportionality between the local surface shear stress vector and the local resolved-scale velocity vector at the first grid level. Because the proportionality coefficient incorporates a surface roughness scale z0 within a functional form taken from law-of-the-wall (LOTW), it is commonly stated that LOTW is ``assumed,'' and therefore ``forced'' on the LES. We show that this is not the case; the LOTW form is the ``drag law'' used to relate friction velocity to mean resolved velocity at the first grid level consistent with z0 as the height where mean velocity vanishes. Whereas standard SSMs do not force LOTW on the prediction, we show that parameterized roughness does not match ``true'' z0 when LOTW is not predicted, or does not exist. By extrapolating mean velocity, we show a serious mismatch between true z0 and parameterized z0 in the presence of a spurious ``overshoot'' in normalized mean velocity gradient. We shall discuss the source of the problem and its potential resolution.

Scale-free networks as an epiphenomenon of memory

NASA Astrophysics Data System (ADS)

Caravelli, F.; Hamma, A.; Di Ventra, M.

2015-01-01

Many realistic networks are scale free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place. However, this mechanism is non-local, in the sense that it requires knowledge of the whole graph in order for the graph to be updated. Instead, if preferential attachment and realistic networks occur in physical systems, these features need to emerge from a local model. In this paper, we propose a local model and show that a possible ingredient (which is often underrated) for obtaining scale-free networks with local rules is memory. Such a model can be realised in solid-state circuits, using non-linear passive elements with memory such as memristors, and thus can be tested experimentally.

A theoretical Deduction from the Hubble law based on a Modified Newtonian Dynamics with field of Yukawa inverse

NASA Astrophysics Data System (ADS)

Falcon, N.

2017-07-01

At cosmic scales the dynamics of the Universe are almost exclusively prescribed by the force of gravity; however the assumption of the law of gravitation, depending on the inverse of the distance, leads to the known problems of the rotation curves of galaxies and missing mass (dark matter). The problem of the coupling of gravity to changes in scale and deviations from the law of the inverse square is an old problem (Laplace, 1805; Seeliger 1898), which has motivated alternatives to Newtonian dynamics compatible with observations. The present paper postulates a modified Newtonian dynamics by adding an inverse Yukawa potential: U(r)≡U0(M)(r-r0)e-α/r is the the potential per unit mass (in N/kg) as a function of the barionic mass that causes the field, r0 is of the order of 50h-1 Mpc and alpha is a coupling constant of the order of 2.5 h-1 Mpc. This potential is zero within the solar system, slightly attractive at interstellar distances, very attractive in galactic range and repulsive at cosmic scales. Its origin is the barionic matter, it allows to include the Milgrow MoND theory to explain the rotation curves, it is compatible with the experiments Eovos type, and allows to deduce the law of Hubble to cosmic scales, in the form H0=100h km/s Mpc≍U0(M)/c, where U0(M)≍ 4pi×6.67 10-11m/s2, is obtained from the Laplace's equation, assuming that the gravitational force is the law of the inverse of the square plus a non-linear term type Yukawa inverse. It is concluded that the modification of the law of gravity with nonlinear terms, allows to model the dynamics of the Universe on a large scale and include non-locality without dark matter. (See Falcon et al. 2014, International Journal of Astronomy and Astrophysics, 4, 551-559).

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

NASA Astrophysics Data System (ADS)

Gaume, Johan; Löwe, Henning; Tan, Shurun; Tsang, Leung

2017-09-01

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number zc of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of zc and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density νc=zcϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Accurate physical laws can permit new standard units: The two laws F→=ma→ and the proportionality of weight to mass

NASA Astrophysics Data System (ADS)

Saslow, Wayne M.

2014-04-01

Three common approaches to F→=ma→ are: (1) as an exactly true definition of force F→ in terms of measured inertial mass m and measured acceleration a→; (2) as an exactly true axiom relating measured values of a→, F→ and m; and (3) as an imperfect but accurately true physical law relating measured a→ to measured F→, with m an experimentally determined, matter-dependent constant, in the spirit of the resistance R in Ohm's law. In the third case, the natural units are those of a→ and F→, where a→ is normally specified using distance and time as standard units, and F→ from a spring scale as a standard unit; thus mass units are derived from force, distance, and time units such as newtons, meters, and seconds. The present work develops the third approach when one includes a second physical law (again, imperfect but accurate)—that balance-scale weight W is proportional to m—and the fact that balance-scale measurements of relative weight are more accurate than those of absolute force. When distance and time also are more accurately measurable than absolute force, this second physical law permits a shift to standards of mass, distance, and time units, such as kilograms, meters, and seconds, with the unit of force—the newton—a derived unit. However, were force and distance more accurately measurable than time (e.g., time measured with an hourglass), this second physical law would permit a shift to standards of force, mass, and distance units such as newtons, kilograms, and meters, with the unit of time—the second—a derived unit. Therefore, the choice of the most accurate standard units depends both on what is most accurately measurable and on the accuracy of physical law.

