Structures and scaling laws of turbulent Couette flow
NASA Astrophysics Data System (ADS)
Oberlack, Martin; Avsarkisov, Victor; Hoyas, Sergio; Rosteck, Andreas; Garcia-Galache, Jose P.; Frank, Andy
2014-11-01
We conducted a set of large scale DNS of turbulent Couette flow with the two key objectives: (i) to better understand large scale coherent structures and (ii) to validate new Lie symmetry based turbulent scaling laws for the mean velocity and higher order moments. Though frequently reported in the literature large scale structures pose a serious constraint on our ability to conduct DNS of turbulent Couette flow as the largest structures grow with increasing Re#, while at the same time Kolmogorov scale decreases. Other than for the turbulent Poiseuille flow a too small box is immediately visible in low order statistics such as the mean and limited our DNS to Reτ = 550 . At the same time we observed that scaling of the mean is peculiar as it involves a certain statistical symmetry which has never been observed for any other parallel wall-bounded turbulent shear flow. Symmetries such as Galilean group lie at the heart of fluid dynamics, while for turbulence statistics due to the multi-point correlation equations (MPCE) additional statistical symmetries are admitted. Most important, symmetries are the essential to construct exact solutions to the MPCE, which with the new above-mentioned special statistical symmetry led to a new turbulent scaling law for the Couette flow. DFG Grant No; KH 257/2-1.
Heat Release Effects on Scaling Laws for Turbulent Shear Flows
NASA Astrophysics Data System (ADS)
Tacina, Kathleen M.; Dahm, Werner J. A.
1996-11-01
Experiments have long suggested apparent differences in the fundamental scaling laws for turbulent shear flows between reacting and nonreacting flows. These differences result from the density changes produced by exothermic reaction, and are here shown to be similar to the changes produced by free-stream density differences in nonreacting flows. Motivated by this, we show that the fundamental scaling laws can be generalized to predict the changes due to heat release. The bilinear dependence of temperature T(ζ) on an appropriately defined conserved scalar ζ allows the density changes to be related to an equivalent nonreacting flow, in which one of the free-stream fluid temperatures is set to a value determined by the adiabatic flame temperature and the overall stoichiometry. This scaling principle is applied to turbulent jet diffusion flames, and leads to a generalized scaling variable d^+ for both reacting and nonreacting flows; it effectively extends the momentum diameter d^* of Thring & Newby (1952) and Ricou & Spalding (1961) to reacting flows. The resulting predicted effects of heat release show good agreement with all available data from momentum-dominated jet flames. (Supported by GRI Contract No. 5093-260-2728.)
Scaling laws and bulk-boundary decoupling in heat flow.
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.
Laws of non-symmetric optimal flow structures, from the macro to the micro scale
NASA Astrophysics Data System (ADS)
Reis, A. Heitor
2012-05-01
Many natural systems and engineering processes occur in which a fluid invades a territory from one entry point (invasion), or conversely is expelled from the territory through an outlet (drainage). In any such situation an evolutionary flow structure develops that bridges the gap between the micro-scale (diffusion dominant) and the macro-scale (convection dominant). The respiratory and circulatory systems of animals are clear examples of complex flow trees in which both the invasion and drainage processes occur. These flow trees display successive bifurcations (almost always non-symmetric) which allow them to cover and serve the entire territory to be bathed. Although they are complex, it is possible to understand its internal structuring in the light of Constructal Law. A scaling law for optimal diameters of symmetric bifurcations was proposed by Murray (1926), while Bejan and co-workers (2000-2006) added a new scaling law for channel lengths, and based scaling laws of tree shaped structures on theoretical grounds. In this work we use the Constructal Law to study the internal structure and scaling laws of non-symmetric flow structures, and show how the results might help understand some flow patterns found in Nature. We show that the global flow resistances depend on the parameter ξ = D2/D1 = L2/L1 defining the degree of asymmetry between branches 1 and 2 in a bifurcation. We also present a more accurate and general form, of Murray's law, as a result of the application of the Constructal law to branching flow structures. We end with a brief analysis of the use of these results in the analysis of flow structures of the human respiratory and circulatory systems.
Scaling laws for fully developed turbulent flow in pipes: Discussion of experimental data
Barenblatt, G. I.; Chorin, A. J.; Prostokishin, V. M.
1997-01-01
We compare mean velocity profiles measured in turbulent pipe flows (and also in boundary layer flows) with the predictions of a recently proposed scaling law; in particular, we examine the results of the Princeton “superpipe” experiment and assess their range of validity. PMID:9023332
Separation Control Using ZNMF Devices: Flow Physics and Scaling Laws
2007-12-31
the baseline uncontrolled flow is massively separated and does not reattached before the trailing edge (i.e. post stall). As mentioned earlier, this... massively leading-edge separated flow. In particular, a recursive ARMARKOV system ID algorithm is used to model the flow dynamics and provide the...3, May-June 2001. Soderstrom, T. and Stoica, P., System Identification, Prentice-Hall, New York, 1989. Song, Q., Tian, Y. and Cattafesta, L., " MIMO
Validity of classical scaling laws in laminar channel flow with periodic spacer-like obstacles
NASA Astrophysics Data System (ADS)
Rohlfs, Wilko; Lienhard, John H.
2015-11-01
Laminar channel flows with periodic obstacles occur in different technical applications involving heat and mass transfer. They are present in membrane technologies such as electro-dialysis or spirally wound membrane modules. For process design, classical scaling laws of heat and mass transfer are typically used. The laws scale the transfer (Sherwood) number, Sh , to the hydrodynamic Reynolds, Re , the fluid specific Schmidt number, Sc , and to some dimensionless geometric parameters, G, in a classical form like Sh = CReα ScβGγ . However, the validity of those classical scaling laws is limited to the region where the concentration boundary layer develops as it is well known that the transfer numbers approach a constant (Reynolds and Schmidt independent) value in the developed region of a laminar channel flow. This study examines numerically the validity of the scaling laws if the channel flow is interrupted periodically by cylindrical obstacles of different size and separation distance. In the developed region, a Schmidt and Reynolds number dependency is found and associated to wall-normal flow induced by the obstacles, for which this dependency varies with obstacle size and separation distance. Funding for WR was provided by the German Academic Exchange Service DAAD.
Kwak, Rhokyun; Pham, Van Sang; Lim, Kian Meng; Han, Jongyoon
2013-03-15
We consider electroconvective fluid flows initiated by ion concentration polarization (ICP) under pressure-driven shear flow, a scenario often found in many electrochemical devices and systems. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of ICP under shear flow: a unidirectional vortex structure, its height selection, and vortex advection. Determined by both the external pressure gradient and the electric body force, the dimensionless height of the sheared electroconvective vortex is shown to scale as (ϕ(2)/U(HP))(1/3), which is a clear departure from the previous diffusion-drift model prediction. To the best of our knowledge, this is the first microscopic characterization of ion concentration polarization under shear flow, and it firmly establishes electroconvection as the mechanism for an overlimiting current in realistic, large-area ion exchange membrane systems such as electrodialysis. The new scaling law has significant implications on the optimization of electrodialysis and other electrochemical systems.
NASA Astrophysics Data System (ADS)
Kwak, Rhokyun; Pham, Van Sang; Lim, Kian Meng; Han, Jongyoon
2013-03-01
We consider electroconvective fluid flows initiated by ion concentration polarization (ICP) under pressure-driven shear flow, a scenario often found in many electrochemical devices and systems. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of ICP under shear flow: a unidirectional vortex structure, its height selection, and vortex advection. Determined by both the external pressure gradient and the electric body force, the dimensionless height of the sheared electroconvective vortex is shown to scale as (ϕ2/UHP)1/3, which is a clear departure from the previous diffusion-drift model prediction. To the best of our knowledge, this is the first microscopic characterization of ion concentration polarization under shear flow, and it firmly establishes electroconvection as the mechanism for an overlimiting current in realistic, large-area ion exchange membrane systems such as electrodialysis. The new scaling law has significant implications on the optimization of electrodialysis and other electrochemical systems.
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.
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.
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
DNS of turbulent Couette flow with transpiration - spectra and symmetry induced scaling laws
NASA Astrophysics Data System (ADS)
Hoyas, Sergio; Kraheberger, Stefanie; Oberlack, Martin
2016-11-01
We present DNS results of turbulent plane Couette flow with constant wall-normal transpiration for Reynolds numbers of Reτ = 250 , 500 , 1000 and several transpiration Reynolds numbers Retr =V0 /Uw . To obtain the DNS data, a pseudo-spectral code, which originally was developed at UP Madrid, see (Hoyas and Jiménez 2006), is used for the simulations. Due to the lack of experimental and DNS data, the convergence of every simulation has been validated using the total shear stress equation and the relation between the friction velocities at the lower and upper wall. Examining the spectra we found that the large and wide structures, which appear in pure Couette flow, see (Avsarkisov et al. 2014), are destroyed as soon as transpiration velocity is different from zero. This and the presence of anomalous spectra near the blowing wall indicates the strong influence of suction on the whole flow, which was observed in (Antonia et al. 1988) as well. As classical scaling laws are not valid due to transpiration, new scaling laws of the mean velocity are derived using Lie symmetry methods. Additionally, suction creates a comparably larger uτ which, in turn, causes a flat and long region in the indicator function for the largest transpiration rate. SH was partially funded by ENE2015-71333-R. SK was funded by DFG under Grant No. OB96/39-1. Computer resources have been provided by LRZ Munich under Grant pr92la.
Revisiting the Nelson-Morfey scaling law for flow noise from duct constrictions
NASA Astrophysics Data System (ADS)
Kårekull, Oscar; Efraimsson, Gunilla; Åbom, Mats
2015-11-01
The semi-empirical scaling law by Nelson and Morfey [1] predicts the noise generation from constrictions in ducts with low Mach number flows. The results presented here demonstrate that the original model loses accuracy for constrictions of high pressure loss. A generalization based on a momentum flux assumption of the dipole forces is suggested and is evaluated against measurement results for orifice geometries of higher pressure loss than earlier evaluated. A prediction model including constrictions at flow duct terminations is also suggested. Improved accuracy for the predictions of the new model is found for orifice geometries of high pressure loss inside and at the end of ducts. The extended model is finally evaluated by measurements on a regular ventilation air terminal device.
NASA Astrophysics Data System (ADS)
Afzal, Noor
2006-11-01
An alternate two layers theory, based on four new scalings for transitional wall roughness variables, is presented for large appropriate roughness Reynolds numbers. For velocity profile the matching of inner and outer layers in the overlap region, by Izakson-Millikan-Kolmogorov hypothesis (Afzal, N. 2005 Proc. Royal Society A: PME 461, 1889-1910) leads to functional solutions that are universal log laws, as well as universal power laws, that explicitly independent of transitional wall roughness, having same constants as in smooth wall case. The universal log or power laws velocity profile and skin friction, if expressed in terms of traditional Reynolds numbers also yield log law and power laws that depend on surface roughness. The skin friction, in traditional variables, is predicted by a single relation for inflectional type of Nikuradse roughness for sand grain type roughness data and Colebrook commercial monotonic roughness. The extensive experimental data for various types of wall transitional roughness provide very good support to present theory of universal log laws as well as new predictions in traditional log laws . The experimental data from various sources (Osaka and Mochizuki, Kameda et al, Antonia and Krogstad, Smalley et al, Schultz and Flack and Leonardi et al for boundary layers and Nikuradse, Shockling and Bakken for pipes/Channels) provide strong support to the new scaling for log and power laws. Moody type diagram for inflectional roughness for boundary layer and pipe flows are presented.
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.
Scaling laws of aquatic locomotion
NASA Astrophysics Data System (ADS)
Sun, BoHua
2017-10-01
In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion C D( Re)2 = ( Sw)2 and its corresponding log law and power law. For power scaling law, ( Sw)2 = β n Re 2-1/ n , which is valid within the full spectrum of the Reynolds number Re = UL/ν from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw = ωAL/ν as Re ∝ ( Sw)σ, with σ = 2 for creeping flows, σ = 4=3 for laminar flows, σ = 10=9 and σ = 14=13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(ln Re+1:287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer's gait A; ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number
Experimental scaling law for the subcritical transition to turbulence in plane Poiseuille flow.
Lemoult, Grégoire; Aider, Jean-Luc; Wesfreid, José Eduardo
2012-02-01
We present an experimental study of the transition to turbulence in a plane Poiseuille flow. Using a well-controlled perturbation, we analyze the flow by using extensive particle image velocimetry and flow visualization (using laser-induced fluorescence) measurements, and use the deformation of the mean velocity profile as a criterion to characterize the state of the flow. From a large parametric study, four different states are defined, depending on the values of the Reynolds number and the amplitude of the perturbation. We discuss the role of coherent structures, such as hairpin vortices, in the transition. We find that the minimal amplitude of the perturbation triggering transition scales asymptotically as Re(-1).
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.
Energy loss as the origin of a universal scaling law of the elliptic flow
NASA Astrophysics Data System (ADS)
Andrés, Carlota; Braun, Mikhail; Pajares, Carlos
2017-03-01
It is shown that the excellent scaling of the elliptic flow found for all centralities, species and energies from RHIC to the LHC for pT less than the saturation momentum is a consequence of the energy lost by a parton interacting with the color field produced in a nucleus-nucleus collision. In particular, the deduced shape of the scaling curve describes correctly all the data. We discuss the possible extensions to higher pT, proton-nucleus and proton-proton collisions as well as higher harmonics.
Scaling laws for homogeneous turbulent shear flows in a rotating frame
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Mhuiris, Nessan Macgiolla
1988-01-01
The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.
2007-01-01
Poiseuille flow . These studies complement our earlier drag-driven structure simulations and analyses. We use the mesoscopic Doi-Marrucci-Greco model...pressure-driven, capillary Poiseuille flow . These studies complement our earlier drag-driven structure simulations and analyses. We use the mesoscopic Doi... Simulations of liquid crystals in Poiseuille flow ,” Computational and Theoretical Polymer Science 11, 389-395 (2001). [10] Doi, M., Edwards, S.F., The Theory of
Instability onset and scaling laws of an auto-oscillating turbulent flow in a complex plasma
NASA Astrophysics Data System (ADS)
Schwabe, M.; Zhdanov, S.; Räth, C.
2017-04-01
We study a complex plasma under microgravity conditions that is first stabilized with an oscillating electric field. Once the stabilization is stopped, the so-called heartbeat instability develops. We study how the kinetic energy spectrum changes during and after the onset of the instability and compare with the double cascade predicted by Kraichnan and Leith for two-dimensional turbulence. The onset of the instability manifests clearly in the ratio of the reduced rates of cascade of energy and enstrophy and in the power-law exponents of the energy spectra.
Scaling laws in cognitive sciences.
Kello, Christopher T; Brown, Gordon D A; Ferrer-I-Cancho, Ramon; Holden, John G; Linkenkaer-Hansen, Klaus; Rhodes, Theo; Van Orden, Guy C
2010-05-01
Scaling laws are ubiquitous in nature, and they pervade neural, behavioral and linguistic activities. A scaling law suggests the existence of processes or patterns that are repeated across scales of analysis. Although the variables that express a scaling law can vary from one type of activity to the next, the recurrence of scaling laws across so many different systems has prompted a search for unifying principles. In biological systems, scaling laws can reflect adaptive processes of various types and are often linked to complex systems poised near critical points. The same is true for perception, memory, language and other cognitive phenomena. Findings of scaling laws in cognitive science are indicative of scaling invariance in cognitive mechanisms and multiplicative interactions among interdependent components of cognition.
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.
Intraspecific scaling laws of vascular trees.
Huo, Yunlong; Kassab, Ghassan S
2012-01-07
A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volume-diameter and flow-length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter-length, flow-diameter and flow-volume scaling laws. The intraspecific scaling predicts the volume-diameter power relation with a theoretical exponent of 3, which is validated by the experimental measurements for the three major coronary arterial trees in swine (where a least-squares fit of these measurements has exponents of 2.96, 3 and 2.98 for the left anterior descending artery, left circumflex artery and right coronary artery trees, respectively). This scaling law as well as others agrees very well with the measured morphometric data of vascular trees in various other organs and species. This study is fundamental to the understanding of morphological and haemodynamic features in a biological vascular tree and has implications for vascular disease.
NASA Astrophysics Data System (ADS)
Guo, H.; Huang, Q. M.; Liu, P. Q.; Feng, T.
2015-08-01
The effects of localized unsteady ejection by synthetic jet with slot-type exit on a turbulent boundary layer at zero pressure gradient conditions were investigated downstream of the slot using hot-wire anemometry. This work is to investigate the influence of unsteady disturbance on turbulent structures at small scales, i.e., in the isotropy recovery range (IRR) and the shear-dominated range (SDR). In the near-slot region, our results show that IRR is extended and SDR is shortened for the perturbed flow in the near-wall region, which contributes to the decrease in anisotropy and intermittency. For the perturbed flow, only one scaling behavior of the longitudinal structure functions similar to the classical Kolmogorov-like scaling is observed in IRR.
Baert, Jonathan; Kinet, Romain; Brognaux, Alison; Delepierre, Anissa; Telek, Samuel; Sørensen, Søren J; Riber, Leise; Fickers, Patrick; Delvigne, Frank
2015-08-01
Noise in gene and protein expression is a major cause for bioprocess deviation. However, this phenomenon has been only scarcely considered in real bioprocessing conditions. In this work, a scaling-law derived from genome-scale studies based on GFP reporter systems has been calibrated to an on-line flow cytometry device, allowing thus to get an insight at the level of promoter activity and associated noise during a whole microbial culture carried out in bioreactor. We show that most of the GFP reporter systems investigated and thus corresponding genes could be included inside the area covered by the scaling-law. The experimental results suggest that this scaling-law could be used to predict the dynamics of promoter activity, as well as the associated noise, in bioprocessing conditions. The knowledge acquired throughout this work could be used for the design of more robust expression systems. Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Constructing cities, deconstructing scaling laws.
Arcaute, Elsa; Hatna, Erez; Ferguson, Peter; Youn, Hyejin; Johansson, Anders; Batty, Michael
2015-01-06
Cities can be characterized and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al. have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realizations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide us enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size, regardless of the definition of the urban boundaries. However, when nonlinear correlations are present, the exponent fluctuates considerably.
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.
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 laws of coronary circulation in health and disease.
Huo, Yunlong; Kassab, Ghassan S
2016-08-16
The heterogeneity and complexity of coronary vasculature (structure) and myocardial flow (function) have fractal-like characteristics and can be described by scaling laws with remarkable simplicity. In contrast with allometric (interspecific) scaling law, intraspecific scaling laws describe the design rules of vascular trees within a species. This paper provides an overview of intraspecific scaling laws of vascular trees and the physiological and clinical implications thereof. The significance and shortcomings of these scaling laws are discussed in relation to diffuse coronary artery disease, Glagov's positive remodeling in early stages of coronary atherosclerosis, treatment guidelines of complex bifurcation lesions, and for estimation of outlet resistance values for computation of blood flow in epicardial coronary arteries. Finally, we summarize the highlights of scaling relations and suggest some future directions.
Fundamental Scaling Laws in Nanophotonics.
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.
Fundamental Scaling Laws in Nanophotonics
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
Scaling laws for radial foil bearings
NASA Astrophysics Data System (ADS)
Honavara Prasad, Srikanth
The effects of fluid pressurization, structural deformation of the compliant members and heat generation in foil bearings make the design and analysis of foil bearings very complicated. The complex fluid-structural-thermal interactions in foil bearings also make modeling efforts challenging because these phenomena are governed by highly non-linear partial differential equations. Consequently, comparison of various bearing designs require detailed calculation of the flow fields (velocities, pressures), bump deflections (structural compliance) and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile etc.,) resulting in extensive computational effort (time/hardware). To obviate rigorous computations and aid in feasibility assessments of foil bearings of various sizes, NASA developed the "rule of thumb" design guidelines for estimation of journal bearing load capacity. The guidelines are based on extensive experimental data. The goal of the current work is the development of scaling laws for radial foil bearings to establish an analytical "rule of thumb" for bearing clearance and bump stiffness. The use of scale invariant Reynolds equation and experimentally observed NASA "rule of thumb" yield scale factors which can be deduced from first principles. Power-law relationships between: a. Bearing clearance and bearing radius, and b. bump stiffness and bearing radius, are obtained. The clearance and bump stiffness values obtained from scaling laws are used as inputs for Orbit simulation to study various cases. As the clearance of the bearing reaches the dimensions of the material surface roughness, asperity contact breaks the fluid film which results in wear. Similarly, as the rotor diameter increases (requiring larger bearing diameters), the load capacity of the fluid film should increase to prevent dry rubbing. This imposes limits on the size of the rotor diameter and consequently bearing diameter. Therefore, this thesis aims
Scaling laws in magnetohydrodynamic turbulence
Campanelli, Leonardo
2004-10-15
We analyze the decay laws of the kinetic and magnetic energies and the evolution of correlation lengths in freely decaying incompressible magnetohydrodynamic (MHD) turbulence. Scale invariance of MHD equations assures that, in the case of constant dissipation parameters (i.e., kinematic viscosity and resistivity) and null magnetic helicity, the kinetic and magnetic energies decay in time as E{approx}t{sup -1}, and the correlation lengths evolve as {xi}{approx}t{sup 1/2}. In the helical case, assuming that the magnetic field evolves towards a force-free state, we show that (in the limit of large magnetic Reynolds number) the magnetic helicity remains constant, and the kinetic and magnetic energies decay as E{sub v}{approx}t{sup -1} and E{sub B}{approx}t{sup -1/2} respectively, while both the kinetic and magnetic correlation lengths grow as {xi}{approx}t{sup 1/2}.
Scaling Laws for Mesoscale and Microscale Systems
Spletzer, Barry
1999-08-23
The set of laws developed and presented here is by no means exhaustive. Techniques have been present to aid in the development of additional scaling laws and to combine these and other laws to produce additional useful relationships. Some of the relationships produced here have yielded perhaps surprising results. Examples include the fifth order scaling law for electromagnetic motor torque and the zero order scaling law for capacitive motor power. These laws demonstrate important facts about actuators in small-scale systems. The primary intent of this introduction into scaling law analysis is to provide needed tools to examine possible areas of the research in small-scale systems and direct research toward more fruitful areas. Numerous examples have been included to show the validity of developing scaling laws based on first principles and how real world systems tend to obey these laws even when many other variables may potentially come into play. Development of further laws may well serve to provide important high-level direction to the continued development of small-scale systems.
Ohm's Law, Fick's Law, Joule's Law, and Ground Water Flow
Narasimhan, T.N.
1999-02-01
Starting from the contributions of Ohm, Fick and Joule during the nineteenth century, an integral expression is derived for a steady-state groundwater flow system. In general, this integral statement gives expression to the fact that the steady-state groundwater system is characterized by two dependent variables, namely, flow geometry and fluid potential. As a consequence, solving the steady-state flow problem implies the finding of optimal conditions under which flow geometry and the distribution of potentials are compatible with each other, subject to the constraint of least action. With the availability of the digital computer and powerful graphics software, this perspective opens up possibilities of understanding the groundwater flow process without resorting to the traditional differential equation. Conceptual difficulties arise in extending the integral expression to a transient groundwater flow system. These difficulties suggest that the foundations of groundwater hydraulics deserve to be reexamined.
Scaling laws for coastal overwash morphology
NASA Astrophysics Data System (ADS)
Lazarus, Eli D.
2016-12-01
Overwash is a physical process of coastal sediment transport driven by storm events and is essential to landscape resilience in low-lying barrier environments. This work establishes a comprehensive set of scaling laws for overwash morphology: unifying quantitative descriptions with which to compare overwash features by their morphological attributes across case examples. Such scaling laws also help relate overwash features to other morphodynamic phenomena. Here morphometric data from a physical experiment are compared with data from natural examples of overwash features. The resulting scaling relationships indicate scale invariance spanning several orders of magnitude. Furthermore, these new relationships for overwash morphology align with classic scaling laws for fluvial drainages and alluvial fans.
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.
Scaling laws of human interaction activity.
Rybski, Diego; Buldyrev, Sergey V; Havlin, Shlomo; Liljeros, Fredrik; Makse, Hernán A
2009-08-04
Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.
RFQ scaling-law implications and examples
Wadlinger, E.A.
1986-01-01
We demonstrate the utility of the RFQ scaling laws that have been previously derived. These laws are relations between accelerator parameters (electric field, fr frequency, etc.) and beam parameters (current, energy, emittance, etc.) that act as guides for designing radio-frequency quadrupoles (RFQs) by showing the various tradeoffs involved in making RFQ designs. These scaling laws give a unique family of curves, at any given synchronous particle phase, that relates the beam current, emittance, particle mass, and space-charge tune depression with the RFQ frequency and maximum vane-tip electric field when assuming equipartitioning and equal longitudinal and transverse tune depressions. These scaling curves are valid at any point in any given RFQ where there is a bunched and equipartitioned beam. We show several examples for designing RFQs, examine the performance characteristics of an existing device, and study various RFQ performance limitations required by the scaling laws.
Scaling laws predict global microbial diversity
Locey, Kenneth J.; Lennon, Jay T.
2016-01-01
Scaling laws underpin unifying theories of biodiversity and are among the most predictively powerful relationships in biology. However, scaling laws developed for plants and animals often go untested or fail to hold for microorganisms. As a result, it is unclear whether scaling laws of biodiversity will span evolutionarily distant domains of life that encompass all modes of metabolism and scales of abundance. Using a global-scale compilation of ∼35,000 sites and ∼5.6⋅106 species, including the largest ever inventory of high-throughput molecular data and one of the largest compilations of plant and animal community data, we show similar rates of scaling in commonness and rarity across microorganisms and macroscopic plants and animals. We document a universal dominance scaling law that holds across 30 orders of magnitude, an unprecedented expanse that predicts the abundance of dominant ocean bacteria. In combining this scaling law with the lognormal model of biodiversity, we predict that Earth is home to upward of 1 trillion (1012) microbial species. Microbial biodiversity seems greater than ever anticipated yet predictable from the smallest to the largest microbiome. PMID:27140646
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
Fluctuation scaling, Taylor's law, and crime.
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.
A power law approach to orifice flow rate calibration.
Rhinehart, R Russell; Gebreyohannes, Solomon; Sridhar, Upasana Manimegalai; Patrachari, Anirudh; Rahaman, M S
2011-04-01
Although standards for orifice flow meter design, installation, and calibration are supported herein, noncompliant devices exist in many pilot-, lab-scale, and on-board applications. For these, a common calibration practice is to preserve the ideal square root relation and determine a device specific discharge coefficient value. This work provides theoretical and empirical analyses to support relaxing the square root relation between orifice pressure drop and flow rate for noncompliant devices. The resulting power law relation is shown to improve accuracy, precision, and rangeability. Whether a device specific square root or power law model is used, it requires off-line or in-line calibration data. As such, a power law calibration model may only be useful for on-board and small-scale applications.
Empirical scaling laws for coronal heating
NASA Technical Reports Server (NTRS)
Golub, L.
1983-01-01
The origins and uses of scaling laws in studies of stellar outer atmospheres are reviewed with particular emphasis on the properties of coronal loops. Some evidence is presented for a fundamental structuring of the solar corona and the thermodynamics of scaling laws are discussed. It is found that magnetic field-related scaling laws can be obtained by relating coronal pressure, temperature, and magnetic field strength. Available data validate this method. Some parameters of the theory, however, must be treated as adjustable, and it is considered necessary to examine data from other stars in order to determine the validity of the parameters. Using detailed observational data, the applicability of single loop models is examined.
Empirical scaling laws for coronal heating
NASA Technical Reports Server (NTRS)
Golub, L.
1983-01-01
The origins and uses of scaling laws in studies of stellar outer atmospheres are reviewed with particular emphasis on the properties of coronal loops. Some evidence is presented for a fundamental structuring of the solar corona and the thermodynamics of scaling laws are discussed. It is found that magnetic field-related scaling laws can be obtained by relating coronal pressure, temperature, and magnetic field strength. Available data validate this method. Some parameters of the theory, however, must be treated as adjustable, and it is considered necessary to examine data from other stars in order to determine the validity of the parameters. Using detailed observational data, the applicability of single loop models is examined.
Scaling law of velocity and conductivity in EK turbulence
NASA Astrophysics Data System (ADS)
Zhao, Wei; Yang, Fang; Wang, Guiren
2014-11-01
In microfluidics, when electrokinetic (EK) flow is applied with sufficiently high electric Rayleigh number (Rae) , turbulence can be achieved, and there can even be an universal equilibrium range of conductivity field. In this flow, a new scaling law region of velocity and conductivity structures where the energy cascade is dominated by electric body force (EBF) can be found. This is similar to the Bolgiano-Obukhov scaling law (BO59) in Rayleigh-Bénard (RB) convection. By both directly analyzing Navier-Stokes (N-S) equation and dimensional analysis, the scaling exponent of the second order moment of velocity structure function is 2/5, while that of conductivity structures is 4/5. Compared to the buoyancy in RB convection which decreases with decreasing length scale, EBF actually increases with decreasing spatial scales. This leads to two different microscales depending on the strength of EBF. The scaling law of velocity fluctuation is verified experimentally in a micro-EK turbulent flow. Although due to the restriction of geometry of our microchannel, the bandwidth of the EBF dominant subrange is narrow. By adjusting Rae and other parameters, a wider EBF dominant subrange is predicable. The work was supported by NSF under Grant No. CAREER CBET-0954977 and MRI CBET-1040227, respectively.
Scaling laws for RFQ design procedures
Wadlinger, E.A.
1985-01-01
Scaling laws are relations between accelerator parameters (electric field, rf wavelength etc.) and beam parameters (current, energy, emittance, etc.) that define surfaces of constant accelerator performance in parameter space. These scaling laws can act as guides for designing radio-frequency quadrupoles (RFQs). We derive several scaling relations to show the various tradeoffs involved in choosing RFQ designs and to provide curves to help choose starting points in parameter space for optimizing an RFQ for a particular requirement. We show that there is a unique scaling curve, at a synchronous particle phase of /sup -/90/sup 0/, that relates the beam current, emittance, particle mass, and space-charge tune depression with the RFQ frequency and maximum vane-tip electric field, provided that we assume equipartitioning and equal longitudinal and transverse tune depressions. This scaling curve indicates the maximum performance limit one can expect at any point in any given RFQ. We show several examples for designing RFQs using this procedure.
Scaling laws for iceberg calving
NASA Astrophysics Data System (ADS)
Åström, Jan; Moore, John
2014-05-01
Over the next century, most additional ocean water will come from ice sheets and glaciers, primarily through calving of ice into the oceans. Calving fluxes are prone to rapid and non-linear variability and therefore have proven difficult to include in models forced by evolving climatic variables. Theoretical and simulation first-principles fracture models are applied to investigating iceberg calving. We demonstrate that calving originates from general behaviour of unstable cracks in elastic media. Cracks in ice trigger calving events that have a striking statistical similarity to avalanches in Abelian sand-pile models. That is, both calving mass distribution and inter-event waiting times are similar to those of sand-pile models. The theoretical results are confirmed by a first-principles simulation model and field observations spanning 12 orders of magnitude in calving size. This suggests that calving termini are self-organized critical systems, hence the difficulty to parameterize calving in large-scale models. Subtle deviation from a critical point towards higher stability will lead to subcritical calving - small and infrequent calving events associated with glacier advance, while subtle deviation towards higher instability will lead to supercritical calving - larger and more frequent events associated with rapid retreat. Such behaviour is consistent with recent worldwide observations of ice shelf disintegration and irreversible tidewater glacier retreat in response to climate warming.
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.
Temperature Scaling Law for Quantum Annealing Optimizers
NASA Astrophysics Data System (ADS)
Albash, Tameem; Martin-Mayor, Victor; Hen, Itay
2017-09-01
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.
Scaling Laws in Supramolecular Polymer Networks
Xu, Donghua; Craig, Stephen L.
2011-01-01
The linear rheological properties of networks formed by adding bis-Pd(II) cross-linkers to poly(4-vinylpyridine) (PVP) solution are examined, and the scaling law relationships between the zero shear viscosity (η0) of the networks versus the concentration of PVP solution (CPVP), the concentration of cross-linkers (CX), and the number density of elastically active chains (vphantom) are experimentally determined. The scaling law relationships are compared to the theoretical expectations of the Sticky Rouse and Sticky Reptation models (Macromolecules 2001, 34, 1058-1068), and both qualitative and quantitative differences are observed. PMID:21765553
Scaling laws for electromagnetic pulsed plasma thrusters
NASA Astrophysics Data System (ADS)
Ziemer, J. K.; Choueiri, E. Y.
2001-08-01
The scaling laws of pulsed plasma thrusters operating in the predominantly electromagnetic acceleration mode (EM-PPT) are investigated theoretically and experimentally using gas-fed pulsed plasma thrusters. A fundamental characteristic velocity that depends on the inductance per unit length and the square root of the capacitance to the initial inductance ratio is identified. An analytical model of the discharge current predicts scaling laws in which the propulsive efficiency is proportional to the EM-PPT performance scaling number, defined here as the ratio of the exhaust velocity to the EM-PPT characteristic velocity. The importance of the effective plasma resistance in improving the propulsive performance is shown. To test the validity of the predicted scaling relations, the performance of two gas-fed pulsed plasma thruster designs (one with coaxial electrodes and the other with parallel-plate electrodes), was measured under 70 different operating conditions using an argon plasma. The measurements demonstrate that the impulse bit scales linearly with the integral of the square of the discharge current as expected for an electromagnetic accelerator. The measured performance scaling is shown to be in good agreement with the theoretically predicted scaling. Normalizing the exhaust velocity and the impulse-to-energy ratio by the EM-PPT characteristic velocity collapses almost all the measured data onto single curves that uphold the general validity of these scaling laws. [12pt]This paper is dedicated to the memory of Dr Daniel Birx
Power laws and fragility in flow networks☆
Shore, Jesse; Chu, Catherine J.; Bianchi, Matt T.
2015-01-01
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence. PMID:26082568
Zipf's law from scale-free geometry
NASA Astrophysics Data System (ADS)
Lin, Henry W.; Loeb, Abraham
2016-03-01
The spatial distribution of people exhibits clustering across a wide range of scales, from household (˜10-2km ) to continental (˜104km ) scales. Empirical data indicate simple power-law scalings for the size distribution of cities (known as Zipf's law) and the population density fluctuations as a function of scale. Using techniques from random field theory and statistical physics, we show that these power laws are fundamentally a consequence of the scale-free spatial clustering of human populations and the fact that humans inhabit a two-dimensional surface. In this sense, the symmetries of scale invariance in two spatial dimensions are intimately connected to urban sociology. We test our theory by empirically measuring the power spectrum of population density fluctuations and show that the logarithmic slope α =2.04 ±0.09 , in excellent agreement with our theoretical prediction α =2 . The model enables the analytic computation of many new predictions by importing the mathematical formalism of random fields.
Scaling Laws of Solar and Stellar Flares
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.; Stern, Robert A.; Güdel, Manuel
2008-01-01
In this study we compile for the first time comprehensive data sets of solar and stellar flare parameters, including flare peak temperatures Tp, flare peak volume emission measures EMp, and flare durations τf from both solar and stellar data, as well as flare length scales L from solar data. Key results are that both the solar and stellar data are consistent with a common scaling law of EMp propto T4.7p, but the stellar flares exhibit ≈250 times higher emission measures (at the same flare peak temperature). For solar flares we observe also systematic trends for the flare length scale L(Tp) propto T0.9p and the flare duration τF(Tp) propto T0.9p as a function of the flare peak temperature. Using the theoretical RTV scaling law and the fractal volume scaling observed for solar flares, i.e., V(L) propto L2.4, we predict a scaling law of EMp propto T4.3p, which is consistent with observations, and a scaling law for electron densities in flare loops, np propto T2p/L propto T1.1p. The RTV-predicted electron densities were also found to be consistent with densities inferred from total emission measures, np = (EMp/qVV)1/2, using volume filling factors of qV = 0.03-0.08 constrained by fractal dimensions measured in solar flares. Solar and stellar flares are expected to have similar electron densities for equal flare peak temperatures Tp, but the higher emission measures of detected stellar flares most likely represent a selection bias of larger flare volumes and higher volume filling factors, due to low detector sensitivity at higher temperatures. Our results affect also the determination of radiative and conductive cooling times, thermal energies, and frequency distributions of solar and stellar flare energies.
NASA Technical Reports Server (NTRS)
Nikuradse, J
1950-01-01
An experimental investigation is made of the turbulent flow of water in pipes with various degrees of relative roughness. The pipes range in size from 25 to 100 millimeters in diameter and from 1800 to 7050 millimeters in length. Flow velocities permitted Reynolds numbers from about 10 (sup. 4) to 10 (sup. 6). The laws of resistance and velocity distributions were obtained as a function of relative roughness and Reynolds number. Mixing length, as described by Prandtl's mixing-length formula, is discussed in relation to the experimental results.
Scaling laws for implicit viscosities in smoothed particle hydrodynamics
NASA Astrophysics Data System (ADS)
Bierwisch, Claas; Polfer, Pit
2017-06-01
Smoothed particle hydrodynamics (SPH) is a particle-based method which solves continuum equations such as the Navier-Stokes equations. A periodic fluidic system under homogeneous shear is studied using SPH in the present work. The total pressure of the system and the shear stress contributions from the SPH interaction terms for pressure and viscosity as well as the contribution caused by velocity fluctuations are analyzed. It is found that the pressure and the shear stress contributions obey certain scaling laws depending on physical properties of the system such as compressibility, viscosity and shear rate as well as the spatial resolution. Some of the identified relations resemble scaling laws for the rheology of dense granular flows. These findings render an assessment of the convergence with respect to the spatial resolution of SPH simulations possible. Furthermore, the similarities between numerical SPH particles and physical grains in dense flow provide a deeper understanding of the nature of the SPH method.
Scaling laws of vascular trees: of form and function.
Kassab, Ghassan S
2006-02-01
The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steady-state conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.
Scaling laws from geomagnetic time series
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.
Scaling Laws for Hydrodynamically Equivalent Implosions
NASA Astrophysics Data System (ADS)
Murakami, Masakatsu
2001-10-01
The EPOC (equivalent physics of confinement) scenario for the proof of principle of high gain inertial confinement fusion is presented, where the key concept "hydrodynamically equivalent implosions" plays a crucial role. Scaling laws on the target and confinement parameters are derived by applying the Lie group analysis to the PDE (partially differential equations) chain of the hydrodynamic system. It turns out that the conventional scaling law based on adiabatic approximation significantly differs from one which takes such energy transport effect as electron heat conduction into account. Confinement plasma parameters of the hot spot such as the central temperature and the areal mass density at peak compression are obtained with a self-similar solution for spherical implosions.
Scaling laws in adsorption on bivariate surfaces.
Bulnes, F; Ramirez-Pastor, A J; Zgrablich, G
2002-03-01
The adsorption of particles with nearest-neighbor attractive and repulsive interactions is studied through Monte Carlo simulation on bivariate surfaces characterized by patches of weak and strong adsorbing sites of size l. Patches are considered to have either a square or a strip geometry and they can be either arranged in a deterministic ordered structure or in a random way. Quantities are identified that scale obeying power laws as a function of the scale length l. The consequences of this finding are discussed for the determination of the energetic topography of the surface from adsorption measurements.
Scaling law in carbon nanotube electromechanical devices.
Lefèvre, R; Goffman, M F; Derycke, V; Miko, C; Forró, L; Bourgoin, J P; Hesto, P
2005-10-28
We report a method for probing electromechanical properties of multiwalled carbon nanotubes (CNTs). This method is based on atomic force microscopy measurements on a doubly clamped suspended CNT electrostatically deflected by a gate electrode. We measure the maximum deflection as a function of the applied gate voltage. Data from different CNTs scale into an universal curve within the experimental accuracy, in agreement with a continuum model prediction. This method and the general validity of the scaling law constitute a very useful tool for designing actuators and in general conducting nanowire-based nanoelectromechanical systems.
Scaling law of Wolff cluster surface energy
NASA Astrophysics Data System (ADS)
Hsiao, Pai-Yi; Monceau, Pascal
2003-05-01
We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension 1
A Surprising New Take on Scaling Laws
NASA Astrophysics Data System (ADS)
Martens, Petrus C.
2006-06-01
I have derived analytical solutions for the 1D energy equation for static solar coronal loops for a set of heating functions parametrized as power-laws. This formalism yields a large set of solutions including loops that are mainly heated at the footpoints, at the looptop, and uniformly. I found that the analytical solutions are indistinguishable from numerical solutions produced the MSU 1D hydro-code.I also find that there is very little difference between the temperature profiles for these very different heating functions. A surprising result is though that the constant of proportionality in the classic RTV scaling law (PL T^3) depends strongly on the heating function used, yielding a potential diagnostic for the type of heating function at work in the solar corona -- assuming most loops have the same heating profile. Loops heated at the base have a large constant of proportionality, leading to overdense loops compared to the case of uniform heating, and v.v. for loops heated at the top -- an effect that had already been noticed in numerical solutions but has been inaccurately been interpreted as a violation of the scaling law.This work is supported by NASA Grant NAS5-38099 for the Transition Region and Coronal Explorer, and NNG04EA00C for the Atmospheric Imaging Assembly through subcontracts with Lockheed-Martin Solar and Astrophysics Lab.
General wave optics propagation scaling law.
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.
Correlations and scaling laws in human mobility.
Wang, Xiang-Wen; Han, Xiao-Pu; Wang, Bing-Hong
2014-01-01
In recent years, several path-breaking findings on human mobility patterns point out a novel issue which is of important theoretical significance and great application prospects. The empirical analysis of the data which can reflect the real-world human mobility provides the basic cognition and verification of the theoretical models and predictive results on human mobility. One of the most noticeable findings in previous studies on human mobility is the wide-spread scaling anomalies, e.g. the power-law-like displacement distributions. Understanding the origin of these scaling anomalies is of central importance to this issue and therefore is the focus of our discussion. In this paper, we empirically analyze the real-world human movements which are based on GPS records, and observe rich scaling properties in the temporal-spatial patterns as well as an abnormal transition in the speed-displacement patterns together with an evidence to the real-world traffic jams. In addition, we notice that the displacements at the population level show a significant positive correlation, indicating a cascading-like nature in human movements. Furthermore, our analysis at the individual level finds that the displacement distributions of users with stronger correlations usually are closer to the power law, suggesting a correlation between the positive correlation of the displacement series and the form of an individual's displacement distribution. These empirical findings make connections between the two basic properties of human mobility, the scaling anomalies on displacement distributions and the positive correlations on displacement series, implying the cascading-like dynamics which is exhibited by the positive correlations would cause the emergence of scaling properties on human mobility patterns. Our findings would inspire further researches on mechanisms and predictions of human mobility.