Scaling of load in communications networks.

PubMed

Narayan, Onuttom; Saniee, Iraj

2010-09-01

We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k)∼k{-γ} , we show that the load is l(k)∼k{η} with η=γ-1 , implying that the probability distribution for the load is p(l)∼1/l{2} independent of γ . The results are obtained through scaling arguments supported by finite size scaling studies. They contradict earlier claims, but are in agreement with the exact solution for the special case of tree graphs. Results are also presented for real communications networks at the IP layer, using the latest available data. Our analysis of the data shows relatively poor power-law degree distributions as compared to the scaling of the load versus degree. This emphasizes the importance of the load in network analysis.

Human dynamics scaling characteristics for aerial inbound logistics operation

NASA Astrophysics Data System (ADS)

Wang, Qing; Guo, Jin-Li

2010-05-01

In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions - that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models.

On Faraday's law in the presence of extended conductors

NASA Astrophysics Data System (ADS)

Bilbao, Luis

2018-06-01

The use of Faraday's Law of induction for calculating the induced currents in an extended conducting body is discussed. In a general case with arbitrary geometry, the solution to the problem of a moving metal object in the presence of a magnetic field is difficult and implies solving Maxwell's equations in a time-dependent situation. In many cases, including cases with good conductors (but not superconductors) Ampère's Law can be neglected and a simpler solution based solely in Faraday's law can be obtained. The integral form of Faraday's Law along any loop in the conducting body is equivalent to a Kirkhhoff's voltage law of a circuit. Therefore, a numerical solution can be obtained by solving a linear system of equations corresponding to a discrete number of loops in the body.

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

PubMed

Gong, Tao; Shuai, Lan

2014-01-01

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

Scaling Laws for Dark Matter Halos in Late-type and Dwarf Spheroidal Galaxies

NASA Astrophysics Data System (ADS)

Kormendy, John; Freeman, K. C.

2016-02-01

Dark matter (DM) halos of Sc-Im and dwarf spheroidal (dSph) galaxies satisfy scaling laws: halos in lower-luminosity galaxies have smaller core radii, higher central densities, and smaller velocity dispersions. These results are based on maximum-disk rotation curve decompositions for giant galaxies and Jeans equation analysis for dwarfs. (1) We show that spiral, Im, and Sph galaxies with absolute magnitudes MV > -18 form a sequence of decreasing baryon-to-DM surface density with decreasing luminosity. We suggest that this is a sequence of decreasing baryon retention versus supernova-driven losses or decreasing baryon capture after cosmological reionization. (2) The structural differences between S+Im and Sph galaxies are small. Both are affected mostly by the physics that controls baryon depletion. (3) There is a linear correlation between the maximum rotation velocities of baryonic disks and the outer circular velocities Vcirc of test particles in their DM halos. Baryons become unimportant at Vcirc = 42 ± 4 km s-1. Smaller galaxies are dim or dark. (4) We find that, absent baryon “depletion” and with all baryons converted into stars, dSph galaxies would be brighter by ˜4.6 mag and dIm galaxies would be brighter by ˜3.5 mag. Both have DM halos that are massive enough to help to solve the “too big to fail” problem with DM galaxy formation. (5) We suggest that there exist many galaxies that are too dark to be discovered by current techniques, as required by cold DM theory. (6) Central surface densities of DM halos are constant from MB ˜ -5 to -22. This implies a Faber-Jackson law with halo mass M ∝ (halo dispersion)4.

SCALING LAWS FOR DARK MATTER HALOS IN LATE-TYPE AND DWARF SPHEROIDAL GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kormendy, John; Freeman, K. C., E-mail: kormendy@astro.as.utexas.edu, E-mail: kenneth.freeman@anu.edu.au

2016-02-01

Dark matter (DM) halos of Sc–Im and dwarf spheroidal (dSph) galaxies satisfy scaling laws: halos in lower-luminosity galaxies have smaller core radii, higher central densities, and smaller velocity dispersions. These results are based on maximum-disk rotation curve decompositions for giant galaxies and Jeans equation analysis for dwarfs. (1) We show that spiral, Im, and Sph galaxies with absolute magnitudes M{sub V} > −18 form a sequence of decreasing baryon-to-DM surface density with decreasing luminosity. We suggest that this is a sequence of decreasing baryon retention versus supernova-driven losses or decreasing baryon capture after cosmological reionization. (2) The structural differences betweenmore » S+Im and Sph galaxies are small. Both are affected mostly by the physics that controls baryon depletion. (3) There is a linear correlation between the maximum rotation velocities of baryonic disks and the outer circular velocities V{sub circ} of test particles in their DM halos. Baryons become unimportant at V{sub circ} = 42 ± 4 km s{sup −1}. Smaller galaxies are dim or dark. (4) We find that, absent baryon “depletion” and with all baryons converted into stars, dSph galaxies would be brighter by ∼4.6 mag and dIm galaxies would be brighter by ∼3.5 mag. Both have DM halos that are massive enough to help to solve the “too big to fail” problem with DM galaxy formation. (5) We suggest that there exist many galaxies that are too dark to be discovered by current techniques, as required by cold DM theory. (6) Central surface densities of DM halos are constant from M{sub B} ∼ −5 to −22. This implies a Faber–Jackson law with halo mass M ∝ (halo dispersion){sup 4}.« less

Out of equilibrium transport through an Anderson impurity: probing scaling laws within the equation of motion approach.

PubMed

Balseiro, C A; Usaj, G; Sánchez, M J

2010-10-27

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing on the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G(2)(T, V) in order to test several scaling laws. We find that G(2)(T, V)/G(2)(T, 0) is a universal function of both eV/T(K) and T/T(K), T(K) being the Kondo temperature. The effect of an in-plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting Δ, the computed differential conductance peak splitting depends only on Δ/T(K), and for large fields approaches the value of 2Δ. Besides studying the traditional two leads setup, we also consider other configurations that mimic recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as ln(eV/T(K)). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.

The second laws of quantum thermodynamics.

PubMed

Brandão, Fernando; Horodecki, Michał; Ng, Nelly; Oppenheim, Jonathan; Wehner, Stephanie

2015-03-17

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.

The second laws of quantum thermodynamics

PubMed Central

Brandão, Fernando; Horodecki, Michał; Ng, Nelly; Oppenheim, Jonathan; Wehner, Stephanie

2015-01-01

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies. PMID:25675476

Exponentially Stabilizing Robot Control Laws

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1990-01-01

New class of exponentially stabilizing laws for joint-level control of robotic manipulators introduced. In case of set-point control, approach offers simplicity of proportion/derivative control architecture. In case of tracking control, approach provides several important alternatives to completed-torque method, as far as computational requirements and convergence. New control laws modified in simple fashion to obtain asymptotically stable adaptive control, when robot model and/or payload mass properties unknown.

A Comparison of Curing Process-Induced Residual Stresses and Cure Shrinkage in Micro-Scale Composite Structures with Different Constitutive Laws

NASA Astrophysics Data System (ADS)

Li, Dongna; Li, Xudong; Dai, Jianfeng; Xi, Shangbin

2018-02-01

In this paper, three kinds of constitutive laws, elastic, "cure hardening instantaneously linear elastic (CHILE)" and viscoelastic law, are used to predict curing process-induced residual stress for the thermoset polymer composites. A multi-physics coupling finite element analysis (FEA) model implementing the proposed three approaches is established in COMSOL Multiphysics-Version 4.3b. The evolution of thermo-physical properties with temperature and degree of cure (DOC), which improved the accuracy of numerical simulations, and cure shrinkage are taken into account for the three models. Subsequently, these three proposed constitutive models are implemented respectively in a 3D micro-scale composite laminate structure. Compared the differences between these three numerical results, it indicates that big error in residual stress and cure shrinkage generates by elastic model, but the results calculated by the modified CHILE model are in excellent agreement with those estimated by the viscoelastic model.

Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence

NASA Astrophysics Data System (ADS)

Andrés, N.; Galtier, S.; Sahraoui, F.

2018-01-01

We derive an exact law for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamic turbulence, without the assumption of isotropy. The Hall current is shown to introduce new flux and source terms that act at the small scales (comparable or smaller than the ion skin depth) to significantly impact the turbulence dynamics. The law provides an accurate means to estimate the energy cascade rate over a broad range of scales covering the magnetohydrodynamic inertial range and the sub-ion dispersive range in 3D numerical simulations and in in situ spacecraft observations of compressible turbulence. This work is particularly relevant to astrophysical flows in which small-scale density fluctuations cannot be ignored such as the solar wind, planetary magnetospheres, and the interstellar medium.

The constructal law of design and evolution in nature.

PubMed

Bejan, Adrian; Lorente, Sylvie

2010-05-12

Constructal theory is the view that (i) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered by a principle (the constructal law): 'for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it'. This law is about the necessity of design to occur, and about the time direction of the phenomenon: the tape of the design evolution 'movie' runs such that existing configurations are replaced by globally easier flowing configurations. The constructal law has two useful sides: the prediction of natural phenomena and the strategic engineering of novel architectures, based on the constructal law, i.e. not by mimicking nature. We show that the emergence of scaling laws in inanimate (geophysical) flow systems is the same phenomenon as the emergence of allometric laws in animate (biological) flow systems. Examples are lung design, animal locomotion, vegetation, river basins, turbulent flow structure, self-lubrication and natural multi-scale porous media. This article outlines the place of the constructal law as a self-standing law in physics, which covers all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes. Nature is configured to flow and move as a conglomerate of 'engine and brake' designs.