Correlations and Scaling Laws in Human Mobility
Wang, Xiang-Wen; Han, Xiao-Pu; Wang, Bing-Hong
2014-01-01
Background In recent years, several path-breaking findings on human mobility patterns point out a novel issue which is of important theoretical significance and great application prospects. The empirical analysis of the data which can reflect the real-world human mobility provides the basic cognition and verification of the theoretical models and predictive results on human mobility. One of the most noticeable findings in previous studies on human mobility is the wide-spread scaling anomalies, e.g. the power-law-like displacement distributions. Understanding the origin of these scaling anomalies is of central importance to this issue and therefore is the focus of our discussion. Methodology/Principal Findings In this paper, we empirically analyze the real-world human movements which are based on GPS records, and observe rich scaling properties in the temporal-spatial patterns as well as an abnormal transition in the speed-displacement patterns together with an evidence to the real-world traffic jams. In addition, we notice that the displacements at the population level show a significant positive correlation, indicating a cascading-like nature in human movements. Furthermore, our analysis at the individual level finds that the displacement distributions of users with stronger correlations usually are closer to the power law, suggesting a correlation between the positive correlation of the displacement series and the form of an individual's displacement distribution. Conclusions/Significance These empirical findings make connections between the two basic properties of human mobility, the scaling anomalies on displacement distributions and the positive correlations on displacement series, implying the cascading-like dynamics which is exhibited by the positive correlations would cause the emergence of scaling properties on human mobility patterns. Our findings would inspire further researches on mechanisms and predictions of human mobility. PMID:24454769
The scaling laws of human travel
NASA Astrophysics Data System (ADS)
Brockmann, D.; Hufnagel, L.; Geisel, T.
2006-01-01
The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools. Human travel, for example, is responsible for the geographical spread of human infectious disease. In the light of increasing international trade, intensified human mobility and the imminent threat of an influenza A epidemic, the knowledge of dynamical and statistical properties of human travel is of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive, and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Using a comprehensive data set of over a million individual displacements, we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale-free random walks known as Lévy flights. Second, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails that attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two-parameter continuous-time random walk model to a surprising accuracy, and conclude that human travel on geographical scales is an ambivalent and effectively superdiffusive process.
Scaling law in target-hunting processes
NASA Astrophysics Data System (ADS)
Yang, Shi-Jie
2004-05-01
We study a hunting process for a target, in which the hunter tracks the goal by smelling odors it emits. The odor intensity is supposed to decrease with the diffusion distance. The Monte Carlo experiment is carried out on a two-dimensional square lattice. Having no idea of the location of the target, the hunter determines its moves only by random attempts in each direction. By sorting the searching time in each simulation and introducing a variable x to reflect the sequence of searching times, we obtain a curve with a wide plateau, indicating the most probable time of successfully finding the target. The simulations reveal a scaling law for the searching time versus the distance to the position of the target. The scaling exponent depends on the sensitivity of the hunter. Our model may be a prototype in studying such searching processes as various food-foraging behaviors of wild animals.
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.
NASA Astrophysics Data System (ADS)
Muhammad, Nawaz; Spiers, Chris; De Bresser, Hans; Peach, Colin
2014-05-01
Bischofite exits in the upper crust with its related minerals carnallite, sylvite and halite, and is known as the most ductile material within the halide family of minerals. It is normally extracted from the subsurface by solution mining in underground caverns. Abandonment of the caverns causes the wall rock to creep towards the inside due to overburden stress, which in turn results in subsidence at the surface. In order to allow reliable prediction of the creep of Bischofite at cavern walls, a well-defined flow law is required that can be applied at strain rates at least as low as 10-9 s-1. Such rates are difficult to achieve in the laboratory. We have conducted new, conventional axi-symmetric compression tests on as-received polycrystalline Bischofite samples from natural cores. The experiments have been carried out at near real in situ conditions of temperature and pressure (70oC and 40 MPa, respectively), using a range of strain rates from 10-5 to 10-8 s-1. All experiments were strain rate stepping experiments including stress relaxation after every step down to strain rates of 3×10-9 s-1. In the relaxation part of the experiments, the deformation piston was arrested at fixed position and the stored elastic energy in the sample and in the machine was allowed to relax through plastic deformation of the sample. The measured mechanical data were used to obtain the stress exponent (n) as included in a conventional (Dorn-type) power law. We observed that during the stress relaxation, the n-value gradually changed from n >5 at 10-5 to n ~1 at 10-9 s-1. The absolute strength of the samples remained higher if the relaxation started at a higher stress, i.e. at a faster rate within the range tested. We interpret this as indicating a difference in microstructure at the initiation of the relaxation, notably a smaller grain size related to dynamical recrystallization during the constant strain rate part of the test just before relaxation. The data thus suggest that there
A generalized quadratic flow law for sheet metals
NASA Astrophysics Data System (ADS)
Jones, S. E.; Gillis, P. P.
1984-01-01
A planar quadratic flow law is proposed for anisotropic sheet materials. This law is similar to the anisotropic strength criterion of Tsai and Wu. It has six experimentally determinable coefficients as compared to four in Hill’s flow law and, thus, allows more experimental information to be accommodated. However, the resulting strain increment vector, while unique, is not necessarily normal to the flow surface.
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.
Scaling Law of Urban Ride Sharing
Tachet, R.; Sagarra, O.; Santi, P.; Resta, G.; Szell, M.; Strogatz, S. H.; Ratti, C.
2017-01-01
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. PMID:28262743
Scaling Law of Urban Ride Sharing
NASA Astrophysics Data System (ADS)
Tachet, R.; Sagarra, O.; Santi, P.; Resta, G.; Szell, M.; Strogatz, S. H.; Ratti, C.
2017-03-01
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.
Filament velocity scaling laws for warm ions
Manz, P.; Carralero, D.; Birkenmeier, G.; Müller, H. W.; Scott, B. D.; Müller, S. H.; Fuchert, G.; Stroth, U.
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 relevant limit regimes are given. These are the sheath dissipation, collisional, and electromagnetic regime.
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.
Allometric scaling laws for water uptake by plant roots.
Biondini, Mario
2008-03-07
This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as r approximately volume(2/(8+a))(0scaling for root radius branches (r(i+1)=beta*r(i)) is of the form beta=f(N)((2*epsilon(N))/(8+a)), where f(N)=A(N)/(n(b)*(1+A(N))), n(b) is the number of branches, and A(N) and epsilon(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, beta converges to the beta from the WBE model. For small N, the beta's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.
Universal scaling laws of diffusion: application to liquid metals.
Samanta, Alok; Musharaf Ali, Sk; Ghosh, Swapan K
2005-08-22
This work focuses on the universal scaling laws, which relate scaled diffusivity to excess entropy in fluids and their mixtures. The derivation of the new scaling law for diffusivity proposed recently [A. Samanta, Sk. M. Ali, and S. K. Ghosh, Phys. Rev. Lett. 92, 145901 (2004)] is discussed in details highlighting the nature of approximations involved. Also the applicability of the scaling law is extended to a new class of liquids, viz., liquid metals. The results calculated based on the scaling laws are shown to be in very good agreement with the simulation results for liquid Rb and Cs metals along the liquid-vapor coexistence curve corresponding to a wide variation of temperature and density. The new universal scaling law discussed here is superior to the earlier empirically proposed scaling laws and provides a very simple route to calculate a dynamical quantity such as diffusivity from an equilibrium property such as the radial distribution function.
Scaling laws in magnetized plasma turbulence
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 of 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 solar
Diffusional Scaling Laws in Oscillatory Systems with Stochastic Forcing
NASA Astrophysics Data System (ADS)
Gao, J. B.; Tung, Wen-wen
2003-08-01
Rhythmic motions are ubiquitous in nature and in man-made systems, such as in low Reynolds number wake flows, breathing, and pathological tremors including essential and Parkinsonian. Due to the presence of external noise, those sinusoidal movements are typically only approximately rhythmic, or aperiodic, thus may be interpreted as chaotic. Although existing tests developed for the analysis of chaotic systems may be able to tell some qualitative differences between these stochastically driven oscillatory motions from true chaotic motions, those differences are often not very instructive, because in the study of chaos, one often monitors the motion on fairly short time scales, to be consistent with the one of the key features of chaos—short-term predictability. In this paper, we report a diffusional scaling law for stochastically driven oscillatory motions. By studying a number of measured data such as the fluctuating velocity signals in the near wake of a circular cylinder and pathological tremor data as well as numerically generated data, we shall show that the time scale range for the diffusional scaling law to be valid starts from about one to several tens of the mean oscillation period. Furthermore, we classify the diffusional oscillatory motions into three categories, depending on whether the diffusional exponent less than, equal to, or large than 0.5, and consider the mechanism for each category. It is found that the case with the exponent larger than 0.5 is an anomalous diffusion and is a pre-cursor for noise to induce chaos.
A scaling law beyond Zipf's law and its relation to Heaps' law
NASA Astrophysics Data System (ADS)
Font-Clos, Francesc; Boleda, Gemma; Corral, Álvaro
2013-09-01
The dependence on text length of the statistical properties of word occurrences has long been considered a severe limitation on the usefulness of quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies that brings to light the robustness of this distribution as text grows. In this way, the shape of the distribution is always the same, and it is only a scale parameter that increases (linearly) with text length. By analyzing very long novels we show that this behavior holds both for raw, unlemmatized texts and for lemmatized texts. In the latter case, the distribution of frequencies is well approximated by a double power law, maintaining the Zipf's exponent value γ ≃ 2 for large frequencies but yielding a smaller exponent in the low-frequency regime. The growth of the distribution with text length allows us to estimate the size of the vocabulary at each step and to propose a generic alternative to Heaps' law, which turns out to be intimately connected to the distribution of frequencies, thanks to its scaling behavior.
Scaling law and microstructure of alginate hydrogel.
Liu, Sijun; Li, Huijun; Tang, Bijun; Bi, Shuguang; Li, Lin
2016-01-01
The gelation of alginate in aqueous solution was studied as a function of Ca(2+) concentration. At each given concentration of alginate, a critical gel concentration [Formula: see text] , was successfully determined for the first time using the Winter-Chambon criterion. The critical gel concentration [Formula: see text] was found to increase linearly with alginate concentration. At the same time, the critical relaxation exponent n decreased and the critical gel strength Sg increased linearly with alginate concentration. An improved egg-box model was proposed to describe the change in gel junction and gel network. In the stable gel state, the plateau modulus Ge of alginate gel depended on Ca(2+) concentration according to a power-law scaling, Ge=kɛ(1.5), where ɛ is the relative distance of a gelling variable (Ca(2+) concentration in this case) from the gel point ( [Formula: see text] ). The FESEM images verified the microstructure of alginate gel in which alginate chains associated into fibrils in the presence of Ca(2+) ions. The fibrillar diameter and network density increased with increasing Ca(2+) ion concentration while alginate concentration had a weak influence on fibrillar diameter.
Investigations of scaling laws for jet impingement
NASA Technical Reports Server (NTRS)
Morton, J. B.; Haviland, J. K.; Catalano, G. D.; Herling, W. W.
1976-01-01
The statistical properties of tangential flows over surfaces were investigated by two techniques. In one, a laser-Doppler velocimeter was used in a smoke-laden jet to measure one-point statistical properties, including mean velocities, turbulent intensities, intermittencies, autocorrelations, and power spectral densities. In the other technique, free stream and surface pressure probes connected to 1/8 inch microphones were used to obtain single point rms and 1/3 octave pressures, as well as two point cross correlations, the latter being converted to auto spectra, amplitude ratios, phase lags, and coherences. The results of these studies support the vortex model of jets, give some insights into the effects of surface impingement, and confirm that jet diameter and velocity are the scaling parameters for circular jets, while Reynolds number is relatively unimportant.
Applicability of flow laws to naturally deformed polyphase rocks
NASA Astrophysics Data System (ADS)
Kilian, Rüdiger; Heilbronner, Renée; Stünitz, Holger
2013-04-01
Small scale shear zones formed in the Gran Paradiso metagranodiorite under lower amphibolite facies conditions (~550°C/0.8 GPa LeGoff & Ballevre, 1990; Brouwer et al.,2002). Based on detailed microstructural work the deformation mechanisms of the different rheological phases have been identified. Polycrystalline quartz aggregates deform by dislocation creep (gbm recrystallization), whereas the polymineralic matrix deforms by diffusion creep (Kilian et al., 2011). Iso - stress conditions (Sachs-average) are assumed based on a constant recrystallized quartz grain size and the formation of shear-parallel layers. Deformed quartz aggregates show higher rotation angle / lower aspect ratio relations, little coalescence, and only minor pinch and swell structures, which altogether suggest that quartz represents the more viscous phase in a somewhat lower viscous matrix. At high strain quartz is completely recrystallized and forms parallel layers with the matrix and does not boudinage. Experimental flow laws for quartz and feldspar from the literature as well as the theoretically derived flow law for Coble creep with the appropriate parameters can reproduce the observed relation between quartz aggregates and matrix suggesting a strain rate ratio below 2 orders of magnitude. A comparison of data from different granitic rocks deformed between 450° to ~ 600°C suggests that a combination of a quartz creep law and a Coble creep law can be used for extrapolation at medium grade, natural conditions. These results provide an indication for the range of reasonable flow law parameters and viscosity ratios which are useful for modeling purposes. References: Kilian, R., Heilbronner, R., Stünitz, H. Quartz grain size reduction in a granitoid rock and the transition from dislocation to diffusion creep. JSG 33,1265-1284,2011. LeGoff, E., Ballevre, M. Geothermobarometry in albite-garnet orthogneisses - a case-study from the Gran-Paradiso Nappe (Western Alps). Lithos, 25,261-280,1990. F
NASA Astrophysics Data System (ADS)
Cheng, Wan; Samtaney, Ravi
2013-11-01
We present results of large eddy simulation (LES) for a smooth-wall, zero-pressure-gradient turbulent boundary layer. We employ the stretched vortex sub-grid-scale model in the simulations augmented by a wall model. Our wall model is based on the virtual-wall model introduced by Chung & Pullin (J. Fluid Mech 2009). An essential component of their wall model is an ODE governing the local wall-normal velocity gradient obtained using inner-scaling ansatz. We test two variants of the wall model based on different similarity laws: one is based on a log-law and the other on a power-law. The specific form of the power law scaling utilized is that proposed by George & Castillo (Appl. Mech. Rev. 1997), dubbed the ``GC Law''. Turbulent inflow conditions are generated by a recycling method, and applying scaling laws corresponding to the two variants of the wall model, and a uniform way to determine the inlet friction velocity. For Reynolds number based on momentum thickness, Reθ , ranging from 104 to 1012 it is found that the velocity profiles generally follow the log law form rather than the power law. For large Reynolds number asymptotic behavior, LES based on different scaling laws the boundary layer thickness and turbulent intensities do not show much difference. Supported by a KAUST funded project on large eddy simulation of turbulent flows. The IBM Blue Gene P Shaheen at KAUST was utilized for the simulations.
Gradient Driven Flow: Lattice Gas, Diffusion Equation and Measurement Scales
2001-01-01
03-200 1 Journal Article (refereed) 2001 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Gradient Driven Flow : Lattice Gas, Diffusion Equation and...time regime, the collective motion exhibits an onset of oscillation. 15. SUBJECT TERMS Diffusion; Fick’s Law; Gradient Driven Flow ; Lattice Gas 16...Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39.18 20010907 062 Gradient driven flow : lattice gas, diffusion equation and measurement scales R.B
Origin of Noncubic Scaling Law in Disordered Granular Packing
NASA Astrophysics Data System (ADS)
Xia, Chengjie; Li, Jindong; Kou, Binquan; Cao, Yixin; Li, Zhifeng; Xiao, Xianghui; Fu, Yanan; Xiao, Tiqiao; Hong, Liang; Zhang, Jie; Kob, Walter; Wang, Yujie
2017-06-01
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.
A constitutive law for dense granular flows.
Jop, Pierre; Forterre, Yoël; Pouliquen, Olivier
2006-06-08
A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.
Unified transport scaling laws for plasma blobs and depletions
NASA Astrophysics Data System (ADS)
Wiesenberger, M.; Held, M.; Kube, R.; Garcia, O. E.
2017-06-01
We study the dynamics of seeded plasma blobs and depletions in an (effective) gravitational field. For incompressible flows, the radial center of mass velocity of blobs and depletions is proportional to the square root of their initial cross-field size and amplitude. If the flows are compressible, this scaling holds only for ratios of amplitude to size larger than a critical value. Otherwise, the maximum blob and depletion velocity depends linearly on the initial amplitude and is independent of size. In both cases, the acceleration of blobs and depletions depends on their initial amplitude relative to the background plasma density and is proportional to gravity and independent of their cross-field size. Due to their reduced inertia plasma, depletions accelerate more quickly than the corresponding blobs. These scaling laws are derived from the invariants of the governing drift-fluid equations for blobs and agree excellently with numerical simulations over five orders of magnitude for both blobs and depletions. We suggest an empirical model that unifies and correctly captures the radial acceleration and maximum velocities of both blobs and depletions.
Trajectory and Mixing Scaling Laws for Confined and Unconfined Transverse Jets
2012-06-01
fluidic thrust vectoring. Although this flow has received extensive research attention over several decades, a lack of universality exists regarding...NUMBER 33SP0795 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER ir Force Research...jet and cross flow. An experimental study was conducted and the results indicate the utility of the new scaling law parameter for defining flow
Trajectory and Mixing Scaling Laws for Confined and Unconfined Transverse Jets
2012-06-01
and fluidic thrust vectoring. Although this flow has received extensive research attention over several decades, a lack of universality exists...NUMBER 5f. WORK UNIT NUMBER 33SP0795 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NO. Air Force Research...the jet and cross flow. An experimental study was conducted and the results indicate the utility of the new scaling law parameter for defining flow
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2015-03-01
The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).
CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS
Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.; Duarte, Lucia D. V.
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 analyze 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.
Scaling laws as a tool of materials informatics
NASA Astrophysics Data System (ADS)
Mendez, Patricio F.; Furrer, Reinhard; Ford, Ryan; Ordóñez, Fernando
2008-03-01
This paper discusses the utility of scaling laws to materials informatics and presents the algorithm Scaling LAW (SLAW), useful to obtain scaling laws from statistical data. These laws can be used to extrapolate known materials property data to untested materials by using other more readily available information. This technique is independent of a characteristic length or time scale, so it is useful for a broad diversity of problems. In some cases, SLAW can reproduce the mathematical expression that would have been obtained through an analytical treatment of the problem. This technique was originally designed for mining statistical data in materials processing and materials behavior at a system level, and it shows promise for the study of the relationship between structure and properties in materials.
Global scale groundwater flow model
NASA Astrophysics Data System (ADS)
Sutanudjaja, Edwin; de Graaf, Inge; van Beek, Ludovicus; Bierkens, Marc
2013-04-01
As the world's largest accessible source of freshwater, groundwater plays vital role in satisfying the basic needs of human society. It serves as a primary source of drinking water and supplies water for agricultural and industrial activities. During times of drought, groundwater sustains water flows in streams, rivers, lakes and wetlands, and thus supports ecosystem habitat and biodiversity, while its large natural storage provides a buffer against water shortages. Yet, the current generation of global scale hydrological models does not include a groundwater flow component that is a crucial part of the hydrological cycle and allows the simulation of groundwater head dynamics. In this study we present a steady-state MODFLOW (McDonald and Harbaugh, 1988) groundwater model on the global scale at 5 arc-minutes resolution. Aquifer schematization and properties of this groundwater model were developed from available global lithological model (e.g. Dürr et al., 2005; Gleeson et al., 2010; Hartmann and Moorsdorff, in press). We force the groundwtaer model with the output from the large-scale hydrological model PCR-GLOBWB (van Beek et al., 2011), specifically the long term net groundwater recharge and average surface water levels derived from routed channel discharge. We validated calculated groundwater heads and depths with available head observations, from different regions, including the North and South America and Western Europe. Our results show that it is feasible to build a relatively simple global scale groundwater model using existing information, and estimate water table depths within acceptable accuracy in many parts of the world.
Scaling law for diffusion coefficients in simple melts
NASA Astrophysics Data System (ADS)
Li, G. X.; Liu, C. S.; Zhu, Z. G.
2005-03-01
Employing realistic many-body potentials for a series of simple melts, including Ag, Al, Au, Co, Cu, Mg, Ni, Pb, Pd, Pt, Rh, and Si, we tested by molecular-dynamics simulation the scaling laws of diffusion coefficients with different expressions of the reduction parameters. Our simulation results give sound support to the universal excess entropy scaling laws proposed by Rosenfeld [Phys. Rev. A 15, 2545 (1977)] and Dzugutov [Nature (London) 381, 137 (1996)] for transport coefficients in liquid metals. In particular, we find that excess entropy (Sex) universally scales with temperature as Sex=-ES/T . When the diffusion coefficient is scaled as Dzugutov suggested, ES is essentially identical to the Arrhenius activation energy, indicating that the entropic component in the Arrhenius activation energy is solely responsible for controlling the diffusion rate. Thus, there exists a link between the scaling law and the Arrhenius law, i.e., the excess entropy scaling law for the diffusion coefficient can be interpreted as a straightforward extension of the Arrhenius law.
Asymptotic scaling in turbulent pipe flow.
McKeon, B J; Morrison, J F
2007-03-15
The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an 'inertial sublayer' in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R+>5 x 10(3), approximately, much higher than was generally thought.
Chiral battery, scaling laws and magnetic fields
NASA Astrophysics Data System (ADS)
Anand, Sampurn; Bhatt, Jitesh R.; Pandey, Arun Kumar
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 T2 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 1030 G at T~ 109 GeV, with a typical length scale of the order of 10-18 cm, which is much smaller than the Hubble radius at that temperature (10-8 cm). Moreover, such a system possess scaling symmetry. We show that the T2 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.
Modified Beer-Lambert law for blood flow
Baker, Wesley B.; Parthasarathy, Ashwin B.; Busch, David R.; Mesquita, Rickson C.; Greenberg, Joel H.; Yodh, A. G.
2014-01-01
We develop and validate a Modified Beer-Lambert law for blood flow based on diffuse correlation spectroscopy (DCS) measurements. The new formulation enables blood flow monitoring from temporal intensity autocorrelation function data taken at single or multiple delay-times. Consequentially, the speed of the optical blood flow measurement can be substantially increased. The scheme facilitates blood flow monitoring of highly scattering tissues in geometries wherein light propagation is diffusive or non-diffusive, and it is particularly well-suited for utilization with pressure measurement paradigms that employ differential flow signals to reduce contributions of superficial tissues. PMID:25426330
Modified Beer-Lambert law for blood flow.
Baker, Wesley B; Parthasarathy, Ashwin B; Busch, David R; Mesquita, Rickson C; Greenberg, Joel H; Yodh, A G
2014-11-01
We develop and validate a Modified Beer-Lambert law for blood flow based on diffuse correlation spectroscopy (DCS) measurements. The new formulation enables blood flow monitoring from temporal intensity autocorrelation function data taken at single or multiple delay-times. Consequentially, the speed of the optical blood flow measurement can be substantially increased. The scheme facilitates blood flow monitoring of highly scattering tissues in geometries wherein light propagation is diffusive or non-diffusive, and it is particularly well-suited for utilization with pressure measurement paradigms that employ differential flow signals to reduce contributions of superficial tissues.
Scaling laws for melting ice avalanches.
Turnbull, B
2011-12-16
This Letter describes an investigation of interfacial melting in ice-bearing granular flows. It is proposed that energy associated with granular collisions causes melting at an ice particle's surface, which can thus occur at temperatures well below freezing. A laboratory experiment has been designed that allows quantification of this process and its effect on the dynamics of a granular shear flow of ice spheres. This experiment employs a rotating drum, half filled with ice particles, situated in a temperature controlled laboratory. Capillary forces between the wetted melted particle surfaces lead to the clumping of particles and enhanced flow speeds, in turn leading to further melting. Dimensional analysis defines a parameter space for further experimentation.
Universal Scaling Laws for Dispersion Interactions
Buhmann, Stefan Yoshi; Scheel, Stefan; Babington, James
2010-02-19
We study the scaling behavior of dispersion potentials and forces under very general conditions. We prove that a rescaling of an arbitrary geometric arrangement by a factor a changes the atom-atom and atom-body potentials in the long-distance limit by factors 1/a{sup 7} and 1/a{sup 4}, respectively, and the Casimir force per unit area by 1/a{sup 4}. In the short-distance regime, electric and magnetic bodies lead to different scaling behavior. As applications, we present scaling functions for two atom-body potentials and display the equipotential lines of a plate-assisted two-atom potential.
Meyer, Perry A.; Kurath, Dean E.; Bamberger, Judith A.; Barnes, Steven M.; Etchells, Arthur W.
2006-03-02
The Waste Treatment Plant (WTP) under construction at the Hanford Site will use pulse jet mixer (PJM) technology for mixing and gas retention control applications in tanks expected to contain waste slurries exhibiting a non-Newtonian rheology. This paper presents the results of theoretical and experimental studies undertaken to establish a methodology to perform reduced-scale mixing tests with PJM systems in non-Newtonian fluids. A theoretical model for mixing cavern formation from steady and pulsed jets is developed and compared with data from a single unsteady jet in a yield stress simulant. Dimensional analysis is used to identify the important dimensionless parameters affecting mixing performance in more complex systems. Scaling laws are proposed based on the modeling and dimensional analysis. Experimental validation of the scaling laws governing unsteady jet mixing in non-Newtonian fluids are also presented. Tests were conducted at three scales using two non-Newtonian simulants. The data were compared non-dimensionally, and the important scale laws were confirmed. The key dimensionless parameters were found to be the Strouhal number (which describes unsteady pulse jet mixer operation), the yield Reynolds number (which governs cavern formation due to non-Newtonian fluid behavior), and the viscous Reynolds number (which determines the flow regime and the degree of turbulence). The experimentally validated scaling laws provide the basis for reduced scale testing of prototypic WTP mixing systems. It is argued that mixing systems developed from reduced scale testing will produce conservative designs at full scale.
Current Density Scaling in Electrochemical Flow Capacitors
Hoyt, NC; Wainright, JS; Savinell, RF
2015-02-18
Electrochemical flow capacitors (EFCs) are a recently developed energy storage technology. One of the principal performance metrics of an EFC is the steady-state electrical current density that it can accept or deliver. Numerical models exist to predict this performance for specific cases, but here we present a study of how the current varies with respect to the applied cell voltage, flow rate, cell dimensions, and slurry properties using scaling laws. The scaling relationships are confirmed by numerical simulations and then subsequently by comparison to results from symmetric cell EFC experiments. This modeling approach permits the delimitation of three distinct operational regimes dependent on the values of two nondimensional combinations of the pertinent variables (specifically, a capacitive Graetz number and a conductivity ratio). Lastly, the models and nondimensional numbers are used to provide design guidance in terms of criteria for proper EFC operation. (C) The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. All rights reserved.
Ohm's law survives to the atomic scale.
Weber, B; Mahapatra, S; Ryu, H; Lee, S; Fuhrer, A; Reusch, T C G; Thompson, D L; Lee, W C T; Klimeck, G; Hollenberg, L C L; Simmons, M Y
2012-01-06
As silicon electronics approaches the atomic scale, interconnects and circuitry become comparable in size to the active device components. Maintaining low electrical resistivity at this scale is challenging because of the presence of conﬁning surfaces and interfaces. We report on the fabrication of wires in silicon--only one atom tall and four atoms wide--with exceptionally low resistivity (~0.3 milliohm-centimeters) and the current-carrying capabilities of copper. By embedding phosphorus atoms within a silicon crystal with an average spacing of less than 1 nanometer, we achieved a diameter-independent resistivity, which demonstrates ohmic scaling to the atomic limit. Atomistic tight-binding calculations conﬁrm the metallicity of these atomic-scale wires, which pave the way for single-atom device architectures for both classical and quantum information processing.
A skin friction law for compressible turbulent flow
NASA Technical Reports Server (NTRS)
Barnwell, Richard W.; Wahls, Richard A.
1989-01-01
An algebraic skin friction law is derived for adiabatic, compressible, equilibrium, turbulent boundary layer flow. An outer solution in terms of the Clauser defect stream function is matched to an inner empirical expression composed of compressible laws of the wall and wake. The modified Crocco temperature-velocity relationship and the Clauser eddy viscousity model are used in the outer solution. The skin friction law pertains for all pressure gradients in the incompressible through supersonic range and for small pressure gradients in the hypersonic range. Excellent comparisons with experiment are obtained in the appropriate parameter ranges. The application to numerical computation is discussed.
Modified Beer-Lambert law for blood flow
NASA Astrophysics Data System (ADS)
Baker, Wesley B.; Parthasarathy, Ashwin B.; Busch, David R.; Mesquita, Rickson C.; Greenberg, Joel H.; Yodh, A. G.
2015-03-01
The modified Beer-Lambert law is among the most widely used approaches for analysis of near-infrared spectroscopy (NIRS) reflectance signals for measurements of tissue blood volume and oxygenation. Briefly, the modified Beer-Lambert paradigm is a scheme to derive changes in tissue optical properties based on continuous-wave (CW) diffuse optical intensity measurements. In its simplest form, the scheme relates differential changes in light transmission (in any geometry) to differential changes in tissue absorption. Here we extend this paradigm to the measurement of tissue blood flow by diffuse correlation spectroscopy (DCS). In the new approach, differential changes of the intensity temporal auto-correlation function at a single delay-time are related to differential changes in blood flow. The key theoretical results for measurement of blood flow changes in any tissue geometry are derived, and we demonstrate the new method to monitor cerebral blood flow in a pig under conditions wherein the semi-infinite geometry approximation is fairly good. Specifically, the drug dinitrophenol was injected in the pig to induce a gradual 200% increase in cerebral blood flow, as measured with MRI velocity flow mapping and by DCS. The modified Beer-Lambert law for flow accurately recovered these flow changes using only a single delay-time in the intensity auto-correlation function curve. The scheme offers increased DCS measurement speed of blood flow. Further, the same techniques using the modified Beer-Lambert law to filter out superficial tissue effects in NIRS measurements of deep tissues can be applied to the DCS modified Beer-Lambert law for blood flow monitoring of deep tissues.
Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure.
Gong, Yanjun; Feng, Yundi; Chen, Xudong; Tan, Wenchang; Huo, Yunlong; Kassab, Ghassan S
2016-11-01
It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.
Newton's Third Law on a Scale Balance
ERIC Educational Resources Information Center
Nopparatjamjomras, Suchai; Panijpan, Bhinyo; Huntula, Jiradawan
2009-01-01
We propose a series of experiments involving balance readings of an object naturally floating or forced to be partially or fully immersed in water contained in a beaker sitting on an electronic scale balance. Students were asked to predict, observe and explain each case. The teacher facilitated the learning by asking probing questions, giving…
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)
Newton's Third Law on a Scale Balance
ERIC Educational Resources Information Center
Nopparatjamjomras, Suchai; Panijpan, Bhinyo; Huntula, Jiradawan
2009-01-01
We propose a series of experiments involving balance readings of an object naturally floating or forced to be partially or fully immersed in water contained in a beaker sitting on an electronic scale balance. Students were asked to predict, observe and explain each case. The teacher facilitated the learning by asking probing questions, giving…
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.
Band gap scaling laws in group IV nanotubes
NASA Astrophysics Data System (ADS)
Wang, Chongze; Fu, Xiaonan; Guo, Yangyang; Guo, Zhengxiao; Xia, Congxin; Jia, Yu
2017-03-01
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.
Band gap scaling laws in group IV nanotubes.
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.
Lorentzian symmetry predicts universality beyond scaling laws
NASA Astrophysics Data System (ADS)
Watson, Stephen J.
2017-06-01
We present a covariant theory for the ageing characteristics of phase-ordering systems that possess dynamical symmetries beyond mere scalings. A chiral spin dynamics which conserves the spin-up (+) and spin-down (-) fractions, μ+ and μ- , serves as the emblematic paradigm of our theory. Beyond a parabolic spatio-temporal scaling, we discover a hidden Lorentzian dynamical symmetry therein, and thereby prove that the characteristic length L of spin domains grows in time t according to L = \\fracβ{\\sqrt{1 - σ^2}}t\\frac{1{2}} , where σ:= μ+ - μ- (the invariant spin-excess) and β is a universal constant. Furthermore, the normalised length distributions of the spin-up and the spin-down domains each provably adopt a coincident universal (σ-independent) time-invariant form, and this supra-universal probability distribution is empirically verified to assume a form reminiscent of the Wigner surmise.
Physical Origins of Statistical Scale Invariance or Scaling in Peak Flows in Real River Networks
NASA Astrophysics Data System (ADS)
Mantilla, R.; Gupta, V. K.; Furey, P.
2005-12-01
For nearly forty years, regional flood frequency analyses in unnested and in nested basins have shown that annual peak-flow quantiles can be related to drainage areas as power laws that arise from the property of scale invariance. This empirical feature has instigated a basic hydrologic question: Can power laws be obtained from physical processes governing rainfall-runoff transformations on real channel networks? There has been steady progress in answering this question since 1990. A physical understanding of peak flow scaling requires the time scales of individual rainfall-runoff events as a first step before going to longer time scales. We have used data from two Agriculture Research Service (ARS) experimental basins in the United States to test the physical basis of scaling in peak flows. The first basin is Goodwin Creek in Mississippi (21 km2), and the second one is Walnut Gulch in Arizona (150 km2). We have tested the hypothesis that scaling parameters of individual flood events on Goodwin Creek vary from one event to the next due to the effect of temporal rainfall variability. On the Walnut Gulch, we have tested the hypothesis that scaling in peak flows for short duration rainfall events is controlled by the river network topological and geometric configuration and the downstream hydraulic-geometric properties. Based on these results we present a gauging strategy to investigate peak flow scaling in the 1100 km2 Whitewater basin in Kansas.
Scaling laws in aeolian sand transport
NASA Astrophysics Data System (ADS)
Valance, Alexandre; Ho, Tuan Duc; Ould El Moctar, Ahmed; Dupont, Pascal
2013-04-01
Via wind tunnel experiments on aeolian sand transport, we provide evidences that over an erodible bed the grain velocity in the saltation layer and the saltation length are almost invariant with the wind strength, whereas over a non-erodible bed these quantities vary significantly with the air friction speed. It results that the particle transport rate over an erodible bed does not exhibit a cubic dependence with the air friction speed, as predicted by Bagnold, but a quadratic one. This contrasts with saltation over a non-erodible bed where the cubic Bagnold scaling holds. Our findings emphasize the crucial role of the boundary conditions at the bed and may have important practical consequences for aeolian sand transport in natural environment. Reference: T.D. Ho, A. Valance, P. Dupont and A. Ould El Moctar, Phys. Rev. Lett. 106, 094501 (2011).
Scaling and power-laws in ecological systems.
Marquet, Pablo A; Quiñones, Renato A; Abades, Sebastian; Labra, Fabio; Tognelli, Marcelo; Arim, Matias; Rivadeneira, Marcelo
2005-05-01
Scaling relationships (where body size features as the independent variable) and power-law distributions are commonly reported in ecological systems. In this review we analyze scaling relationships related to energy acquisition and transformation and power-laws related to fluctuations in numbers. Our aim is to show how individual level attributes can help to explain and predict patterns at the level of populations that can propagate at upper levels of organization. We review similar relationships also appearing in the analysis of aquatic ecosystems (i.e. the biomass spectra) in the context of ecological invariant relationships (i.e. independent of size) such as the 'energetic equivalence rule' and the 'linear biomass hypothesis'. We also discuss some power-law distributions emerging in the analysis of numbers and fluctuations in ecological attributes as they point to regularities that are yet to be integrated with traditional scaling relationships and which we foresee as an exciting area of future research.
Scaling range of power laws that originate from fluctuation analysis.
Grech, Dariusz; Mazur, Zygmunt
2013-05-01
We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R^{2} of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.
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.
The linewidth-size scaling law of molecular gas revisited
NASA Astrophysics Data System (ADS)
Falgarone, Edith; McKee, Christopher F.
The origin of the linewidth-size (LWS) scaling law, first noticed by Larson three decades ago and ascribed to turbulence, is still a highly debated issue. Not unexpectedly, its properties depend on the environment and on the line tracer used. When the optically thick 12CO (J=1-0) line is used, a specific medium is sampled: the translucent molecular gas of moderate density that builds up the bulk of the molecular interstellar medium in galaxies like the Milky Way. The sensitivity of the 12CO line to this gas is such that the LWS is found to hold over almost five orders of magnitude in lengthscale, although with a considerable scatter (+/- 0.5 dex). It also appears to split into two regimes, depending on the gas mass surface density: below a given threshold that is proposed to be linked to the galactic structure, it bears the signature of a turbulent cascade, while above it, the scaling law is ascribed to virial balance. Large deviations from the LWS scaling law are observed at small scales where signatures of turbulent intermittency appear. The mass-size scaling law built with the 12CO (J=1-0) line also splits into two regimes. The mass surface density is uniform (also with a large scatter) above lengthscales ~ 10pc and increases with size at smaller scales, following turbulence predictions. The two thresholds define an average gas density n H ~ 300 cm-3.
Universal scaling law of electrical turbulence in the mammalian heart
Noujaim, Sami F.; Berenfeld, Omer; Kalifa, Jérôme; Cerrone, Marina; Nanthakumar, Kumaraswamy; Atienza, Felipe; Moreno, Javier; Mironov, Sergey; Jalife, José
2007-01-01
Many biological processes, such as metabolic rate and life span, scale with body mass (BM) according to the universal law of allometric scaling: Y = aBMb (Y, biological process; b, scaling exponent). We investigated whether the temporal properties of ventricular fibrillation (VF), the major cause of sudden and unexpected cardiac death, scale with BM. By using high-resolution optical mapping, numerical simulations and metaanalysis of VF data in 11 mammalian species, we demonstrate that the interbeat interval of VF scales as VFcycle length = 53 × BM1/4, spanning more than four orders of magnitude in BM from mouse to horse. PMID:18093948
Scale-Dependent Models for Atmospheric Flows
NASA Astrophysics Data System (ADS)
Klein, Rupert
2010-01-01
Atmospheric flows feature length scales from 10-5 to 105 m and timescales from microseconds to weeks or more. For scales above several kilometers and minutes, there is a natural scale separation induced by the atmosphere's thermal stratification, together with the influences of gravity and Earth's rotation, and the fact that atmospheric-flow Mach numbers are typically small. A central aim of theoretical meteorology is to understand the associated scale-specific flow phenomena, such as internal gravity waves, baroclinic instabilities, Rossby waves, cloud formation and moist convection, (anti-)cyclonic weather patterns, hurricanes, and a variety of interacting waves in the tropics. Single-scale asymptotics yields reduced sets of equations that capture the essence of these scale-specific processes. For studies of interactions across scales, techniques of multiple-scales asymptotics have received increasing recognition in recent years. This article recounts the most prominent scales and associated scale-dependent models and summarizes recent multiple-scales developments.
Scaling laws and fluctuations in the statistics of word frequencies
NASA Astrophysics Data System (ADS)
Gerlach, Martin; Altmann, Eduardo G.
2014-11-01
In this paper, we combine statistical analysis of written texts and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. The average vocabulary of an ensemble of fixed-length texts is known to scale sublinearly with the total number of words (Heaps’ law). Analyzing the fluctuations around this average in three large databases (Google-ngram, English Wikipedia, and a collection of scientific articles), we find that the standard deviation scales linearly with the average (Taylor's law), in contrast to the prediction of decaying fluctuations obtained using simple sampling arguments. We explain both scaling laws (Heaps’ and Taylor) by modeling the usage of words using a Poisson process with a fat-tailed distribution of word frequencies (Zipf's law) and topic-dependent frequencies of individual words (as in topic models). Considering topical variations lead to quenched averages, turn the vocabulary size a non-self-averaging quantity, and explain the empirical observations. For the numerous practical applications relying on estimations of vocabulary size, our results show that uncertainties remain large even for long texts. We show how to account for these uncertainties in measurements of lexical richness of texts with different lengths.
Scaling laws and properties of compositional data
NASA Astrophysics Data System (ADS)
Buccianti, Antonella; Albanese, Stefano; Lima, AnnaMaria; Minolfi, Giulia; De Vivo, Benedetto
2016-04-01
Many random processes occur in geochemistry. Accurate predictions of the manner in which elements or chemical species interact each other are needed to construct models able to treat presence of random components. Geochemical variables actually observed are the consequence of several events, some of which may be poorly defined or imperfectly understood. Variables tend to change with time/space but, despite their complexity, may share specific common traits and it is possible to model them stochastically. Description of the frequency distribution of the geochemical abundances has been an important target of research, attracting attention for at least 100 years, starting with CLARKE (1889) and continued by GOLDSCHMIDT (1933) and WEDEPOHL (1955). However, it was AHRENS (1954a,b) who focussed on the effect of skewness distributions, for example the log-normal distribution, regarded by him as a fundamental law of geochemistry. Although modeling of frequency distributions with some probabilistic models (for example Gaussian, log-normal, Pareto) has been well discussed in several fields of application, little attention has been devoted to the features of compositional data. When compositional nature of data is taken into account, the most typical distribution models for compositions are the Dirichlet and the additive logistic normal (or normal on the simplex) (AITCHISON et al. 2003; MATEU-FIGUERAS et al. 2005; MATEU-FIGUERAS and PAWLOWSKY-GLAHN 2008; MATEU-FIGUERAS et al. 2013). As an alternative, because compositional data have to be transformed from simplex space to real space, coordinates obtained by the ilr transformation or by application of the concept of balance can be analyzed by classical methods (EGOZCUE et al. 2003). In this contribution an approach coherent with the properties of compositional information is proposed and used to investigate the shape of the frequency distribution of compositional data. The purpose is to understand data-generation processes
Geometrically-controlled drop evaporation: Dynamics and universal scaling law
NASA Astrophysics Data System (ADS)
Sefiane, Khellil; Saenz, Pedro; Wray, Alexander; Che, Zhizhao; Matar, Omar; Valluri, Prashant; Kim, Jungho
2016-11-01
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 present an investigation of well-defined, non-spherical evaporating drops of pure liquids and binary mixtures. We deduce a new 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 and spatially-dependent thresholds for thermocapillary instabilities. In the case of binary mixtures, geometry dictates the spatial segregation of the more volatile component as it is depleted. In the light of our results, we believe that the drop geometry can be exploited to facilitate precise local control over the particle deposition and evaporative dynamics of pure drops and the mixing characteristics of multicomponent drops. Memphis Multiphase (EPSRC EP/K003976/1) & ThermaPOWER (EU IRSESPIRSES GA-2011-294905).