Renormalization group approach to power-law modeling of complex metabolic networks.

PubMed

Hernández-Bermejo, Benito

2010-08-07

In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations. Copyright 2010 Elsevier Ltd. All rights reserved.

Power law expansion of the early universe for a V (a) = kan potential

NASA Astrophysics Data System (ADS)

Freitas, Augusto S.

2018-01-01

In a recent paper, He, Gao and Cai [Phys. Rev. D 89, 083510 (2014)], found a rigorous proof, based on analytical solutions of the Wheeler-DeWitt (WDWE) equation, of the spontaneous creation of the universe from nothing. The solutions were obtained from a classical potential V = ka2, where a is the scale factor. In this paper, we present a complementary (to that of He, Gao and Cai) solution to the WDWE equation with V = kan. I have found an exponential expansion of the true vacuum bubble for all scenarios. In all scenarios, we found a power law behavior of the scale factor result which is in agreement with another studies.

Universities scale like cities.

PubMed

van Raan, Anthony F J

2013-01-01

Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the 'gross university income' in terms of total number of citations over 'size' in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities--the top-100 European universities--we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment.

Universities Scale Like Cities

PubMed Central

van Raan, Anthony F. J.

2013-01-01

Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the ‘gross university income’ in terms of total number of citations over ‘size’ in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities -the top-100 European universities- we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment. PMID:23544062

An Investigation of Mentoring and Socialization among Law Faculty

ERIC Educational Resources Information Center

Haynes, Ray K.; Petrosko, Joseph M.

2009-01-01

This study examined mentoring and organizational socialization among law faculty at American Bar Association (ABA) approved law schools. Data obtained from respondents (n = 298) captured the types of mentoring (formal or informal) occurring in law schools and faculty perceptions of the effectiveness of each type of mentoring. Comparative analysis…

Computing beyond Moore's Law

DOE PAGES

Shalf, John M.; Leland, Robert

2015-12-01

Here, photolithography systems are on pace to reach atomic scale by the mid-2020s, necessitating alternatives to continue realizing faster, more predictable, and cheaper computing performance. If the end of Moore's law is real, a research agenda is needed to assess the viability of novel semiconductor technologies and navigate the ensuing challenges.

The one scale that rules them all

NASA Astrophysics Data System (ADS)

Ouellette, Jennifer

2017-05-01

There are very real constraints on how large a complex organism can grow. This is the essence of all modern-day scaling laws, and the subject of Geoffrey West's provocative new book Scale: the Universal Laws of Life and Death in Organisms, Cities and Companies

32 CFR Appendix B to Part 275 - Obtaining Customer Authorization

Code of Federal Regulations, 2010 CFR

2010-07-01

... 32 National Defense 2 2010-07-01 2010-07-01 false Obtaining Customer Authorization B Appendix B to... OF 1978 Pt. 275, App. B Appendix B to Part 275—Obtaining Customer Authorization A. A DoD law... feasible, obtain the customer's consent. B. Any authorization obtained under paragraph A. of this appendix...

THE KILOPARSEC-SCALE STAR FORMATION LAW AT REDSHIFT 4: WIDESPREAD, HIGHLY EFFICIENT STAR FORMATION IN THE DUST-OBSCURED STARBURST GALAXY GN20

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hodge, J. A.; Riechers, D.; Decarli, R.

2015-01-01

We present high-resolution observations of the 880 μm (rest-frame FIR) continuum emission in the z = 4.05 submillimeter galaxy GN20 from the IRAM Plateau de Bure Interferometer (PdBI). These data resolve the obscured star formation (SF) in this unlensed galaxy on scales of 0.''3 × 0.''2 (∼2.1 × 1.3 kpc). The observations reveal a bright (16 ± 1 mJy) dusty starburst centered on the cold molecular gas reservoir and showing a bar-like extension along the major axis. The striking anti-correlation with the Hubble Space Telescope/Wide Field Camera 3 imaging suggests that the copious dust surrounding the starburst heavily obscures the rest-frame UV/optical emission. A comparison with 1.2 mm PdBI continuummore » data reveals no evidence for variations in the dust properties across the source within the uncertainties, consistent with extended SF, and the peak star formation rate surface density (119 ± 8 M {sub ☉} yr{sup –1} kpc{sup –2}) implies that the SF in GN20 remains sub-Eddington on scales down to 3 kpc{sup 2}. We find that the SF efficiency (SFE) is highest in the central regions of GN20, leading to a resolved SF law with a power-law slope of Σ{sub SFR} ∼ Σ{sub H{sub 2}{sup 2.1±1.0}}, and that GN20 lies above the sequence of normal star-forming disks, implying that the dispersion in the SF law is not due solely to morphology or choice of conversion factor. These data extend previous evidence for a fixed SFE per free-fall time to include the star-forming medium on ∼kiloparsec scales in a galaxy 12 Gyr ago.« less