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.
Reconstruction of flow topology and percolation scalings
NASA Astrophysics Data System (ADS)
Bakunin, Oleg
2005-11-01
The essential deviation of transport processes in turbulent fluids and plasma from the classical behavior leads to the necessity of search for new approaches and scaling laws [1]. A variety of turbulence forms requires not only special description methods, but also an analysis of general mechanisms for different turbulence types. One such mechanism is the percolation transport [1,2]. Its description is based on the idea of long-range correlations, borrowed from theory of phase transitions and critical phenomena. The present paper considers the influence of zonal flow and time-dependence effects on the passive scalar behavior in the framework of the percolation approach. It is suggested to modify the renormalization condition of the small parameter of percolation model in accordance with the additional external influences superimposed on the system [3-4]. This approach makes it possible to consider simultaneously both parameters: the characteristic drift velocity Ud and the characteristic perturbation frequency w. The effective diffusion coefficient Deff ˜ w^7/10 satisfactory describes the low-frequency region w in which the long-range correlation effects play a significant role. This scaling agrees well with the analogous expressions that describe low frequency regimes of transport [1,2]. [1] Isichenko M B 1992 Rev. Mod. Phys. 64 961 [2] Bakunin O G 2004 Reports on Progress in Physics 67 965 [3] Bakunin O G 2005 Physica A 345 1 [4] Bakunin O G 2005 J. Plasma Physics 71 756.
Scaling laws for dual radio-frequency capacitively coupled discharges
Chung, T.H.
2005-10-01
The characteristics of dual radio-frequency capacitively coupled discharges are studied based on a homogeneous analytic model. We are considering a planar plasma device that can be approximated using a one-dimensional model. A set of equations describing the dynamics of the system are presented and used to give the analytic scaling laws. Scaling laws relating the drive frequencies and the applied voltages of dual radio-frequency sources to operating functions such as plasma density and plasma potential are examined and compared with numerical simulations.
Scaling laws for resonance line photons in an absorbing medium
NASA Astrophysics Data System (ADS)
Frisch, H.
1980-07-01
Resonance line scattering in the presence of a source of continuous absorption is studied for very small values of the ratio of the continuous to line opacity, beta. Scaling laws for the thermalization length, the thermalization frequency, the mean number of scatterings and the mean path length are extracted from an asymptotic analysis of the equation of transfer in the limit as beta approaches 0. An interpretation is given for asymptotic scaling laws inferred from numerical data by Hummer and Kunasz (1978) and Bonilha et al. (1979).
Constructal law of vascular trees for facilitation of flow.
Razavi, Mohammad S; Shirani, Ebrahim; Salimpour, Mohammad Reza; Kassab, Ghassan S
2014-01-01
Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.
Constructal Law of Vascular Trees for Facilitation of Flow
Razavi, Mohammad S.; Shirani, Ebrahim; Salimpour, Mohammad Reza; Kassab, Ghassan S.
2014-01-01
Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures. PMID:25551617
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.
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.
Robust regression on noisy data for fusion scaling laws
Verdoolaege, Geert
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.
Fluctuation Scaling, Taylor’s Law, and Crime
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
Batchelor scaling in fast-flowing soap films.
Amarouchene, Y; Kellay, H
2004-11-19
The dynamics of a passive scalar such as a dye in the far dissipative range of fluid turbulence is a central problem in nonlinear physics. An important prediction for this problem was made by Batchelor over 40 years ago and is known as Batchelor's scaling law. We here present strong evidence in favor of this law for the thickness fluctuations in the flow of a soap film past a flat plate. The results also capture the dissipative range of the scalar which turns out to have universal features. The probability density function of the scalar increments and their structure functions come out in nice agreement with theoretical predictions.
Batchelor Scaling in Fast-Flowing Soap Films
NASA Astrophysics Data System (ADS)
Amarouchene, Y.; Kellay, H.
2004-11-01
The dynamics of a passive scalar such as a dye in the far dissipative range of fluid turbulence is a central problem in nonlinear physics. An important prediction for this problem was made by Batchelor over 40years ago and is known as Batchelor's scaling law. We here present strong evidence in favor of this law for the thickness fluctuations in the flow of a soap film past a flat plate. The results also capture the dissipative range of the scalar which turns out to have universal features. The probability density function of the scalar increments and their structure functions come out in nice agreement with theoretical predictions.
NASA Astrophysics Data System (ADS)
Starchenko, S. V.
2014-11-01
Scaling laws for hydromagnetic dynamo in planets initially express the characteristic strength of the magnetic field through the primary values, such as the size of the conductive core of the planet, the angular rotation rate, electrical conductivity and energy flows. Most of the earlier proposed scaling laws based only on observations and assumptions about force balances. Recent and my new approaches to fully take into account the energy and induction balance has additionally expressed here in terms of primary values such important characteristics as forces, magnitudes, energies, scales and orientations of hydromagnetic fields. The direct numerical simulation of the hydromagnetic dynamo and modeling ability in a fairly wide range of parameters for the first time allowed direct test such laws. The obtained numerical geodynamo-like results for the Earth, Jupiter and partially Saturn postulated previously not identified analytically simplest law that predicts the field strength is only depended on the specific energy density of convection and the size of the dynamo area. This simplest and already widely used law was original way analytically grounded here along with other previously known and new laws. This analytic identifies the physics determining geomagnetic periodicities for jerk, secular variations and inversions. Mean period between the inversions is found to be roughly proportional to the intensity of the geomagnetic field that is confirmed by some paleomagnetic researches. Possible dynamos in Mercury, Ganymede, Uranus and Neptune are also discussed.
Transition in the Flow of Power-Law Fluids through Isotropic Porous Media.
Zami-Pierre, F; de Loubens, R; Quintard, M; Davit, Y
2016-08-12
We use computational fluid dynamics to explore the creeping flow of power-law fluids through isotropic porous media. We find that the flow pattern is primarily controlled by the geometry of the porous structure rather than by the nonlinear effects in the rheology of the fluid. We further highlight a macroscale transition between a Newtonian and a non-Newtonian regime, which is the signature of a coupling between the viscosity of the fluid and the structure of the porous medium. These complex features of the flow can be condensed into an effective length scale, which defines both the non-Newtonian transition and the Newtonian permeability.
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.
Practical Predictability of Flows with Many Scales of Motion
NASA Astrophysics Data System (ADS)
Snyder, C.
2016-12-01
With advances in both observational and computational capabilities, data assimilation and prediction that treat a range of spatial or temporal scales simultaneously are increasingly feasible. This raises the question of predictability in practice, for a given observing network, across that range of scales. Basic insights follow from generalizing Lorenz's (1969) model for the intrinsic predictability of isotropic, homogeneous turbulence to include data assimilation. When the exponent of the flow's kinetic-energy power law is -3 (the situation that characterizes atmospheric motions for scales larger than roughly 400 km), even scales smaller than the resolution of the observational network can be analyzed and predicted skillfully. For an exponent of -5/3 (the situation that characterizes atmospheric scales below roughly 400 km), recovery of unobserved scales by the assimilation scheme is much more limited and skillful prediction is possible only for observed scales.
Scale relativity theory and integrative systems biology: 1. Founding principles and scale laws.
Auffray, Charles; Nottale, Laurent
2008-05-01
In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, and discuss how scale laws of increasing complexity can be used to model and understand the behaviour of complex biological systems. In scale relativity theory, the geometry of space is considered to be continuous but non-differentiable, therefore fractal (i.e., explicitly scale-dependent). One writes the equations of motion in such a space as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the non-differentiable and fractal geometry. In this first review paper, the scale laws that describe the new dependence on resolutions of physical quantities are obtained as solutions of differential equations acting in the scale space. This leads to several possible levels of description for these laws, from the simplest scale invariant laws to generalized laws with variable fractal dimensions. Initial applications of these laws to the study of species evolution, embryogenesis and cell confinement are discussed.
NASA Astrophysics Data System (ADS)
Stephenson, David; Patronis, Alexander; Holland, David M.; Lockerby, Duncan A.
2015-11-01
Murray's law states that the volumetric flow rate is proportional to the cube of the radius in a cylindrical channel optimized to require the minimum work to drive and maintain the fluid. However, application of this principle to the biomimetic design of micro/nano fabricated networks requires optimization of channels with arbitrary cross-sectional shape (not just circular) and smaller than is valid for Murray's original assumptions. We present a generalized law for symmetric branching that (a) is valid for any cross-sectional shape, providing that the shape is constant through the network; (b) is valid for slip flow and plug flow occurring at very small scales; and (c) is valid for networks with a constant depth, which is often a requirement for lab-on-a-chip fabrication procedures. By considering limits of the generalized law, we show that the optimum daughter-parent area ratio Γ, for symmetric branching into N daughter channels of any constant cross-sectional shape, is Γ=N-2 /3 for large-scale channels, and Γ=N-4 /5 for channels with a characteristic length scale much smaller than the slip length. Our analytical results are verified by comparison with a numerical optimization of a two-level network model based on flow rate data obtained from a variety of sources, including Navier-Stokes slip calculations, kinetic theory data, and stochastic particle simulations.
Catalina Segura; Davide Lazzati; Arumugam Sankarasubramanian
2013-01-01
A recent study employed a broken power-law (BPL) distribution for understanding the scaling frequency of bankfull discharge in snowmelt-dominated basins. This study, grounded from those findings, investigated the ability of a BPL function to describe the distribution of daily flows above the mean annual flow in 1217 sites across the conterminous U.S. (CONUS). The...
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).
Two-dimensional electromagnetic Child-Langmuir law of a short-pulse electron flow
Chen, S. H.; Tai, L. C.; Liu, Y. L.; Ang, L. K.; Koh, W. S.
2011-02-15
Two-dimensional electromagnetic particle-in-cell simulations were performed to study the effect of the displacement current and the self-magnetic field on the space charge limited current density or the Child-Langmuir law of a short-pulse electron flow with a propagation distance of {zeta} and an emitting width of W from the classical regime to the relativistic regime. Numerical scaling of the two-dimensional electromagnetic Child-Langmuir law was constructed and it scales with ({zeta}/W) and ({zeta}/W){sup 2} at the classical and relativistic regimes, respectively. Our findings reveal that the displacement current can considerably enhance the space charge limited current density as compared to the well-known two-dimensional electrostatic Child-Langmuir law even at the classical regime.
Scaling laws of gelatin hydrogels for steady dynamic friction
NASA Astrophysics Data System (ADS)
Gupta, Vinit; Singh, Arun K.
2016-09-01
In this article, we use population balance based dynamic friction model for steady sliding to develop scaling laws in the terms of mesh size of gelatin hydrogels. First of all, it is observed in the sliding experiments that shear modulus of gelatin hydrogels depends on sliding velocity. This dependence is more evident in the case of low sliding velocity. Moreover, relaxation time constant of a dangling chain at the sliding interface scales with the same exponent as its stiffness. The scaling law is also developed for chain density and viscous retardation at the sliding interface. It is also established that the Hookean-based dynamic friction model is sufficient to study frictional behaviour of hydrogels. The reason for this observation is attributed to the weak bonding between a gelatin hydrogel and glass interface.
Universal Scaling Law for the Collapse of Viscous Nanopores.
Lu, Jiakai; Yu, Jiayun; Corvalan, Carlos M
2015-08-11
Below a threshold size, a small pore nucleated in a fluid sheet will contract to minimize the surface energy. Such behavior plays a key role in nature and technology, from nanopores in biological membranes to nanopores in sensors for rapid DNA and RNA sequencing. Here we show that nanopores nucleated in viscous fluid sheets collapse following a universal scaling law for the pore radius. High-fidelity numerical simulations reveal that the scaling is largely independent of the initial conditions, including the size, shape, and thickness of the original nanopore. Results further show that the scaling law yields a constant speed of collapse as observed in recent experiments. Nanopores in fluid sheets of moderate viscosity also attain this constant terminal speed provided that they are sufficiently close to the singularity.
Generalizing Microdischarge Breakdown Scaling Laws for Pressure and Gas
NASA Astrophysics Data System (ADS)
Loveless, Amanda; Garner, Allen
2016-10-01
Shrinking device dimensions for micro- and nanoelectromechanical systems necessitates accurate breakdown voltage predictions for reliable operation. Additionally, one must accurately predict breakdown voltage to optimize system geometry for applications in microplasmas and micropropulsion. Traditional approaches use Paschen's law (PL) to predict breakdown, but PL fails at small gap distances ( 15 μm) where field emission dominates. Subsequent work derived scaling laws and analytic expressions for breakdown voltage in argon at atmospheric pressure. Applications at high (e.g. combustion) and low (e.g. vacuum nanoelectronics) pressures for various gases motivate the generalization of these models for pressure and gas. This work addresses these concerns by deriving scaling laws generalized for gap distance, pressure, and gas, while also specifically incorporating and exploring the impact of field enhancement and work function. We compare these analytic scaling laws to experimental data and particle-in-cell simulations. Funded by a U.S. Nuclear Regulatory Commission Nuclear Education Program Faculty Development Grant Program at Purdue University.
Statistical conservation law in two- and three-dimensional turbulent flows.
Frishman, Anna; Boffetta, Guido; De Lillo, Filippo; Liberzon, Alex
2015-03-01
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance R(t) between two neutrally buoyant particles, raised to the power -d and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two- and three-dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In two dimensions we show that, as an extension of the conservation law, an Evans-Cohen-Morriss or Gallavotti-Cohen type fluctuation relation exists. We also analyze data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012)], finding that although it probes small scales they are not in the smooth regime. Thus instead of 〈R-3〉, we look for a similar, power-law-in-separation conservation law. We show that the existence of an initially slowly varying function of this form can be predicted but that it does not turn into a conservation law. We suggest that the conservation of 〈R-d〉, demonstrated here, can be used as a check of isotropy, incompressibility, and flow dimensionality in numerical and laboratory experiments that focus on small scales.
Statistical conservation law in two- and three-dimensional turbulent flows
NASA Astrophysics Data System (ADS)
Frishman, Anna; Boffetta, Guido; De Lillo, Filippo; Liberzon, Alex
2015-03-01
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013), 10.1103/PhysRevLett.110.214502] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d -dimensional flow the distance R (t ) between two neutrally buoyant particles, raised to the power -d and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two- and three-dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In two dimensions we show that, as an extension of the conservation law, an Evans-Cohen-Morriss or Gallavotti-Cohen type fluctuation relation exists. We also analyze data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012), 10.1016/j.physd.2011.07.008], finding that although it probes small scales they are not in the smooth regime. Thus instead of
Scaling laws for spreading of a liquid under pressure
NASA Astrophysics Data System (ADS)
Nag, Soma; Dutta, Suparna; Tarafdar, Sujata
2009-10-01
We study squeeze flow of two different fluids (castor oil and ethylene glycol) between a pair of glass plates and a pair of perspex plates, under an applied load. The film thickness is found to vary with time as a power-law, where the exponent increases with load. After a certain time interval the area of fluid-solid contact saturates to a nearly steady value. This saturation area, increases with load at different rates for different fluid-solid combinations.
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
A laboratory scale supersonic combustive flow system
Sams, E.C.; Zerkle, D.K.; Fry, H.A.; Wantuck, P.J.
1995-02-01
A laboratory scale supersonic flow system [Combustive Flow System (CFS)] which utilizes the gaseous products of methane-air and/or liquid fuel-air combustion has been assembled to provide a propulsion type exhaust flow field for various applications. Such applications include providing a testbed for the study of planar two-dimensional nozzle flow fields with chemistry, three-dimensional flow field mixing near the exit of rectangular nozzles, benchmarking the predictive capability of various computational fluid dynamic codes, and the development and testing of advanced diagnostic techniques. This paper will provide a detailed description of the flow system and data related to its operation.
Macroscopic laws for immiscible two-phase flow in porous media: Results From numerical experiments
NASA Astrophysics Data System (ADS)
Rothman, Daniel H.
1990-06-01
Flow through porous media may be described at either of two length scales. At the scale of a single pore, fluids flow according to the Navier-Stokes equations and the appropriate boundary conditions. At a larger, volume-averaged scale, the flow is usually thought to obey a linear Darcy law relating flow rates to pressure gradients and body forces via phenomenological permeability coefficients. Aside from the value of the permeability coefficient, the slow flow of a single fluid in a porous medium is well-understood within this framework. The situation is considerably different, however, for the simultaneous flow of two or more fluids: not only are the phenomenological coefficients poorly understood, but the form of the macroscopic laws themselves is subject to question. I describe a numerical study of immiscible two-phase flow in an idealized two-dimensional porous medium constructed at the pore scale. Results show that the macroscopic flow is a nonlinear function of the applied forces for sufficiently low levels of forcing, but linear thereafter. The crossover, which is not predicted by conventional models, occurs when viscous forces begin to dominate capillary forces; i.e., at a sufficiently high capillary number. In the linear regime, the flow may be described by the linear phenomenological law ui = ΣjLijfj, where the flow rate ui of the ith fluid is related to the force fj applied to the jth fluid by the matrix of phenomenological coefficients Lij which depends on the relative concentrations of the two fluids. The diagonal terms are proportional to quantities commonly referred to as "relative permeabilities." The cross terms represent viscous coupling between the two fluids; they are conventionally assumed to be negligible and require special experimental procedures to observe in a laboratory. In contrast, in this numerical study the cross terms are straightforward to measure and are found to be of significant size. The cross terms are additionally observed to
Universal Scaling Law in Long Gamma-Ray Bursts
NASA Astrophysics Data System (ADS)
Tsutsui, Ryo; Shigeyama, Toshikazu
2013-06-01
The overwhelming diversity of long gamma-ray bursts (LGRBs), discovered after the launch of the Swift satellite,is a major obstacle to LGRB studies. Recently, it was shown that the prompt emission of LGRBs can be classified into three subclasses: Type I and Type II LGRBs, populating separate fundamental planes in a 3D space defined by the peak luminosity, the duration, and the spectral peak energy, and outliers belonging to none of these planes. Here, we show that Type I LGRBs exhibit different shapes of light curves from that of Type II LGRBs. Furthermore, we demonstrate that this classification has uncovered a new scaling law concerning the light curve of Type II LGRBs, over a span of 8 orders of magnitude ranging from the prompt emission to the late X-ray afterglow one. The scaled light curve has four distinct phases. The first phase has a characteristic time-scale, while the three subsequent phases exhibit power-law behaviors with different exponents. We attempt a new interpretation in terms of the emission from an optically thick fireball propagating in the cricumstellar matter at relativistic speed, and argue that the four observed phases correspond to its hydrodynamical phases. Our classification scheme succeeds in pinning down intrinsic luminosities of Type II LGRBs through the scaling law with a sample of polymorphic GRBs. Further refinements of this scheme and scaling law will make it possible to use a subclass of LGRBs as new standard candles with the same reliability and accuracy as Type Ia supernovae in more distant universe than the light from supernovae can reach.
Modeling expiratory flow from excised tracheal tube laws.
Aljuri, N; Freitag, L; Venegas, J G
1999-11-01
Flow limitation during forced exhalation and gas trapping during high-frequency ventilation are affected by upstream viscous losses and by the relationship between transmural pressure (Ptm) and cross-sectional area (A(tr)) of the airways, i.e., tube law (TL). Our objective was to test the validity of a simple lumped-parameter model of expiratory flow limitation, including the measured TL, static pressure recovery, and upstream viscous losses. To accomplish this objective, we assessed the TLs of various excised animal tracheae in controlled conditions of quasi-static (no flow) and steady forced expiratory flow. A(tr) was measured from digitized images of inner tracheal walls delineated by transillumination at an axial location defining the minimal area during forced expiratory flow. Tracheal TLs followed closely the exponential form proposed by Shapiro (A. H. Shapiro. J. Biomech. Eng. 99: 126-147, 1977) for elastic tubes: Ptm = K(p) [(A(tr)/A(tr0))(-n) - 1], where A(tr0) is A(tr) at Ptm = 0 and K(p) is a parametric factor related to the stiffness of the tube wall. Using these TLs, we found that the simple model of expiratory flow limitation described well the experimental data. Independent of upstream resistance, all tracheae with an exponent n < 2 experienced flow limitation, whereas a trachea with n > 2 did not. Upstream viscous losses, as expected, reduced maximal expiratory flow. The TL measured under steady-flow conditions was stiffer than that measured under expiratory no-flow conditions, only if a significant static pressure recovery from the choke point to atmosphere was assumed in the measurement.
Scaling laws for the distribution of natural resources
NASA Astrophysics Data System (ADS)
Blenkinsop, Thomas
2014-05-01
If scaling laws can be established for the distribution of natural resources, they would have important economic consequences. For example, they can be used to estimate total resources, they can dictate exploration strategies, and they can also point to processes by which natural resources form. A scaling law for the spatial distribution of natural resources can be proposed as: M(r) ~ r-D where M(r) is the mass of resource within a circle of radius r. If the mass of individual occurrences of resources is unity, this law describes the Mass Dimension D of the resource, commonly analysed by the number-in-circle method. In this case D is simply interpreted as a measure of the clustering of the resource distribution. Space filling or random distributions have D = 2: lower values indicate a decrease in density with distance. If the mass of resource varies at each occurrence (as typical in nature), then M(r) ~ r-D is a general scaling law, with an exponent that is referred to here as the Mass-Radius scaling exponent. This exponent can have values greater than 2. Mass Dimensions and Mass-Radius scaling exponents have been determined in this study for Archean gold deposits in Zimbabwe, direct use of geothermal energy in Oregon, geothermal energy use in New Zealand and conventional and unconventional gas production in Pennsylvania. Mass Dimensions vary between 0.4 and 2, reflecting the variable clustering of the data sets. The highest values are from conventional gas production, while unconventional gas production and geothermal energy have lower values. In general Mass Dimensions and Mass-Radius scaling exponents are similar in any data sets. An interesting consequence is that an approximate value for the Mass-Radius scaling exponent can be given by the Mass Dimension. It is commonly hard to measure the Mass-Radius scaling exponent because accurate data for mass is difficult to obtain. The similarity of the two exponents suggests that substituting the Mass Dimension for the
Goldilocks and the Three Complex Crater Scaling Laws
NASA Technical Reports Server (NTRS)
McKinnon, William B.; Schenk, Paul M.; Moore, Jeffrey M.
2003-01-01
Formed in the gravity regime, complex craters are larger than their simple crater equivalents, due to a combination of slumping and uplift. Just how much larger is a matter of great interest for, for example, age dating studies. We examine three empirical scaling laws for complex crater size, examining their strengths and weaknesses, as well as asking how well they accord with previously published and new data from lunar, terrestrial, and Venusian craters.
Goldilocks and the Three Complex Crater Scaling Laws
NASA Technical Reports Server (NTRS)
McKinnon, William B.; Schenk, Paul M.; Moore, Jeffrey M.
2003-01-01
Formed in the gravity regime, complex craters are larger than their simple crater equivalents, due to a combination of slumping and uplift. Just how much larger is a matter of great interest for, for example, age dating studies. We examine three empirical scaling laws for complex crater size, examining their strengths and weaknesses, as well as asking how well they accord with previously published and new data from lunar, terrestrial, and venusian craters.
Goldilocks and the Three Complex Crater Scaling Laws
NASA Technical Reports Server (NTRS)
McKinnon, William B.; Schenk, Paul M.; Moore, Jeffrey M.
2003-01-01
Formed in the gravity regime, complex craters are larger than their simple crater equivalents, due to a combination of slumping and uplift. Just how much larger is a matter of great interest for, for example, age dating studies. We examine three empirical scaling laws for complex crater size, examining their strengths and weaknesses, as well as asking how well they accord with previously published and new data from lunar, terrestrial, and venusian craters.
The Second Law of Thermodynamics at the Microscopic Scale
NASA Astrophysics Data System (ADS)
Josset, Thibaut
2017-09-01
In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this paper, we investigate how the relaxation toward equilibrium is made possible through interactions that do not lead to significant exchange of energy, and argue for the validity of the second law of thermodynamics at the microscopic scale.
Scaling laws for buckling instability in monolayer networks
NASA Technical Reports Server (NTRS)
Noever, David A.
1992-01-01
In this comment a power law is argued to govern the thickening of cell widths relative to their lengths in buckling monolayer networks. A scaling relation is derived for general instabilities in cellular networks, and a reply is given that questions the use of the amplitude of the buckling undulation in an already buckled wall in the Euler relation. Both treatments provided shed light on the stability/instability of wavelengths for buckling monolayer networks.
X-ray scaling laws for galaxy clusters and groups
NASA Astrophysics Data System (ADS)
Horner, Donald John
Scaling laws between galaxy cluster properties, such as the x-ray luminosity- temperature relation (L-T), the total mass-temperature relation (M-T), and velocity dispersion-temperature relation (?-T) reflect the underlying physics in clus ter formation and evolution. The differences between empirically determined and theoretically predicted scaling laws can give useful insights into physical processes happening in clusters. To determine these scaling laws, we have developed a data reduction pipeline for clusters observed by the ASCA x-ray satellite to create a sample of 273 clusters and groups with measured x-ray luminosities, average temperatures, and metal abundances. This is the largest such sample yet created and will form a baseline for future studies with improved instruments like Chandra and XMM-Newton. We compare our ASCA cluster catalog to data in the literature to examine some of the biases and systematics that affect measurement of x-ray properties, and illuminate issues that affect the science results derived from such x-ray samples. We derive the L-T relationship over several orders of magnitude in luminosity, from rich clusters to groups. In combination with data from the literature, we examine the M-T relationship for a variety of mass estimators. We then examine the ?-T relationship and other correlations between the optical and x-ray propertie s of galaxy clusters. In general, we find that these scaling laws are affected by non-gravitational processes which require additional physics, e.g., energy injection by supernovae. We also see little evolution of galaxy cluster properties with redshift to z - 0.5.
Scaling laws for particle growth in plasma reactors
Lemons, D.S.; Keinigs, R.K.; Winske, D.; Jones, M.E.
1996-01-01
We quantify a model which incorporates observed features of contaminant particle growth in plasma processing reactors. According to the model, large {open_quote}{open_quote}predator{close_quote}{close_quote} particles grow by adsorbing smaller, typically neutral, {open_quote}{open_quote}prey{close_quote}{close_quote} protoparticles. The latter are supplied by an assumed constant mass injection of contaminant material. Scaling laws and quantitative predictions compare favorably with published experimental results. {copyright} {ital 1996 American Institute of Physics.}
MAGNETIC SCALING LAWS FOR THE ATMOSPHERES OF HOT GIANT EXOPLANETS
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 laws 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.
Scaling law for electrocaloric temperature change in antiferroelectrics
Lisenkov, S.; Mani, B. K.; Glazkova, E.; Miller, C. W.; Ponomareva, I.
2016-01-01
A combination of theoretical and first-principles computational methods, along with experimental evidence from the literature, were used to predict the existence of a scaling law for the electrocaloric temperature change in antiferroelectric materials. We show that the temperature change scales quadratically with electric field, allowing a simple transformation to collapse the set of ΔT(E) onto a single curve. This offers a unique method that can be used to predict electrocaloric behavior beyond the limits of present measurement ranges or in regions where data are not yet available. PMID:26796343
Scaling law for electrocaloric temperature change in antiferroelectrics
NASA Astrophysics Data System (ADS)
Lisenkov, S.; Mani, B. K.; Glazkova, E.; Miller, C. W.; Ponomareva, I.
2016-01-01
A combination of theoretical and first-principles computational methods, along with experimental evidence from the literature, were used to predict the existence of a scaling law for the electrocaloric temperature change in antiferroelectric materials. We show that the temperature change scales quadratically with electric field, allowing a simple transformation to collapse the set of ΔT(E) onto a single curve. This offers a unique method that can be used to predict electrocaloric behavior beyond the limits of present measurement ranges or in regions where data are not yet available.
Scaling law for electrocaloric temperature change in antiferroelectrics.
Lisenkov, S; Mani, B K; Glazkova, E; Miller, C W; Ponomareva, I
2016-01-22
A combination of theoretical and first-principles computational methods, along with experimental evidence from the literature, were used to predict the existence of a scaling law for the electrocaloric temperature change in antiferroelectric materials. We show that the temperature change scales quadratically with electric field, allowing a simple transformation to collapse the set of ΔT(E) onto a single curve. This offers a unique method that can be used to predict electrocaloric behavior beyond the limits of present measurement ranges or in regions where data are not yet available.
Fluctuation scaling in complex systems: Taylor's law and beyond
NASA Astrophysics Data System (ADS)
Eisler, Zoltán; Bartos, Imre; Kertész, János
2008-01-01
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form 'fluctuations ≈ constant × averageα', where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.
Commuting flows and conservation laws for noncommutative Lax hierarchies
Hamanaka, Masashi
2005-05-01
We discuss commuting flows and conservation laws for Lax hierarchies on noncommutative spaces in the framework of the Sato theory. On commutative spaces, the Sato theory has revealed essential aspects of the integrability for wide class of soliton equations which are derived from the Lax hierarchies in terms of pseudodifferential operators. Noncommutative extension of the Sato theory has been already studied by the author and Toda, and the existence of various noncommutative Lax hierarchies are guaranteed. In this paper, we present conservation laws for the noncommutative Lax hierarchies with both space-space and space-time noncommutativities and prove the existence of infinite number of conserved densities. We also give the explicit representations of them in terms of Lax operators. Our results include noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera, modified KdV equation and so on.
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.
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.
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.
Conductivity scaling in supercritical percolation of nanoparticles--not a power law.
Li, Jiantong; Östling, Mikael
2015-02-28
The power-law behavior widely observed in supercritical percolation systems of conductive nanoparticles may merely be a phenomenological approximation to the true scaling law not yet discovered. In this work, we derive a comprehensive yet simple scaling law and verify its extensive applicability to various experimental and numerical systems. In contrast to the power law which lacks theoretical backing, the new scaling law is explanatory and predictive, and thereby helpful to gain more new insights into percolation systems of conductive nanoparticles.
1d Numerical Simulation of A Swiss Debris Flow: Comparison of Flow Laws
NASA Astrophysics Data System (ADS)
McArdell, B. W.; Graf, Ch.; Naef, D.; Rickenmann, D.
Efforts to numerically model debris flows have been limited by a lack of appropriate numerical tools. Here we report on our efforts to systematically evaluate different flow laws using a numerical tool under development at our institute. The model, DFEM, is a finite element solution of the shallow water equations in one or two dimensions and is based on the FEMTOOL libraries from Rutschmann (1993). Debris flow constitu- tive relations or flow laws include turbulent (e.g. Manning, Chézy, Voellmy), laminar (Bingham, Newtonian laminar), and inertial formulations (dilatant/grain shearing) as well as combinations of flow laws when appropriate. The model is applied to a recent debris flow event from the Schipfenbach torrent, Switzerland (Hürlimann, submitted), where we maintain an automated debris flow observation station. Observations include flow depth measurements from ultrasonic depth measurement devices, reach-averaged velocities estimated from the travel time between ultrasonic gages and geophones, velocity and flow behavior from video cam- eras situated near the flow retention basin on the fan, and post-event field surveys. Preliminary results suggest that the flow of debris in the steep reaches of the torrent channel can be reasonably described by a simple turbulent flow law (e.g. Manning- Strickler or Chézy) with a large overall flow resistance, and that both the flow in the channel and the deposition on the fan can be satisfactorily simulated using the Voellmy fluid approach. The results using the Voellmy fluid approach are in agree- ment with results calculated from the AVAL-1D snow avalanche simulation code and input parameters for debris instead of snow, corroborating the implementation in the DFEM model. The AVAL-1D code is commercially available, providing another tool that may be used by workers in the natural hazards field for debris flow routing in torrent channels and on alluvial fans. References: Hürlimann, M., Rickenmann, D. and Graf, Ch., Field
Rheological flow laws for multiphase magmas: An empirical approach
NASA Astrophysics Data System (ADS)
Pistone, Mattia; Cordonnier, Benoît; Ulmer, Peter; Caricchi, Luca
2016-07-01
The physical properties of magmas play a fundamental role in controlling the eruptive dynamics of volcanoes. Magmas are multiphase mixtures of crystals and gas bubbles suspended in a silicate melt and, to date, no flow laws describe their rheological behaviour. In this study we present a set of equations quantifying the flow of high-viscosity (> 105 Pa·s) silica-rich multiphase magmas, containing both crystals (24-65 vol.%) and gas bubbles (9-12 vol.%). Flow laws were obtained using deformation experiments performed at high temperature (673-1023 K) and pressure (200-250 MPa) over a range of strain-rates (5 · 10- 6 s- 1 to 4 · 10- 3 s- 1), conditions that are relevant for volcanic conduit processes of silica-rich systems ranging from crystal-rich lava domes to crystal-poor obsidian flows. We propose flow laws in which stress exponent, activation energy, and pre-exponential factor depend on a parameter that includes the volume fraction of weak phases (i.e. melt and gas bubbles) present in the magma. The bubble volume fraction has opposing effects depending on the relative crystal volume fraction: at low crystallinity bubble deformation generates gas connectivity and permeability pathways, whereas at high crystallinity bubbles do not connect and act as ;lubricant; objects during strain localisation within shear bands. We show that such difference in the evolution of texture is mainly controlled by the strain-rate (i.e. the local stress within shear bands) at which the experiments are performed, and affect the empirical parameters used for the flow laws. At low crystallinity (< 44 vol.%) we observe an increase of viscosity with increasing strain-rate, while at high crystallinity (> 44 vol.%) the viscosity decreases with increasing strain-rate. Because these behaviours are also associated with modifications of sample textures during the experiment and, thus, are not purely the result of different deformation rates, we refer to ;apparent shear-thickening; and
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.
Scaling laws for impact fragmentation of spherical solids.
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.
Power-law citation distributions are not scale-free
NASA Astrophysics Data System (ADS)
Golosovsky, Michael
2017-09-01
We analyze time evolution of statistical distributions of citations to scientific papers published in the same year. While these distributions seem to follow the power-law dependence we find that they are nonstationary and the exponent of the power-law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of the low-cited and highly cited papers. By measuring citation trajectories of papers we found that citation careers of the low-cited papers come to saturation after 10-15 years while those of the highly cited papers continue to increase indefinitely: The papers that exceed some citation threshold become runaways. Thus, we show that although citation distribution can look as a power-law dependence, it is not scale free and there is a hidden dynamic scale associated with the onset of runaways. We compare our measurements to our recently developed model of citation dynamics based on copying-redirection-triadic closure and find explanations to our empirical observations.
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework.
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.
Site-Scale Saturated Zone Flow Model
G. Zyvoloski
2003-12-17
The purpose of this model report is to document the components of the site-scale saturated-zone flow model at Yucca Mountain, Nevada, in accordance with administrative procedure (AP)-SIII.lOQ, ''Models''. This report provides validation and confidence in the flow model that was developed for site recommendation (SR) and will be used to provide flow fields in support of the Total Systems Performance Assessment (TSPA) for the License Application. The output from this report provides the flow model used in the ''Site-Scale Saturated Zone Transport'', MDL-NBS-HS-000010 Rev 01 (BSC 2003 [162419]). The Site-Scale Saturated Zone Transport model then provides output to the SZ Transport Abstraction Model (BSC 2003 [164870]). In particular, the output from the SZ site-scale flow model is used to simulate the groundwater flow pathways and radionuclide transport to the accessible environment for use in the TSPA calculations. Since the development and calibration of the saturated-zone flow model, more data have been gathered for use in model validation and confidence building, including new water-level data from Nye County wells, single- and multiple-well hydraulic testing data, and new hydrochemistry data. In addition, a new hydrogeologic framework model (HFM), which incorporates Nye County wells lithology, also provides geologic data for corroboration and confidence in the flow model. The intended use of this work is to provide a flow model that generates flow fields to simulate radionuclide transport in saturated porous rock and alluvium under natural or forced gradient flow conditions. The flow model simulations are completed using the three-dimensional (3-D), finite-element, flow, heat, and transport computer code, FEHM Version (V) 2.20 (software tracking number (STN): 10086-2.20-00; LANL 2003 [161725]). Concurrently, process-level transport model and methodology for calculating radionuclide transport in the saturated zone at Yucca Mountain using FEHM V 2.20 are being
Scaling laws for jet pulsations associated with high-resolution electrohydrodynamic printing
NASA Astrophysics Data System (ADS)
Choi, Hong Kyoon; Park, Jang-Ung; Park, O. Ok; Ferreira, Placid M.; Georgiadis, John G.; Rogers, John A.
2008-03-01
This paper presents simple scaling laws that describe the intrinsic pulsation of a liquid jet that forms at the tips of fine nozzles under electrohydrodynamically induced flows. The jet diameter is proportional to the square root of the nozzle size and inversely proportional to the electric field strength. The fundamental pulsation frequency is proportional to the electric field strength raised to the power of 1.5. These scaling relationships are confirmed by experiments presented here and by data from the literature. The results are important for recently developed high-resolution ink jet printing techniques and other applications using electrohydrodynamics.
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
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.
Universal Scaling Laws in Quantum Theory and Cosmology
NASA Astrophysics Data System (ADS)
Rauscher, Elizabeth A.; Hurtak, James J.; Hurtak, D. E.
2013-09-01
We have developed a hyperdimensional geometry, Dn or Descartes space of dimensionality of n > 4, for our consideration n = 10. This model introduces a formation in terms of the conditions of constants as the space that allows us to calculate a unique set of scaling laws from the lower end scale of the quantum vacuum foam to the current universe. A group theoretical matrix formalism is made for the ten and eleven dimensional model of this space. For the eleven dimensional expressions of this geometry, a fundamental frequency is introduced and utilized as an additional condition on the topology. The constraints on the Dn space are imposed by the relationship of the universal constraints of nature expressed in terms of physical variables. The quantum foam picture can be related to the Fermi-Dirac vacuum model. Consideration is made for the lower limit of a universal size scaling from the Planck length, l = 10-33 cm, temporal component, t = 10-44 sec, density, 1093 gm/cm3 and additional Planck units of quantized variables. The upper limit of rotational frequency in the Dn space is given as 1043 Hz, as conditions or constraints that apply to the early universe which are expressed uniquely in terms of the universal constants, h, Planck's constant, the G, the gravitational constant and c, the velocity of light. We have developed a scaling law for cosmogenesis from the early universe to our present day universe. We plot the physical variables of the ten and eleven dimensional space versus a temporal evolution of these parameters. From this formalism, in order to maintain the compatibility of Einstein's General Relativity with the current model of cosmology, we replace Guth's inflationary model with a matter creation term. Also we have developed a fundamental scaling relationship between the "size scale" of organized matter with their associated fundamental frequency.
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.
Scaling Law for Irreversible Entropy Production in Critical Systems
Hoang, Danh-Tai; Prasanna Venkatesh, B.; Han, Seungju; Jo, Junghyo; Watanabe, Gentaro; Choi, Mahn-Soo
2016-01-01
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. The initially ordered spins become disordered by quenching the ferromagnetic coupling constant. For a sudden quench, the deviation from the Jarzynski equality evaluated from the ideal ensemble average could, in principle, depend on the reduced coupling constant ε0 of the initial state and the system size L. We find that, instead of depending on ε0 and L separately, this deviation exhibits a scaling behavior through a universal combination of ε0 and L for a given tolerance parameter, inherited from the critical scaling laws of second-order phase transitions. A similar scaling law can be obtained for the finite-speed quench as well within the Kibble-Zurek mechanism. PMID:27277558
Scaling Law for Irreversible Entropy Production in Critical Systems
NASA Astrophysics Data System (ADS)
Hoang, Danh-Tai; Prasanna Venkatesh, B.; Han, Seungju; Jo, Junghyo; Watanabe, Gentaro; Choi, Mahn-Soo
2016-06-01
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. The initially ordered spins become disordered by quenching the ferromagnetic coupling constant. For a sudden quench, the deviation from the Jarzynski equality evaluated from the ideal ensemble average could, in principle, depend on the reduced coupling constant ε0 of the initial state and the system size L. We find that, instead of depending on ε0 and L separately, this deviation exhibits a scaling behavior through a universal combination of ε0 and L for a given tolerance parameter, inherited from the critical scaling laws of second-order phase transitions. A similar scaling law can be obtained for the finite-speed quench as well within the Kibble-Zurek mechanism.
Scale effect on overland flow connectivity at the plot scale
NASA Astrophysics Data System (ADS)
Peñuela, A.; Javaux, M.; Bielders, C. L.
2012-06-01
A major challenge in present-day hydrological sciences is to enhance the performance of existing distributed hydrological models through a better description of subgrid processes, in particular the subgrid connectivity of flow paths. The relative surface connection function (RSC) was proposed by Antoine et al. (2009) as a functional indicator of runoff flow connectivity. For a given area, it expresses the percentage of the surface connected to the outflow boundary (C) as a function of the degree of filling of the depression storage. This function explicitly integrates the flow network at the soil surface and hence provides essential information regarding the flow paths' connectivity. It has been shown that this function could help improve the modeling of the hydrogram at the square meter scale, yet it is unknown how the scale affects the RSC function, and whether and how it can be extrapolated to other scales. The main objective of this research is to study the scale effect on overland flow connectivity (RSC function). For this purpose, digital elevation data of a real field (9 × 3 m) and three synthetic fields (6 × 6 m) with contrasting hydrological responses were used, and the RSC function was calculated at different scales by changing the length (l) or width (w) of the field. Border effects, at different extents depending on the microtopography, were observed for the smaller scales, when decreasing l or w, which resulted in a strong decrease or increase of the maximum depression storage, respectively. There was no scale effect on the RSC function when changing w. On the contrary, a remarkable scale effect was observed in the RSC function when changing l. In general, for a given degree of filling of the depression storage, C decreased as l increased. This change in C was inversely proportional to the change in l. This observation applied only up to approx. 50-70% (depending on the hydrological response of the field) of filling of depression storage, after which
Scale effect on overland flow connectivity at the plot scale
NASA Astrophysics Data System (ADS)
Peñuela, A.; Javaux, M.; Bielders, C. L.
2013-01-01
A major challenge in present-day hydrological sciences is to enhance the performance of existing distributed hydrological models through a better description of subgrid processes, in particular the subgrid connectivity of flow paths. The Relative Surface Connection (RSC) function was proposed by Antoine et al. (2009) as a functional indicator of runoff flow connectivity. For a given area, it expresses the percentage of the surface connected to the outflow boundary (C) as a function of the degree of filling of the depression storage. This function explicitly integrates the flow network at the soil surface and hence provides essential information regarding the flow paths' connectivity. It has been shown that this function could help improve the modeling of the hydrograph at the square meter scale, yet it is unknown how the scale affects the RSC function, and whether and how it can be extrapolated to other scales. The main objective of this research is to study the scale effect on overland flow connectivity (RSC function). For this purpose, digital elevation data of a real field (9 × 3 m) and three synthetic fields (6 × 6 m) with contrasting hydrological responses were used, and the RSC function was calculated at different scales by changing the length (l) or width (w) of the field. To different extents depending on the microtopography, border effects were observed for the smaller scales when decreasing l or w, which resulted in a strong decrease or increase of the maximum depression storage, respectively. There was no scale effect on the RSC function when changing w, but a remarkable scale effect was observed in the RSC function when changing l. In general, for a given degree of filling of the depression storage, C decreased as l increased, the change in C being inversely proportional to the change in l. However, this observation applied only up to approx. 50-70% (depending on the hydrological response of the field) of filling of depression storage, after which no
Scaled Experimental Modeling of VHTR Plenum Flows
ICONE 15
2007-04-01
Abstract The Very High Temperature Reactor (VHTR) is the leading candidate for the Next Generation Nuclear Power (NGNP) Project in the U.S. which has the goal of demonstrating the production of emissions free electricity and hydrogen by 2015. Various scaled heated gas and water flow facilities were investigated for modeling VHTR upper and lower plenum flows during the decay heat portion of a pressurized conduction-cooldown scenario and for modeling thermal mixing and stratification (“thermal striping”) in the lower plenum during normal operation. It was concluded, based on phenomena scaling and instrumentation and other practical considerations, that a heated water flow scale model facility is preferable to a heated gas flow facility and to unheated facilities which use fluids with ranges of density to simulate the density effect of heating. For a heated water flow lower plenum model, both the Richardson numbers and Reynolds numbers may be approximately matched for conduction-cooldown natural circulation conditions. Thermal mixing during normal operation may be simulated but at lower, but still fully turbulent, Reynolds numbers than in the prototype. Natural circulation flows in the upper plenum may also be simulated in a separate heated water flow facility that uses the same plumbing as the lower plenum model. However, Reynolds number scaling distortions will occur at matching Richardson numbers due primarily to the necessity of using a reduced number of channels connected to the plenum than in the prototype (which has approximately 11,000 core channels connected to the upper plenum) in an otherwise geometrically scaled model. Experiments conducted in either or both facilities will meet the objectives of providing benchmark data for the validation of codes proposed for NGNP designs and safety studies, as well as providing a better understanding of the complex flow phenomena in the plenums.
Scaling laws for drop impingement on porous films and papers.
Joung, Young Soo; Buie, Cullen R
2014-01-01
This study investigates drop impingement on highly wetting porous films and papers. Experiments reveal previously unexplored impingement modes on porous surfaces designated as necking, spreading, and jetting. Dimensional analysis yields a nondimensional parameter, denoted the Washburn-Reynolds number, relating droplet kinetic energy and surface energy. The impingement modes correlate with Washburn-Reynolds number variations spanning four orders of magnitude and a corresponding energy conservation analysis for droplet spreading shows good agreement with the experimental results. The simple scaling laws presented will inform the investigation of dynamic interactions between porous surfaces and liquid drops.
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 for Pulsed Chain-Reaction Chemical Lasers.
1981-08-07
HOFLANO, J3 S WHITTIER FOR701-SO-C-OOB1 UCASFE0TR-006i167213 -1 SO-TR-61-57 N MEL LEYELi two Scaling Laws for Pulsed Chain-Reaction Chemical Lasers H...44 CNN u-i LU C=, C= Ca . C= -IN HAND Mil C C" 41 U c-iG- Ca1 ~-J4J -~40) c.Ji C-4- C= G’H Io sifld 83ld A91:3N3 1i7- For small K,te is of the order
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.
Microdischarges of xenon sustained by microwaves: Determination of scaling laws
Lacoste, A.; Maulat, O.; Latrasse, L.; Arnal, Y.; Pelletier, J.
2005-04-04
The threshold conditions to maintain millimeter and submillimeter-size discharges of xenon with microwaves are experimentally determined. The threshold electric field required to sustain the plasma is reported as a function of gas pressure. The influence of the size of the dielectric cell in which the discharge is produced is also shown. The scaling laws are deduced from the threshold electric field measurements, assuming a few additional simplifying assumptions. The results are compared with data obtained with argon discharges sustained by surface waves in capillary tubes and the hypotheses assumed for the calculations are discussed.
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 and modeling of turbulent suspension flows
NASA Technical Reports Server (NTRS)
Chen, C. P.
1989-01-01
Scaling factors determining various aspects of particle-fluid interactions and the development of physical models to predict gas-solid turbulent suspension flow fields are discussed based on two-fluid, continua formulation. The modes of particle-fluid interactions are discussed based on the length and time scale ratio, which depends on the properties of the particles and the characteristics of the flow turbulence. For particle size smaller than or comparable with the Kolmogorov length scale and concentration low enough for neglecting direct particle-particle interaction, scaling rules can be established in various parameter ranges. The various particle-fluid interactions give rise to additional mechanisms which affect the fluid mechanics of the conveying gas phase. These extra mechanisms are incorporated into a turbulence modeling method based on the scaling rules. A multiple-scale two-phase turbulence model is developed, which gives reasonable predictions for dilute suspension flow. Much work still needs to be done to account for the poly-dispersed effects and the extension to dense suspension flows.
Large-scale instabilities of helical flows
NASA Astrophysics Data System (ADS)
Cameron, Alexandre; Alexakis, Alexandros; Brachet, Marc-Étienne
2016-10-01
Large-scale hydrodynamic instabilities of periodic helical flows of a given wave number K are investigated using three-dimensional Floquet numerical computations. In the Floquet formalism the unstable field is expanded in modes of different spacial periodicity. This allows us (i) to clearly distinguish large from small scale instabilities and (ii) to study modes of wave number q of arbitrarily large-scale separation q ≪K . Different flows are examined including flows that exhibit small-scale turbulence. The growth rate σ of the most unstable mode is measured as a function of the scale separation q /K ≪1 and the Reynolds number Re. It is shown that the growth rate follows the scaling σ ∝q if an AKA effect [Frisch et al., Physica D: Nonlinear Phenomena 28, 382 (1987), 10.1016/0167-2789(87)90026-1] is present or a negative eddy viscosity scaling σ ∝q2 in its absence. This holds both for the Re≪1 regime where previously derived asymptotic results are verified but also for Re=O (1 ) that is beyond their range of validity. Furthermore, for values of Re above a critical value ReSc beyond which small-scale instabilities are present, the growth rate becomes independent of q and the energy of the perturbation at large scales decreases with scale separation. The nonlinear behavior of these large-scale instabilities is also examined in the nonlinear regime where the largest scales of the system are found to be the most dominant energetically. These results are interpreted by low-order models.
Scaling Laws and Critical Properties for fcc and hcp Metals.
Desgranges, Caroline; Widhalm, Leanna; Delhommelle, Jerome
2016-06-16
The determination of the critical parameters of metals has remained particularly challenging both experimentally, because of the very large temperatures involved, and theoretically, because of the many-body interactions that take place in metals. Moreover, experiments have shown that these systems exhibit an unusually strong asymmetry of their binodal. Recent theoretical work has led to new similarity laws, based on the calculation of the Zeno line and of the underlying Boyle parameters, which provided results for the critical properties of atomic and molecular systems in excellent agreement with experiments. Using the recently developed expanded Wang-Landau (EWL) simulation method, we evaluate the grand-canonical partition function, over a wide range of conditions, for 11 fcc and hcp metals (Ag, Al, Au, Be, Cu, Ir, Ni, Pb, Pd, Pt, and Rh), modeled with a many-body interaction potential. This allows us to calculate the binodal, Zeno line, and Boyle parameters and, in turn, obtain the critical properties for these systems. We also propose two scaling laws for the enthalpy and entropy of vaporization, and identify critical exponents of 0.4 and 1.22 for these two laws, respectively.
Dimensionless parameters, scaling laws, and the implications for ETG
Castle, G.G.
1995-04-20
ETG will be useful in resolving several physical issues relevant to Spherical Tokamak Reactor concepts. First, it will provide a test of whether transport is Bohm or gyro-Bohm in nature. The second point is that ETG will operate in a completely different range of {rho}* space from other high performance machines, opening up a previously inaccessible region of parameter space. ETG is also a (very) high-{beta} machine. It would be the only device that would have all of its parameters except {rho}* similar to those of a Spherical tokamak Reactor. If it turns out that the transport scales definitively as either Bohm or gyro-Bohm, then extrapolation to reactor conditions with significantly lower values of {rho}* would become more credible. It is also shown that in general one cannot obtain a power law relation in the dimensionless variables for the confinement tim from a power law fit to the engineering variables. It is shown, however, that if T{sub i}/T{sub e} and n{sub i}/n{sub e} are constant or if a modified definition of certain dimensionless variables is adopted, then such a power law conversion is possible.
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.
Scale effect on overland flow connectivity, at the interill scale
NASA Astrophysics Data System (ADS)
Penuela Fernandez, A.; Bielders, C.; Javaux, M.
2012-04-01
The relative surface connection function (RSC) was proposed by Antoine et al. (2009) as a functional indicator of runoff flow connectivity. For a given area, it expresses the percentage of the surface connected to the outlet (C) as a function of the degree of filling of the depression storage. This function explicitly integrates the flow network at the soil surface and hence provides essential information regarding the flow paths' connectivity. It has been shown that this function could help improve the modeling of the hydrogram at the square meter scale, yet it is unknown how the scale affects the RSC function, and whether and how it can be extrapolated to other scales. The main objective of this research is to study the scale effect on overland flow connectivity (RSC function). For this purpose, digital elevation data of a real field (9 x 3 m) and three synthetic fields (6 x 6 m) with contrasting hydrological responses was used, and the RSC function was calculated at different scales by changing the length (L) or width (l) of the field. Border effects were observed for the smaller scales. In most of cases, for L or l smaller than 750mm, increasing L or l, resulted in a strong increase or decrease of the maximum depression storage, respectively. There was no scale effect on the RSC function when changing l. On the contrary, a remarkable scale effect was observed in the RSC function when changing L. In general, for a given degree of filling of the depression storage, C decreased as L increased. This change in C was inversely proportional to the change in L. This observation applied only up to approx. 50-70% (depending on the hydrological response of the field) of filling of depression storage, after which no correlation was found between C and L. The results of this study help identify the critical scale to study overland flow connectivity. At scales larger than the critical scale, the RSC function showed a great potential to be extrapolated to other scales.
On the Small-Scale Morphology of Asthenospheric Flow
NASA Astrophysics Data System (ADS)
Vidal, V.; Davaille, A.; Crambes, C.
2003-12-01
We investigated the interaction of small-scale cold instabilities dripping from a cooling lithosphere with a shear flow confined in the asthenosphere, using analog experiments. Rayleigh numbers ranged between 104 and 108. The fluids were either polymer solutions (constant viscosity), sugar or corn syrups (viscosity depending on temperature), or wax (phase transition). When cooling away from the ridge, the thickening lithosphere becomes thermally unstable and develops small-scale convective instabilities at its bottom. For sufficiently fast asthenospheric flow, these instabilities are sheared and remain trapped in the asthenosphere, following a helicoidal path aligned with the direction of plate motion. A phase diagram and scaling laws for the flow characteristics were determined. The observed helicoidal pattern could explain some geophysical observables such as small wavelength lineations in the terrestrial gravity field, or seismic anisotropy anomalies under the Pacific plate. Moreover, the distance from the ridge at which the small-scale instabilities form depends on the underlying mantle temperature: for a hotter mantle, they are generated closer to the ridge. Therefore, in the case of a ridge-centered plume, the hot temperature anomaly due to the plume triggers small-scale instabilities almost at the ridge. The heat transfer out of the mantle is accelerated, and the thickening of the lithosphere away from the ridge is delayed. Therefore, a groove at the bottom of the lithosphere may be expected along the track of a ridge-centred hotspot.
Growth, ageing and scaling laws of coronary arterial trees
Chen, Xi; Niu, Pei; Niu, Xiaolong; Shen, Wenzeng; Duan, Fei; Ding, Liang; Wei, Xiliang; Gong, Yanjun; Huo, Yong; Kassab, Ghassan S.; Tan, Wenchang; Huo, Yunlong
2015-01-01
Despite the well-known design principles of vascular systems, it is unclear whether the vascular arterial tree obeys some scaling constraints during normal growth and ageing in a given species. Based on the micro-computed tomography measurements of coronary arterial trees in mice at different ages (one week to more than eight months), we show a constant exponent of 3/4, but age-dependent scaling coefficients in a length–volume scaling law ( Lc is the crown length, Vc is the crown volume, Klength–volume is the age-dependent scaling coefficient) during normal growth and ageing. The constant 3/4 exponent represents the self-similar fractal-like branching pattern (i.e. basic mechanism to regulate the development of vascular trees within a species), whereas the age-dependent scaling coefficients characterize the structural growth or resorption of vascular trees during normal growth or ageing, respectively. This study enhances the understanding of age-associated changes in vascular structure and function. PMID:26701881
Growth, ageing and scaling laws of coronary arterial trees.
Chen, Xi; Niu, Pei; Niu, Xiaolong; Shen, Wenzeng; Duan, Fei; Ding, Liang; Wei, Xiliang; Gong, Yanjun; Huo, Yong; Kassab, Ghassan S; Tan, Wenchang; Huo, Yunlong
2015-12-06
Despite the well-known design principles of vascular systems, it is unclear whether the vascular arterial tree obeys some scaling constraints during normal growth and ageing in a given species. Based on the micro-computed tomography measurements of coronary arterial trees in mice at different ages (one week to more than eight months), we show a constant exponent of 3/4, but age-dependent scaling coefficients in a length-volume scaling law (Lc=K(length-volume) · Vc³/⁴; Lc is the crown length, Vc is the crown volume, K(length-volume) is the age-dependent scaling coefficient) during normal growth and ageing. The constant 3/4 exponent represents the self-similar fractal-like branching pattern (i.e. basic mechanism to regulate the development of vascular trees within a species), whereas the age-dependent scaling coefficients characterize the structural growth or resorption of vascular trees during normal growth or ageing, respectively. This study enhances the understanding of age-associated changes in vascular structure and function.
Crater ejecta scaling laws - Fundamental forms based on dimensional analysis
NASA Technical Reports Server (NTRS)
Housen, K. R.; Schmidt, R. M.; Holsapple, K. A.
1983-01-01
Self-consistent scaling laws are developed for meteoroid impact crater ejecta. Attention is given to the ejection velocity of material as a function of the impact point, the volume of ejecta with a threshold velocity, and the thickness of ejecta deposit in terms of the distance from the impact. Use is made of recently developed equations for energy and momentum coupling in cratering events. Consideration is given to scaling of laboratory trials up to real-world events and formulations are developed for calculating the ejection velocities and ejecta blanket profiles in the gravity and strength regimes of crater formation. It is concluded that, in the gravity regime, the thickness of an ejecta blanket is the same in all directions if the thickness and range are expressed in terms of the crater radius. In the strength regime, however, the ejecta velocities are independent of crater size, thereby allowing for asymmetric ejecta blankets. Controlled experiments are recommended for the gravity/strength transition.
Gompertz mortality law and scaling behavior of the Penna model.
Coe, J B; Mao, Y
2005-11-01
The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.
Gompertz mortality law and scaling behavior of the Penna model
NASA Astrophysics Data System (ADS)
Coe, J. B.; Mao, Y.
2005-11-01
The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism’s genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.
Crater ejecta scaling laws - Fundamental forms based on dimensional analysis
NASA Technical Reports Server (NTRS)
Housen, K. R.; Schmidt, R. M.; Holsapple, K. A.
1983-01-01
Self-consistent scaling laws are developed for meteoroid impact crater ejecta. Attention is given to the ejection velocity of material as a function of the impact point, the volume of ejecta with a threshold velocity, and the thickness of ejecta deposit in terms of the distance from the impact. Use is made of recently developed equations for energy and momentum coupling in cratering events. Consideration is given to scaling of laboratory trials up to real-world events and formulations are developed for calculating the ejection velocities and ejecta blanket profiles in the gravity and strength regimes of crater formation. It is concluded that, in the gravity regime, the thickness of an ejecta blanket is the same in all directions if the thickness and range are expressed in terms of the crater radius. In the strength regime, however, the ejecta velocities are independent of crater size, thereby allowing for asymmetric ejecta blankets. Controlled experiments are recommended for the gravity/strength transition.
Universal scaling laws for the disintegration of electrified drops
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
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.
Scale effects in gas nano flows
NASA Astrophysics Data System (ADS)
Barisik, Murat; Beskok, Ali
2014-05-01
Most previous studies on gas transport in nano-scale confinements assume dynamic similarity with rarefied gas flows, and employ kinetic theory based models. This approach is incomplete, since it neglects the van der Waals forces imposed on gas molecules by the surfaces. Using three-dimensional molecular dynamics (MD) simulations of force driven gas flows, we show the significance of wall force field in nano-scale confinements by defining a new dimensionless parameter (B) as the ratio of the wall force-penetration length to the channel height. Investigation of gas transport in different nano-channels at various Knudsen numbers show the importance of wall force field for finite B values, where the dynamic similarity between the rarefied and nano-scale gas flows break down. Comparison of MD results employing molecularly structured three-dimensional walls versus reflection of gas molecules from a two-dimensional planar surface with Maxwell distribution show that the nano-confinement effects cannot be resolved by the latter approach, frequently used in kinetic theory calculations. Molecularly structured walls determine the bulk flow physics by setting a proper tangential momentum accommodation coefficient, and they also determine the transport in the near wall region. Gas nano-flows with finite B exhibit significant differences in the local density and velocity profiles, affecting the mass flow rate and the formation of Knudsen's minimum in nano-channels.
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 law analysis of paraffin thin films on different surfaces
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 substrates 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.
Anomalous scaling law of strength and toughness of cellulose nanopaper
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
Universal geometrical scaling of the elliptic flow
NASA Astrophysics Data System (ADS)
Andrés, C.; Dias de Deus, J.; Moscoso, A.; Pajares, C.; Salgado, Carlos A.
2015-03-01
The presence of scaling variables in experimental observables provide very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the Color Glass Condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from RHIC to LHC, with a simple generalization of the scaling previously found for other observables and systems. Interestingly, the case of the photons, difficult to reconcile in most formalisms, nicely fit the scaling curve. We discuss on the possible interpretations of this finding in terms of initial or final state effects.
Empirical Solar Abundance Scaling Laws of Supernova {gamma} Process Isotopes
Hayakawa, Takehito; Iwamoto, Nobuyuki; Kajino, Toshitaka; Shizum, Toshiyuki; Umeda, Hideyuki; Nomoto, Ken'Ichi
2008-11-11
Analyzing the solar system abundances, we have found two empirical abundance scaling laws concerning the p- and s-nuclei with the same atomic number. They are evidence that the 27 p-nuclei are synthesized by the supernova {gamma}-process. The scalings lead to a novel concept of 'universality of {gamma}-process' that the s/p and p/p ratios of nuclei produced by individual {gamma}-processes are almost constant, respectively. We have calculated the ratios of materials produced by the {gamma}-process based on core-collapse supernova explosion models under various astrophysical conditions and found that the scalings hold for individual {gamma}-processes independent of the conditions assumed. The results further suggest an extended universality that the s/p ratios in the {gamma}-process layers are not only constant but also centered on a specific value of 3. With this specific value and the scaling of the s/p ratios, we estimate that the ratios of the s-process abundance contributions from the AGB stars to the massive stars are almost 6.7 for the s-nuclei of A>90 in the solar system.
The scaling laws of human travel - A message from George
NASA Astrophysics Data System (ADS)
Brockmann, Dirk
2006-03-01
In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic the knowledge of dynamical and statistical properties of human travel is of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive and the assumption that humans disperse diffusively still prevails in models. I will report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Based on a comprehensive dataset of over a million individual displacements we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale free random walks known as L'evy flights. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraic tails which attenuate the superdiffusive spread. We show that human travel can be described mathematically on many spatiotemporal scales by a two parameter continuous time random walk model to a surprising accuracy and conclude that human travel on geographical scales is an ambivalent effectively superdiffusive process.
Scaling up debris-flow experiments on a centrifuge
NASA Astrophysics Data System (ADS)
Hung, C.; Capart, H.; Crone, T. J.; Grinspum, E.; Hsu, L.; Kaufman, D.; Li, L.; Ling, H.; Reitz, M. D.; Smith, B.; Stark, C. P.
2013-12-01
Boundary forces generated by debris flows can be powerful enough to erode bedrock and cause considerable damage to infrastructure during runout. Formulation of an erosion-rate law for debris flows is therefore a high priority, and it makes sense to build such a law around laboratory experiments. However, running experiments big enough to generate realistic boundary forces is a logistical challenge to say the least [1]. One alternative is to run table-top simulations with unnaturally weak but fast-eroding pseudo-bedrock, another is to extrapolate from micro-erosion of natural substrates driven by unnaturally weak impacts; hybrid-scale experiments have also been conducted [2]. Here we take a different approach in which we scale up granular impact forces by running our experiments under enhanced gravity in a geotechnical centrifuge [3]. Using a 40cm-diameter rotating drum [2] spun at up to 100g, we generate debris flows with an effective depth of over several meters. By varying effective gravity from 1g to 100g we explore the scaling of granular flow forces and the consequent bed and wall erosion rates. The velocity and density structure of these granular flows is monitored using laser sheets, high-speed video, and particle tracking [4], and the progressive erosion of the boundary surfaces is measured by laser scanning. The force structures and their fluctuations within the granular mass and at the boundaries are explored with contact dynamics numerical simulations that mimic the lab experimental conditions [5]. In this presentation we summarize these results and discuss how they can contribute to the formulation of debris-flow erosion law. [1] Major, J. J. (1997), Journal of Geology 105: 345-366, doi:10.1086/515930 [2] Hsu, L. (2010), Ph.D. thesis, University of California, Berkeley [3] Brucks, A., et al (2007), Physical Review E 75, 032301, doi:10.1103/PhysRevE.75.032301 [4] Spinewine, B., et al (2011), Experiments in Fluids 50: 1507-1525, doi: 10.1007/s00348
Flow topologies and turbulence scales in a jet-in-cross-flow
Oefelein, Joseph C.; Ruiz, Anthony M.; Lacaze, Guilhem
2015-04-03
This study presents a detailed analysis of the flow topologies and turbulence scales in the jet-in-cross-flow experiment of [Su and Mungal JFM 2004]. The analysis is performed using the Large Eddy Simulation (LES) technique with a highly resolved grid and time-step and well controlled boundary conditions. This enables quantitative agreement with the first and second moments of turbulence statistics measured in the experiment. LES is used to perform the analysis since experimental measurements of time-resolved 3D fields are still in their infancy and because sampling periods are generally limited with direct numerical simulation. A major focal point is the comprehensivemore » characterization of the turbulence scales and their evolution. Time-resolved probes are used with long sampling periods to obtain maps of the integral scales, Taylor microscales, and turbulent kinetic energy spectra. Scalar-fluctuation scales are also quantified. In the near-field, coherent structures are clearly identified, both in physical and spectral space. Along the jet centerline, turbulence scales grow according to a classical one-third power law. However, the derived maps of turbulence scales reveal strong inhomogeneities in the flow. From the modeling perspective, these insights are useful to design optimized grids and improve numerical predictions in similar configurations.« less
Flow topologies and turbulence scales in a jet-in-cross-flow
Oefelein, Joseph C.; Ruiz, Anthony M.; Lacaze, Guilhem
2015-04-03
This study presents a detailed analysis of the flow topologies and turbulence scales in the jet-in-cross-flow experiment of [Su and Mungal JFM 2004]. The analysis is performed using the Large Eddy Simulation (LES) technique with a highly resolved grid and time-step and well controlled boundary conditions. This enables quantitative agreement with the first and second moments of turbulence statistics measured in the experiment. LES is used to perform the analysis since experimental measurements of time-resolved 3D fields are still in their infancy and because sampling periods are generally limited with direct numerical simulation. A major focal point is the comprehensive characterization of the turbulence scales and their evolution. Time-resolved probes are used with long sampling periods to obtain maps of the integral scales, Taylor microscales, and turbulent kinetic energy spectra. Scalar-fluctuation scales are also quantified. In the near-field, coherent structures are clearly identified, both in physical and spectral space. Along the jet centerline, turbulence scales grow according to a classical one-third power law. However, the derived maps of turbulence scales reveal strong inhomogeneities in the flow. From the modeling perspective, these insights are useful to design optimized grids and improve numerical predictions in similar configurations.
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
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
Constitutive Law and Flow Mechanism in Diamond Deformation
Yu, Xiaohui; Raterron, Paul; Zhang, Jianzhong; ...
2012-11-19
Constitutive laws and crystal plasticity in diamond deformation have been the subjects of substantial interest since synthetic diamond was made in 1950's. To date, however, little is known quantitatively regarding its brittle-ductile properties and yield strength at high temperatures. In this paper, we report, for the first time, the strain-stress constitutive relations and experimental demonstration of deformation mechanisms under confined high pressure. The deformation at room temperature is essentially brittle, cataclastic, and mostly accommodated by fracturing on {111} plane with no plastic yielding at uniaxial strains up to 15%. At elevated temperatures of 1000°C and 1200°C diamond crystals exhibit significantmore » ductile flow with corresponding yield strength of 7.9 and 6.3 GPa, indicating that diamond starts to weaken when temperature is over 1000°C. Finally, at high temperature the plastic deformation and ductile flow is meditated by the <110>{111} dislocation glide and a very active {111} micro-twinning.« less
Constitutive Law and Flow Mechanism in Diamond Deformation
Yu, Xiaohui; Raterron, Paul; Zhang, Jianzhong; Lin, Zhijun; Wang, Liping; Zhao, Yusheng
2012-11-19
Constitutive laws and crystal plasticity in diamond deformation have been the subjects of substantial interest since synthetic diamond was made in 1950's. To date, however, little is known quantitatively regarding its brittle-ductile properties and yield strength at high temperatures. In this paper, we report, for the first time, the strain-stress constitutive relations and experimental demonstration of deformation mechanisms under confined high pressure. The deformation at room temperature is essentially brittle, cataclastic, and mostly accommodated by fracturing on {111} plane with no plastic yielding at uniaxial strains up to 15%. At elevated temperatures of 1000°C and 1200°C diamond crystals exhibit significant ductile flow with corresponding yield strength of 7.9 and 6.3 GPa, indicating that diamond starts to weaken when temperature is over 1000°C. Finally, at high temperature the plastic deformation and ductile flow is meditated by the <110>{111} dislocation glide and a very active {111} micro-twinning.
Neptune radio emission - Predictions based on planetary scaling laws
NASA Technical Reports Server (NTRS)
Desch, Michael D.
1988-01-01
In this paper a prediction is advanced concerning Neptune's low-frequency radio emission based on the radiometric Bode's law for radio planets in combination with the magnetostrophic scaling law for magnetized planets. The total emitted radio power is predicted to be about 1.6 x 10 to the 7th W, very nearly the same as that predicted and observed for Uranus. Possible emission spectral shapes, based on Saturn and earth-like models, are shown. Using these models, the radio emission frequency range is predicted to extend from approximately 100 to just over 1000 kHz, with a spectral peak between 350 and 500 kHz. If radiation is beamed approximately in the sunward direction, Neptune should be detectable by the planetary radio astronomy experiment onboard the Voyager spacecraft sometime between 45 and 90 days before closest approach. This detection is likely to represent the first direct evidence of a Neptune magnetic field. Possible implications for Neptune's magnetosphere with regard to the time of first detection are discussed.
Species survival and scaling laws in hostile and disordered environments.
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.
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.
Scaling laws for van der Waals interactions in nanostructured materials.
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.
Scaling laws for the inner structure of the radiation belts
NASA Astrophysics Data System (ADS)
Mourenas, D.; Ma, Q.; Artemyev, A. V.; Li, W.
2017-04-01
Accurately modeling the evolution of the electron radiation belts within the plasmasphere represents both an imperative goal for space weather forecasting and a great challenge. Combining previously developed approximate analytical expressions of electron lifetimes with recent statistical models of plasma density, ULF, whistler-mode, and electromagnetic ion cyclotron waves, we demonstrate that geomagnetic activity and plasma density actually govern the inner structure of the radiation belts through several simple analytical scaling laws when Kp < 3. Many of the observed characteristic features of electron fluxes in the energy versus L shell parameter space are straightforwardly explained. In particular, the upper energy limit of significant electron fluxes at L = 1.5 is estimated as ˜1 MeV in agreement with recent satellite observations. This approximate analytical model represents a very simple and powerful tool for exploring and better understanding the complex variations of the inner structure of the radiation belts with geomagnetic activity during relatively quiet times.
Coastal microbial fuel cell: scaling laws and systems
NASA Astrophysics Data System (ADS)
Bandyopadhyay, Promode R.; McNeilly, Frank J.; Thivierge, Daniel P.; Fredette, Albert R.
2006-05-01
Microbes, like Geobacters, have inhabited the seafloors around the world since the early days of earth. Such regions are anaerobic and they gain energy by using the widely prevalent iron oxides and organic matters. Because they appear to colonize conducting surfaces that act as sinks of electrons, microbial fuel cells have been shown to convert organic matter to electricity. A microbial fuel cell system has been deployed in Narragansett Bay in Newport, Rhode Island for a year. Currently, the cathode and anode areas are of the order of that of a small wind mill. Measurements have been carried out to determine the marine scaling laws of power harvesting in passive benthic microbial fuel cells. The focus has been on the ocean engineering aspects such as marine scaling laws and the integration of the biochemical and the electronic systems. The characteristics examined are: the relationship of electrode surface area and power produced, the stabilization rates of ionic paths, that is, the effects of location depth of cathodes on stabilization after deployment, the effects of solar and lunar cycles in the Narragansett Bay on the dynamic components of power produced, and the hysteresis effects between periods of active power harvesting and dormancy; the effects of 'on sediment surface' versus 'in sediment' anode deployment have been examined for smaller electrode areas so far. A capacitance model of power consumption and harvesting has been proposed for the marine environment. It is assumed that the primordial benthic microbe laden layer of the earth acts like a giant capacitor. In the microbial fuel cell, this charged benthic layer acts in series with a smaller constant voltage DC power source. This giant benthic capacitance is a result of untapped accumulated charge from the microbes while the DC source originates from the real-time production due to the microbes. Finally, the microbial fuel cell is integrated with a power conversion system to intermittently energize a
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.
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.
Scaling law for bubbles rising near vertical walls
NASA Astrophysics Data System (ADS)
Dabiri, Sadegh; Bhuvankar, Pramod
2016-06-01
This paper examines the rising motion of a layer of gas bubbles next to a vertical wall in a liquid in the presence of an upward flow parallel to the wall to help with the understanding of the fluid dynamics in a bubbly upflow in vertical channels. Only the region near the wall is simulated with an average pressure gradient applied to the domain that balances the weight of the liquid phase. The upward flow is created by the rising motion of the bubbles. The bubbles are kept near the wall by the lateral lift force acting on them as a result of rising in the shear layer near the wall. The rise velocity of the bubbles sliding on the wall and the average rise velocity of the liquid depend on three dimensionless parameters, Archimedes number, Ar, Eötvös number, Eo, and the average volume fraction of bubbles on the wall. In the limit of small Eo, bubbles are nearly spherical and the dependency on Eo becomes negligible. In this limit, the scaling of the liquid Reynolds number with Archimedes number and the void fraction is presented. A scaling argument is presented based on viscous dissipation analysis that matches the numerical findings. Viscous dissipation rates are found to be high in a thin film region between the bubble and the wall. A scaling of the viscous dissipation and steady state film thickness between the bubble and the wall with Archimedes number is presented.
Cross-flow Ultrafiltration Scaling Considerations
Duignan, M
2006-04-10
One legacy of the nuclear age is radioactive waste and it must be stabilized to be stored in a safe manner. An important part of the stabilization process is the separation of radioactive solids from the liquid wastes by cross-flow ultrafiltration. The performance of this technology with the wastes to be treated was unknown and, therefore, had to be obtained. However, before beginning a filter study the question of experimental scale had to be addressed. Of course, carrying out experiments using full-size equipment is always ideal, but rarely practical when dealing with plant size processes. Flow loops that will handle millions of liters of slurries, which are either highly caustic or acidic, with flow rates of 10,000 lpm make full-scale tests prohibitively expensive. Moreover, when the slurries happen to be radioactive such work is also very dangerous. All of these considerations lend themselves to investigations at smaller scales and in many situations can be treated with computational analyses. Unfortunately, as scale is reduced it becomes harder to provide prototypic results and the two and three phase multi-component mixtures challenge accurate computational results. To obtain accurate and representative filter results the use of two scales were chosen: (1) Small-scale--would allow the testing with actual radioactive waste samples and compare results with simulated wastes that were not radioactive. For this scale the feed tank held 6 liters of waste and it had a single cross-flow filter tube 0.61 m long. (2) Pilot-scale--would be restricted to use simulated non-radioactive wastes. At this larger scale the feed tank held 120 liters of waste and the filter unit was prototypic to the planned plant facility in pore size (0.1 micron), length (2.29 m), diameter (0.0127 m inside and 0.0159 m outside diameter), and being multi-tubed. The small-scale apparatus is convenient, easy to use, and can test both radioactive and non-radioactive wastes; therefore, there is a
Scaling Laws for liquid and ion transport in nanochannels grafted with polyelectrolyte brushes
NASA Astrophysics Data System (ADS)
Chen, Guang; Sinha, Shayandev; Das, Siddhartha; Soft Matter, Interfaces,; Energy Laboratory (Smiel) Team
Grafting nanochannels with polyelectrolyte (PE) brushes renders tremendous functionality to the nanochannels, making them capable of applications such as ion manipulation, ion sensing, current rectification, nanofluidic diode fabrication, and flow control. PE brush is a special case of polymers at interfaces; such brush-like structure is possible only when the grafting density (σ) is beyond a critical value. In this study, we shall propose scaling laws that identify σ-N(N is the size of the PE molecule) combination that simultaneously ensure that the grafted PE molecules adopt ''brush''-like configuration and the height of the PE brushes are smaller than the nanochannel half height. Secondly, we pinpoint the scaling conditions where the electrostatic effects associated with the PE brushes can be decoupled from the corresponding PE excluded volume and elastic effects; such de-coupling has tremendous connotation in context of modeling of electrostatics and transport at PE-brush-covered interfaces. Thirdly, we provide scaling arguments to quantify the dependence of the flow penetration depth into the PE brush as a function of the σ-N combination. Finally, our scaling estimates pinpoint the conditions where the flow or electric field induced deformation of the grafted nanochannel PE brushes can be neglected while modeling the pressure-driven or electroosmotic transport or ionic current in such nanochannels.
Scaling Laws for Inter-droplet Ice Bridging
NASA Astrophysics Data System (ADS)
Nath, Saurabh; Ahmadi, Farzad; Boreyko, Jonathan
2016-11-01
In this work, we study the dynamics of an ice bridge growing from a frozen droplet towards its neighboring supercooled liquid droplet. Experiments were done on a Peltier stage inside a humidity chamber with deposited or condensed droplets where the substrate temperature and ambient humidity could be controlled. Following a quasi-steady diffusion-driven model, we develop scaling laws to show how the growth rate depends on the substrate temperature, droplet sizes and inter-droplet distances over and above other environmental parameters such as air temperature and humidity. The growth rate as well as the success or failure of an ice bridge to connect to its neighboring liquid droplet depend on a nondimensional number called the separation parameter S*, defined as the ratio of the initial inter-droplet spacing to the diameter of the evaporating liquid droplet. It is shown that the maximum value of S* for connection scales as 1 as long as frozen drop is larger than the liquid droplet. For the converse case of a larger water drop, there are at least three separate regimes of critical S*, depending on whether the water drop is a puddle, a spherical cap or if the frozen drop is a puddle.
Cope's Rule and the Universal Scaling Law of Ornament Complexity.
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.
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.
Mixing lengths scaling in a gravity flow
Ecke, Robert E; Rivera, Micheal; Chen, Jun; Ecke, Robert E
2009-01-01
We present an experimental study of the mixing processes in a gravity current. The turbulent transport of momentum and buoyancy can be described in a very direct and compact form by a Prandtl mixing length model [1]: the turbulent vertical fluxes of momentum and buoyancy are found to scale quadraticatly with the vertical mean gradients of velocity and density. The scaling coefficient is the square of the mixing length, approximately constant over the mixing zone of the stratified shear layer. We show in this paper how, in different flow configurations, this length can be related to the shear length of the flow {radical}({var_epsilon}/{partial_derivative}{sub z}u{sup 3}).
Finite scale equations for compressible fluid flow
Margolin, Len G
2008-01-01
Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier-Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volume-averaged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier-Stokes equations.
Scaling of flow and transport behavior in heterogeneous groundwater systems
NASA Astrophysics Data System (ADS)
Scheibe, Timothy; Yabusaki, Steven
1998-11-01
Three-dimensional numerical simulations using a detailed synthetic hydraulic conductivity field developed from geological considerations provide insight into the scaling of subsurface flow and transport processes. Flow and advective transport in the highly resolved heterogeneous field were modeled using massively parallel computers, providing a realistic baseline for evaluation of the impacts of parameter scaling. Upscaling of hydraulic conductivity was performed at a variety of scales using a flexible power law averaging technique. A series of tests were performed to determine the effects of varying the scaling exponent on a number of metrics of flow and transport behavior. Flow and transport simulation on high-performance computers and three-dimensional scientific visualization combine to form a powerful tool for gaining insight into the behavior of complex heterogeneous systems. Many quantitative groundwater models utilize upscaled hydraulic conductivity parameters, either implicitly or explicitly. These parameters are designed to reproduce the bulk flow characteristics at the grid or field scale while not requiring detailed quantification of local-scale conductivity variations. An example from applied groundwater modeling is the common practice of calibrating grid-scale model hydraulic conductivity or transmissivity parameters so as to approximate observed hydraulic head and boundary flux values. Such parameterizations, perhaps with a bulk dispersivity imposed, are then sometimes used to predict transport of reactive or non-reactive solutes. However, this work demonstrates that those parameters that lead to the best upscaling for hydraulic conductivity and head do not necessarily correspond to the best upscaling for prediction of a variety of transport behaviors. This result reflects the fact that transport is strongly impacted by the existence and connectedness of extreme-valued hydraulic conductivities, in contrast to bulk flow which depends more strongly on
Diffusivity-free Scaling Laws for Earth and Planetary Dynamos: A Reassessment
NASA Astrophysics Data System (ADS)
Fournier, A.; Gastine, T.; Aubert, J.
2016-12-01
Numerical dynamo models notoriously do not operate in the adequate region of parameter space, since the stiffnessof the problem at hand makes it mandatory to resort to enhanced values of transport properties for a solution to be within reach. Accordingly, the application of scaling laws derived from numerical simulations to planetaryinteriors implicitly assumes that simulations operate in the adequate dynamical regime. Christensen and Aubert (2006, CA06 henceforth) proposed along these lines power-based, diffusivity-free scaling laws for magnetic field strength and flow speed, based on the analysis of an ensemble of such simulations. The CA06 laws were subsequently applied to a large number of bodies in the solar system, including Earth. They have received some criticism in the past few years, in particular with regard to a residual effect of diffusivites on the properties deduced from the CA06 dataset. In view of providing a refreshing look at this issue, and noting that simulation have improved since 2006, we complement the CA06 dataset with simulations performed during the last decade. This amounts to doubling the size of the dataset (from O(100) to 0(200) members), while enabling a broader sampling of parameter space. Physics-based selection criteria (most notably the magnetic energy to kinetic energy ratio) further allow us to select those dynamos which we think are indeed in the appropriate dynamical regime. This reduced dataset (comprising O(5O) members) convincingly reveals power-based, diffusion-free scalings for magnetic field strength and flow speed. We further discuss the exponents found in light of the theoretical predictions of Davidson (2013), which rest on the assumption that the main departure from geostrophy in planetary cores is achieved through a Magnetic-Archimedean-Coriolis 3-term force balance.
The nature of the two scaling laws in interfacial fracture.
NASA Astrophysics Data System (ADS)
Stormo, Arne; Lengliné, Olivier; Schmittbuhl, Jean
2014-05-01
brittle. When we introduce a gradient to the model we get an interface between a large group of broken fibers, and a large group of surviving fibers. By interpreting the interface between these two groups as a developing fracture front, we can reconstruct the scaling laws found in the laboratory. When we investigate the release of energy in our model, we find that the amount released in each event is distributed as a power-law, similar to the Gutenberg Richter distribution. The exponent of this distribution is dependant on the properties of the system. We thus want to find a connection to the exponent of the Gutenberg Richter distribution, especially the varying exponent found during the hydraulic injection of the deep geothermal reservoirs at Soultz-sous Forêts.
Scaling of peak flows with constant flow velocity in random self-similar networks
Troutman, Brent M.; Mantilla, Ricardo; Gupta, Vijay K.
2011-01-01
A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters pi and pe, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β(E) and φ(E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β(E) and φ(E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ(E) and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios
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
Scale invariance of subsurface flow patterns and its limitation
NASA Astrophysics Data System (ADS)
Hergarten, Stefan; Winkler, Gerfried; Birk, Steffen
2015-04-01
The morphology of river networks at the Earth's surface has been addressed in numerous studies. Numerical simulations of fluvial erosion processes and concepts of optimization have provided a rather comprehensive understanding about the scale invariance of river networks. Less is known about the structure of preferential flow patterns in the subsurface because these are only accessible by indirect measurements in most cases. As preferential flow patterns are crucial for all transport processes in the subsurface, unraveling their structure is a major challenge in subsurface hydrology. Transferring the idea of optimization from surface flow to subsurface flow it was recently suggested that preferential subsurface flow patterns should also have a dendritic, scale-invariant structure similar to that of river networks. In this study we analyzed the mean discharges of serval thousand springs with respect to scale invariance. For this purpose we reanalyzed a data set comprising about 17,000 springs from Spain already published in the literature and three new data sets from the Eastern Alps in Austria. We found that the probability density f(Q) of the discharge distribution can be described by a power law with an exponential cutoff, f(Q) ≈ Q-τe- QQc. The scaling exponent τ was found to be about 1.6, which is slightly larger than the exponent τ = 1.5 of river networks. In contrast to rivers, the distributions of the spring discharges are characterized by a significant cutoff at large discharges. This cutoff strongly depends on the lithology of the aquifers, while the scaling exponent τ ˜ 1.6 seems to be universal. The highest cutoff was found for limestones being one of the primary host rocks for karstic aquifers. We found Qc ˜ 6000 l/s for the limestones in the data set from Spain, suggesting a scale-invariant subsurface flow pattern up to catchment sizes of several thousand square kilometers. At the other edge, we found a cutoff at catchment sizes in the order of
Universal geometrical scaling of the elliptic flow
NASA Astrophysics Data System (ADS)
Andrés, C.; de Deus, J. Dias; Moscoso, A.; Pajares, C.; Salgado, Carlos A.