The evolution of Zipf's law indicative of city development

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2016-02-01

Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban scientists. However, the three-parameter model and another type of two-parameter model have not attracted attention. This paper is devoted to exploring the conditions and scopes of application of these Zipf models. By mathematical reasoning and empirical analysis, new discoveries are made as follows. First, if the size distribution of cities in a geographical region cannot be described with the one- or two-parameter model, maybe it can be characterized by the three-parameter model with a scaling factor and a scale-translational factor. Second, all these Zipf models can be unified by hierarchical scaling laws based on cascade structure. Third, the patterns of city-size distributions seem to evolve from three-parameter mode to two-parameter mode, and then to one-parameter mode. Four-year census data of Chinese cities are employed to verify the three-parameter Zipf's law and the corresponding hierarchical structure of rank-size distributions. This study is revealing for people to understand the scientific laws of social systems and the property of urban development.

Electromagnetic scattering laws in Weyl systems.

PubMed

Zhou, Ming; Ying, Lei; Lu, Ling; Shi, Lei; Zi, Jian; Yu, Zongfu

2017-11-09

Wavelength determines the length scale of the cross section when electromagnetic waves are scattered by an electrically small object. The cross section diverges for resonant scattering, and diminishes for non-resonant scattering, when wavelength approaches infinity. This scattering law explains the colour of the sky as well as the strength of a mobile phone signal. We show that such wavelength scaling comes from the conical dispersion of free space at zero frequency. Emerging Weyl systems, offering similar dispersion at non-zero frequencies, lead to new laws of electromagnetic scattering that allow cross sections to be decoupled from the wavelength limit. Diverging and diminishing cross sections can be realized at any target wavelength in a Weyl system, providing the ability to tailor the strength of wave-matter interactions for radiofrequency and optical applications.

A scaling law derived from optimal dendritic wiring

PubMed Central

Cuntz, Hermann; Mathy, Alexandre; Häusser, Michael

2012-01-01

The wide diversity of dendritic trees is one of the most striking features of neural circuits. Here we develop a general quantitative theory relating the total length of dendritic wiring to the number of branch points and synapses. We show that optimal wiring predicts a 2/3 power law between these measures. We demonstrate that the theory is consistent with data from a wide variety of neurons across many different species and helps define the computational compartments in dendritic trees. Our results imply fundamentally distinct design principles for dendritic arbors compared with vascular, bronchial, and botanical trees. PMID:22715290

Anomalous Hall effect scaling in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Grigoryan, Vahram L.; Xiao, Jiang; Wang, Xuhui; Xia, Ke

2017-10-01

We propose a scaling law for anomalous Hall effect in ferromagnetic thin films. Our approach distinguishes multiple scattering sources, namely, bulk impurity, phonon for Hall resistivity, and most importantly the rough surface contribution to longitudinal resistivity. In stark contrast to earlier laws that rely on temperature- and thickness-dependent fitting coefficients, this scaling law fits the recent experimental data excellently with constant parameters that are independent of temperature and film thickness, strongly indicating that this law captures the underlying physical processes. Based on a few data points, this scaling law can even fit all experimental data in full temperature and thickness range. We apply this law to interpret the experimental data for Fe, Co, and Ni and conclude that (i) the phonon-induced skew scattering is unimportant as expected; (ii) contribution from the impurity-induced skew scattering is negative; (iii) the intrinsic (extrinsic) mechanism dominates in Fe (Co), and both the extrinsic and intrinsic contributions are important in Ni.

On the apparent power law in CDM halo pseudo-phase space density profiles

NASA Astrophysics Data System (ADS)

Nadler, Ethan O.; Oh, S. Peng; Ji, Suoqing

2017-09-01

We investigate the apparent power-law scaling of the pseudo-phase space density (PPSD) in cold dark matter (CDM) haloes. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log-log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar; scalelengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inwards, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.

Parental consent for abortion: impact of the Massachusetts law.

PubMed Central

Cartoof, V G; Klerman, L V

1986-01-01

This study assessed the impact of Massachusetts' parental consent law, which requires unmarried women under age 18 to obtain parental or judicial consent before having an abortion. Data were analyzed on monthly totals of abortions and births to Massachusetts minors prior to and following the April 1981 implementation of the law. Findings indicate that half as many minors obtained abortions in the state during the 20 months after the law went into effect as had done so previously. More than 1,800 minors residing in Massachusetts traveled to five surrounding states during these 20 months to avoid the statute's mandates. This group accounts for the reduction in in-state abortions. A small number of minors (50 to 100) bore children rather than aborting during 1982, perhaps because of the law. Findings suggest that this state's parental consent law had little effect on adolescent's pregnancy-resolution behavior. PMID:3953915