2015-09-01
The presence of scaling variables in experimental observables provides very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the color glass condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from the BNL Relativistic Heavy Ion Collider to the CERN Large Hadron Collider, with a simple generalization of the scaling previously found for other observables and systems. Interestingly the case of the photons, difficult to reconcile in most formalisms, nicely fits the scaling curve. We discuss the possible interpretations of this finding in terms of initial or final state effects.
Scaling laws in functional genome content across prokaryotic clades and lifestyles.
Molina, Nacho; van Nimwegen, Erik
2009-06-01
For high-level functional categories that are represented in almost all prokaryotic genomes, the numbers of genes in these categories scale as power-laws in the total number of genes. We present a comprehensive analysis of the variation in these scaling laws across prokaryotic clades and lifestyles. For the large majority of functional categories, including transcription regulators, the inferred scaling laws are statistically indistinguishable across clades and lifestyles, supporting the simple hypothesis that these scaling laws are universally shared by all prokaryotes.
Scaling law governing the roughness of the swash edge line
NASA Astrophysics Data System (ADS)
Bormashenko, E.; Musin, A.; Grynyov, R.
2014-09-01
The paper is devoted to the analysis of the shape of the swash edge line. Formation of the swash boundary is treated as an interfacial phenomenon. The simplest quantitative characteristic of the roughness of interface is its width w, defined as the root-mean-square fluctuation around the average position. For rough interfaces, the scaling with size of the system L is observed in the form w(L)~Lζ. The concept of scaling supplies a simple framework for classifying interfaces. It is suggested that the fine structure of the swash boundary results from the combined action of the pinning force applied by random defects of the beach and elasticity of distorted swash boundary. The roughness of the swash front was studied at the Mediterranean Sea coast for uprush and backwash flows. Value of exponent ζ for receding swash front line was 0.64 +/- 0.02, when in the case of advancing swash the value 0.73 +/- 0.03 was calculated. The scaling exponent established for the receding phase of the swash is very close to the values of the exponent established for the roughness of the triple line for water droplets deposited on rough surfaces, crack propagation front in Plexiglas, and for the motion of a magnetic domain walls.
Scaling law governing the roughness of the swash edge line
Bormashenko, E.; Musin, A.; Grynyov, R.
2014-01-01
The paper is devoted to the analysis of the shape of the swash edge line. Formation of the swash boundary is treated as an interfacial phenomenon. The simplest quantitative characteristic of the roughness of interface is its width w, defined as the root-mean-square fluctuation around the average position. For rough interfaces, the scaling with size of the system L is observed in the form w(L)∝Lζ. The concept of scaling supplies a simple framework for classifying interfaces. It is suggested that the fine structure of the swash boundary results from the combined action of the pinning force applied by random defects of the beach and elasticity of distorted swash boundary. The roughness of the swash front was studied at the Mediterranean Sea coast for uprush and backwash flows. Value of exponent ζ for receding swash front line was 0.64 ± 0.02, when in the case of advancing swash the value 0.73 ± 0.03 was calculated. The scaling exponent established for the receding phase of the swash is very close to the values of the exponent established for the roughness of the triple line for water droplets deposited on rough surfaces, crack propagation front in Plexiglas, and for the motion of a magnetic domain walls. PMID:25175319
Scaling thermal effects in radial flow
NASA Astrophysics Data System (ADS)
Hudspeth, R. T.; Guenther, R. B.; Roley, K. L.; McDougal, W. G.
To adequately evaluate the environmental impact of siting nuclear waste repositories in basalt aquicludes, it is essential to know the effects on parameter identification algorithms of thermal gradients that exist in these basaltic aquicludes. Temperatures of approximately 60°C and pressures of approximately 150 atm can be expected at potential repository sites located at depths of approximately 1000 m. The phenomenon of over-recovery has been observed in some pumping tests conducted at the Hanford Nuclear Reservation located in the Pasco Basin adjacent to the Columbia River in the state of Washington, USA. This over-recovery phenomenon may possibly be due to variations in the fluid density caused by thermal gradients. To assess the potential effects of these thermal gradients on indirect parameter identification algorithms, a systematic scaling of the governing field equations is required in order to obtain dimensionless equations based on the principle of similarity. The constitutive relationships for the specific weight of the fluid and for the porosity of the aquiclude are shown to be exponentially dependent on the pressure gradient. The dynamic pressure is converted to the piezometric head and the flow equation for the piezometric head is then scaled in radial coordinates. Order-of-magnitude estimates are made for all variables in unsteady flow for a typical well test in a basaltic aquiclude. Retaining all nonlinear terms, the parametric dependency of the flow equation on the classical dimensionless thermal and hydraulic parameters is demonstrated. These classical parameters include the Batchelor, Fourier, Froude, Grashof, and Reynolds Numbers associated with thermal flows. The flow equation is linearized from order-of-magnitude estimates based on these classical parameters for application in parameter identification algorithms.
The rank-size scaling law and entropy-maximizing principle
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2012-02-01
The rank-size regularity known as Zipf's law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely successful. By introducing a pivotal constraint condition, I present here a set of new derivations based on the self-similar hierarchy of cities. First, I derive a pair of exponent laws by postulating local entropy maximizing. From the two exponential laws follows a general hierarchical scaling law, which implies the general form of Zipf's law. Second, I derive a special hierarchical scaling law with the exponent equal to 1 by postulating global entropy maximizing, and this implies the pure form of Zipf's law. The rank-size scaling law has proven to be one of the special cases of the hierarchical scaling law, and the derivation suggests a certain scaling range with the first or the last data point as an outlier. The entropy maximization of social systems differs from the notion of entropy increase in thermodynamics. For urban systems, entropy maximizing suggests the greatest equilibrium between equity for parts/individuals and efficiency of the whole.
NASA Astrophysics Data System (ADS)
Blackwell, D. D.; Thakur, M.
2007-12-01
Birch (1968) first showed the linear correlation of surface heat flow and radioactive heat production (Qs = Qo + bAs ) in granites in New England, USA and discussed implications to the vertical scale of radioactive heat generation in the crust. Subsequently similar relationships have been found worldwide and numerous papers written describing more details and expanding the implications of Birch's Law. The results are a powerful contribution from heat flow research to the understanding of the lithosphere and its evolution. Models are both well constrained experimentally and simple in implications. However, there still exist thermal models of the crust and lithosphere that do not have the same firm foundation and involve unnecessary ad hoc assumptions. A main point of confusion has been that the several of the original relationships were so low in error as to be considered by some to be "fortuitous". Interestingly a "similar" relationship has been proposed based on regional scale averaging of Qs -As data. A second point of confusion is that one admissible crustal radioactivity distribution model (the constant heat generation to depth b) has been criticized as unrealistic for a number of reasons, including the effect of erosion. However, it is appropriate to refer to the Qs -As relationship as a law because in fact the relationship holds as long as the vertical distribution is "geologically realistic." as will be demonstrated in this paper. All geologic and geophysical models of the continental crust imply decreasing heat production as a function of depth (i.e. the seismic layering for example) except in very special cases. This general decrease with depth is the only condition required for the existence of a "linear" Qs -As relationship. A comparison of all the Qs -As relationships proposed for terrains not affected by thermal events over the last 150 to 200 Ma shows a remarkably uniformity in slope (10 ± 3 km) and intercept value (30 ± 5 mWm-2 ). Therefore these
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).
Scaling Laws for van der Waals Interactions in Nanostructured Materials
NASA Astrophysics Data System (ADS)
Gobre, Vivekanand; Tkatchenko, Alexandre
2014-03-01
Van der Waals (vdW) forces originate from interactions between fluctuating multipoles in matter and play a significant role in the structure and stability of nanostructured materials. Many models used to describe vdW interactions in nanomaterials are based on a simple pairwise-additive approximation, neglecting the strong electrodynamic response effects caused by long-range fluctuations in matter. We develop and utilize an efficient microscopic method to demonstrate that vdW 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 vdW 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.
Ignition scaling laws and their application to capsule design
NASA Astrophysics Data System (ADS)
Herrmann, Mark C.; Tabak, Max; Lindl, John D.
2001-05-01
This paper investigates the amount of energy required to ensure the ignition of an inertial confinement fusion capsule. First, a series of one-dimensional LASNEX [G. B. Zimmerman and W. L. Kruer, Plasma Phys. Controlled Fusion 2, 51 (1975)] simulations are performed to create a database of barely ignited capsules that span the parameter regime of interest. This database is used to develop scaling laws for the ignition energy in terms of both the stagnated capsule parameters and the in-flight capsule parameters, and to explore the connection between these two parameter sets. We then examine how much extra energy is required to overcome the effect of the inevitable surface imperfections that are amplified during the implosion process. These perturbations can lead to break up of the capsule in flight or to mix of cold fuel into the hot spot, both of which can cause the capsule to fail. As an example, a family of capsules with fixed adiabat, drive pressure, and absorbed energy is studied; the capsule from this family that is maximally robust to these failure modes is found.
Scaling laws in annealed LiCoOx films
NASA Astrophysics Data System (ADS)
Kleinke, M. U.; Davalos, J.; Polo da Fonseca, C.; Gorenstein, A.
1999-03-01
The surface morphology evolution due to the annealing process of LiCoOx thin films deposited by rf sputtering is studied by means of an atomic force microscope. Linear relationships were observed in log-log plots of interface width versus window length, as predicted by scaling laws. For as-grown films, only one growth exponent α is evidenced. For annealed films two different slopes α1 and α2 were observed, indicating distinct growth dynamics in the system. The roughness exponent for the as-grown film and the internal morphology of the crystalline grains for the annealed films can be described by a diffusional process. The macrostructure shows characteristics of a Kardar-Parisi-Zhang system [M. Kardar, G. Parisi, Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986); J. Krim and G. Palasantzas, Int. J. Mod. Phys. B 9, 599 (1995)]. An activation energy Ed=(0.11±0.01) eV is determined for the diffusion process.
The history and role of the cubic law for fluid flow in fractured rocks
NASA Astrophysics Data System (ADS)
Zimmerman, R. W.
2012-12-01
The hydraulic transmissivity of a channel bounded by two smooth parallel walls that are separated by an aperture h is exactly equal to h3/12. As this is the most obvious and simplest model for flow through a rock fracture, fluid flow through a rock fracture is said to follow the cubic law. But the walls of actual rock fractures are not smooth and parallel; rather, they have roughness at various scales, and are in contact at discrete asperities that correspond to local regions of zero aperture. The existence of spatially varying apertures raises the question of whether it is systematically possible to compute a priori a hydraulic aperture, such that the transmissivity is related to the hydraulic aperture by the cubic law. Another approach is to use some appropriate mean aperture (arithmetic, geometric, etc.), and account for the effect of aperture variability and contact area by suitable multiplicative factors. An important related issue is that, as a normal stress will reduce the aperture, but not in a uniform manner, all three factors (mean aperture, aperture variability and contact area) will influence the manner in which the transmissivity changes due to a normal stress. Although the cubic law holds for flow between parallel walls up to the laminar-turbulent transition that occurs at Reynolds numbers of about 2000, deviations from a linear relationship between pressure drop and flowrate in a rough-walled fracture occur at much lower Reynolds numbers, on the order of about 10, during laminar flow. Each of the issues outlined above were identified and studied in the 1980 paper ``Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture'', by P. A. Witherspoon, J. S. Y. Wang, K. Iwai, and J. E. Gale (Water Resources Research, vol. 16, pp. 1016-1024). In this talk, I will review the various advances that have been made during the past three decades to clarify these issues, with specific reference to the contributions of Paul Witherspoon and his colleagues
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.
Yuan, Fuping Wu, Xiaolei
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 density 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.
NASA Astrophysics Data System (ADS)
Yuan, Fuping; Wu, Xiaolei
2014-12-01
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 density 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.
Scaling laws for the movement of people between locations in a large city.
Chowell, G; Hyman, J M; Eubank, S; Castillo-Chavez, C
2003-12-01
Large scale simulations of the movements of people in a "virtual" city and their analyses are used to generate insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these interactions, can be used in optimizing traffic flow, slowing the spread of infectious diseases, or predicting the change in cell phone usage in a disaster. We analyzed cumulative and aggregated data generated from the simulated movements of 1.6 x 10(6) individuals in a computer (pseudo-agent-based) model during a typical day in Portland, Oregon. This city is mapped into a graph with 181,206 nodes representing physical locations such as buildings. Connecting edges model individual's flow between nodes. Edge weights are constructed from the daily traffic of individuals moving between locations. The number of edges leaving a node (out-degree), the edge weights (out-traffic), and the edge weights per location (total out-traffic) are fitted well by power-law distributions. The power-law distributions also fit subgraphs based on work, school, and social/recreational activities. The resulting weighted graph is a "small world" and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes. We observe a strong linear correlation between the out-degree and total out-traffic distributions and significant levels of clustering. We discuss how these network features can be used to characterize social networks and their relationship to dynamic processes.
Scaling laws for the movement of people between locations in a large city
NASA Astrophysics Data System (ADS)
Chowell, G.; Hyman, J. M.; Eubank, S.; Castillo-Chavez, C.
2003-12-01
Large scale simulations of the movements of people in a “virtual” city and their analyses are used to generate insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these interactions, can be used in optimizing traffic flow, slowing the spread of infectious diseases, or predicting the change in cell phone usage in a disaster. We analyzed cumulative and aggregated data generated from the simulated movements of 1.6×106 individuals in a computer (pseudo-agent-based) model during a typical day in Portland, Oregon. This city is mapped into a graph with 181 206 nodes representing physical locations such as buildings. Connecting edges model individual’s flow between nodes. Edge weights are constructed from the daily traffic of individuals moving between locations. The number of edges leaving a node (out-degree), the edge weights (out-traffic), and the edge weights per location (total out-traffic) are fitted well by power-law distributions. The power-law distributions also fit subgraphs based on work, school, and social/recreational activities. The resulting weighted graph is a “small world” and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes. We observe a strong linear correlation between the out-degree and total out-traffic distributions and significant levels of clustering. We discuss how these network features can be used to characterize social networks and their relationship to dynamic processes.
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.
Remotely Sensed, catchment scale, estimations of flow resistance
NASA Astrophysics Data System (ADS)
Carbonneau, P.; Dugdale, S. J.
2009-12-01
Despite a decade of progress in the field of fluvial remote sensing, there are few published works using this new technology to advance and explore fundamental ideas and theories in fluvial geomorphology. This paper will apply remote sensing methods in order to re-visit a classic concept in fluvial geomorphology: flow resistance. Classic flow resistance equations such as those of Strickler and Keulegan typically use channel slope, channel depth or hydraulic radius and some measure channel roughness usually equated to the 50th or 84th percentile of the bed material size distribution. In this classic literature, empirical equations such as power laws are usually calibrated and validated with a maximum of a few hundred data points. In contrast, fluvial remote sensing methods are now capable of delivering millions of high resolution data points in continuous, catchment scale, surveys. On the river Tromie in Scotland, a full dataset or river characteristics is now available. Based on low altitude imagery and NextMap topographic data, this dataset has a continuous sampling of channel width at a resolution of 3cm, of depth and median grain size at a resolution of 1m, and of slope at a resolution of 5m. This entire data set is systematic and continuous for the entire 20km length of the river. When combined with discharge at the time of data acquisition, this new dataset offers the opportunity to re-examine flow resistance equations with a 2-4 orders of magnitude increase in calibration data. This paper will therefore re-examine the classic approaches of Strickler and Keulagan along with other more recent flow resistance equations. Ultimately, accurate predictions of flow resistance from remotely sensed parameters could lead to acceptable predictions of velocity. Such a usage of classic equations to predict velocity could allow lotic habitat models to account for microhabitat velocity at catchment scales without the recourse to advanced and computationally intensive
Sen, Amrik; Mininni, Pablo D; Rosenberg, Duane; Pouquet, Annick
2012-09-01
Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two-dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale Lf, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the inverse cascade range at a small but fixed Rossby number, Rof≈0.05. Several numerical simulations with helical and nonhelical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with reasonably large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a ∼k⊥-5/3 scaling, and the other that corresponds to a steeper ∼k⊥-3 spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to the 2D modes. The spectrum that emerges depends on the anisotropy of the forcing function, the former solution prevailing for forcings in which more energy is injected into the 2D modes while the latter prevails for isotropic forcing. In the case of anisotropic forcing, whence the energy goes from the 2D to the 3D modes at low wave numbers, large-scale shear is created, resulting in a time scale τsh, associated with shear, thereby producing a ∼k-1 spectrum for the total energy with the horizontal energy of the 2D modes still following a ∼k⊥-5/3 scaling.
Peak Sediment Flow Scaling in a Small Hortonian Watershed
NASA Astrophysics Data System (ADS)
Abebe, N. A.; Ogden, F. L.
2008-12-01
. Estimation of fine-sediment delivery rates at the watershed-scale is a long-standing problem. We investigated this problem using data from the Goodwin Creek Experimental Watershed (GCEW) located in the Northern-central Mississippi. The GCEW is a Hortonian catchment with 13 nested sub-catchments and a total area of 21.3 km2. Previous studies in this catchment showed that flood quantiles in nearly all sub- catchments are self-similar as described by simple scaling theory. We analyzed sixteen years of peak suspended sediment data from 12 gauging stations. Results showed that simple scaling holds better for peak sediment flow quantiles for the larger sub-catchments with slopes similar to the average slope of the catchment. In the same manner, predictions using derived power-law relations showed better performance for the larger sub-catchments. The log-transform of peak sediment flow and the computed event-total sediment volume showed a strong relation, which could be exploited in estimating the total sediment volume from single measured sediment concentrations. We hypothesize that the relatively uniform distribution of precipitation and land use and the similarity in slope of many of the subcatchments contributes to simple scaling behavior in the GCEW. Moreover, the balance between deposition and re-suspension of sediment along the river reach, which enables channels to have a relatively uniform sediment concentration, helps the peak suspended sediment flux to be proportional to the flow peak and area for larger sub-catchments with similar slopes.
Fractal scaling and fluid flow in fracture networks in rock
Barton, C.C.
1996-12-31
Recovery of oil and gas resources and injection of toxic waste materials requires quantitative models to describe and predict the movement of fluids in rock. Existing models based on pore-space flow are inappropriate for study of the more rapid process of fluid flow through fracture networks. This type of flow is not a simple function of the fracture characteristics at any particular scale, but rather the integration of fracture contributions at all scales. The mathematical constructs of fractal geometry are well suited to quantify and model relationships within complex systems that are statistically self-similar over a wide range of scales. Analyses show that fracture traces mapped on two-dimensional slices through three-dimensional nature fracture networks in rock follow a fractal scaling law over six orders of magnitude. Detailed measurements of 17 two-dimensional samples of fracture networks (at diverse scales in rocks of dissimilar age, lithology, and tectonic setting) show similar fractal dimensions in the range 1.3-1.7. The range in fractal dimension implies that a single physical process of rock fracturing operates over a wide range of scales, from microscopic cracks to large, regional fault systems. The knowledge that rock-fracture networks are fractal allows the use of data from a one-dimensional drill-hole sample to predict the two- and three-dimensional scaling of the fracture system. The spacing of fractures in drill holes is a fractal Cantor distribution, and the range of fractal dimension is 0.4-0.6, which is an integer dimension less than that of fracture-trace patterns exposed on two-dimensional, planar sections. A reconstruction of the fracture history at the point of initial connectivity across the network (percolation) has a fractal dimension of 1.35 as compared to a dimension of 1.9 for the percolation cluster in a two-dimensional model. Paleo flow was mapped based on the deposition of aqueous minerals on the fracture surface.
Fractal scaling and fluid flow in fracture networks in rock
Barton, C.C. )
1996-01-01
Recovery of oil and gas resources and injection of toxic waste materials requires quantitative models to describe and predict the movement of fluids in rock. Existing models based on pore-space flow are inappropriate for study of the more rapid process of fluid flow through fracture networks. This type of flow is not a simple function of the fracture characteristics at any particular scale, but rather the integration of fracture contributions at all scales. The mathematical constructs of fractal geometry are well suited to quantify and model relationships within complex systems that are statistically self-similar over a wide range of scales. Analyses show that fracture traces mapped on two-dimensional slices through three-dimensional nature fracture networks in rock follow a fractal scaling law over six orders of magnitude. Detailed measurements of 17 two-dimensional samples of fracture networks (at diverse scales in rocks of dissimilar age, lithology, and tectonic setting) show similar fractal dimensions in the range 1.3-1.7. The range in fractal dimension implies that a single physical process of rock fracturing operates over a wide range of scales, from microscopic cracks to large, regional fault systems. The knowledge that rock-fracture networks are fractal allows the use of data from a one-dimensional drill-hole sample to predict the two- and three-dimensional scaling of the fracture system. The spacing of fractures in drill holes is a fractal Cantor distribution, and the range of fractal dimension is 0.4-0.6, which is an integer dimension less than that of fracture-trace patterns exposed on two-dimensional, planar sections. A reconstruction of the fracture history at the point of initial connectivity across the network (percolation) has a fractal dimension of 1.35 as compared to a dimension of 1.9 for the percolation cluster in a two-dimensional model. Paleo flow was mapped based on the deposition of aqueous minerals on the fracture surface.
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…
Scaling laws of reflection coefficients of quantum waves at a Cantor-like potential
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Ogawana, Taichi
2017-03-01
We reconsider a one-dimensional scattering problem in the Schrödinger equation with a Cantor-like potential. The reflection coefficient obeys a scaling law for sufficiently large wave number k . The scaling law is expressed with a universal function characterized by a multifractal.
Scaling laws of reflection coefficients of quantum waves at a Cantor-like potential.
Sakaguchi, Hidetsugu; Ogawana, Taichi
2017-03-01
We reconsider a one-dimensional scattering problem in the Schrödinger equation with a Cantor-like potential. The reflection coefficient obeys a scaling law for sufficiently large wave number k. The scaling law is expressed with a universal function characterized by a multifractal.
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…
Onset of power-law scaling behavior in idiotypic random and scale-free networks
NASA Astrophysics Data System (ADS)
Claudino, Elder S.; Lyra, M. L.; Gleria, Iram; Campos, Paulo R. A.; Bertrand, Delvis
2012-10-01
We numerically study the dynamics of model immune networks with random and scale-free topologies. We observe that a memory state is reached when the antigen is attached to the most connected sites of the network, whereas a percolation state may occur when the antigen attaches to the less connected sites. For increasing values of the connectivity of the antibody directly binded to the antigen, its population converges exponentially to the asymptotic value of the memory state. On the other hand, the next-nearest populations evolve slowly as power-laws towards the virgin-like state.
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.
Water-Rock Differentiation of Icy Bodies by Darcy law, Stokes law, and Two-Phase Flow
NASA Astrophysics Data System (ADS)
Neumann, Wladimir; Breuer, Doris; Spohn, Tilman
2016-10-01
The early Solar system produced a variety of bodies with different properties. Among the small bodies, objects that contain notable amounts of water ice are of particular interest. Water-rock separation on such worlds is probable and has been confirmed in some cases. We couple accretion and water-rock separation in a numerical model. The model is applicable to Ceres, icy satellites, and Kuiper belt objects, and is suited to assess the thermal metamorphism of the interior and the present-day internal structures. The relative amount of ice determines the differentiation regime according to porous flow or Stokes flow. Porous flow considers differentiation in a rock matrix with a small degree of ice melting and is typically modelled either with the Darcy law or two-phase flow. We find that for small icy bodies two-phase flow differs from the Darcy law. Velocities derived from two-phase flow are at least one order of magnitude smaller than Darcy velocities. The latter do not account for the matrix resistance against the deformation and overestimate the separation velocity. In the Stokes regime that should be used for large ice fractions, differentiation is at least four orders of magnitude faster than porous flow with the parameters used here.
Scaled Rocket Testing in Hypersonic Flow
NASA Technical Reports Server (NTRS)
Dufrene, Aaron; MacLean, Matthew; Carr, Zakary; Parker, Ron; Holden, Michael; Mehta, Manish
2015-01-01
NASA's Space Launch System (SLS) uses four clustered liquid rocket engines along with two solid rocket boosters. The interaction between all six rocket exhaust plumes will produce a complex and severe thermal environment in the base of the vehicle. This work focuses on a recent 2% scale, hot-fire SLS base heating test. These base heating tests are short-duration tests executed with chamber pressures near the full-scale values with gaseous hydrogen/oxygen engines and RSRMV analogous solid propellant motors. The LENS II shock tunnel/Ludwieg tube tunnel was used at or near flight duplicated conditions up to Mach 5. Model development was strongly based on the Space Shuttle base heating tests with several improvements including doubling of the maximum chamber pressures and duplication of freestream conditions. Detailed base heating results are outside of the scope of the current work, rather test methodology and techniques are presented along with broader applicability toward scaled rocket testing in supersonic and hypersonic flow.
Titius-Bode laws in the solar system. 1: Scale invariance explains everything
NASA Astrophysics Data System (ADS)
Graner, F.; Dubrulle, B.
1994-02-01
According to the Titius-Bode law, the planetary distances to the sun follow a geometric progression. We review the major interpretations and explanations of the law. We show that most derivations of Titius-Bode law are implicitely based on the assumption of both rotational and scale invariance. In absence of any radial length scale, linear instabilities cause periodic perturbations in the variable x = ln(r/r0). Since maxima equidistant in x obey a geometric progression in the variable r, Titius-Bode type of laws are natural outcome of the linear regime of systems in which both symmetries are present; we discuss possible nonlinear corrections to the law. Thus, if Titius-Bode law is real, it is probably only a consequence of the scale invariance of the disk which gave rise to the planets.
Analysis of electroosmotic flow of power-law fluids in a slit microchannel.
Zhao, Cunlu; Zholkovskij, Emilijk; Masliyah, Jacob H; Yang, Chun
2008-10-15
Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.
Palva, J Matias; Zhigalov, Alexander; Hirvonen, Jonni; Korhonen, Onerva; Linkenkaer-Hansen, Klaus; Palva, Satu
2013-02-26
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.
Deformation of a Capsule in a Power-Law Shear Flow.
Tian, Fang-Bao
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
A numerical model for dynamic crustal-scale fluid flow
NASA Astrophysics Data System (ADS)
Sachau, Till; Bons, Paul; Gomez-Rivas, Enrique; Koehn, Daniel
2015-04-01
Fluid flow in the crust is often envisaged and modeled as continuous, yet minimal flow, which occurs over large geological times. This is a suitable approximation for flow as long as it is solely controlled by the matrix permeability of rocks, which in turn is controlled by viscous compaction of the pore space. However, strong evidence (hydrothermal veins and ore deposits) exists that a significant part of fluid flow in the crust occurs strongly localized in both space and time, controlled by the opening and sealing of hydrofractures. We developed, tested and applied a novel computer code, which considers this dynamic behavior and couples it with steady, Darcian flow controlled by the matrix permeability. In this dual-porosity model, fractures open depending on the fluid pressure relative to the solid pressure. Fractures form when matrix permeability is insufficient to accommodate fluid flow resulting from compaction, decompression (Staude et al. 2009) or metamorphic dehydration reactions (Weisheit et al. 2013). Open fractures can close when the contained fluid either seeps into the matrix or escapes by fracture propagation: mobile hydrofractures (Bons, 2001). In the model, closing and sealing of fractures is controlled by a time-dependent viscous law, which is based on the effective stress and on either Newtonian or non-Newtonian viscosity. Our simulations indicate that the bulk of crustal fluid flow in the middle to lower upper crust is intermittent, highly self-organized, and occurs as mobile hydrofractures. This is due to the low matrix porosity and permeability, combined with a low matrix viscosity and, hence, fast sealing of fractures. Stable fracture networks, generated by fluid overpressure, are restricted to the uppermost crust. Semi-stable fracture networks can develop in an intermediate zone, if a critical overpressure is reached. Flow rates in mobile hydrofractures exceed those in the matrix porosity and fracture networks by orders of magnitude
NASA Astrophysics Data System (ADS)
Peluso, E.; Gelfusa, M.; Murari, A.; Lupelli, I.; Gaudio, P.
The H mode of confinement in Tokamaks is characterized by a thin region of high gradients, located at the edge of the plasma and called the Edge Transport Barrier. Even if various theoretical models have been proposed for the interpretation of the edge physics, the main empirical scaling laws of the plasma confinement time are expressed in terms of global plasma parameters and they do not discriminate between the edge and core regions. Moreover all the scaling laws are assumed to be power law monomials. In the present paper, a new methodology is proposed to investigate the validity of both assumptions. The approach is based on Symbolic Regression via Genetic Programming and allows first the extraction of the most statistically reliable models from the available experimental data in the ITPA database. Non linear fitting is then applied to the mathematical expressions found by Symbolic regression. The obtained scaling laws are compared with the traditional scalings in power law form.
State of stress in the lithosphere: Inferences from the flow laws of olivine
Kirby, S.H.
1977-01-01
The experimental flow data for rocks and minerals are reviewed and found to fit a law of the form {Mathematical expression} where {Mathematical expression} This law reduces to the familiar power-law stress dependency at low stress and to an exponential stress dependency at high stress. Using the material flow law parameters for olivine, stress profiles with depth and strain rate are computed for a representative range of temperature distributions in the lithosphere. The results show that the upper 15 to 25 km of the oceanic lithosphere must behave elastically or fail by fracture and that the remainder deforms by exponential law flow at intermediate depths and by power-law flow in the rest. A model computation of the gravitational sliding of a lithospheric plate using olivine rheology exhibits a very sharp decoupling zone which is a consequence of the combined effects of increasing stress and temperature on the flow law, which is a very sensitive function of both. ?? 1977 Birkha??user Verlag.
Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation.
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.
Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation
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
Scaling laws of coronal loops compared to a 3D MHD model of an active region
NASA Astrophysics Data System (ADS)
Bourdin, Ph.-A.; Bingert, S.; Peter, H.
2016-05-01
Context. The structure and heating of coronal loops have been investigated for decades. Established scaling laws relate fundamental quantities like the loop apex temperature, pressure, length, and coronal heating. Aims: We test these scaling laws against a large-scale 3D magneto-hydrodynamics (MHD) model of the solar corona, which became feasible with current high-performance computing. Methods: We drove an active region simulation with photospheric observations and find strong similarities to the observed coronal loops in X-rays and extreme-ultraviolet (EUV) wavelength. A 3D reconstruction of stereoscopic observations shows that our model loops have a realistic spatial structure. We compared scaling laws to our model data extracted along an ensemble of field lines. Finally, we fit a new scaling law that represents hot loops and also cooler structures, which was not possible before based only on observations. Results: Our model data gives some support for scaling laws that were established for hot and EUV-emissive coronal loops. For the Rosner-Tucker-Vaiana (RTV) scaling law we find an offset to our model data, which can be explained by 1D considerations of a static loop with a constant heat input and conduction. With a fit to our model data we set up a new scaling law for the coronal heat input along magnetic field lines. Conclusions: RTV-like scaling laws were fitted to hot loops and therefore do not predict well the coronal heat input for cooler structures that are barely observable. The basic differences between 1D and self-consistent 3D modeling account for deviations between earlier scaling laws and ours. We also conclude that a heating mechanism by MHD-turbulent dissipation within a braided flux tube would heat the corona stronger than is consistent with our model corona.
Large-Scale Analysis of Zipf's Law in English Texts.
Moreno-Sánchez, Isabel; Font-Clos, Francesc; Corral, Álvaro
2016-01-01
Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been confronted to a representatively large number of texts. So, we can summarize the current support of Zipf's law in texts as anecdotic. We try to solve these issues by studying three different versions of Zipf's law and fitting them to all available English texts in the Project Gutenberg database (consisting of more than 30 000 texts). To do so we use state-of-the art tools in fitting and goodness-of-fit tests, carefully tailored to the peculiarities of text statistics. Remarkably, one of the three versions of Zipf's law, consisting of a pure power-law form in the complementary cumulative distribution function of word frequencies, is able to fit more than 40% of the texts in the database (at the 0.05 significance level), for the whole domain of frequencies (from 1 to the maximum value), and with only one free parameter (the exponent).
The scaling of blood flow resistance: from a single vessel to the entire distal tree.
Huo, Yunlong; Kassab, Ghassan S
2009-01-01
Although the flow resistance of a single vessel segment is easy to compute, the equivalent resistance of a network of vessel segments or the entire vasculature of an organ is difficult to determine in an analytic form. Here, we propose what we believe is a novel resistance scaling law for a vascular tree (i.e., the resistance of a vessel segment scales with the equivalent resistance of the corresponding distal tree). The formulation can be written as (R(s)/R(c)) proportional, variant(L(s)/L(c)) (where R(s) and L(s) are the resistance and length of a vessel segment, respectively, and R(c) and L(c) are the equivalent resistance and total length of the corresponding distal tree, respectively), which was validated for the coronary vascular systems of the heart. The scaling law was also shown to apply to the vascular systems of the lung, mesentery, muscle, eye, and so on. The novel resistance scaling law, coupled with the 3/4-power scaling law for metabolic rates, can predict several structure-function relations of vascular trees, albeit with a different exponent. In particular, the self-similar nature of the scaling law may serve as a diagnostic tool with the help of noninvasive imaging modalities.
Preferential flow across scales: how important are plot scale processes for a catchment scale model?
NASA Astrophysics Data System (ADS)
Glaser, Barbara; Jackisch, Conrad; Hopp, Luisa; Klaus, Julian
2017-04-01
Numerous experimental studies showed the importance of preferential flow for solute transport and runoff generation. As a consequence, various approaches exist to incorporate preferential flow in hydrological models. However, few studies have applied models that incorporate preferential flow at hillslope scale and even fewer at catchment scale. Certainly, one main difficulty for progress is the determination of an adequate parameterization for preferential flow at these spatial scales. This study applies a 3D physically based model (HydroGeoSphere) of a headwater region (6 ha) of the Weierbach catchment (Luxembourg). The base model was implemented without preferential flow and was limited in simulating fast catchment responses. Thus we hypothesized that the discharge performance can be improved by utilizing a dual permeability approach for a representation of preferential flow. We used the information of bromide irrigation experiments performed on three 1m2 plots to parameterize preferential flow. In a first step we ran 20.000 Monte Carlo simulations of these irrigation experiments in a 1m2 column of the headwater catchment model, varying the dual permeability parameters (15 variable parameters). These simulations identified many equifinal, yet very different parameter sets that reproduced the bromide depth profiles well. Therefore, in the next step we chose 52 parameter sets (the 40 best and 12 low performing sets) for testing the effect of incorporating preferential flow in the headwater catchment scale model. The variability of the flow pattern responses at the headwater catchment scale was small between the different parameterizations and did not coincide with the variability at plot scale. The simulated discharge time series of the different parameterizations clustered in six groups of similar response, ranging from nearly unaffected to completely changed responses compared to the base case model without dual permeability. Yet, in none of the groups the
Passive scalar scaling regimes in a rapidly decorrelating turbulent flow
NASA Astrophysics Data System (ADS)
Kramer, Peter Roland
This thesis is concerned with some issues pertaining to the small scale structure of a passive scalar field advected by a turbulent flow, and driven by external stochastic pumping and/or interaction with a background passive scalar gradient. We analyze and apply two previously developed simplified mathematical models: the Simple Shear Model of Andrew Majda and Marco Avellaneda, and the Rapid Decorrelation in Time (RDT) Model of Robert Kraichnan. The fundamental representation of the passive scalar statistics in these models is presented from a consideration of Lagrangian tracer trajectories. This permits an easy extension of the Simple Shear Model to incorporate driving, and an alternative derivation of the governing mathematical equations in the RDT Model. Using a Simple Shear Poisson Blob Model of Majda and Avellaneda, we provide an example in which the correlation time of the velocity field becomes very small, but the passive scalar statistics do not converge to those of the RDT model. The RDT Model therefore only describes passive scalar advection for a velocity field with short correlation time in a certain sense. We next apply the RDT Model to investigate scaling regimes in the spectral density of a random passive scalar field advected by a turbulent flow. First, we rigorously derive three scaling regimes, and test some physical theories against these exact results. We find most predictions to succeed, but indicate an apparent gap in the reasoning behind the inertial-diffusive theory of Carl Gibson. Next, motivated by a recent experimental controversy, we consider whether, in the RDT Model, anisotropies in the external pumping could disrupt the k-1 viscous- convective scaling law at high Schmidt number. We find that the k-1 law persists. Finally, we test two asymptotic procedures, the Intermediate Asymptotic (IA) approach as described by G. I. Barenblatt and the Renormalization Group (RG) method of Lin-Yuan Chen et al. on an exactly solvable ODE arising in
Similarity laws of lunar and terrestrial volcanic flows
NASA Technical Reports Server (NTRS)
Pai, S. I.; Hsu, Y.; Okeefe, J. A.
1977-01-01
A mathematical model of a one dimensional, steady duct flow of a mixture of a gas and small solid particles (rock) was analyzed and applied to the lunar and the terrestrial volcanic flows under geometrically and dynamically similar conditions. Numerical results for the equilibrium two phase flows of lunar and terrestrial volcanoes under similar conditions are presented. The study indicates that: (1) the lunar crater is much larger than the corresponding terrestrial crater; (2) the exit velocity from the lunar volcanic flow may be higher than the lunar escape velocity but the exit velocity of terrestrial volcanic flow is much less than that of the lunar case; and (3) the thermal effects on the lunar volcanic flow are much larger than those of the terrestrial case.
Paniagua, F A; Black, S A; O'Boyle, M; Jones, P
1999-06-01
42 middle-aged and older adults, ranging in age from 51 to 85 years, completed 10 items dealing with the assessment of knowledge regarding laws regulating issues related to HIV and AIDS. Participants also completed 40 items involving knowledge of risks for HIV infection. The Cronbach coefficient alpha and test-retest reliability coefficient on the HIV/AIDS and the Law Scale were .74 and .83, respectively. Over-all, the grand mean for correct answers was 46.9%, whereas the grand means for incorrect answers and "don't know" responses were 13.6% and 39.5%, suggesting substantial lack of knowledge of laws regulating issues related to HIV and AIDS. Women (50%) and younger participants (51 to 66 years old; 48.2%) showed more of this knowledge (50%) than men (43.0%) and older participants (46.2%). The sample reported a substantial amount of knowledge regarding HIV transmission assessed with factual (92.2% correct) and misconception (87.5% correct) items. The correlation between this knowledge and knowledge of laws regulating issues related to HIV and AIDS was .42 (p < .01). Research with this scale using adolescents and young adults as well as the utility of the scale in areas of clinical, legal, and policy development are discussed.
NASA Astrophysics Data System (ADS)
Alderweireld, Thomas; Nuyts, Jean
2004-01-01
The technique of Padé approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more “microscopic” level.
Toward a general understanding of the scaling laws in human and animal mobility
NASA Astrophysics Data System (ADS)
Hu, Yanqing; Zhang, Jiang; Huan, Di; Di, Zengru
2011-11-01
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general optimization model, a random walker following scaling laws (whose traveling distances in each step obey a power law distribution with exponent α) tries to diversify its visiting places under a given total traveling distance with a home-return probability. The results show that different optimal exponents in between 1 and 2 can emerge naturally. Therefore, the scaling property of human and animal mobility can be understood in our framework where the discrepancy of the scaling law exponents is due to the home-return constraint under the maximization of the visiting places diversity.
Scaling laws for ignition at the National Ignition Facility from first principles.
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.
Principles of physics in surgery: the laws of flow dynamics physics for surgeons - Part 1.
Srivastava, Anurag; Sood, Akshay; Joy, S Parijat; Woodcock, John
2009-08-01
In the field of medicine and surgery many principles of physics find numerous applications. In this article we have summarized some prominent applications of the laws of fluid mechanics and hydrodynamics in surgery. Poiseuille's law sets the limits of isovolaemic haemodilution, enumerates limiting factors during fluid resuscitation and is a guiding principle in surgery for vascular stenoses. The equation of continuity finds use in non-invasive measurement of blood flow. Bernoulli's theorem explains the formation of post-stenotic dilatation. Reynolds number explains the origin of murmurs, haemolysis and airflow disturbances. Various forms of oxygen therapy are a direct application of the gas laws. Doppler effect is used in ultrasonography to find the direction and velocity of blood flow. In this first part of a series of articles we describe some applications of the laws of hydrodynamics governing the flow of blood and other body fluids.
Interception efficiency in flow of power-law fluids past confined porous bodies
NASA Astrophysics Data System (ADS)
Shahsavari, Setareh; McKinley, Gareth
2014-11-01
Understanding the flow of power-law fluids through porous media is important for a wide range of filtration and sedimentation processes. In this study, the mobility of power-law fluids through porous media is investigated numerically and we use parametric studies to systematically understand the individual roles of geometrical characteristics, rheological properties as well as flow conditions. In addition, an analytical solution is presented that can be used as a modified Darcy law for generalized Newtonian fluids. Building on this modified Darcy law, the incompressible laminar flow of power-law and Carreau fluids past a confined porous body is modeled numerically. From the simulations we calculate the flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector. Finally, the interception efficiency of power-law fluids are compared with the case of a Newtonian fluid. The focus of this work is principally for flow of inelastic fluids in fibrous media; however, the methodology can also be extended to other porous media.
Similarity laws of lunar and terrestrial volcanic flows
NASA Technical Reports Server (NTRS)
Pai, S. I.; Hsu, Y.
1977-01-01
A mathematical model for the terrestrial and lunar volcanic flows is proposed. This mathematical model, which is one-dimensional, steady duct flow of a mixture of a gas and small solid particles (rock), has been analyzed in detail. The similarities and the differences of the essential features of lunar and terrestrial volcanic flows are determined. Numerical results for the equilibrium two-phase flows of lunar and terrestrial volcanics under similar conditions are presented. The main results of the theoretical model are: the lunar crater is much larger than the corresponding terrestrial crater; the exit velocity from the lunar volcanic flow may be higher than the lunar escape velocity but the exit velocity of terrestrial volcanic flow is much less than that of the linear case (this result confirms the hypothesis that Australian tektites came from the moon, as a stream of rock and gas of extremely high speed), and the thermal effects on the lunar volcanic flow are much larger than those in the terrestrial case.
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.
Wall scaling laws for turbulent BL before and after the Reynolds shear stress maxima
NASA Astrophysics Data System (ADS)
Afzal, Noor; Seena, Abu; Afzal, Bushra; Noor Afzal Collaboration; Abu Seena Team; Bushra Afzal Team
2015-11-01
The turbulent shear flow has a critical point due to maximas of Reynolds stress tensor has significant role. Three layers with length scales (inner ν /uτ , meso √{ νδ /uτ }, outer δ) have been analyzed. Below this crucial point the mesolayer inner limit matches with with outer limit of wall layer. Above this crucial point the outer limit of mesolayer matches with inner limit of outer layer. The log law velocity and Reynolds in two overlap regions, above and below the critical point, have been presented. The Reynolds shear stress maxima τmax /τw occurs at a point where ratio of mesolayer to outer lengths is of order Rτ-1 / 2 (= √{ ν / δuτ }), and at this point DNS and experimental data predict Um /Ue = 2 / 3 (where Um = mesolayer velocity and Ue = velocity at boundary edge). The turbulent burst time period also scale with mesolayer time. The shape factor in a TBL shows linear behavior with non-dimensional mesolayer length scale. In special case Um /Ue = 1 / 2 , is due to Izakson and Millikan. The above predictions are supported by experimental and DNS data.
Alves, Luiz G. A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.; Mendes, Renio S.
2013-01-01
We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach has proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law. PMID:23940525
Alves, Luiz G A; Ribeiro, Haroldo V; Lenzi, Ervin K; Mendes, Renio S
2013-01-01
We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach has proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as [Formula: see text] the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, [Formula: see text] the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and [Formula: see text] a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law.
Universal scaling laws of diffusion in two-dimensional granular liquids.
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.
Test of the Universal Scaling Law of Diffusion in Colloidal Monolayers
NASA Astrophysics Data System (ADS)
Ma, Xiaoguang; Chen, Wei; Wang, Ziren; Peng, Yuan; Han, Yilong; Tong, Penger
2013-02-01
Using the techniques of optical microscopy and particle tracking, we measure the pair correlation function and Brownian diffusion in monolayers of strongly interacting colloidal particles suspended at or near three different interfaces and test the universal scaling law of the normalized diffusion coefficient, D˜≃eαΔS, as a function of the excess entropy ΔS for a wide range of particle concentrations. It is found that the universal scaling law with α=1 holds well for highly charged polystyrene spheres suspended at an air-water interface, where the strong electrostatic interactions play a dominant role. For monolayer suspensions of hard-sphere-like particles, where hydrodynamic interactions become important, deviations from the universal scaling law are observed. The experiment indicates that the hydrodynamic corrections could be incorporated into the universal scaling law of diffusion with an exponent α<1.
Finite size scaling analysis on Nagel-Schreckenberg model for traffic flow
NASA Astrophysics Data System (ADS)
Balouchi, Ashkan; Browne, Dana
2015-03-01
The traffic flow problem as a many-particle non-equilibrium system has caught the interest of physicists for decades. Understanding the traffic flow properties and though obtaining the ability to control the transition from the free-flow phase to the jammed phase plays a critical role in the future world of urging self-driven cars technology. We have studied phase transitions in one-lane traffic flow through the mean velocity, distributions of car spacing, dynamic susceptibility and jam persistence -as candidates for an order parameter- using the Nagel-Schreckenberg model to simulate traffic flow. The length dependent transition has been observed for a range of maximum velocities greater than a certain value. Finite size scaling analysis indicates power-law scaling of these quantities at the onset of the jammed phase.
Tectonics of China: Continental scale cataclastic flow
NASA Astrophysics Data System (ADS)
Gallagher, John J., Jr.
Stratigraphic, structural, and earthquake evidence indicates that cataclastic flow, that is, flow by brittle mechanisms (e.g., fracture and slip), was dominant in China from late Paleozoic. This process has operated over a range of scales including the continental scale. China is made up of large brittle basement elements immersed in ductile zones which are analogous to porphyroclasts (large, often brittle fragments) surrounded by fluxion (foliation or flow) structures in cataclastic rocks, respectively. This basement fabric for China is seen on Landsat imagery and on tectonic maps and is comparable to cataclastic rock fabrics seen in fault zones, on outcrops, and in thin sections. Brittle basement elements are broken into two or more large rigid blocks, and the dimensions of elements and blocks are within 1 order of magnitude of each other. Ductile zones are made up of fragments which are many orders of magnitude smaller than the ductile zones. Rigid blocks and fragments are identified, and their dimensions are measured through earthquake, fault, and fracture patterns. Rigid basement blocks are surrounded by earthquakes. The sedimentary rocks over the basement faults at the block boundaries seem to be affected by fault movements because they are characterized by facies changes, thickness changes, high-angle faults, and forced folds. Ductile basement zones are earthquake prone, and deformation of the ductile basement affects the overlying sedimentary rocks, as is demonstrated by unconformities and by a wide variety of structures. Thrust faults, buckle folds, and strike slip faults are common in and adjacent to western ductile zones. Structures are most intensely developed where ductile zones abut brittle elements. Both brittle elements and ductile zones are rifted and cut by strike slip faults in eastern China. The mechanical fabric of China and the boundary conditions acting on China are now and always have been determined by its plate tectonic history. This
Scaling laws and complexity in fire regimes [Chapter 2
Donald McKenzie; Maureen Kennedy
2011-01-01
Use of scaling terminology and concepts in ecology evolved rapidly from rare occurrences in the early 1980s to a central idea by the early 1990s (Allen and Hoekstra 1992; Levin 1992; Peterson and Parker 1998). In landscape ecology, use of "scale" frequently connotes explicitly spatial considerations (Dungan et al. 2002), notably grain and extent. More...
Modified gravity and large scale flows, a review
NASA Astrophysics Data System (ADS)
Mould, Jeremy
2017-02-01
Large scale flows have been a challenging feature of cosmography ever since galaxy scaling relations came on the scene 40 years ago. The next generation of surveys will offer a serious test of the standard cosmology.
Scaling of two-phase flow regimes in a rod bundle with freon
Symolon, P.D.
1990-07-01
Fluid to fluid modeling of the thermal-hydraulics of steam/water systems using Freon has been the subject of research for the past 25 years. However, there is as yet no universally accepted set of scaling laws to define the geometry and velocity scaling requirements of an equivalent Freon test of the full scale steam/water system being simulated. This paper describes a scaling concept where the Weber and Froud numbers of the Freon model are matched to that of the prototype being simulated, thus creating a comparable balance among inertia, surface tension and buoyancy forces. In this test it was demonstrated that similar flow regime transitions are observed in a half scale Freon simulation of a full scale steam/water test run at Dynatech. It is also shown using a two fluid analytical model and existing correlations for friction and interfacial momentum exchange from the open literature, that a half scale simulation leads to nearly the same slip ratio as for full scale steam/water, while the slip ratio for a full scale Freon simulation is too high. A comparison of the predicted flow distribution in the 4-rod bundle is made using the COBRA-IV code for a full scale simulation using Freon, a half scale simulation using Freon and full scale test with water. The COBRA results demonstrated that a half scale test section model using Freon yields a subchannel flow distribution similar to the steam/water case, while a full scale Freon simulation results in a distorted subchannel flow distribution. It is concluded that the appropriate geometric scale factor for Freon simulation of two-phase steam/water flow in tube bundles is one-half for a broad range of thermal-hydraulic conditions. 24 refs., 12 figs., 4 tabs.
Firms growth dynamics, competition and power-law scaling
NASA Astrophysics Data System (ADS)
Gupta, Hari M.; Campanha, José R.
2003-05-01
We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive business world. The detailed quantitative agreement of the theory with empirical results of firms growth based on a large economic database spanning over 20 years is good with a single set of the parameters for all the curves. Further, the empirical data of the variation of the standard deviation of the growth rate with the size of the firm are in accordance with the present theory rather than a simple power law.
Two-threshold model for scaling laws of noninteracting snow avalanches
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.
The flow of power law fluids in elastic networks and porous media.
Sochi, Taha
2016-02-01
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.
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.).
Scaling and Pedotransfer in Numerical Simulations of Flow and Transport in Soils
NASA Astrophysics Data System (ADS)
Pachepsky, Y. A.; Yakirevich, A.; Guber, A.; Gish, T.; Cady, R.; Nicholson, T. J.
2013-12-01
Flow and transport parameters in numerical simulations need to be defined at the support volume of computational cells. This volume can be substantially larger than the support volume in laboratory of field measurements of those parameters. Parameter estimates obtained from measured values with pedotransfer functions are also defined at the measurement rather than simulation cell support scale. The scale dependence of flow and transport parameters essentially precludes the direct use of measured or pedotransfer estimated parameter values in numerical simulations. The hypothesis of this work was that a support volume-based scaling law could be introduced that could convert pedotransfer-estimated saturated hydraulic conductivity values into values to be used over grid cells for finite element-based simulations of water flow and tracer transport in variable saturated soils. A four month-long experiment was conducted at the USDA-ARS experimental site where tracer was applied with a pulse of irrigation water and its transport in groundwater and variably saturated shallow soils was monitored in three rows of wells on daily basis. The complementary weather data collection and runoff volume measurements were performed. The HYDRUS-3D software was used to set and calibrate the Richards model for flow simulations and the convective-dispersive equation for transport simulations. Saturated hydraulic conductivity values were estimated with class pedotransfer functions derived from the USDA database containing results of about 1000 measurements in soils of different textures and bulk density. A power law scaling law for the saturated hydraulic conductivity was derived from literature data and was applied at the OPE3 site. Using the scaled saturated hydraulic conductivity values resulted in the accuracy of simulations that was similar to the accuracy of the calibrated model results. Scaling of pedotransfer-estimated saturated hydraulic conductivities can provide reasonable
Effective Actuation: High Bandwidth Actuators and Actuator Scaling Laws
2007-11-02
5c. PROGRAM ELEMENT NUMBER I-ioh Bandwidth Actiintorv and Actuator 9clinp Iaw-, 65502F 6. AUTHOR(S) 5d. PROJECT NUMBER A. B. Cain, G. R. Raman , and E...of possible applications include the high frequency excitation for supprc~sion of flow induced resonance in weapons bay cavities (see Raman et al...systems. Adaptive high bandwidth actuators are required to adapt to changes in flow speed and conditions during flight. Raman et al. (2000) and Stanek et
NASA Astrophysics Data System (ADS)
Cueto-Felgueroso, L.; Fu, X.; Juanes, R.
2016-12-01
The description of multicomponent flows with complex phase behavior remains an open challenge in pore-scale modeling. Darcy-scale general purpose simulators assume local thermodynamic equilibrium, and perform equation-of-state-based calculations to make phase equilibrium predictions; that is, to determine the phase volume fractions and their compositions from overall component mole fractions. What remains unclear is whether the thermodynamic equilibrium assumption is valid given the flow conditions, complex structure of the pore space and characteristic time scales for flow. Diffuse-interface theories of multiphase flow have recently emerged as promising tools to understand and simulate complex processes involving the simultaneous flow of two or more immiscible fluid phases. The common goal in these approaches is to formulate thermodynamically consistent stress tensors and mesoscale balance laws, including the impact of surface tension on the momentum balance, as well as properly tracking interfacial dynamics and mass transfer. We propose a phase-field model of multiphase, multicomponent flow, which we use to address the following research questions: What is the impact of the wetting conditions at the pore scale on upscaled descriptions of multiphase flow? What is the impact of the displacement dynamics, pore space structure and wetting conditions on the phase behavior of multicomponent mixtures? We finally investigate upscaling procedures to incorporate non-equilibrium phase behavior at the continuum scale.
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 Laws for Shapes of Food Fragments by Human Mastication
NASA Astrophysics Data System (ADS)
Kobayashi, Naoki; Kohyama, Kaoru; Sasaki, Yo; Matsushita, Mitsugu
2007-04-01
Scaling property of the shape of fragments which were produced by masticating raw carrots has been studied experimentally and theoretically. Mastication experiments showed that most fragments have more or less isotropic shapes which are independent of the number of chewing strokes, whereas larger fragments than a crossover size have complicated shapes. Since the crossover size had the structure which was dependent on the number of chewing strokes, we have tried to propose dynamic scaling hypothesis analogous to the case of growing self-affine interface. It was found that the dynamic scaling yields fairly accurate values of the scaling exponents. Our results will provide a new observation and insight of not only sequential fragmentation but also construction for physiological measurement.
ERIC Educational Resources Information Center
Walker, W. R.; Cox, W. E.
1978-01-01
Presents a literature review of the legal issues relative to water quality covering publications of 1977. Consideration is given to federal laws, Supreme Court cases, and the impact of federal environmental laws on local government. A list of 47 references is also presented. (HM)
ERIC Educational Resources Information Center
Walker, W. R.; Cox, W. E.
1978-01-01
Presents a literature review of the legal issues relative to water quality covering publications of 1977. Consideration is given to federal laws, Supreme Court cases, and the impact of federal environmental laws on local government. A list of 47 references is also presented. (HM)
Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas.
Andrés, N; Galtier, S; Sahraoui, F
2016-12-01
We derive exact scaling laws for a three-dimensional incompressible helical two-fluid plasma, without the assumption of isotropy. For each ideal invariant of the two-fluid model, i.e., the total energy, the electron helicity, and the proton helicity, we derive simple scaling laws in terms of two-point increment correlation functions expressed in terms of the velocity field of each species and the magnetic field. These variables are appropriate for comparison with direct numerical simulation data and with in situ measurements in the near-Earth space over a broad range of spatial scales. Finally, using the exact scaling laws and dimensional analysis we predict the magnetic energy and electron helicity spectra for different ranges of scales.
Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas
NASA Astrophysics Data System (ADS)
Andrés, N.; Galtier, S.; Sahraoui, F.
2016-12-01
We derive exact scaling laws for a three-dimensional incompressible helical two-fluid plasma, without the assumption of isotropy. For each ideal invariant of the two-fluid model, i.e., the total energy, the electron helicity, and the proton helicity, we derive simple scaling laws in terms of two-point increment correlation functions expressed in terms of the velocity field of each species and the magnetic field. These variables are appropriate for comparison with direct numerical simulation data and with in situ measurements in the near-Earth space over a broad range of spatial scales. Finally, using the exact scaling laws and dimensional analysis we predict the magnetic energy and electron helicity spectra for different ranges of scales.
Application of composite flow laws to grain size distributions derived from polar ice cores
NASA Astrophysics Data System (ADS)
Binder, Tobias; de Bresser, Hans; Jansen, Daniela; Weikusat, Ilka; Garbe, Christoph; Kipfstuhl, Sepp
2014-05-01
Apart from evaluating the crystallographic orientation, focus of microstructural analysis of natural ice during the last decades has been to create depth-profiles of mean grain size. Several ice flow models incorporated mean grain size as a variable. Although such a mean value may coincide well with the size of a large proportion of the grains, smaller/larger grains are effectively ignored. These smaller/larger grains, however, may affect the ice flow modeling. Variability in grain size is observed on centimeter, meter and kilometer scale along deep polar ice cores. Composite flow laws allow considering the effect of this variability on rheology, by weighing the contribution of grain-size-sensitive (GSS, diffusion/grain boundary sliding) and grain-size-insensitive (GSI, dislocation) creep mechanisms taking the full grain size distribution into account [1]. Extraction of hundreds of grain size distributions for different depths along an ice core has become relatively easy by automatic image processing techniques [2]. The shallow ice approximation is widely adopted in ice sheet modeling and approaches the full-Stokes solution for small ratios of vertical to horizontal characteristic dimensions. In this approximation shear stress in the vertical plain dominates the strain. This assumption is not applicable at ice divides or dome structures, where most deep ice core drilling sites are located. Within the upper two thirds of the ice column longitudinal stresses are not negligible and ice deformation is dominated by vertical strain. The Dansgaard-Johnsen model [3] predicts a dominating, constant vertical strain rate for the upper two thirds of the ice sheet, whereas in the lower ice column vertical shear becomes the main driver for ice deformation. We derived vertical strain rates from the upper NEEM ice core (North-West Greenland) and compared them to classical estimates of strain rates at the NEEM site. Assuming intervals of constant accumulation rates, we found a
Law machines: scale models, forensic materiality and the making of modern patent law.
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.
Deformation of a Capsule in a Power-Law Shear Flow
2016-01-01
An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values. PMID:27840656
NASA Astrophysics Data System (ADS)
Biluš, Ignacijo; Ternik, Primož; Žunič, Zoran
2011-11-01
The steady flow of generalized Newtonian fluid around a stationary cylinder placed between two parallel plates was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of the Reynolds number Re and the Power law index n values. The values of the Reynolds number, based on physical and rheological properties, cylinder radius and bulk velocity, were varied between 0.0001≤Re≤10, while the Power law index values mapped the 0.50≤n≤1.50 range, allowing for the investigation of both shear-thinning and shear-thickening effects at the creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on the most important characteristics of fluid flow past circular cylinder. It is shown that for the creeping flow regime there exist finite sized redevelopment length, drag and loss coefficient. Last but not least, the present numerical results indicate that the shear-thinning viscous behaviour decreases the onset of flow separation.
Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow
NASA Astrophysics Data System (ADS)
Matsubara, Yoshitsugu; Hieida, Yasuhiro; Tadaki, Shin-ichi
2013-09-01
Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.
A scaling law for random walks on networks
Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick
2014-01-01
The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870
Two-Dimensional Axisymmetric Child-Langmuir Scaling Law
NASA Astrophysics Data System (ADS)
Ragan-Kelley, Benjamin; Verboncoeur, John
2007-11-01
The classical one-dimensional Child-Langmuir law has been extended to two dimensions by numerical simulation in planar geometries [1]. By considering an axisymmetric cylindrical system with emission radius r, outer radius R > r, and gap length L, we further examine the space charge limit in two dimensions. The ratio of the observed current density limit JCL2 to the theoretical one-dimensional value JCL1 is found to be a monotonically decreasing function of the ratio of emission area (r^2) to gap separation (L). This result is in agreement with the planar results, where the emission area is proportional to the cathode width (r) [1]. The simulations were run in the particle in cell code, OOPIC [2]. [1] J. W. Luginsland, Y. Y. Lau, and R. M. Gilgenbach, Phys. Rev. Lett. 77, 4668 (1996). [2] J. P. Verboncoeur, A. B. Langdon, and N. T. Gladd, Comp. Phys. Comm. 87, 199 (1995).
Scaling laws and edge effects for polymer surface discharges
NASA Technical Reports Server (NTRS)
Balmain, K. G.
1979-01-01
Specimens of Mylar sheet were exposed to a 20 kV electron beam. The resulting surface discharge arcs were photographed and the discharge current into a metal backing plate measured as a function of time. The area of the Mylar sheet was defined by a round aperture in a close-fitting metal mask, and the current pulse characteristics were plotted against area on log-log paper. The plots appear as straight lines (due to power-law behavior) with slopes of 0.50 for the peak current, 1.00 for the charge released, 1.49 for the energy and 0.55 for the pulse duration. Evidence is presented for the occurrence of banded charge distributions near grounded edges, on both Teflon and Mylar.
A scaling law for random walks on networks
NASA Astrophysics Data System (ADS)
Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick
2014-10-01
The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.
The origin of allometric scaling laws in biology.
Demetrius, Lloyd
2006-12-21
The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon-specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.
Classical and generalized Horton laws for peak flows in rainfall-runoff events.
Gupta, Vijay K; Ayalew, Tibebu B; Mantilla, Ricardo; Krajewski, Witold F
2015-07-01
The discovery of the Horton laws for hydrologic variables has greatly lagged behind geomorphology, which began with Robert Horton in 1945. We define the classical and the generalized Horton laws for peak flows in rainfall-runoff events, which link self-similarity in network geomorphology with river basin hydrology. Both the Horton laws are tested in the Iowa River basin in eastern Iowa that drains an area of approximately 32 400 km(2) before it joins the Mississippi River. The US Geological Survey continuously monitors the basin through 34 stream gauging stations. We select 51 rainfall-runoff events for carrying out the tests. Our findings support the existence of the classical and the generalized Horton laws for peak flows, which may be considered as a new hydrologic discovery. Three different methods are illustrated for estimating the Horton peak-flow ratio due to small sample size issues in peak flow data. We illustrate an application of the Horton laws for diagnosing parameterizations in a physical rainfall-runoff model. The ideas and developments presented here offer exciting new directions for hydrologic research and education.
Classical and generalized Horton laws for peak flows in rainfall-runoff events
NASA Astrophysics Data System (ADS)
Gupta, Vijay K.; Ayalew, Tibebu B.; Mantilla, Ricardo; Krajewski, Witold F.
2015-07-01
The discovery of the Horton laws for hydrologic variables has greatly lagged behind geomorphology, which began with Robert Horton in 1945. We define the classical and the generalized Horton laws for peak flows in rainfall-runoff events, which link self-similarity in network geomorphology with river basin hydrology. Both the Horton laws are tested in the Iowa River basin in eastern Iowa that drains an area of approximately 32 400 km2 before it joins the Mississippi River. The US Geological Survey continuously monitors the basin through 34 stream gauging stations. We select 51 rainfall-runoff events for carrying out the tests. Our findings support the existence of the classical and the generalized Horton laws for peak flows, which may be considered as a new hydrologic discovery. Three different methods are illustrated for estimating the Horton peak-flow ratio due to small sample size issues in peak flow data. We illustrate an application of the Horton laws for diagnosing parameterizations in a physical rainfall-runoff model. The ideas and developments presented here offer exciting new directions for hydrologic research and education.
Scaling laws in {sup 3}He induced nuclear fission
Rubehn, T.; Jing, K.X.; Moretto, L.G.; Phair, L.; Tso, K.; Wozniak, G.J.
1996-12-01
Fission excitation functions of compound nuclei in a mass region where shell effects are expected to be very strong are shown to scale exactly according to the transition state prediction once these shell effects are accounted for. Furthermore, the method applied in this paper allows for the model-independent determination of the nuclear shell effects. {copyright} {ital 1996 The American Physical Society.}
NASA Technical Reports Server (NTRS)
Hamaker, Frank M; Neice, Stanford E; Wong, Thomas J
1953-01-01
The similarity law for nonsteady, inviscid, hypersonic flow about slender three-dimensional shapes is derived. Conclusions drawn are shown to be valid for rotational flow. Requirements for dynamic similarity of related shapes in free flight are obtained. The law is examined for steady flow about related three-dimensional shapes. Results of an experimental investigation of the pressures acting on two inclined cones are found to check the law as it applies to bodies of revolution.
Multi-scale roughness spectra of Mount St. Helens debris flows
NASA Technical Reports Server (NTRS)
Austin, Richard T.; England, Anthony W.
1993-01-01
A roughness spectrum allows surface structure to be interpreted as a sum of sinusoidal components with differing wavelengths. Knowledge of the roughness spectrum gives insight into the mechanisms responsible for electromagnetic scattering at a given wavelength. Measured spectra from 10-year-old primary debris flow surfaces at Mount St. Helens conform to a power-law spectral model, suggesting that these surfaces are scaling over the measured range of spatial frequencies. Measured spectra from water-deposited surfaces deviate from this model.
Multi-scale roughness spectra of Mount St. Helens debris flows
NASA Technical Reports Server (NTRS)
Austin, Richard T.; England, Anthony W.
1993-01-01
A roughness spectrum allows surface structure to be interpreted as a sum of sinusoidal components with differing wavelengths. Knowledge of the roughness spectrum gives insight into the mechanisms responsible for electromagnetic scattering at a given wavelength. Measured spectra from 10-year-old primary debris flow surfaces at Mount St. Helens conform to a power-law spectral model, suggesting that these surfaces are scaling over the measured range of spatial frequencies. Measured spectra from water-deposited surfaces deviate from this model.
A study of flame spread in engineered cardboard fuelbeds: Part II: Scaling law approach
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...
ERIC Educational Resources Information Center
Hull, R. Bruce, IV; Buhyoff, Gregory J.
1981-01-01
Intransitives in observers' preference judgements for multidimensional natural landscape scenes are examined. Thurstone's Law of Comparative Judgement (LCJ) psychophysical scaling routine is used to scale landscape preference. Both the method of Rank Ordering (RO) and the method of Paired Comparisons (PC) are used to gather the raw data necessary…
ERIC Educational Resources Information Center
Hull, R. Bruce, IV; Buhyoff, Gregory J.
1981-01-01
Intransitives in observers' preference judgements for multidimensional natural landscape scenes are examined. Thurstone's Law of Comparative Judgement (LCJ) psychophysical scaling routine is used to scale landscape preference. Both the method of Rank Ordering (RO) and the method of Paired Comparisons (PC) are used to gather the raw data necessary…
On the Kennicutt-Schmidt scaling law of submillimetre galaxies
NASA Astrophysics Data System (ADS)
Miettinen, O.; Delvecchio, I.; Smolčić, V.; Aravena, M.; Brisbin, D.; Karim, A.
2017-05-01
Context. The star formation rate (SFR) per unit area correlates well with the gas surface density for different types of galaxies. However, this Kennicutt-Schmidt (K-S) law has not yet been examined for a large, homogeneously selected sample of submillimetre galaxies (SMGs), which could provide useful SF implementation information for models of massive galaxy formation and evolution. Aims: We aim at determining the K-S law parameters for the first time for a well-selected, statistical sample of SMGs. Methods: We used the Atacama Large Millimetre/submillimetre Array (ALMA) to conduct a high resolution (0.̋2), 870 μm continuum imaging survey of 40 SMGs, which were initially selected at 1.1 mm in the COSMOS field. We analysed a sample of 32 out of the 40 target SMGs, for which our new ALMA 870 μm data provide information about the spatial extent of dust emission, and all of which have dust-obscured SFR and dust-based gas mass estimates available from our previous study. Results: We divided our sample into equally large subsamples of main-sequence (MS) objects and starbursts (factor of > 3 above the MS), and found their K-S relations to be of the form ΣSFR ∝Σgas0.81±0.01 and ΣSFR ∝Σgas0.84±0.39, respectively. Conclusions: The slightly sub-linear K-S slopes we derived suggest that the SF efficiency (SFE) is nearly constant across the Σgas range probed. Under the assumption of a Galactic CO-to-H2 conversion factor (αCO) for the whole sample, the MS SMGs obey a constant global SFE of about 21% per 100 Myr, while that of starburst SMGs is about 27% per 100 Myr. The corresponding gas depletion times are 480 Myr and 370 Myr. On average, our SMGs have Σgas ≳ 103.9 M⊙ pc-2, which suggests that they are Eddington-limited. This is consistent with the theoretical expectation of a linear K-S relation for such systems. However, size measurements of the CO-emitting regions of SMGs, and the αCO values of SMGs are needed to further constrain their Σgas values.
Scaling law for total electron-impact ionization cross sections of Li-like ions
Ancarani, L.U.; Hervieux, P.-A.
2005-09-15
Experimental total cross sections for direct electron-impact ionization of the valence electron of several Li-like ions are seen to follow a new ab initio scaling law which is inspired by a Coulomb-Born model and the frozen-core Hartree-Fock approximation. The predictive character of this scaling law should be very useful to experimentalists and can be used to complete data tables needed for plasma or astrophysical studies. A single-parameter fit of the best available experimental data, once scaled, provides us with a single formula, for moderately charged Li-like ions, which is more accurate than Lotz semiempirical formula.
The Origin of Universal Scaling Laws in Biology from Molecules and Cells to Whales
NASA Astrophysics Data System (ADS)
West, Geoffrey B.
1999-10-01
Even though biological systems are the most complex physical systems known, they satisfy remarkably simple scaling laws. For example, metabolic rate (the power needed to sustain life) scales like the -power of mass over 26 orders of magnitude ranging from the molecular respiratory complex within mitochondria up through the smallest unicellular organism (mycoplasma) to the largest animals (whales) and plants (giant sequoia). Other scaling laws relate how organismal features change with size over many orders of magnitude; these include time-scales (such as lifespan and heart-rate) and sizes (such as the radius of a tree trunk or the aorta). All of these can be expressed as power laws with exponents which are typically simple multiples of . Their phenomenology will be discussed and a quantitative, unified model presented that can explain their origin, including that of the universal -power.
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.
Fifth dimension of life and the 4/5 allometric scaling law for human brain.
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.
On a Possible Unified Scaling Law for Volcanic Eruption Durations.
Cannavò, Flavio; Nunnari, Giuseppe
2016-03-01
Volcanoes constitute dissipative systems with many degrees of freedom. Their eruptions are the result of complex processes that involve interacting chemical-physical systems. At present, due to the complexity of involved phenomena and to the lack of precise measurements, both analytical and numerical models are unable to simultaneously include the main processes involved in eruptions thus making forecasts of volcanic dynamics rather unreliable. On the other hand, accurate forecasts of some eruption parameters, such as the duration, could be a key factor in natural hazard estimation and mitigation. Analyzing a large database with most of all the known volcanic eruptions, we have determined that the duration of eruptions seems to be described by a universal distribution which characterizes eruption duration dynamics. In particular, this paper presents a plausible global power-law distribution of durations of volcanic eruptions that holds worldwide for different volcanic environments. We also introduce a new, simple and realistic pipe model that can follow the same found empirical distribution. Since the proposed model belongs to the family of the self-organized systems it may support the hypothesis that simple mechanisms can lead naturally to the emergent complexity in volcanic behaviour.
On a Possible Unified Scaling Law for Volcanic Eruption Durations
NASA Astrophysics Data System (ADS)
Cannavò, Flavio; Nunnari, Giuseppe
2016-03-01
Volcanoes constitute dissipative systems with many degrees of freedom. Their eruptions are the result of complex processes that involve interacting chemical-physical systems. At present, due to the complexity of involved phenomena and to the lack of precise measurements, both analytical and numerical models are unable to simultaneously include the main processes involved in eruptions thus making forecasts of volcanic dynamics rather unreliable. On the other hand, accurate forecasts of some eruption parameters, such as the duration, could be a key factor in natural hazard estimation and mitigation. Analyzing a large database with most of all the known volcanic eruptions, we have determined that the duration of eruptions seems to be described by a universal distribution which characterizes eruption duration dynamics. In particular, this paper presents a plausible global power-law distribution of durations of volcanic eruptions that holds worldwide for different volcanic environments. We also introduce a new, simple and realistic pipe model that can follow the same found empirical distribution. Since the proposed model belongs to the family of the self-organized systems it may support the hypothesis that simple mechanisms can lead naturally to the emergent complexity in volcanic behaviour.
On a Possible Unified Scaling Law for Volcanic Eruption Durations
Cannavò, Flavio; Nunnari, Giuseppe
2016-01-01
Volcanoes constitute dissipative systems with many degrees of freedom. Their eruptions are the result of complex processes that involve interacting chemical-physical systems. At present, due to the complexity of involved phenomena and to the lack of precise measurements, both analytical and numerical models are unable to simultaneously include the main processes involved in eruptions thus making forecasts of volcanic dynamics rather unreliable. On the other hand, accurate forecasts of some eruption parameters, such as the duration, could be a key factor in natural hazard estimation and mitigation. Analyzing a large database with most of all the known volcanic eruptions, we have determined that the duration of eruptions seems to be described by a universal distribution which characterizes eruption duration dynamics. In particular, this paper presents a plausible global power-law distribution of durations of volcanic eruptions that holds worldwide for different volcanic environments. We also introduce a new, simple and realistic pipe model that can follow the same found empirical distribution. Since the proposed model belongs to the family of the self-organized systems it may support the hypothesis that simple mechanisms can lead naturally to the emergent complexity in volcanic behaviour. PMID:26926425
Two-dimensional axisymmetric Child-Langmuir scaling law
Ragan-Kelley, Benjamin; Verboncoeur, John; Feng Yang
2009-10-15
The classical one-dimensional (1D) Child-Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit J{sub CL2} to the theoretical 1D value J{sub CL1} is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional axisymmetric electrostatic particle-in-cell simulations were used to produce these results.
Structural similitude and scaling laws for laminated beam-plates
NASA Technical Reports Server (NTRS)
Simitses, George J.; Rezaeepazhand, Jalil
1992-01-01
The establishment of similarity conditions between two structural systems is discussed. Similarity conditions provide the relationship between a scale model and its prototype and can be used to predict the behavior of the prototype by extrapolating the experimental data of the corresponding small-scale model. Since satisfying all the similarity conditions simultaneously is difficult or even impossible, distorted models with partial similarity (with at least one similarity condition relaxed) are more practical. Establishing similarity conditions based on both dimensional analysis and direct use of governing equations is discussed, and the possibility of designing distorted models is investigated. The method is demonstrated through analysis of the cylindrical bending of orthotropic laminated beam-plates subjected to transverse line loads.
Coronal Heating, Weak MHD Turbulence, and Scaling Laws
NASA Technical Reports Server (NTRS)
Rappazzo, A. F.; Velli, M.; Einaudi, G.; Dahlburg, R. B.
2007-01-01
Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B, which depends on the spectral index of total energy for given loop parameters, must vary from B3/2 for weak fields to B2 for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.
Coronal Heating, Weak MHD Turbulence, and Scaling Laws
NASA Technical Reports Server (NTRS)
Rappazzo, A. F.; Velli, M.; Einaudi, G.; Dahlburg, R. B.
2007-01-01
Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B, which depends on the spectral index of total energy for given loop parameters, must vary from B3/2 for weak fields to B2 for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.
Scaling laws for the catastrophic collisions of asteroids
NASA Astrophysics Data System (ADS)
Holsapple, K. A.; Housen, K. R.
Collisions of asteroids have traditionally been studied through laboratory experiments involving targets with masses some 15 to 20 orders of magnitude less than the bodies they are intended to simulate. Here the problem of extrapolation of experimental results up to the size regimes of interest is considered. Scaling relations are developed for the shattering threshold and the size and velocity distributions of collisional fragments. A methodology which has often been used assumes that collisional outcomes (e.g., the size of the largest remaining fragment) are completely characterized by Q, the kinetic energy of the impactor normalized by the mass of the target body. This scaling is shown to be an unlikely special case of a more general scaling theory which indicates that collisional outcomes should depend on target size and encounter velocity, even when Q is held constant. In particular, as target size increases, the critical value of Q required to shatter a body, and the characteristic fragment velocities should initially decrease (in qualitative agreement with the recent model of Farinella et al., 1982) up to an asteroid size of perhaps 40 to 50 km; then, as the gravitational forces start to dominate, the value of Q will again increase (in qualitative agreement with the recent model of Davis et al., 1983 and 1985).
Simulation of Flow and Transport at the Micro (Pore) Scale
Trebotich, D; Miller, G H
2007-04-05
An important problem in porous media involves the ability of micron and submicron-sized biological particles such as viruses or bacteria to move in groundwater systems through geologic media characterized by rock or mixed gravel, clay and sand materials. Current simulation capabilities require properly upscaled (continuum) models of colloidal filtration and adsorption to augment existing theories of fluid flow and chemical transport. Practical models typically address flow and transport behavior in aquifers over distances of 1 to 10 km where, for example, fluid momentum balance is governed by the simple Darcy's Law as a function of a pressure gradient, elevation gradient and a medium-dependent permeability parameter. In addition to fluid advection, there are multiple transport processes occurring in these systems including diffusion, dispersion and chemical interactions with solids or other aqueous chemical species. Particle transport is typically modeled in the same way as dissolved species, except that additional loss terms are incorporated to model particle filtration (physical interception), adsorption (chemical interception) and inactivation. Proper resolution of these processes at the porous medium continuum scale constitutes an important closure problem in subsurface science. We present a new simulation capability based on enabling technologies developed for microfluidics applications to model transport of colloidal-sized particles at the microscale, with relevance to the pore scale in geophysical subsurface systems. Particulate is represented by a bead-rod polymer model and is fully-coupled to a Newtonian solvent described by Navier-Stokes. Finite differences are used to discretize the interior of the domain; a Cartesian grid embedded boundary/volume-of-fluid method is used near boundaries and interfaces. This approach to complex geometry is amenable to direct simulation on grids obtained from surface extractions of tomographic image data. Short
Scaling of multiphase pipeline flow behavior at high gas density
Crowley, C.J.
1988-01-01
This report contains data that demonstrates the scaling of flow regime, pressure drop, and holdup multiphase flow with pipe diameter. In addition, entrance length effects, the onset of liquid entrainment, and interfacial shear modeling at high gas density are studied for purposes of validating multiphase flow design methods. Stratified, slug and annular flow regimes have been observed. Air, freon, and water have been used to represent pipeline fluids.
A friction to flow constitutive law and its application to a 2-D modeling of earthquakes
NASA Astrophysics Data System (ADS)
Shimamoto, Toshihiko; Noda, Hiroyuki
2014-11-01
Establishment of a constitutive law from friction to high-temperature plastic flow has long been a challenging task for solving problems such as modeling earthquakes and plate interactions. Here we propose an empirical constitutive law that describes this transitional behavior using only friction and flow parameters, with good agreements with experimental data on halite shear zones. The law predicts steady state and transient behaviors, including the dependence of the shear resistance of fault on slip rate, effective normal stress, and temperature. It also predicts a change in velocity weakening to velocity strengthening with increasing temperature, similar to the changes recognized for quartz and granite gouge under hydrothermal conditions. A slight deviation from the steady state friction law due to the involvement of plastic deformation can cause a large change in the velocity dependence. We solved seismic cycles of a fault across the lithosphere with the law using a 2-D spectral boundary integral equation method, revealing dynamic rupture extending into the aseismic zone and rich evolution of interseismic creep including slow slip prior to earthquakes. Seismic slip followed by creep is consistent with natural pseudotachylytes overprinted with mylonitic deformation. Overall fault behaviors during earthquake cycles are insensitive to transient flow parameters. The friction-to-flow law merges "Christmas tree" strength profiles of the lithosphere and rate dependency fault models used for earthquake modeling on a unified basis. Strength profiles were drawn assuming a strain rate for the flow regime, but we emphasize that stress distribution evolves reflecting the fault behavior. A fault zone model was updated based on the earthquake modeling.
NASA Astrophysics Data System (ADS)
Wesfreid, Eva; Billat, Véronique
2009-02-01
Data power law scaling behavior is observed in many fields. Velocity of fully developed turbulent flow, telecommunication traffic in networks, financial time series are some examples among many others. The goal of the present contribution is to show the scaling behavior of physiological time series in marathon races using wavelet leaders and the Detrended Fluctuation Analysis. Marathon race is an exhausting exercise, it is referenced as being a model for studying the limits of human ambulatory abilities. We analyzed the athlete's heart rate and speed time series recorded simultaneously. We find that the heart cost time series, number of heart beats per meter, increases with the fatigue appearing during the marathon race, its tendency grows in the second half of the race for all athletes. For most physiological time series, we observed a concave behavior of the wavelet leaders scaling exponents which suggests a multifractal behavior. Otherwise, the Detrended Fluctuation Analysis shows short and long range time-scale power law exponents with the same break point for each physiological time series and each athlete. The short range time-scale exponent increases with fatigue in most physiological signals.
Double K-shell photoionization and universal scaling laws
NASA Astrophysics Data System (ADS)
Hoszowska, J.; Kheifets, A. K.; Dousse, J.-Cl; Berset, M.; Bray, I.; Cao, W.; Fennane, K.; Kayser, Y.; Kavčič, M.; Szlachetko, J.; Szlachetko, M.
2009-11-01
The photon energy dependence of the double K-shell ionization cross sections for light atoms and He-like ions is reported. The K-shell double photoionization DPI cross-sections for hollow atom production are compared to those of the corresponding He-like counterparts. The relative contribution of the initial-state correlations and final-state electron-electron interactions to the K-shell DPI is addressed. A semiempirical universal scaling of the double photoionization cross sections with the effective nuclear charge for neutral atoms in the range 2 <= Z <= 47 is established.
Critical scaling laws and a classical equation of state
NASA Astrophysics Data System (ADS)
van Pelt, A.; Jin, G. X.; Sengers, J. V.
1994-07-01
In this paper we present a method which modifies a classical equation of state by incorporating the nonclassical critical behavior. As an example we have applied our procedure to the Carnahan-Starling-DeSantis (CSD) equation of state. The resulting equation reproduces the universal scaling behavior near the critical point and reduces to the universal ideal-gas behavior at low densities. We show that the renormalized CSD equation yields an improved and consistent representation of both mechanical and caloric thermodynamic properties. In addition, the suppression of the critical temperature due to the critical fluctuations is clearly demonstrated.
Scaling laws for nonlinear electromagnetic responses of Dirac fermion
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Nagaosa, Naoto
2016-03-01
We theoretically propose that the Dirac fermion in two dimensions shows the giant nonlinear responses to electromagnetic fields in the terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic fields E /Eω and B /Bω , where the characteristic electric (magnetic) field Eω(Bω) depends on the frequency ω as ℏ ω2/e vF(ℏ ω2/e vF2) , and is typically of the order of 80 V/cm (8 mT) in the terahertz region. Applications of the present theory to graphene and surface state of a topological insulator are discussed.
Atomic-scale thermocapillary flow in focused ion beam milling
Das, K.; Johnson, H. T.; Freund, J. B.
2015-05-15
Focused ion beams provide a means of nanometer-scale manufacturing and material processing, which is used for applications such as forming nanometer-scale pores in thin films for DNA sequencing. We investigate such a configuration with Ga{sup +} bombardment of a Si thin-film target using molecular dynamics simulation. For a range of ion intensities in a realistic configuration, a recirculating melt region develops, which is seen to flow with a symmetrical pattern, counter to how it would flow were it driven by the ion momentum flux. Such flow is potentially important for the shape and composition of the formed structures. Relevant stress scales and estimated physical properties of silicon under these extreme conditions support the importance thermocapillary effects. A flow model with Marangoni forcing, based upon the temperature gradient and geometry from the atomistic simulation, indeed reproduces the flow and thus could be used to anticipate such flows and their influence in applications.
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
Influence of debris flow scale on equilibrium bed slope
NASA Astrophysics Data System (ADS)
Itoh, T.; Egashira, S.; Papa, M.; Miyamoto, K.
2003-04-01
Results obtained from both of flume tests and theory suggest that an equilibrium bed slope in flow over an erodible bed is determined only by sediment discharge rate when the movements of sediment particles are laminar and thus no suspended transportation take place. This means that the static friction force is dominant in debris flow and that sediment concentration is determined by shear stress balance on the bed surface; i.e., the external shear stress must be equal to the resisting static shear stress of sediment particles, as seen in our previous studies. On the other hand, if part of sediment particles in debris flow body is transported in suspension, sediment concentration will be larger in comparison with that in case of laminar motion of sediment particles and the equilibrium bed slope will decrease. These facts are supported Egashira et al.'s experimental data. The present study discusses an influence of flow scales on an equilibrium bed slope and flow structure experimentally and theoretically. Equilibrium bed slopes and velocity profiles are measured for many flow conditions in flume tests. Those results emphasize that the equilibrium bed slope decreases with increasing of flow scale if part of debris flow body is turbulent, and it is predicted corresponding to increase of mass density of fluid phase. Experimental data for velocity profiles are compared to the results predicted by authors' constitutive equations for non-cohesive sediment and water mixture. When no turbulent diffusions take place, flow characteristics such as velocity profiles and flow resistance are predicted very well by our equations. However, the equations will underestimate the flow resistance if a part of the flow body becomes turbulent because of increase of flow scale. These suggest that the changes of equilibrium bed slope and flow structure are caused by phase-shift from solid phase to fluid phase depending on debris flow scale.