Kelvin Absolute Temperature Scale Identified as Length Scale and Related to de Broglie Thermal Wavelength

NASA Astrophysics Data System (ADS)

Sohrab, Siavash

Thermodynamic equilibrium between matter and radiation leads to de Broglie wavelength λdβ = h /mβvrβ and frequency νdβ = k /mβvrβ of matter waves and stochastic definitions of Planck h =hk =mk <λrk > c and Boltzmann k =kk =mk <νrk > c constants, λrkνrk = c , that respectively relate to spatial (λ) and temporal (ν) aspects of vacuum fluctuations. Photon massmk =√{ hk /c3 } , amu =√{ hkc } = 1 /No , and universal gas constant Ro =No k =√{ k / hc } result in internal Uk = Nhνrk = Nmkc2 = 3 Nmkvmpk2 = 3 NkT and potential pV = uN\\vcirc / 3 = N\\ucirc / 3 = NkT energy of photon gas in Casimir vacuum such that H = TS = 4 NkT . Therefore, Kelvin absolute thermodynamic temperature scale [degree K] is identified as length scale [meter] and related to most probable wavelength and de Broglie thermal wavelength as Tβ =λmpβ =λdβ / 3 . Parallel to Wien displacement law obtained from Planck distribution, the displacement law λwS T =c2 /√{ 3} is obtained from Maxwell -Boltzmann distribution of speed of ``photon clusters''. The propagation speeds of sound waves in ideal gas versus light waves in photon gas are described in terms of vrβ in harmony with perceptions of Huygens. Newton formula for speed of long waves in canals √{ p / ρ } is modified to √{ gh } =√{ γp / ρ } in accordance with adiabatic theory of Laplace.

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

The constructal law of design and evolution in nature

PubMed Central

Bejan, Adrian; Lorente, Sylvie

2010-01-01

Constructal theory is the view that (i) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered by a principle (the constructal law): ‘for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it’. This law is about the necessity of design to occur, and about the time direction of the phenomenon: the tape of the design evolution ‘movie’ runs such that existing configurations are replaced by globally easier flowing configurations. The constructal law has two useful sides: the prediction of natural phenomena and the strategic engineering of novel architectures, based on the constructal law, i.e. not by mimicking nature. We show that the emergence of scaling laws in inanimate (geophysical) flow systems is the same phenomenon as the emergence of allometric laws in animate (biological) flow systems. Examples are lung design, animal locomotion, vegetation, river basins, turbulent flow structure, self-lubrication and natural multi-scale porous media. This article outlines the place of the constructal law as a self-standing law in physics, which covers all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes. Nature is configured to flow and move as a conglomerate of ‘engine and brake’ designs. PMID:20368252

China's Marriage Law: a model for family responsibilities and relationships.

PubMed

Hare-Mustin, R T

1982-12-01

China's Marriage Law of 1981 is presented with a brief commentary. The law encompasses the responsibilities of spouses, parents, children, grandparents, and siblings to one another. The new law is contrasted with the 1950 Marriage Law, which prohibited such feudal practices of former times as arranged marriages and child betrothals. The 1981 law is concerned with equality and the lawful needs of women, children, and the aged. Family planning is encouraged. Divorce is made easier to obtain. Adoptees and stepchildren are provided for. The law provides a legislative model for personal relationships.

Animal Construction as a Free Boundary Problem: Evidence of Fractal Scaling Laws

NASA Astrophysics Data System (ADS)

Nicolis, S. C.

2014-12-01

We suggest that the main features of animal construction can be understood as the sum of locally independent actions of non-interacting individuals subjected to the global constraints imposed by the nascent structure. We first formulate an analytically tractable oscopic description of construction which predicts a 1/3 power law for how the length of the structure grows with time. We further show how the power law is modified when biases in random walk performed by the constructors as well as halting times between consecutive construction steps are included.

Scales and scaling in turbulent ocean sciences; physics-biology coupling

NASA Astrophysics Data System (ADS)

Schmitt, Francois

2015-04-01

Geophysical fields possess huge fluctuations over many spatial and temporal scales. In the ocean, such property at smaller scales is closely linked to marine turbulence. The velocity field is varying from large scales to the Kolmogorov scale (mm) and scalar fields from large scales to the Batchelor scale, which is often much smaller. As a consequence, it is not always simple to determine at which scale a process should be considered. The scale question is hence fundamental in marine sciences, especially when dealing with physics-biology coupling. For example, marine dynamical models have typically a grid size of hundred meters or more, which is more than 105 times larger than the smallest turbulence scales (Kolmogorov scale). Such scale is fine for the dynamics of a whale (around 100 m) but for a fish larvae (1 cm) or a copepod (1 mm) a description at smaller scales is needed, due to the nonlinear nature of turbulence. The same is verified also for biogeochemical fields such as passive and actives tracers (oxygen, fluorescence, nutrients, pH, turbidity, temperature, salinity...) In this framework, we will discuss the scale problem in turbulence modeling in the ocean, and the relation of Kolmogorov's and Batchelor's scales of turbulence in the ocean, with the size of marine animals. We will also consider scaling laws for organism-particle Reynolds numbers (from whales to bacteria), and possible scaling laws for organism's accelerations.