Testing the gravitational inverse-square law at centimeter scales
NASA Astrophysics Data System (ADS)
Bonicalzi, Ricco
Many attempts to unify gravity with the Standard Model entail a gravitational inverse-square-law violation (ISLV) at some low level. This dissertation reports on the initial phase of a torsion-pendulum null experiment searching for such a violation in the interaction between two macroscopic bodies with a characteristic separation of 12 cm. Central to the experimental design is the special configuration of the mass distributions of both the pendulum and source mass to provide high-sensitivity to the horizontal gradient of the Laplacian of the interaction potential (a signature of ISLV), while strongly suppressing coupling through Newtonian gravity. Specifically, this design ensures that gravitational systematic effects arise only at second order in the fabrication errors of the pendulum and source mass. A key aspect of this work is the choice of the second-harmonic amplitude of pendulum oscillation as the torque observable, instead of the traditional oscillation frequency. This relatively recent torsion-pendulum method is markedly less sensitive to changes in torsion-fiber temperature and enables the ambient-temperature instrumentation of the initial phase to achieve necessary noise performance without heroic efforts to stabilize temperature. As details of the second-harmonic method have not yet been published, the presentation here dwells on a number of subtleties involved in analyzing the data. Experimental results are reported assuming a Yukawa-type interaction anomaly, where a is the strength of the Yukawa term relative to Newtonian gravity. A preliminary set of 34 data runs, each around a day in duration, produced a value of alpha = (-6.3 +/- 7.5) x 10-5. In the absence of significant systematic effects, even this interim result would have placed tighter bounds on ISLV than previously appearing in the literature. Unfortunately, an accelerated Department of Energy deadline for demolition of our Hanford laboratory facility compelled a shift of focus to the
Power law scaling in synchronization of brain signals depends on cognitive load.
Tinker, Jesse; Velazquez, Jose Luis Perez
2014-01-01
As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors.
Small Scale Mass Flow Plug Calibration
NASA Technical Reports Server (NTRS)
Sasson, Jonathan
2015-01-01
A simple control volume model has been developed to calculate the discharge coefficient through a mass flow plug (MFP) and validated with a calibration experiment. The maximum error of the model in the operating region of the MFP is 0.54%. The model uses the MFP geometry and operating pressure and temperature to couple continuity, momentum, energy, an equation of state, and wall shear. Effects of boundary layer growth and the reduction in cross-sectional flow area are calculated using an in- integral method. A CFD calibration is shown to be of lower accuracy with a maximum error of 1.35%, and slower by a factor of 100. Effects of total pressure distortion are taken into account in the experiment. Distortion creates a loss in flow rate and can be characterized by two different distortion descriptors.
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2017-02-01
Boundary-layer solutions to Banks' problem for the flow induced by power-law stretching of a plate are obtained for two generalizations that include arbitrary transverse plate shearing motion. In one extension an arbitrary transverse shearing motion is the product of the power-law stretching. In the other extension the streamwise stretching coordinate is added to an arbitrary transverse shearing and together raised to the power of stretching. In addition we find that Banks' power law stretching may be accompanied by orthogonal power-law shear. In all cases, the original boundary-value problem of Banks [1] is recovered. Results are illustrated with velocity profiles both at the plate and at fixed height in the fluid above the plate.
Nonlinear Generation of shear flows and large scale magnetic fields by small scale
NASA Astrophysics Data System (ADS)
Aburjania, G.
2009-04-01
EGU2009-233 Nonlinear Generation of shear flows and large scale magnetic fields by small scale turbulence in the ionosphere by G. Aburjania Contact: George Aburjania, g.aburjania@gmail.com,aburj@mymail.ge
On universality of scaling law describing roughness of triple line.
Bormashenko, Edward; Musin, Albina; Whyman, Gene; Barkay, Zahava; Zinigrad, Michael
2015-01-01
The fine structure of the three-phase (triple) line was studied for different liquids, various topographies of micro-rough substrates and various wetting regimes. Wetting of porous and pillar-based micro-scaled polymer surfaces was investigated. The triple line was visualized with the environmental scanning electron microscope and scanning electron microscope for the "frozen" triple lines. The value of the roughness exponent ζ for water (ice)/rough polymer systems was located within 0.55-0.63. For epoxy glue/rough polymer systems somewhat lower values of the exponent, 0.42 < ζ < 0.54, were established. The obtained values of ζ were close for the Cassie and Wenzel wetting regimes, different liquids, and different substrates' topographies. Thus, the above values of the exponent are to a great extent universal. The switch of the exponent, when the roughness size approaches to the correlation length of the defects, is also universal.
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.
Leidenfrost effect: Accurate drop shape modeling and refined scaling laws
NASA Astrophysics Data System (ADS)
Sobac, B.; Rednikov, A.; Dorbolo, S.; Colinet, P.
2014-11-01
We here present a simple fitting-parameter-free theory of the Leidenfrost effect (droplet levitation above a superheated plate) covering the full range of stable shapes, i.e., from small quasispherical droplets to larger puddles floating on a pocketlike vapor film. The geometry of this film is found to be in excellent quantitative agreement with the interferometric measurements of Burton et al. [Phys. Rev. Lett. 109, 074301 (2012), 10.1103/PhysRevLett.109.074301]. We also obtain new scalings generalizing classical ones derived by Biance et al. [Phys. Fluids 15, 1632 (2003), 10.1063/1.1572161] as far as the effect of plate superheat is concerned and highlight the relative role of evaporation, gravity, and capillarity in the vapor film. To further substantiate these findings, a treatment of the problem by matched asymptotic expansions is also presented.
Leidenfrost effect: Accurate drop shape modeling and refined scaling laws.
Sobac, B; Rednikov, A; Dorbolo, S; Colinet, P
2014-11-01
We here present a simple fitting-parameter-free theory of the Leidenfrost effect (droplet levitation above a superheated plate) covering the full range of stable shapes, i.e., from small quasispherical droplets to larger puddles floating on a pocketlike vapor film. The geometry of this film is found to be in excellent quantitative agreement with the interferometric measurements of Burton et al. [Phys. Rev. Lett. 109, 074301 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.074301]. We also obtain new scalings generalizing classical ones derived by Biance et al. [Phys. Fluids 15, 1632 (2003)PHFLE61070-663110.1063/1.1572161] as far as the effect of plate superheat is concerned and highlight the relative role of evaporation, gravity, and capillarity in the vapor film. To further substantiate these findings, a treatment of the problem by matched asymptotic expansions is also presented.
Likert scales, levels of measurement and the "laws" of statistics.
Norman, Geoff
2010-12-01
Reviewers of research reports frequently criticize the choice of statistical methods. While some of these criticisms are well-founded, frequently the use of various parametric methods such as analysis of variance, regression, correlation are faulted because: (a) the sample size is too small, (b) the data may not be normally distributed, or (c) The data are from Likert scales, which are ordinal, so parametric statistics cannot be used. In this paper, I dissect these arguments, and show that many studies, dating back to the 1930s consistently show that parametric statistics are robust with respect to violations of these assumptions. Hence, challenges like those above are unfounded, and parametric methods can be utilized without concern for "getting the wrong answer".
Time-average based on scaling law in anomalous diffusions
NASA Astrophysics Data System (ADS)
Kim, Hyun-Joo
2015-05-01
To solve the obscureness in measurement brought about from the weak ergodicity breaking appeared in anomalous diffusions, we have suggested the time-averaged mean squared displacement (MSD) /line{δ 2 (τ )}τ with an integral interval depending linearly on the lag time τ. For the continuous time random walk describing a subdiffusive behavior, we have found that /line{δ 2 (τ )}τ ˜ τ γ like that of the ensemble-averaged MSD, which makes it be possible to measure the proper exponent values through time-average in experiments like a single molecule tracking. Also, we have found that it has originated from the scaling nature of the MSD at an aging time in anomalous diffusion and confirmed them through numerical results of the other microscopic non-Markovian model showing subdiffusions and superdiffusions with the origin of memory enhancement.
Resistance law for a turbulent Taylor-Couette flow at very large Taylor numbers
NASA Astrophysics Data System (ADS)
Balonishnikov, A. M.
2016-11-01
Based on the semi-empirical model of the transport of the specific rate of turbulence energy dissipation, it has been concluded that the resistance laws are observed for a turbulent Taylor-Couette flow between independently rotating coaxial cylinders for very large Taylor numbers.
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.
Power-law statistics and universal scaling in the absence of criticality
NASA Astrophysics Data System (ADS)
Touboul, Jonathan; Destexhe, Alain
2017-01-01
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
Vortex clustering and universal scaling laws in two-dimensional quantum turbulence.
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.
Goldsmith, Randall H; Wasielewski, Michael R; Ratner, Mark A
2007-10-31
The ability of multiple spatial pathways to sum coherently and facilitate charge transfer is examined theoretically. The role of multiple spatial pathways in mediating charge transfer has been invoked several times in the recent literature while discussing charge transfer in proteins, while multiple spatial pathways are known to contribute to charge transport in metal-molecule-metal junctions. We look at scaling laws for charge transfer in donor-bridge-acceptor (D-B-A) molecules and show that these scaling laws change significantly when environment-induced dephasing is included. In some cases, D-B-A systems are expected to show no enhancement in the rate of charge transfer with the addition of multiple degenerate pathways. The origins of these different scaling laws are investigated by looking at which Liouville space pathways are active in different dephasing regimes.
A phase-field study of the scaling law in free-standing ferroelectric thin films.
Yin, Binglun; Mao, Huina; Qu, Shaoxing
2015-12-18
The scaling law for ferroelectric stripe domains is investigated in free-standing BaTiO3 and PbTiO3 thin films via phase-field simulations. The results agree with the Kittel law, where the square of the domain width is found to be proportional to the thin film thickness. After being rescaled by the corresponding domain wall thickness, the generalized scaling law is also demonstrated, with the dimensionless scaling constant M estimated to be ∼3.3 in two ferroelectric materials. Moreover, we predict the effect of the exchange constant which is incorporated in Ginzburg-Landau theory on the equilibrium domain width and the critical thickness of the ferroelectric thin films.
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.
Power-law statistics and universal scaling in the absence of criticality.
Touboul, Jonathan; Destexhe, Alain
2017-01-01
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
Scaling and design of landslide and debris-flow experiments
Iverson, Richard M.
2015-01-01
Scaling plays a crucial role in designing experiments aimed at understanding the behavior of landslides, debris flows, and other geomorphic phenomena involving grain-fluid mixtures. Scaling can be addressed by using dimensional analysis or – more rigorously – by normalizing differential equations that describe the evolving dynamics of the system. Both of these approaches show that, relative to full-scale natural events, miniaturized landslides and debris flows exhibit disproportionately large effects of viscous shear resistance and cohesion as well as disproportionately small effects of excess pore-fluid pressure that is generated by debris dilation or contraction. This behavioral divergence grows in proportion to H3, where H is the thickness of a moving mass. Therefore, to maximize geomorphological relevance, experiments with wet landslides and debris flows must be conducted at the largest feasible scales. Another important consideration is that, unlike stream flows, landslides and debris flows accelerate from statically balanced initial states. Thus, no characteristic macroscopic velocity exists to guide experiment scaling and design. On the other hand, macroscopic gravity-driven motion of landslides and debris flows evolves over a characteristic time scale (L/g)1/2, where g is the magnitude of gravitational acceleration and L is the characteristic length of the moving mass. Grain-scale stress generation within the mass occurs on a shorter time scale, H/(gL)1/2, which is inversely proportional to the depth-averaged material shear rate. A separation of these two time scales exists if the criterion H/L < < 1 is satisfied, as is commonly the case. This time scale separation indicates that steady-state experiments can be used to study some details of landslide and debris-flow behavior but cannot be used to study macroscopic landslide or debris-flow dynamics.
Scaling and design of landslide and debris-flow experiments
NASA Astrophysics Data System (ADS)
Iverson, Richard M.
2015-09-01
Scaling plays a crucial role in designing experiments aimed at understanding the behavior of landslides, debris flows, and other geomorphic phenomena involving grain-fluid mixtures. Scaling can be addressed by using dimensional analysis or - more rigorously - by normalizing differential equations that describe the evolving dynamics of the system. Both of these approaches show that, relative to full-scale natural events, miniaturized landslides and debris flows exhibit disproportionately large effects of viscous shear resistance and cohesion as well as disproportionately small effects of excess pore-fluid pressure that is generated by debris dilation or contraction. This behavioral divergence grows in proportion to H3, where H is the thickness of a moving mass. Therefore, to maximize geomorphological relevance, experiments with wet landslides and debris flows must be conducted at the largest feasible scales. Another important consideration is that, unlike stream flows, landslides and debris flows accelerate from statically balanced initial states. Thus, no characteristic macroscopic velocity exists to guide experiment scaling and design. On the other hand, macroscopic gravity-driven motion of landslides and debris flows evolves over a characteristic time scale (L/g)1/2, where g is the magnitude of gravitational acceleration and L is the characteristic length of the moving mass. Grain-scale stress generation within the mass occurs on a shorter time scale, H/(gL)1/2, which is inversely proportional to the depth-averaged material shear rate. A separation of these two time scales exists if the criterion H/L < < 1 is satisfied, as is commonly the case. This time scale separation indicates that steady-state experiments can be used to study some details of landslide and debris-flow behavior but cannot be used to study macroscopic landslide or debris-flow dynamics.
AN-107 (C) Simulant Bench-Scale LAW Evaporation with Organic Regulatory Analysis
Saito, H.H.
2001-05-15
The overall objective of this work is to develop preliminary operating data including expected concentration endpoints using a C waste envelope simulant. The data is to be used for the preliminary Hanford RPP flow sheet development and LAW Melter Feed Evaporator design.
Shock-driven transition to turbulence: Emergence of power-law scaling
NASA Astrophysics Data System (ADS)
Olmstead, D.; Wayne, P.; Simons, D.; Trueba Monje, I.; Yoo, J. H.; Kumar, S.; Truman, C. R.; Vorobieff, P.
2017-05-01
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. 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 maps of fluorescent tracer premixed with heavy gas. 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∘).
Shock-driven transition to turbulence: Emergence of power-law scaling
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
Scaling Laws of Turbulence and Heating of Fast Solar Wind: The Role of Density Fluctuations
Carbone, V.; Sorriso-Valvo, L.; Bruno, R.
2009-08-07
Incompressible and isotropic magnetohydrodynamic turbulence in plasmas can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar poles observed by the Ulysses spacecraft, where the turbulence is in an Alfvenic state. An analogous phenomenological scaling law, suitably modified to take into account compressible fluctuations, is observed more frequently in the same data set. Large-scale density fluctuations, despite their low amplitude, thus play a crucial role in the basic scaling properties of turbulence. The turbulent cascade rate in the compressive case can, moreover, supply the energy dissipation needed to account for the local heating of the nonadiabatic solar wind.
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 of turbulence and heating of fast solar wind: the role of density fluctuations.
Carbone, V; Marino, R; Sorriso-Valvo, L; Noullez, A; Bruno, R
2009-08-07
Incompressible and isotropic magnetohydrodynamic turbulence in plasmas can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar poles observed by the Ulysses spacecraft, where the turbulence is in an Alfvénic state. An analogous phenomenological scaling law, suitably modified to take into account compressible fluctuations, is observed more frequently in the same data set. Large-scale density fluctuations, despite their low amplitude, thus play a crucial role in the basic scaling properties of turbulence. The turbulent cascade rate in the compressive case can, moreover, supply the energy dissipation needed to account for the local heating of the nonadiabatic solar wind.
On the scaling of velocity and vorticity variances in turbulent channel flow
NASA Astrophysics Data System (ADS)
Leonard, A.
2015-11-01
The availability of new DNS-based statistics for turbulent channel flow (Lee & Moser, JFM 2015) along with previous results (e.g., Hoyas & Jiménez, Phys. Flu. 2006) has provided the opportunity for another look at the scaling laws for this flow. For example, data from the former (fig. 4(e)) for the streamwise velocity variance in the outer region clearly indicate a modified log law for that quantity at Reτ = 5200 , i.e., + =C0 -C1 ln (y / δ) -C2 ln (y / δ)2 where δ is the channel half height. We find that this result fits the the data very well for 0 . 1 < y / δ < 0 . 8 . The Reynolds number (5200) is still apparently too low to observe the much-discussed log law (above with C2 = 0), which, presumably, would appear for roughly y / δ < 0 . 1 , as it does in high Reτ pipe flow (Hultmark et al., PRL 2012) with δ replaced by R. On the other hand, the above modified log law with the same values for C1 and C2 is a good fit for the pipe data at Reτ = 98 ×105 for y / R > 0 . 12 (fig. 4 of Hultmark et al.).
NASA Astrophysics Data System (ADS)
Segura, Catalina; Lazzati, Davide; Sankarasubramanian, Arumugam
2013-11-01
A recent study employed a broken power-law (BPL) distribution for understanding the scaling frequency of bankfull discharge in snowmelt-dominated basins. This study, grounded from those findings, investigated the ability of a BPL function to describe the distribution of daily flows above the mean annual flow in 1217 sites across the conterminous U.S. (CONUS). The hydrologic regime in all the sites is unregulated and spans a wide range in drainage areas (2-120,000 km2) and elevation (0-3000 m). Available daily flow records in all sites varied between 15 and 108 years. Comparing the performance of BPL distribution and the traditionally used lognormal distribution, we found that BPL provides stronger fit in ˜80% of the sites. Thus the BPL function provides a suitable tool to model daily flows in most areas of the CONUS. The potential for developing a model for predicting the frequency distribution of daily flows in ungauged sites was analyzed. We found that such model is possible using drainage area, mean basin elevation, and mean annual precipitation as predicting variables for any site located above 600 m across the CONUS. We also found strong continental-wide correlations between 3 of the 4 parameters that describe the BPL and basin characteristics. Our results indicate that the BPL function provides a robust alternative to traditional functions such as the lognormal to model the statistical variation of daily flows above the mean annual in most basins of the CONUS.
Compact star matter: EoS with new scaling law
NASA Astrophysics Data System (ADS)
Kim, Kyungmin; Lee, Hyun Kyu; Lee, Jaehyun
In this paper, we present a simple discussion on the properties of compact stars using an EoS obtained in effective field theory anchored on scale and hidden-local symmetric Lagrangian endowed with topology change and a unequivocal prediction on the deformation of the compact star, that could be measured in gravitational waves. The objective is not to offer a superior or improved EoS for compact stars but to confront with a forthcoming astrophysical observable, the given model formulated in what is considered to be consistent with the premise of quantum chromodynamics (QCD). The model so obtained is found to satisfactorily describe the observation of a two-solar mass neutron star [P. B. Demorest et al., Nature 467 (2010) 1081, J. Antoniadis et al., Science 340 (2013) 1233232] with a minimum number of parameters. Specifically, the observable we are considering in this paper is the tidal deformability parameter λ (equivalently the Love number k2), which affects gravitational wave forms at the late period of inspiral stage. The forthcoming aLIGO and aVirgo observations of gravitational waves from binary neutron star system will provide a valuable guidance for arriving at a better understanding of highly compressed baryonic matter.
SCALING LAW OF RELATIVISTIC SWEET-PARKER-TYPE MAGNETIC RECONNECTION
Takahashi, Hiroyuki R.; Kudoh, Takahiro; Masada, Youhei; Matsumoto, Jin
2011-10-01
Relativistic Sweet-Parker-type magnetic reconnection is investigated by relativistic resistive magnetohydrodynamic (RRMHD) simulations. As an initial setting, we assume anti-parallel magnetic fields and a spatially uniform resistivity. A perturbation imposed on the magnetic fields triggers magnetic reconnection around a current sheet, and the plasma inflows into the reconnection region. The inflows are then heated due to ohmic dissipation in the diffusion region and finally become relativistically hot outflows. The outflows are not accelerated to ultrarelativistic speeds (i.e., Lorentz factor {approx_equal} 1), even when the magnetic energy dominates the thermal and rest mass energies in the inflow region. Most of the magnetic energy in the inflow region is converted into the thermal energy of the outflow during the reconnection process. The energy conversion from magnetic to thermal energy in the diffusion region results in an increase in the plasma inertia. This prevents the outflows from being accelerated to ultrarelativistic speeds. We find that the reconnection rate R obeys the scaling relation R{approx_equal}S{sup -0.5}, where S is the Lundquist number. This feature is the same as that of non-relativistic reconnection. Our results are consistent with the theoretical predictions of Lyubarsky for Sweet-Parker-type magnetic reconnection.
Tests of the gravitational inverse-square law below the dark-energy length scale.
Kapner, D J; Cook, T S; Adelberger, E G; Gundlach, J H; Heckel, B R; Hoyle, C D; Swanson, H E
2007-01-12
We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 microm, probing distances less than the dark-energy length scale lambda(d)=[4 -root](variant Planck's over 2pic/rho(d) approximately 85 microm. We find with 95% confidence that the inverse-square law holds (|alpha|
The geomagnetic dynamos of the moon and Venus - Comparisons with a recent scaling law
NASA Technical Reports Server (NTRS)
Russell, C. T.; Goldstein, B. E.
1976-01-01
The evidence for the existence of an ancient lunar dynamo is reviewed along with the data on the magnetic field of Venus. These facts are then discussed in terms of Dolginov's scaling law for predicting magnetic moment of planets with a precession-driven dynamo. The precessional dynamo mechanism of Dolginov comes close to predicting the inferred magnetic moment of Venus, but this is viewed as a coincidence, for the Dolginov scaling law is based on an ad hoc force balance for which little justification is given. It assumes that the interiors of the planets have similar densities, conductivities, and precessional characteristics, whereas they clearly do not.
On the trajectory scaling of tandem twin jets in cross-flow in close proximity
NASA Astrophysics Data System (ADS)
New, T. H.; Zang, B.
2015-11-01
An experimental study has been conducted on tandem twin jets in cross-flow (JICF) in close proximity to investigate the relationships between their trajectories, separation distances and velocity ratios. Results show that the front and rear jets, each with initially distinct jet trajectory, merge into a single trajectory shortly after they exhaust into the cross-flow. Furthermore, the merged tandem JICF attains deeper cross-flow penetration than that of a single JICF at the same velocity ratio. The front jet is also observed to provide `shielding' for the rear jet such that the latter penetrates relatively deeper into the cross-flow, which corroborates observations made by earlier studies. In particular, the present study demonstrates that it is possible to collapse the tandem JICF merged trajectories by ` rD'-scaling, where A and B coefficients show slight reductions and increments, respectively, with increasing separation distance. Collapsing the merged trajectories by using single JICF A and B coefficients leads to the notion of effective velocity ratio for tandem JICF, which enable the authors to propose a modification in the ` rD'-scaling law for tandem JICF. Lastly, the modified ` rD'-scaling law is applied to trajectory data from an earlier tandem JICF study, and its validity is demonstrated by the resulting good collapse.
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
Segregation time-scales in model granular flows
NASA Astrophysics Data System (ADS)
Staron, Lydie; Phillips, Jeremy C.
2016-04-01
Segregation patterns in natural granular systems offer a singular picture of the systems evolution. In many cases, understanding segregation dynamics may help understanding the system's history as well as its future evolution. Among the key questions, one concerns the typical time-scales at which segregation occurs. In this contribution, we present model granular flows simulated by means of the discrete Contact Dynamics method. The granular flows are bi-disperse, namely exhibiting two grain sizes. The flow composition and its dynamics are systematically varied, and the segregation dynamics carefully analyzed. We propose a physical model for the segregation that gives account of the observed dependence of segregation time scales on composition and dynamics. References L. Staron and J. C. Phillips, Stress partition and micro-structure in size-segregating granular flows, Phys. Rev. E 92 022210 (2015) L. Staron and J. C. Phillips, Segregation time-scales in bi-disperse granular flows, Phys. Fluids 26 (3), 033302 (2014)
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.
DOES A SCALING LAW EXIST BETWEEN SOLAR ENERGETIC PARTICLE EVENTS AND SOLAR FLARES?
Kahler, S. W.
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-ray 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.
Martian Meanders: Wavelength-Width Scaling and Flow Duration
NASA Astrophysics Data System (ADS)
Gregoire-Mazzocco, H.; Stepinski, T. F.; McGovern, P. J.; Lanzoni, S.; Frascati, A.; Rinaldo, A.
2006-03-01
Martian meanders reveals linear wavelength/width scaling with a coef. k~10, that can be used to estimate discharges. Simulations of channel evolution are used to determine flow duration from sinuosity. Application to Nirgal Vallis yields 200 yrs.
Toward a dynamical understanding of planetary-scale flow regimes.
NASA Astrophysics Data System (ADS)
Marshall, J.; Molteni, F.
1993-06-01
A strategy for diagnosing and interpreting flow regimes that is firmly rooted in dynamical theory is presented and applied to the study of observed and modeled planetary-scale regimes of the wintertime circulation in the Northern Hemisphere.
Bauer, Wolfgang R; Nadler, Walter
2005-06-22
A generalized macroscopic Fick's first diffusion law is derived which describes steady-state particle flow between two baths explicitly as a function of the concentration gradient, acting as the thermodynamic driving force, times a functional of the first passage time. The latter is shown to be the ratio of the number of particles trapped between the baths and the first passage time. Particle trapping is shown to be a powerful mechanism by which flow can be enhanced. This is analyzed for two examples: a potential and an entropy trap.
Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow
NASA Astrophysics Data System (ADS)
Armstrong, Ryan T.; McClure, James E.; Berrill, Mark A.; Rücker, Maja; Schlüter, Steffen; Berg, Steffen
2016-10-01
In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.
Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow.
Armstrong, Ryan T; McClure, James E; Berrill, Mark A; Rücker, Maja; Schlüter, Steffen; Berg, Steffen
2016-10-01
In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.
Two-threshold model for scaling laws of noninteracting snow avalanches.
Faillettaz, Jerome; Louchet, Francois; Grasso, Jean-Robert
2004-11-12
The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity-driven systems, we introduce a two-threshold 2D cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceding the lattice system breakdown are power-law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power-law exponents observed for land, rock, or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.
NASA Astrophysics Data System (ADS)
Chen, Wen-Yau; Lai, Jeng-You; Young, D. L.
2010-11-01
Asymptotic and transient stability analyses of unbounded uniform granular shear flow at high solids volume fractions were carried out in the paper, based on a model composed of the viscoplastic constitutive law [P. Jop, Y. Forterre, and O. Pouliquen, Nature (London) 441, 727 (2006)] and the dilatancy law [O. Pouliquen et al., J. Stat. Mech.: Theory Exp. (2006) P07020]. We refer to this model as the VPDL (meaning of the "viscoplastic and dilatancy laws") thereinafter. In this model, dense granular flows were treated as a viscoplastic fluid with a Drucker-Prager-like yielding criterion. We compared our results to those obtained using the frictional-kinetic model (FKM) [M. Alam and P. R. Nott, J. Fluid Mech. 343, 267 (1997)]. Our main result is that unbounded uniform dense granular shear flows are always asymptotically stable at large time based on the VPDL model, at least for two-dimensional perturbations. This is valid for disturbances of layering modes (i.e., the perturbations whose wavenumber vectors are aligned along the transverse coordinate) as well as for nonlayering modes (the streamwise component of the wavenumber vector is nonzero). By contrast, layering modes can be unstable based on the FKM constitutive laws. Interestingly, in the framework of the VPDL, the analysis shows that significant transient growth may occur owing to the non-normality of the linear system, although disturbances eventually decay at large time.
Organised convection embedded in a large-scale flow
NASA Astrophysics Data System (ADS)
Naumann, Ann Kristin; Stevens, Bjorn; Hohenegger, Cathy
2017-04-01
In idealised simulations of radiative convective equilibrium, convection aggregates spontaneously from randomly distributed convective cells into organized mesoscale convection despite homogeneous boundary conditions. Although these simulations apply very idealised setups, the process of self-aggregation is thought to be relevant for the development of tropical convective systems. One feature that idealised simulations usually neglect is the occurrence of a large-scale background flow. In the tropics, organised convection is embedded in a large-scale circulation system, which advects convection in along-wind direction and alters near surface convergence in the convective areas. A large-scale flow also modifies the surface fluxes, which are expected to be enhanced upwind of the convective area if a large-scale flow is applied. Convective clusters that are embedded in a large-scale flow therefore experience an asymmetric component of the surface fluxes, which influences the development and the pathway of a convective cluster. In this study, we use numerical simulations with explicit convection and add a large-scale flow to the established setup of radiative convective equilibrium. We then analyse how aggregated convection evolves when being exposed to wind forcing. The simulations suggest that convective line structures are more prevalent if a large-scale flow is present and that convective clusters move considerably slower than advection by the large-scale flow would suggest. We also study the asymmetric component of convective aggregation due to enhanced surface fluxes, and discuss the pathway and speed of convective clusters as a function of the large-scale wind speed.
Scaling behavior of immersed granular flows
NASA Astrophysics Data System (ADS)
Amarsid, L.; Delenne, J.-Y.; Mutabaruka, P.; Monerie, Y.; Perales, F.; Radjai, F.
2017-06-01
The shear behavior of granular materials immersed in a viscous fluid depends on fluid properties (viscosity, density), particle properties (size, density) and boundary conditions (shear rate, confining pressure). Using computational fluid dynamics simulations coupled with molecular dynamics for granular flow, and exploring a broad range of the values of parameters, we show that the parameter space can be reduced to a single parameter that controls the packing fraction and effective friction coefficient. This control parameter is a modified inertial number that incorporates viscous effects.
Direct simulation Monte Carlo of rarefied hypersonic flow on power law shaped leading edges
NASA Astrophysics Data System (ADS)
Santos, Wilson Fernando Nogueira Dos
A numerical study of several parameters that influence the flowfield structure, aerodynamic surface quantities and shock wave structure at rarefied hypersonic flow conditions is conducted on power law shaped leading edges. The calculations are performed with a detailed computer code that properly accounts for nonequilibrium effects and that has been demonstrated to yield excellent comparisons with flight- and ground-test data. The flowfield structure, aerodynamic surface quantities and shock wave structure of power law shaped leading edges are examined in order to provide information on how well these shapes could stand as possible candidates for blunting geometries of hypersonic leading edges. Newtonian flow analysis has shown that these shapes exhibit both blunt and sharp aerodynamic properties. Moreover, computational investigation of minimum-drag bodies at supersonic and moderate hypersonic speeds has indicated that power law shapes for certain exponents yield the lowest wave drag. These qualities make power law shapes strong candidates for leading edge design. A very detailed description of the impact on the flow properties, such as velocity, density, temperature and pressure, has been presented separately in the vicinity of the nose of the leading edges due to changes in their shapes. Numerical solutions show that the shape of the leading edge disturbed the flowfield far upstream, where the domain of influence decreased as the leading edge became aerodynamically sharp. A detailed procedure is presented to predict the pressure gradient along the body surface in a rarefied environment. Numerical solutions show that the pressure gradient behavior follows that predicted by Newtonian theory. It is found that the pressure gradient along the body surface goes to zero at the nose of the leading edge for power law exponents less than 2/3, a characteristic of a blunt body. It is finite for power law exponent of 2/3 and goes to minus infinite for power law exponents
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.
Scaling laws for capillary vessels of mammals at rest and in exercise.
Dawson, Thomas H
2003-01-01
A general derivation is presented for the scaling laws governing the size and number of capillary blood vessels in mammals. The derivation is based on the assumption of three idealized similarity principles known to apply, at least approximately, to resting mammals: (i) size-invariant blood pressure; (ii) size-invariant fraction of blood in the capillaries; and (iii) size-invariant oxygen consumption and uptake, per unit of body mass, during each heart cycle. Results indicate that the radius and length of capillaries, and the number that are open and active in the resting state, should scale with mammal mass to the powers 1/12, 5/24 and 5/8, respectively, consistent with earlier work by the author. Measurements are presented supporting the results. Physiological changes accompanying strenuous exercise are accounted for by a change in the scaling law for capillary number, from scaling exponent 5/8 to 3/4. PMID:12713751
Scaling Laws in City Growth: Setting Limitations with Self-Organizing Maps
Sobczyński, Maciej
2016-01-01
Do scaling relations always provide the means to anticipate the relationships between the size of cities, costs of maintenance, and the socio-economic benefits resulting from their growth? Scaling laws are considered a universal principle that describes the development of complex systems such as cities. It seems that regardless of their location or history, the growth of cities is associated with the super-linear or sublinear scaling of features such as the amount of space required, infrastructure, or human activities. However, the results of our research, based on grouping by Self-Organizing Maps, reveal some limitations in the application of scaling laws: the trends of urban growth behave in a different manner when we consider both a large and diverse collection of cities and a subset of cities alike. This finding complements the existing body of knowledge on the growth of cities and allows for a more accurate prediction of their future. PMID:28005994
NASA Astrophysics Data System (ADS)
Yang, Soohyun; Paik, Kyungrock
Horton’s laws have long served as fundamental principles for fractal organization of a drainage basin. Scaling ratios of stream number, length, area, and side tributary have been proposed but the definitions of these basic variables are inconsistent. The concept of eigenarea can be utilized to resolve this issue. Here, we investigated the relationships among Hortonian scaling ratios using the concept of eigenarea. We found that the eigenarea ratio, likewise other scaling ratios, is invariant within a stream network, the law of eigenarea. We analytically revealed that the eigenarea ratio is equivalent to the stream length ratio. Our examination implies that Horton’s original two ratios of stream number and length can represent most Hortonian scaling ratios except Tokunaga ratio.
Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces
NASA Astrophysics Data System (ADS)
Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye
1998-11-01
The well-known translation between the power law of the 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.
Diversity of individual mobility patterns and emergence of aggregated scaling laws
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
Diversity of individual mobility patterns and emergence of aggregated scaling laws.
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.
Glass transitions and scaling laws within an alternative mode-coupling theory
NASA Astrophysics Data System (ADS)
Götze, Wolfgang; Schilling, Rolf
2015-04-01
Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014), 10.1016/j.physa.2013.10.028]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the correlation functions. It is also demonstrated for a schematic model that the TMCT does not lead to the MCT scenarios either for transition-line crossings or for the appearance of higher-order glass-transition singularities.
Glass transitions and scaling laws within an alternative mode-coupling theory.
Götze, Wolfgang; Schilling, Rolf
2015-04-01
Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014)]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the correlation functions. It is also demonstrated for a schematic model that the TMCT does not lead to the MCT scenarios either for transition-line crossings or for the appearance of higher-order glass-transition singularities.
Scale invariance of subsurface flow patterns and its limitation
NASA Astrophysics Data System (ADS)
Hergarten, S.; Winkler, G.; Birk, S.
2016-05-01
Preferential flow patterns in the subsurface are of great importance for the availability and the quality of water resources. However, knowledge of their spatial structure is still behind their importance, so that understanding the nature of preferential flow patterns is a major issue in subsurface hydrology. Comparing the statistics of river catchment sizes and spring discharges, we found that the morphology of preferential subsurface flow patterns is probably scale invariant and similar to that of dendritic river networks. This result is not limited to karstic aquifers where the occurrence of dendritic structures has been known at least qualitatively for a long time. The scale invariance even seems to be independent of the lithology of the aquifer. However, scale invariance of river patterns seems to be only limited by the continental scale, while scale invariance of subsurface flow patterns breaks down at much smaller scales. The upper limit of scale invariance in subsurface flow patterns is highly variable. We found a range from thousands of square kilometers for limestone aquifers down to less than 1 km2 in the weathered zone and debris accumulations of crystalline rocks.
Evaluating flow laws for dynamically recrystallized quartz based on field data
NASA Astrophysics Data System (ADS)
Peters, Max; Herwegh, Marco
2013-04-01
The extrapolation of experimentally controlled deformation conditions, and the resulting relations between physical parameters acting during ductile deformation, to nature is considered controversial (see Herwegh et al., 2005 and references therein). Whereas the relationship between flow stress and recrystallized grain size can be empirically derived from lab experiments using paleopiezometers (e.g. Stipp & Tullis, 2003), the relation between recrystallized grain size, strain rate, differential stress, temperature and activation energy for dislocation creep requires further constraints. For these relations, various power law flow laws for dynamically recrystallized quartz were proposed over the past years (Paterson & Luan, 1990; Luan & Paterson, 1992; Gleason & Tullis, 1995; Hirth et al., 2001, Rutter & Brodie, 2004). The variations in the flow laws are mainly characterized by different starting materials, experimental conditions, the activation energy for dislocation creep and the stress exponent n. In this study we compare and evaluate experimentally derived flow laws regarding their reliability for the prediction of rheology of background deformation of naturally deformed crystalline samples from mylonites of the Aar massif (Swiss Central Alps). The majority of samples comprises highly deformed rocks (e.g. Central Aare granite), which exhibit severe grain size reduction. This reduction dominantly occurred by subgrain rotation (SGR), in the case of low temperature overprint by bulging recrystallization (BLG). Towards elevated temperatures, grain boundary migration (GBM) and SGR recrystallization were active. Along the metamorphic gradient (300 - 475°C) quartz microstructures and associated recrystallized grain size distributions indicate steady state mean grain sizes. The quantification of the metamorphic gradient (temperature, pressure, water fugacity) over the sampling area allowed the application of flow laws, yielding variations of 6 orders of magnitude in
Capacitance scaling law for diatomic molecules and prediction of their electron detachment energies
Ellenbogen, James C.
2010-07-15
The variation or 'scaling' of the quantum capacitances is explored for 45 diatomic molecules as a function of their dimensions. Scaling trends in the capacitances of these diatomic molecules dictate an 'atoms-in-molecules' view of their valence energetics. That is, experimentally derived quantum capacitances for both homonuclear and heteronuclear diatomic molecules scale linearly with the average of the mean radii for the outermost orbitals of their component atoms. This is in accord with Maxwell's law for classical capacitors formed from two conducting atom-sized spheres in tangential contact. However, the scaling behavior for the molecules has some nonclassical features. Notably, the quantum capacitances extrapolate to nonzero values at zero dimensions. Radius-capacitance points of the homonuclear diatomics lie primarily along five scaling lines, with each determined by points for molecules composed of atoms with the same atomic symmetry (i.e., atoms from the same column in the periodic table). Five scaling lines for heteronuclear diatomics each are determined by points for molecules of the same or similar molecular symmetries. The molecules' quantum capacitances are calculated from their ionization potentials (IPs) and electron affinities (EAs). Thus, equations or laws for the scaling lines impose mutual consistency conditions among these electron detachment energies for different diatomics of similar symmetries. By taking advantage of this, the linear quantum capacitance scaling laws and ab initio atomic mean radii are used to predict IPs for two diatomics with known EAs (Ga{sub 2} and SeO), but for which there is no standard value of the IP. Similarly, the laws are used to predict EAs that were unknown or uncertain for several diatomics (Li{sub 2}, LiF, CSe, PN, BF, BCl, SiO, GeO, NCl, CaO, SrO, and BaO) with known IPs.
The Scaling Relations and Star Formation Laws of Mini-starburst Complexes
NASA Astrophysics Data System (ADS)
Nguyen-Luong, Quang; Nguyen, Hans V. V.; Motte, Fredérique; Schneider, Nicola; Fujii, Michiko; Louvet, Fabien; Hill, Tracey; Sanhueza, Patricio; Chibueze, James O.; Didelon, Pierre
2016-12-01
The scaling relations and star formation laws for molecular cloud complexes (MCCs) in the Milky Way are investigated. MCCs are mostly large (R > 50 pc), massive (˜106 {\\text{}}{M}⊙ ) gravitationally unbound cloud structures. We compare their masses {M}{gas}, mass surface densities {{{Σ }}}{M{gas}}, radii R, velocity dispersions σ, star formation rates (SFRs), and SFR densities {{{Σ }}}{SFR} with those of structures ranging from cores, clumps, and giant molecular clouds, to MCCs, and galaxies, spanning eight orders of magnitudes in size and 13 orders of magnitudes in mass. This results in the following universal relations:σ ˜ {R}0.5,{M}{gas}˜ {R}2,{{{Σ }}}{SFR}˜ {{{Σ }}}{M{gas}}1.5, {SFR}˜ {{M}{gas}}0.9, {and} {SFR}˜ {σ }2.7. Variations in the slopes and coefficients of these relations are found at individual scales, signifying different physics acting at different scales. Additionally, there are breaks at the MCC scale in the σ {--}R relation and between starburst and normal star-forming objects in the {SFR}{--}{M}{gas} and {{{Σ }}}{SFR}-{{{Σ }}}{{{M}}{gas}} relations. Therefore, we propose to use the Schmidt-Kennicutt diagram to distinguish starburst from normal star-forming structures by applying a {{{Σ }}}{M{gas}} threshold of ˜100 {\\text{}}{M}⊙ pc-2 and a {{{Σ }}}{SFR} threshold of 1 {\\text{}}{M}⊙ yr-1 kpc-2. Mini-starburst complexes are gravitationally unbound MCCs that have enhanced {{{Σ }}}{SFR} (>1 {\\text{}}{M}⊙ yr-1 kpc-2), probably caused by dynamic events such as radiation pressure, colliding flows, or spiral arm gravitational instability. Because of dynamical evolution, gravitational boundedness does not play a significant role in regulating the star formation activity of MCCs, especially the mini-starburst complexes, which leads to the dynamical formation of massive stars and clusters. We emphasize the importance of understanding mini-starbursts in investigating the physics of starburst galaxies.
Universal scaling laws of diffusion in two-dimensional granular liquids
NASA Astrophysics Data System (ADS)
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 S2* follow two distinct scaling laws: D*˜eS2* for dense liquids and D*˜e3 S2* 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), 10.1038/381137a0; A. Samanta et al., Phys. Rev. Lett. 92, 145901 (2004), 10.1103/PhysRevLett.92.145901]. In the dilute regime, a power law [Y. Rosenfeld, J. Phys.: Condens. Matter 11, 5415 (1999), 10.1088/0953-8984/11/28/303] 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.
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…
Scaling Laws for the Lifetimes of Governments in the Sznajd Democracy
NASA Astrophysics Data System (ADS)
Schneider, Johannes J.; Hirtreiter, Christian
We investigate the lifetimes of governments in the original and a randomized one-dimensional Sznajd model. We find various scaling laws for the lifetime of the democracy and for the reigning time of governments in this model, depending on the system size N.
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…
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Advances in modelling of biomimetic fluid flow at different scales.
Saha, Sujoy Kumar; Celata, Gian Piero
2011-04-15
The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed.