Anthropometry of Law Enforcement Officers

DTIC Science & Technology

1975-09-10

were obtained in a sur- vey of Air Force women with regard to height, although they tended to underestimate their weight (table 8). Although the...ESTIMATED BODY DIMENSIONS. Measured Height (in) Estimated Difference Law Enforcement Officers Army Men* Air Force Women** 70.04 68.71 63.82 71.07...69.81 64.80 1.03 0.90 0.98 Measured Weight (lb) Estimated Difference Law Enforcement Officers Army Men* Air Force Women** 189.60 159.10

Universal scaling laws in metro area election results.

PubMed

Bokányi, Eszter; Szállási, Zoltán; Vattay, Gábor

2018-01-01

We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948-2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single parameter only, and one of the parties always shows superlinear scaling and drives the process, while the sublinear exponent of the other party is merely the consequence of probability conservation. Based on the recently developed model of urban scaling, we give a microscopic model of voter behavior in which we replace diversity characterizing humans in creative aspects with social diversity and tolerance. The model can also predict new political developments such as the fragmentation of the left and the immigration paradox.

Ohm's law for a current sheet

NASA Technical Reports Server (NTRS)

Lyons, L. R.; Speiser, T. W.

1985-01-01

The paper derives an Ohm's law for single-particle motion in a current sheet, where the magnetic field reverses in direction across the sheet. The result is considerably different from the resistive Ohm's law often used in MHD studies of the geomagnetic tail. Single-particle analysis is extended to obtain a self-consistency relation for a current sheet which agrees with previous results. The results are applicable to the concept of reconnection in that the electric field parallel to the current is obtained for a one-dimensional current sheet with constant normal magnetic field. Dissipated energy goes directly into accelerating particles within the current sheet.

Methods for Scaling Icing Test Conditions

NASA Technical Reports Server (NTRS)

Anderson, David N.

1995-01-01

This report presents the results of tests at NASA Lewis to evaluate several methods to establish suitable alternative test conditions when the test facility limits the model size or operating conditions. The first method was proposed by Olsen. It can be applied when full-size models are tested and all the desired test conditions except liquid-water content can be obtained in the facility. The other two methods discussed are: a modification of the French scaling law and the AEDC scaling method. Icing tests were made with cylinders at both reference and scaled conditions representing mixed and glaze ice in the NASA Lewis Icing Research Tunnel. Reference and scale ice shapes were compared to evaluate each method. The Olsen method was tested with liquid-water content varying from 1.3 to .8 g/m(exp3). Over this range, ice shapes produced using the Olsen method were unchanged. The modified French and AEDC methods produced scaled ice shapes which approximated the reference shapes when model size was reduced to half the reference size for the glaze-ice cases tested.

Articulated Multimedia Physics, Lesson 14, Gases, The Gas Laws, and Absolute Temperature.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

As the fourteenth lesson of the Articulated Multimedia Physics Course, instructional materials are presented in this study guide with relation to gases, gas laws, and absolute temperature. The topics are concerned with the kinetic theory of gases, thermometric scales, Charles' law, ideal gases, Boyle's law, absolute zero, and gas pressures. The…

Universal scaling laws in metro area election results

PubMed Central

Szállási, Zoltán; Vattay, Gábor

2018-01-01

We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948–2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single parameter only, and one of the parties always shows superlinear scaling and drives the process, while the sublinear exponent of the other party is merely the consequence of probability conservation. Based on the recently developed model of urban scaling, we give a microscopic model of voter behavior in which we replace diversity characterizing humans in creative aspects with social diversity and tolerance. The model can also predict new political developments such as the fragmentation of the left and the immigration paradox. PMID:29470518

Divergent conservation laws in hyperbolic thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present study is devoted to the problem of formulation of conservation laws in divergent form for hyperbolic thermoelastic continua. The field formalism is applied to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are formulated. A special form of the first variation of the action is employed to obtain 4-covariant divergent conservation laws. Differential field equations and constitutive laws are derived from a special form of the first variation of the action integral. The objectivity of constitutive equations is provided by the rotationally invariant forms of the Lagrangian employed.

Scaling Laws and the Water Strider.

ERIC Educational Resources Information Center

Huetink, Linda

1996-01-01

Presents activities designed to build an understanding of why the physical characteristics of small animals such as the water strider, water spider, and the basilisk make it possible for the animals to use the surface tension of water to their advantage. Discusses the concept of geometrical scaling. (JRH)

A constitutive law for degrading bioresorbable polymers.

PubMed

Samami, Hassan; Pan, Jingzhe

2016-06-01

This paper presents a constitutive law that predicts the changes in elastic moduli, Poisson's ratio and ultimate tensile strength of bioresorbable polymers due to biodegradation. During biodegradation, long polymer chains are cleaved by hydrolysis reaction. For semi-crystalline polymers, the chain scissions also lead to crystallisation. Treating each scission as a cavity and each new crystal as a solid inclusion, a degrading semi-crystalline polymer can be modelled as a continuum solid containing randomly distributed cavities and crystal inclusions. The effective elastic properties of a degrading polymer are calculated using existing theories for such solid and the tensile strength of the degrading polymer is predicted using scaling relations that were developed for porous materials. The theoretical model for elastic properties and the scaling law for strength form a complete constitutive relation for the degrading polymers. It is shown that the constitutive law can capture the trend of the experimental data in the literature for a range of biodegradable polymers fairly well. Copyright © 2016 Elsevier Ltd. All rights reserved.

A study of the dust distribution and extinction law in Mon R2

NASA Technical Reports Server (NTRS)

Natta, A.; Beckwith, S.; Beck, S. C.; Evans, N. J., II; Moorwood, A. F. M.

1986-01-01

Observations were obtained at wavelengths from 1.5 to 7.5 microns with beams varying in diameter from 4 to 28 arcsec of infrared hydrogen recombination lines toward the Mon R2 IRS1 H II region. It is found that the data cannot be fitted with the extinction law which characterizes the interstellar medium unless the obscuring matter is clumped on a small scale of not greater than 0.3 arcsec; in which case considerable fluctuations in the amount of extinction on scales smaller than 1 arcsec are expected. The data of Simon et al. (1983) suggest a dip in the extinction about 5 arcsec from the 2-micron and radio continuum peak, and rule out models with uniform dust and clump distributions.

Identification of a constitutive law for trabecular bone samples under remodeling in the framework of irreversible thermodynamics

NASA Astrophysics Data System (ADS)

Louna, Zineeddine; Goda, Ibrahim; Ganghoffer, Jean-François

2018-01-01

We construct in the present paper constitutive models for bone remodeling based on micromechanical analyses at the scale of a representative unit cell (RUC) including a porous trabecular microstructure. The time evolution of the microstructure is simulated as a surface remodeling process by relating the surface growth remodeling velocity to a surface driving force incorporating a (surface) Eshelby tensor. Adopting the framework of irreversible thermodynamics, a 2D constitutive model based on the setting up of the free energy density and a dissipation potential is identified from FE simulations performed over a unit cell representative of the trabecular architecture obtained from real bone microstructures. The static and evolutive effective properties of bone at the scale of the RUC are obtained by combining a methodology for the evaluation of the average kinematic and static variables over a prototype unit cell and numerical simulations with controlled imposed first gradient rates. The formulated effective growth constitutive law at the scale of the homogenized set of trabeculae within the RUC is of viscoplastic type and relates the average growth strain rate to the homogenized stress tensor. The postulated model includes a power law function of an effective stress chosen to depend on the first and second stress invariants. The model coefficients are calibrated from a set of virtual testing performed over the RUC subjected to a sequence of loadings. Numerical simulations show that overall bone growth does not show any growth kinematic hardening. The obtained results quantify the strength and importance of different types of external loads (uniaxial tension, simple shear, and biaxial loading) on the overall remodeling process and the development of elastic deformations within the RUC.

A convenient method of obtaining percentile norms and accompanying interval estimates for self-report mood scales (DASS, DASS-21, HADS, PANAS, and sAD).

PubMed

Crawford, John R; Garthwaite, Paul H; Lawrie, Caroline J; Henry, Julie D; MacDonald, Marie A; Sutherland, Jane; Sinha, Priyanka

2009-06-01

A series of recent papers have reported normative data from the general adult population for commonly used self-report mood scales. To bring together and supplement these data in order to provide a convenient means of obtaining percentile norms for the mood scales. A computer program was developed that provides point and interval estimates of the percentile rank corresponding to raw scores on the various self-report scales. The program can be used to obtain point and interval estimates of the percentile rank of an individual's raw scores on the DASS, DASS-21, HADS, PANAS, and sAD mood scales, based on normative sample sizes ranging from 758 to 3822. The interval estimates can be obtained using either classical or Bayesian methods as preferred. The computer program (which can be downloaded at www.abdn.ac.uk/~psy086/dept/MoodScore.htm) provides a convenient and reliable means of supplementing existing cut-off scores for self-report mood scales.

Kidneys for transplant--"opting out" law in Singapore.

PubMed

Iyer, T K

1987-01-01

This paper is about the legislative attempt in Singapore to obtain more cadaver kidneys for transplants. It is a brief account of the major features of the bill which has become law since this note was written. The bill and the law are identical in this case.