Advances in modelling of biomimetic fluid flow at different scales
2011-01-01
The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed. PMID:21711847
NASA Astrophysics Data System (ADS)
Nimmo, J. R.; Perkins, K. S.; Gaten-Slahor, L.
2015-12-01
A traditional assumption for unsaturated flow is that the pores are either water-filled and conducting or empty and nonconducting. Evidence from lab and field investigations, however, shows that substantial preferential flow can occur in macropores that are partially filled. Such flow can transmit large fluxes of water. Rates of transport can exceed the saturated hydraulic conductivity, because of possible reductions of friction and buoyancy effects. These conditions reduce the influence of capillarity on energy state, driving force, and the configuration of water-filled space. Influences such as gravity, inertia, and chaotic liquid-phase irregularities then take on increased importance. Perhaps most important is that with partial filling, the flux of water entering the pore is a determining influence on the configuration of air and water phases. Hence the incoming flux itself influences the pore's conductance, and Darcy's law cannot be expected to apply. Flow through partially-filled macropores thus requires new or revised concepts of flow pathways in unsaturated soil, and new ways of quantifying their effect. Flow modes can include free-surface films, rivulets that are not fully confined by capillarity, pulse flow, and sliding drops. Gravity dominates the driving force. Because capillarity does not establish complete geometrical confinement for these modes of flow, the mathematical relation between flux and force is not the direct Darcian proportionality, but rather a mode-specific relation involving incoming flux and flow-stream dimensions. In swelling soils there is the further complication that flow may switch from one mode to another because macropore size, shape, and connectedness vary dynamically with changing water content. This presentation evaluates commonalities and divergences among different partially-filled flow modes and compares them with commonly-assumed Poiseuille flow modes. Mathematical relations for the physical processes of these flow modes
An animal-to-human scaling law for blast-induced traumatic brain injury risk assessment.
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.
Baseline neoclassical scaling law on H-mode pedestal width from XGC0 kinetic simulation
NASA Astrophysics Data System (ADS)
Park, Gunyoung; Chang, C. S.; Ku, S.
2009-11-01
In the H-mode pedestal before the ELM onset, nonlocal neoclassical self-organization is an important physical effect, to set the baseline pedestal width scaling law. Deviation from the neoclassical scaling will define the anomalous scaling. The neoclassical self-organization includes effects from the self-consistent radial electric field shear, strong magnetic field shear, ion-orbit loss across the last closed magnetic surface, finite ion banana width, particle source from neutral ionization, heat flux from the core plasma, and collisional transport. XGC0 code is used to perform an inter-machine study of the neoclassical pedestal scaling law between two representative devices DIII-D (low-B, low collisionality) and C- Mod (high-B, high collisionality). Anomalous scaling component in the experimental pedestal width data will be separated out from the neoclassical component. Prediction for ITER pedestal will be attempted based upon the combined neoclassical (theoretical) and anomalous (empirical) scaling laws obtained in this study. This ion-electron study indicates that the neoclassical pedestal width is broader than the previous ion only study results, closer to experimental pedestal width.
Behavior of local dissipation scales in turbulent pipe flow
NASA Astrophysics Data System (ADS)
Bailey, Sean; Hultmark, Marcus; Schumacher, Joerg; Yakhot, Victor; Smits, Alexander
2010-11-01
Classically, dissipation of turbulence has been thought to occur around the Kolmogorov scales. However, the Kolmogorov scales are prescribed using mean dissipation rate, whereas dissipation is spatially intermittent. It therefore seems natural to instead describe dissipation using a continuum of local length scales rather than a single scale. By connecting a local dissipation scale η to the velocity increment across this scale δuη, it is possible to derive a probability density function (PDF) of η which show how the dissipation is contained in scales larger and smaller than the Kolmogorov scale. Here we present a comparison between measured PDFs in turbulent pipe flow, the analytically derived PDF, and PDFs determined from direct numerical simulation of homogeneous isotropic turbulence. It was found that there is good general agreement between experiment, simulation and theory amongst both homogeneous and inhomogeneous turbulent flows, pointing to universality in the dissipation scales amongst different flows. It was also found that the PDFs are invariant with distance from the wall except for a region very near the wall (y^+<80), where dissipation was found to occur at increasingly larger length scales as the wall is approached.
A multiple-scale model for compressible turbulent flows
NASA Technical Reports Server (NTRS)
Liou, William W.; Shih, Tsan-Hsing
1993-01-01
A multiple-scale model for compressible turbulent flows is proposed. It is assumed that turbulent eddy shocklets are formed primarily by the 'collisions' of large energetic eddies. The extra straining of the large eddy, due to their interactions with shocklets, enhances the energy cascade to smaller eddies. Model transport equations are developed for the turbulent kinetic energies and the energy transfer rates of the different scale. The turbulent eddy viscosity is determined by the total turbulent kinetic energy and the rate of energy transfer from the large scale to the small scale, which is different from the energy dissipation rate. The model coefficients in the modeled turbulent transport equations depend on the ratio of the turbulent kinetic energy of the large scale to that of the small scale, which renders the model more adaptive to the characteristics of individual flow. The model is tested against compressible free shear layers. The results agree satisfactorily with measurements.
Temporal and Spatial Power Laws of River Peak Flows and Flood Frequency Estimation
NASA Astrophysics Data System (ADS)
Krajewski, W. F.; Mantilla, R.; Perez, G.
2016-12-01
It is well known that the quantiles of annual peak flows (floods) are related as power law functions of basin drainage areas. These relationships constitute the basis for the current methods of regional flood frequency estimation. It is less well known that flood events obey similar laws but with different and varied (from event to event) parameters. It has also been demonstrated that power law probability distributions offer very good fit to flood data and lead to more conservative estimates of extreme events compared to the standard methods. The authors review some of the previous findings and show additional analyses of temporal flood data from Iowa. They supplement the data-based analyses with simulations from a space-time model. The overall goal of the research is to connect the spatial and temporal aspects of flood genesis and improve our understanding of the physical aspects that control flood frequency.
Convergence of Beer's Law for Radiation Transmission in Particle-Laden Turbulent Flows
NASA Astrophysics Data System (ADS)
Frankel, Ari; Rauenzahn, Rick; Iaccarino, Gianluca; Mani, Ali
2015-11-01
Discrete random particulate media have been shown to produce significant deviations from Beer's law for radiation transmission. Though particle-resolved ray tracing models can exactly resolve the transmission, the computational expense of such approaches can be prohibitive in settings involving many particles where the radiative transfer equation must be solved at every time step. In this work we investigate the validity of projecting Lagrangian particles onto an Eulerian concentration field and using Beer's law on a local basis. We take particle distributions produced from clustering in turbulent flows and perform both particle-resolved Monte Carlo ray tracing and Beer's law computations. We show that the error in the calculated transmission decreases as the grid is refined, but that the homogenization error increases rapidly as the grid size approaches the particle diameter. This work was supported by the PSAAP2 program at Stanford University.
Log law of the wall revisited in Taylor-Couette flows at intermediate Reynolds numbers.
Singh, Harminder; Suazo, Claudio Alberto Torres; Liné, Alain
2016-11-01
We provide Reynolds averaged azimuthal velocity profiles, measured in a Taylor-Couette system in turbulent flow, at medium Reynolds (7800 < Re < 18000) number with particle image velocimetry technique. We find that in the wall regions, close to the inner and outer cylinders, the azimuthal velocity profile reveals a significant deviation from classical logarithmic law. In order to propose a new law of the wall, the profile of turbulent mixing length was estimated from data processing; it was shown to behave nonlinearly with the radial wall distance. Based on this turbulent mixing length expression, a law of the wall was proposed for the Reynolds averaged azimuthal velocity, derived from momentum balance and validated by comparison to different data. In addition, the profile of viscous dissipation rate was investigated and compared to the global power needed to maintain the inner cylinder in rotation.
Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts
NASA Astrophysics Data System (ADS)
Lima, J. A.; Pereira, L. M.; Macêdo, E. N.; Chaves, C. L.; Quaresma, J. N. N.
The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical-analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.
Log law of the wall revisited in Taylor-Couette flows at intermediate Reynolds numbers
NASA Astrophysics Data System (ADS)
Singh, Harminder; Suazo, Claudio Alberto Torres; Liné, Alain
2016-11-01
We provide Reynolds averaged azimuthal velocity profiles, measured in a Taylor-Couette system in turbulent flow, at medium Reynolds (7800 < Re < 18000) number with particle image velocimetry technique. We find that in the wall regions, close to the inner and outer cylinders, the azimuthal velocity profile reveals a significant deviation from classical logarithmic law. In order to propose a new law of the wall, the profile of turbulent mixing length was estimated from data processing; it was shown to behave nonlinearly with the radial wall distance. Based on this turbulent mixing length expression, a law of the wall was proposed for the Reynolds averaged azimuthal velocity, derived from momentum balance and validated by comparison to different data. In addition, the profile of viscous dissipation rate was investigated and compared to the global power needed to maintain the inner cylinder in rotation.
Testing of Large-Scale ICV Glasses with Hanford LAW Simulant
Hrma, Pavel R.; Kim, Dong-Sang; Vienna, John D.; Matyas, Josef; Smith, Donald E.; Schweiger, Michael J.; Yeager, John D.
2005-03-01
Preliminary glass compositions for immobilizing Hanford low-activity waste (LAW) by the in-container vitrification (ICV) process were initially fabricated at crucible- and engineering-scale, including simulants and actual (radioactive) LAW. Glasses were characterized for vapor hydration test (VHT) and product consistency test (PCT) responses and crystallinity (both quenched and slow-cooled samples). Selected glasses were tested for toxicity characteristic leach procedure (TCLP) responses, viscosity, and electrical conductivity. This testing showed that glasses with LAW loading of 20 mass% can be made readily and meet all product constraints by a far margin. Glasses with over 22 mass% Na2O can be made to meet all other product quality and process constraints. Large-scale testing was performed at the AMEC, Geomelt Division facility in Richland. Three tests were conducted using simulated LAW with increasing loadings of 12, 17, and 20 mass% Na2O. Glass samples were taken from the test products in a manner to represent the full expected range of product performance. These samples were characterized for composition, density, crystalline and non-crystalline phase assemblage, and durability using the VHT, PCT, and TCLP tests. The results, presented in this report, show that the AMEC ICV product with meets all waste form requirements with a large margin. These results provide strong evidence that the Hanford LAW can be successfully vitrified by the ICV technology and can meet all the constraints related to product quality. The economic feasibility of the ICV technology can be further enhanced by subsequent optimization.
A New Scaling Law of Resonance in Total Scattering Cross Section in Gases
NASA Astrophysics Data System (ADS)
Raju, Gorur Govinda
2009-10-01
Electrical discharges in gases continue to be an active area of research because of industrial applications such as power systems, environmental clean up, laser technology, semiconductor fabrication etc. A fundamental knowledge of electron-gas neutral interaction is indispensable and, the total scattering cross section is one of the quantities that have been measured extensively. The energy dependence of the total cross sections shows peaks or resonance processes that are operative in the collision process. These peaks and the energies at which they occur are shown to satisfy a broad relationship involving the polarizability and the dipole moment of the target particle. Data on 62 target particles belonging to the following species are analyzed. (Eq 1) Rare gas atoms (Eq 2) Di-atomic molecules with combinations of polar, non-polar, attaching, and non-attaching properties Poly-atomic molecules with combinations of polar, non-polar, attaching, and non-attaching properties. Methods of improving the newly identified scaling law and possible application have been identified. 1 INTRODUCTION: Data on electron-neutral interactions are one of the most fundamental in the study of gaseous electronics and an immense literature, both experimental and theoretical, has become available since about the year 1920. [1-5]. In view of the central role which these data play in all facets of gas discharges and plasma science, it is felt that a critical review of available data is timely, mainly for the community of high voltage engineers and industries connected with plasma science in general. The electron-neutral interaction, often referred to as scattering in the scientific literature, is quantified by using the quantity called the total scattering cross section (QT, m^2). In the literature on cross section, total cross section and total scattering cross section are terms used synonymously and we follow the same practice. A definition may be found in reference [1]. This paper concerns
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.
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.
Taylor's power law and fluctuation scaling explained by a central-limit-like convergence
NASA Astrophysics Data System (ADS)
Kendal, Wayne S.; Jørgensen, Bent
2011-06-01
A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.
Taylor's power law and fluctuation scaling explained by a central-limit-like convergence.
Kendal, Wayne S; Jørgensen, Bent
2011-06-01
A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.
A psychometric appraisal of the Jefferson Scale of Empathy using law students
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
Size and shape characteristics of drumlins, derived from a large sample, and associated scaling laws
NASA Astrophysics Data System (ADS)
Clark, Chris D.; Hughes, Anna L. C.; Greenwood, Sarah L.; Spagnolo, Matteo; Ng, Felix S. L.
2009-04-01
Ice sheets flowing across a sedimentary bed usually produce a landscape of blister-like landforms streamlined in the direction of the ice flow and with each bump of the order of 10 2 to 10 3 m in length and 10 1 m in relief. Such landforms, known as drumlins, have mystified investigators for over a hundred years. A satisfactory explanation for their formation, and thus an appreciation of their glaciological significance, has remained elusive. A recent advance has been in numerical modelling of the land-forming process. In anticipation of future modelling endeavours, this paper is motivated by the requirement for robust data on drumlin size and shape for model testing. From a systematic programme of drumlin mapping from digital elevation models and satellite images of Britain and Ireland, we used a geographic information system to compile a range of statistics on length L, width W, and elongation ratio E (where E = L/ W) for a large sample. Mean L, is found to be 629 m ( n = 58,983), mean W is 209 m and mean E is 2.9 ( n = 37,043). Most drumlins are between 250 and 1000 metres in length; between 120 and 300 metres in width; and between 1.7 and 4.1 times as long as they are wide. Analysis of such data and plots of drumlin width against length reveals some new insights. All frequency distributions are unimodal from which we infer that the geomorphological label of 'drumlin' is fair in that this is a true single population of landforms, rather than an amalgam of different landform types. Drumlin size shows a clear minimum bound of around 100 m (horizontal). Maybe drumlins are generated at many scales and this is the minimum, or this value may be an indication of the fundamental scale of bump generation ('proto-drumlins') prior to them growing and elongating. A relationship between drumlin width and length is found (with r2 = 0.48) and that is approximately W = 7 L 1/2 when measured in metres. A surprising and sharply-defined line bounds the data cloud plotted in E- W
Flow excursion time scales in the advanced neutron source reactor
Sulfredge, C.D.
1995-04-01
Flow excursion transients give rise to a key thermal limit for the proposed Advanced Neutron Source (ANS) reactor because its core involves many parallel flow channels with a common pressure drop. Since one can envision certain accident scenarios in which the thermal limits set by flow excursion correlations might be exceeded for brief intervals, a key objective is to determine how long a flow excursion would take to bring about a system failure that could lead to fuel damage. The anticipated time scale for flow excursions has been examined by subdividing the process into its component phenomena: bubble nucleation and growth, deceleration of the resulting two-phase flow, and finally overcoming thermal inertia to heat up the reactor fuel plates. Models were developed to estimate the time required for each individual stage. Accident scenarios involving sudden reduction in core flow or core exit pressure have been examined, and the models compared with RELAP5 output for the ANS geometry. For a high-performance reactor like the ANS, flow excursion time scales were predicted to be in the millisecond range, so that even very brief transients might lead to fuel damage. These results should prove useful whenever one must determine the time involved in any portion of a flow excursion transient.
Meso-scale simulation of shocked particle laden flows and construction of metamodels
NASA Astrophysics Data System (ADS)
Sen, Oishik; Davis, Sean; Jacobs, Gustaaf; Udaykumar, H. S.
2015-06-01
In a typical multi-scale modeling problem, such as shock interaction with a dusty gas, information needs to be communicated between disparate length scales, for example between the system scale (order of meters) and the particle scale (order of microns). For the passage of a shock through a cloud of particles, the particle-gas interphase transfer terms in the macro-scale equations are typically based on empirical models of the drag force around a single particle embedded in a shocked flow. Often physical experiments to construct empirical models are restricted in parameter space and difficult or even impossible to perform for a wide range of parameters (Mach number, solid fraction, Reynolds numbers etc.). The goal of the current work is to use high-resolution meso-scale computational experiments as surrogates to physical experiments; a metamodeling approach is developed to ``lift'' information from the particle scale to the macro-scale. The research compares different metamodeling techniques and demonstrates the efficient use of metamodels to close the macro-scale equations; the meso-scale simulations provide a numerical drag law which can be readily used as a source term in macro-scale governing equations. We gratefully acknowledge the financial support by the Air Force Office of Scientific Research under Grant Number FA9550-12-1-0115 and the National Science Foundation under Grant Number DMS-115631.
Conductivity independent scaling laws for convection and magnetism in fast rotating planets
NASA Astrophysics Data System (ADS)
Starchenko, S.
2012-09-01
In the limit of negligible molecular diffusivity, viscosity and magnetic diffusivity effects, I derive scaling laws for convection and magnetism from the first principles for fast rotating planets. In the Earth, Jupiter, Saturn and ancient dynamo active Mars it is reasonable to suppose domination of magnetic energy over kinetic one that results in the typical magnetic field B proportional to the third root of the buoyancy flux F [3] driving the convection, while B is independent on conductivity σ and angular rotation rate Ω. The same scaling law was previously obtained via compilation of many numerical planetary dynamo simulations [1-3]. Besides, I obtained scaling laws for typical hydrodynamic scale h, velocity V, Archimedean acceleration A, electromagnetic scale d and sinus of the angle between magnetic and velocity vector s. In Uranus, Neptune and Ganymede a local magnetic Reynolds number rm=μσVd~1 with magnetic permeability in vacuum μ. Correspondent magnetic energy could be of order kinetic energy resulting in relatively lower magnetic field strength B=(μρ)1/2V with density ρ. That may explain magnetic field values and nondipolar structures in Uranus, Neptune and Ganymede.
Transport coefficient free scaling laws for convection and magnetism in fast rotating planets
NASA Astrophysics Data System (ADS)
Starchenko, S. V.
2013-09-01
In the limit of negligible molecular diffusivity, viscosity and magnetic diffusivity effects, Scaling laws for convection and magnetism are derived for fast rotating planets. In the Earth, Jupiter, Saturn and ancient dynamo active Mars it is reasonable to suppose domination of magnetic energy over kinetic one that results in the typical magnetic field B proportional to the third root of the buoyancy flux F [3] driving the convection, while B is independent on conductivity σ and angular rotation rate Ω. The same scaling law was previously obtained via compilation of many numerical planetary dynamo simulations [1-3]. Besides, new scaling laws are obtained for typical hydrodynamic scale h, velocity V, Archimedean acceleration A, electromagnetic scale d and sinus of the angle between magnetic and velocity vector s. In Uranus, Neptune and Ganymede a local magnetic Reynolds number rm=μσVd~1 with magnetic permeability in vacuum μ. Correspondent magnetic energy could be of order kinetic energy resulting in relatively lower magnetic field strength B=(μρ)1/2V with density ρ. That may explain magnetic field values and non-dipolar structures in Uranus, Neptune and Ganymede.
Spectral scaling laws of solar wind fluctuations at 1 AU: Part 2
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 spacecraft measurements are briefly reviewed. The first part of this review, Part 1, is contained in a separate paper in these proceedings.
Generalized scaling laws for ionization of atomic states by ultra-short electromagnetic pulses
NASA Astrophysics Data System (ADS)
Rosmej, F. B.; Astapenko, V. A.; Lisitsa, V. S.
2016-01-01
It is demonstrated that in the framework of the perturbation theory on laser field strength and the Fermi equivalent photon method expressions for photon transition, probabilities can be obtained that permit the derivation of scaling laws in terms of atomic state quantum numbers and pulse duration. A unified approach is developed that identifies universal scaling parameters for energy and pulse duration that allow analytical investigation of the interrelation of scaling laws for the two important regimes of above and below-threshold ionization. Numerical studies are presented that illuminate the conditions for linear and nonlinear regimes of photoionization, as dependent on the cycle number and carrier frequencies. We also discuss analytical asymptotic forms of the different regimes of photoionization. Finally, we develop a generalized unified approach that permits studies in terms of principal and orbital quantum numbers as well as in pulse duration for any regime of carrier frequencies.
Deviations from uniform power-law scaling due to exposure to high altitude
NASA Astrophysics Data System (ADS)
Posiewnik, A.
2002-12-01
A major challenge in biological physics is the analysis of time series that are typically highly nonstationary. Viswanathan et al. (Phys. Rev. E 55 (1) (1997) 845-899) using techniques based on the Fano factor and the Allan factor functions, as well as on detrended fluctuation analysis showed that the scaling properties of the dynamics of healthy physiological systems in normal conditions are more stable than those of pathological systems-there is underlying loss of uniform power-law scaling in disease. Here we test, using the same techniques as Viswanathan et al. (1997), the hypothesis that deviations from uniform power-law scaling, similar to those seen in heart failure and deep apnea syndrome occur also for healthy subjects under pathological conditions (hypoxaemic stress during exposure to high altitude, over 6000 m).
Identifying all moiety conservation laws in genome-scale metabolic networks.
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.
Entropy-scaling laws for diffusion coefficients in liquid metals under high pressures
Cao, Qi-Long Shao, Ju-Xiang; Wang, Fan-Hou; Wang, Pan-Pan
2015-04-07
Molecular dynamic simulations on the liquid copper and tungsten are used to investigate the empirical entropy-scaling laws D{sup *}=A exp(BS{sub ex}), proposed independently by Rosenfeld and Dzugutov for diffusion coefficient, under high pressure conditions. We show that the scaling laws hold rather well for them under high pressure conditions. Furthermore, both the original diffusion coefficients and the reduced diffusion coefficients exhibit an Arrhenius relationship D{sub M}=D{sub M}{sup 0} exp(−E{sub M}/K{sub B}T), (M=un,R,D) and the activation energy E{sub M} increases with increasing pressure, the diffusion pre-exponential factors (D{sub R}{sup 0} and D{sub D}{sup 0}) are nearly independent of the pressure and element. The pair correlation entropy, S{sub 2}, depends linearly on the reciprocal temperature S{sub 2}=−E{sub S}/T, and the activation energy, E{sub S}, increases with increasing pressure. In particular, the ratios of the activation energies (E{sub un}, E{sub R}, and E{sub D}) obtained from diffusion coefficients to the activation energy, E{sub S}, obtained from the entropy keep constants in the whole pressure range. Therefore, the entropy-scaling laws for the diffusion coefficients and the Arrhenius law are linked via the temperature dependence of entropy.
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies
NASA Technical Reports Server (NTRS)
Mirels, Harold
1959-01-01
Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows
NASA Astrophysics Data System (ADS)
Anbarlooei, H. R.; Cruz, D. O. A.; Ramos, F.; Silva Freire, A. P.
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed.
The law-of-the-wall in mixed convection flow in a vertical channel
NASA Astrophysics Data System (ADS)
Sutherland, Duncan; Chung, Daniel; Ooi, Andrew; Bou-Zeid, Elie
2015-11-01
Direct numerical simulations (DNS) of mixed convection in a plane vertical channel are conducted over a range of Richardson numbers. The direction of the buoyant forces are parallel and anti parallel to the direction of the imposed mean flow resulting in buoyancy-aided flow on the hot wall and buoyancy opposed flow on the cold wall. In the absence of buoyant forces the mean normal velocity profile is logarithmic and independent of the orientation of the wall. In the case of a horizontal channel, where buoyancy is orthogonal to the direction of mean flow, a correction to the log-law for the mean normal velocity is given by Moinin-Ohbukov similarity theory in terms of empirically determined universal functions of momentum and temperature. We attempt an an analysis of the law-of-the-wall for the aiding and opposing flows near the walls in a differentially heated vertical channel and develop analogous universal functions for temperature and momentum from the DNS data. Study supported by the Bushfire and Natural Hazards Cooperative Research Centre.
Scaling Approach to the Growth Equation with a Generalized Conservation Law
NASA Astrophysics Data System (ADS)
Tang, Gang; Zhang, Li-Ping; Wu, Yu-Xi; Xia, Hui; Hao, Da-Peng; Chen, Hua
2003-11-01
The Flory-type scaling approach proposed by Hentschel and Family [Phys. Rev. Lett. 66 (1991) 1982] is generalized to the analysis of the growth equation with a generalized conservation law, which contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and molecular-beam epitaxy growth equations as special cases and allows for a unified investigation of growth equations. The scaling exponents obtained here can be in agreement well with the corresponding results derived by the dynamic renormalization group theory and the previous scaling analyses.
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.
NASA Astrophysics Data System (ADS)
Gonnermann, Helge M.; Jellinek, A. Mark; Richards, Mark A.; Manga, Michael
2004-09-01
We report results from analog laboratory experiments, in which a large-scale flow is imposed upon natural convection from a hot boundary layer at the base of a large tank of corn syrup. The experiments show that the subdivision of the convective flow into four regions provides a reasonable conceptual framework for interpreting the effects of large-scale flow on plumes. Region I includes the area of the hot thermal boundary layer (TBL) that is thinned by the large-scale flow, thereby suppressing plumes. Region II encompasses the critically unstable boundary layer where plumes form. Region III is the area above the boundary layer that is devoid of plumes. Region IV comprises the area of hot upwelling and plume conduits. Quantitative analysis of our experiments results in a scaling law for heat flux from the hot boundary and for the spatial extent of plume suppression. When applied to the Earth's core-mantle boundary (CMB), our results suggest that large-scale mantle flow, due to sinking lithospheric plates, can locally thin the TBL and suppress plume formation over large fractions of the CMB. Approximately 30% of heat flow from the core may be due to increased heat flux from plate-scale flow. Furthermore, CMB heat flux is non-uniformly distributed along the CMB, with large areas where heat flux is increased on average by a factor of 2. As a consequence, the convective flow pattern in the outer core may be affected by CMB heat-flux heterogeneity and sensitive to changes in plate-scale mantle flow. Because of plume suppression and 'focusing' of hot mantle from the CMB into zones of upwelling flow, plume conduits (hotspots) are expected to be spatially associated with lower-mantle regions of low seismic velocities, inferred as hot upwelling mantle flow.
Barenblatt, G I; Chorin, A J; Prostokishin, V M
2000-04-11
In a turbulent boundary layer over a smooth flat plate with zero pressure gradient, the intermediate structure between the viscous sublayer and the free stream consists of two layers: one adjacent to the viscous sublayer and one adjacent to the free stream. When the level of turbulence in the free stream is low, the boundary between the two layers is sharp, and both have a self-similar structure described by Reynolds-number-dependent scaling (power) laws. This structure introduces two length scales: one-the wall-region thickness-determined by the sharp boundary between the two intermediate layers and the second determined by the condition that the velocity distribution in the first intermediate layer be the one common to all wall-bounded flows and in particular coincide with the scaling law previously determined for pipe flows. Using recent experimental data, we determine both these length scales and show that they are close. Our results disagree with the classical model of the "wake region."
Interactions between butterfly scales and unsteady flows during flapping flight
NASA Astrophysics Data System (ADS)
Jones, Robert; Lang, Amy
2008-11-01
Recent research has shown that the highly flexible wings of butterflies in flapping flight develop vortices along their leading and trailing edges. Butterfly scales (approximately 100 microns) have a shingled pattern and extend into the boundary layer. These scales could play a part in controlling separation in this 3-dimensional complex flow field. Biomimetic applications of butterfly scales may aid in the development of flapping wing micro air vehicles. In this study, we observed that the orientation of the scales may relate to the local flow field, and might move or shift during flight. Monarch butterflies were trained to fly in a low speed smoke tunnel for visualization. Scales were removed from the leading and trailing edges and specimens were photographed at 500 frames per second. Variation in flapping pattern and flight fitness are discussed.
Natural Length Scales Shape Liquid Phase Continuity in Unsaturated Flows
NASA Astrophysics Data System (ADS)
Assouline, S.; Lehmann, P. G.; Or, D.
2015-12-01
Unsaturated flows supporting soil evaporation and internal drainage play an important role in various hydrologic and climatic processes manifested at a wide range of scales. We study inherent natural length scales that govern these flow processes and constrain the spatial range of their representation by continuum models. These inherent length scales reflect interactions between intrinsic porous medium properties that affect liquid phase continuity, and the interplay among forces that drive and resist unsaturated flow. We have defined an intrinsic length scale for hydraulic continuity based on pore size distribution that controls soil evaporation dynamics (i.e., stage 1 to stage 2 transition). This simple metric may be used to delineate upper bounds for regional evaporative losses or the depth of soil-atmosphere interactions (in the absence of plants). A similar length scale governs the dynamics of internal redistribution towards attainment of field capacity, again through its effect on hydraulic continuity in the draining porous medium. The study provides a framework for guiding numerical and mathematical models for capillary flows across different scales considering the necessary conditions for coexistence of stationarity (REV), hydraulic continuity and intrinsic capillary gradients.
Blood Flow: Multi-scale Modeling and Visualization (July 2011)
2011-01-01
Multi-scale modeling of arterial blood flow can shed light on the interaction between events happening at micro- and meso-scales (i.e., adhesion of red blood cells to the arterial wall, clot formation) and at macro-scales (i.e., change in flow patterns due to the clot). Coupled numerical simulations of such multi-scale flow require state-of-the-art computers and algorithms, along with techniques for multi-scale visualizations. This animation presents early results of two studies used in the development of a multi-scale visualization methodology. The fisrt illustrates a flow of healthy (red) and diseased (blue) blood cells with a Dissipative Particle Dynamics (DPD) method. Each blood cell is represented by a mesh, small spheres show a sub-set of particles representing the blood plasma, while instantaneous streamlines and slices represent the ensemble average velocity. In the second we investigate the process of thrombus (blood clot) formation, which may be responsible for the rupture of aneurysms, by concentrating on the platelet blood cells, observing as they aggregate on the wall of an aneruysm. Simulation was performed on Kraken at the National Institute for Computational Sciences. Visualization was produced using resources of the Argonne Leadership Computing Facility at Argonne National Laboratory.
On solute residence time in the storage zones of small streams - experimental study and scaling law
NASA Astrophysics Data System (ADS)
Schmid, Bernhard
2013-04-01
Transient storage has a major influence on solute transport in streams, on biogeochemical cycling, water quality and on the functioning of aquatic ecosystems. The first part of the research reported here focuses on surface transient storage (STS) zones between groins along small streams. Such groins are used to protect banks, but also to increase habitat diversity and are, thus, not restricted to large rivers. Repeated tracer dilution experiments on the Mödlingbach, a small stream in Austria some 30 km south of Vienna, have been analyzed to determine the solute residence time between groins and to characterize the exchange processes between dead zones and main stream. Pairs of related breakthrough curves were measured in main stream and storage zones, resp., and used subsequently to estimate the solute residence time in the surface dead zones under study. Following previous work (Weitbrecht et al., 2008; Jackson et al., 2012) these residence times were, in turn, expressed as T = -W-.hD- k ?u hE (1) with W denoting groin length, u main stream flow velocity, hD mean water depth between the groins and hE depth at the interface dead zone - main stream. Coefficient k, finally, is thought to depend on a type of hydraulic radius, RD = W.L/(W+L), with L denoting the distance between the groins, measured in main flow direction. Using both the Mödlingbach STS zone data and the results of the aforementioned study (Weitbrecht et al., 2008) the following regression equation was derived (hS denotes main stream water depth): k = 0.00282? RD + 0.00802 hS (2) The second part of this research focuses on the dependency of solute residence time on flow rate, which is important for an improved understanding of longitudinal solute transport in streams and for the application of mathematical models. The scaling law proposed here is based on a physics-related theory combined with extensive data sets available form a decade of stream tracer experiments on the Mödlingbach stream
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.
NASA Astrophysics Data System (ADS)
Ormerod, Paul; Mounfield, Craig
2001-04-01
Power law distributions of macroscopic observables are ubiquitous in both the natural and social sciences. They are indicative of correlated, cooperative phenomena between groups of interacting agents at the microscopic level. In this paper, we argue that when one is considering aggregate macroeconomic data (annual growth rates in real per capita GDP in the seventeen leading capitalist economies from 1870 through to 1994) the magnitude and duration of recessions over the business cycle do indeed follow power law like behaviour for a significant proportion of the data (demonstrating the existence of cooperative phenomena amongst economic agents). Crucially, however, there are systematic deviations from this behaviour when one considers the frequency of occurrence of large recessions. Under these circumstances the power law scaling breaks down. It is argued that it is the adaptive behaviour of the agents (their ability to recognise the changing economic environment) which modifies their cooperative behaviour.
The linewidth-size scaling law of molecular gas in the Galaxy
NASA Astrophysics Data System (ADS)
Falgarone, Edith G.; McKee, Christopher
2015-08-01
The origin of the linewidth-size (LWS) scaling law, first noticed by Larson three decades ago and ascribed to turbulence, is still a highly debated issue. Not unexpectedly, its properties depend on the environment and on the line tracer used.When the optically thick 12CO (J=1-0) line is used, a specific medium is sampled: the translucent molecular gas of moderate density that builds up the bulk of the molecular interstellar medium in galaxies like ours. The sensitivity of the 12CO line to this gas is such that the LWS is found to hold over almost five orders of magnitude in lengthscale, although with a considerable scatter (1 dex). It reveals an invariant of the cascade, the specific kinetic energy tranfer rate. It also appears to split into two regimes, depending on the gas mass surface density: below a given threshold that is proposed to be linked to the galactic dynamics, it bears the signature of a turbulent cascade, while above that threshold, the scaling law is ascribed to virial balance between turbulent energy and gravity. Large deviations from the scaling law are observed at small scales where signatures of turbulent intermittency may be present.
Huo, Yunlong; Choy, Jenny Susana; Wischgoll, Thomas; Luo, Tong; Teague, Shawn D.; Bhatt, Deepak L.; Kassab, Ghassan S.
2013-01-01
Glagov's positive remodelling in the early stages of coronary atherosclerosis often results in plaque rupture and acute events. Because positive remodelling is generally diffused along the epicardial coronary arterial tree, it is difficult to diagnose non-invasively. Hence, the objective of the study is to assess the use of scaling power law for the diagnosis of positive remodelling of coronary arteries based on computed tomography (CT) images. Epicardial coronary arterial trees were reconstructed from CT scans of six Ossabaw pigs fed on a high-fat, high-cholesterol, atherogenic diet for eight months as well as the same number of body-weight-matched farm pigs fed on a lean chow (101.9±16.1 versus 91.5±13.1 kg). The high-fat diet Ossabaw pig model showed diffuse positive remodelling of epicardial coronary arteries. Good fit of measured coronary data to the length–volume scaling power law ( where Lc and Vc are crown length and volume) were found for both the high-fat and control groups (R2 = 0.95±0.04 and 0.99±0.01, respectively). The coefficient, KLV, decreased significantly in the high-fat diet group when compared with the control (14.6±2.6 versus 40.9±5.6). The flow–length scaling power law, however, was nearly unaffected by the positive remodelling. The length–volume and flow–length scaling power laws were preserved in epicardial coronary arterial trees after positive remodelling. KLV < 18 in the length–volume scaling relation is a good index of positive remodelling of coronary arteries. These findings provide a clinical rationale for simple, accurate and non-invasive diagnosis of positive remodelling of coronary arteries, using conventional CT scans. PMID:23365197
Granular flow down an inclined plane: Bagnold scaling and rheology.
Silbert, L E; Ertaş, D; Grest, G S; Halsey, T C; Levine, D; Plimpton, S J
2001-11-01
We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.
Relativistic thermal electron scale instabilities in sheared flow plasma
NASA Astrophysics Data System (ADS)
Miller, Evan D.; Rogers, Barrett N.
2016-04-01
> The linear dispersion relation obeyed by finite-temperature, non-magnetized, relativistic two-fluid plasmas is presented, in the special case of a discontinuous bulk velocity profile and parallel wave vectors. It is found that such flows become universally unstable at the collisionless electron skin-depth scale. Further analyses are performed in the limits of either free-streaming ions or ultra-hot plasmas. In these limits, the system is highly unstable in the parameter regimes associated with either the electron scale Kelvin-Helmholtz instability (ESKHI) or the relativistic electron scale sheared flow instability (RESI) recently highlighted by Gruzinov. Coupling between these modes provides further instability throughout the remaining parameter space, provided both shear flow and temperature are finite. An explicit parameter space bound on the highly unstable region is found.
Role of Zonal Flow in Turbulent Transport Scaling
Z. Lin; T.S. Hahm; J.A. Krommes; W.W. Lee; J. Lewandowski; H. Mynick; H. Qin; G. Rewoldt; W.M. Tang; R. White
2000-11-15
Transport scalings with respect to collisionality (n*) and device size (r*) are obtained from massively parallel gyrokinetic particle simulations of toroidal ion-temperature-gradient (ITG) turbulence in the presence of zonal flows. Simulation results show that ion thermal transport from electrostatic ITG turbulence depends on ion-ion collisions due to the neo-classical damping of self-generated EXB zonal flows that regulate the turbulence. Fluctuations and heat transport levels exhibit bursting behavior with a period corresponding to the collisional damping time of poloidal flows. Results from large-scale full torus simulations with device-size scans for realistic parameters show that Bohm-like transport can be driven by microscopic scale fluctuations in the ITG turbulence with isotropic spectra. These simulation results resolve some apparent physics contradictions between experimental observations and turbulent transport theories.
Glen's Law++: Transition to a Rate-Weakening Flow Law As a New Framework for Damage Evolution
NASA Astrophysics Data System (ADS)
Borstad, C. P.; Morlighem, M.; Khazendar, A.; Scheuchl, B.; Larour, E. Y.; Rignot, E. J.
2014-12-01
Continuum damage mechanics is gaining increasing acceptance as a framework for modeling flow enhancement caused by fractures in glaciers and ice shelves. To date, the temporal evolution of viscous damage has been handled using a transport equation with some kind of source term for damage. A number of empirical formulations for such a source term have been adopted, though no clear physical foundation exists for treating damage using flux terms. Furthermore, it remains to be demonstrated that the parameters of such a source term can be determined from observations. Here, we introduce a new framework for damage evolution that does not require specifying a damage source term and that results in a more intuitive physical interpretation of the coupled evolution of stress and damage. By postulating an explicit rate-weakening flow law above a threshold stress, damage can be calculated analytically from the results of a stress balance computation. A transport equation is still applied to advect damage, but the evolution of damage is explicitly linked to the evolving stress balance. This new damage formulation requires only two new parameters, both of which have clear physical interpretations and can be inferred from observations. Using the Ice Sheet System Model (ISSM), we determine values for both parameters by inverting for damage for the remnant Larsen B ice shelf using a time series of InSAR velocity data covering the years 2000-2010. The inferred patterns of damage and strain rate, in both space and time, are used to quantify the rate-weakening constitutive parameters using nonlinear regression. The resulting damage evolution framework is then applied in perturbation experiments to determine the conditions and timescales under which the remnant Larsen B ice shelf may collapse. We conclude by discussing advantages of this approach to damage evolution and applications to problems in iceberg calving, ice shelf stability, and buttressing at the grounding line.
The role of freestream turbulence scale in subsonic flow separation
NASA Technical Reports Server (NTRS)
Potter, J. L.; Seebaugh, W. R.; Barnett, R. J.; Gokhale, R. B.
1984-01-01
The ojective of this work is the clarification of the role of freestream turbulence scale in determining the location of boundary layer separation. An airfoil in subsonic wind tunnel flow is the specific case studied. Hot-film and hot-wire anemometry, liquid-film visualization and pressure measurements are the principal diagnostic techniques in use. The Vanderbilt University subsonic wind tunnel is the flow facility being used.
The cooling law and the search for a good temperature scale, from Newton to Dalton
NASA Astrophysics Data System (ADS)
Besson, Ugo
2011-03-01
The research on the cooling law began with an article by Newton published in 1701. Later, many studies were performed by other scientists confirming or confuting Newton's law. This paper presents a description and an interpretation of Newton's article, provides a short overview of the research conducted on the topic during the 18th century, and discusses the relationships between the research on cooling laws and the definition of a temperature scale, as it was treated in Newton's article and in the work of Dalton, including Dalton's search for the absolute zero of temperature. It is shown that these scientists considered the exponential cooling law as a fundamental principle rather than a conjecture to be tested by means of experiments. The faith in the simplicity of natural laws and the spontaneous idea of proportionality between cause and effect seem to have strongly influenced Newton and Dalton. The topic is developed in a way that can be suitable for both undergraduate students and general physicists.
Extension of Murray's law using a non-Newtonian model of blood flow
Revellin, Rémi; Rousset, François; Baud, David; Bonjour, Jocelyn
2009-01-01
Background So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. Modeling In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. ΣRc = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. Results We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. Conclusion It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid. PMID:19445663
Extension of Murray's law using a non-Newtonian model of blood flow.
Revellin, Rémi; Rousset, François; Baud, David; Bonjour, Jocelyn
2009-05-15
So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.
Research on the Diffusion Law of Oncomelania Along with the Flow Through a Side-weir.
Liu, A M
2014-01-01
Schistosomiasis is a parasitic disease mostly found in areas along the Changjiang River, Oncomelanias is the only intermediate host of schistosomiasis. Oncomelania entering into farmland or the residential zones through the flood discharge or irrigation system is the main reason of spreading schistosomiasis. Therefore it is most essential and effective way to control diffusion of oncomelanias along with flow for preventing epidemic of schistosomiasis disease. In order to simulate the flood discharge when the river dike break or the flow from main to branch channel, a side-weir flow system is set up in this paper, And furtherly the flow characteristic is studied by experiment and mathematical modeling, Finally the research on the diffusion law of oncomelania along with side-weir flow is carried out using the experimental test. The results show that oncomelanias do not equally distribute at floodplain areas, but place where flow velocity is small, i.e. in the vortex areas during oncomelanias moving along with side-weir flow. The settling positions of oncomelanias are obtained, Which lay a good foundation for eliminating oncomelanias.
Collision-dependent power law scalings in two dimensional gyrokinetic turbulence
Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.
2014-08-15
Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.
Compressor Performance Scaling in the Presence of Non-Uniform Flow
NASA Astrophysics Data System (ADS)
Hill, David Jarrod
Fuselage-embedded engines in future aircraft will see increased flow distortions due to the ingestion of airframe boundary layers. This reduces the required propulsive power compared to podded engines. Inlet flow distortions mean that localized regions of flow within the fan and first stage compressor are operating at off-design conditions. It is important to weigh the benefit of increased vehicle propulsive efficiency against the resultant reduction in engine efficiency. High computational cost has limited most past research to single distortion studies. The objective of this thesis is to extract scaling laws for transonic compressor performance in the presence of various distortion patterns and intensities. The machine studied is the NASA R67 transonic compressor. Volumetric source terms are used to model rotor and stator blade rows. The modelling approach is an innovative combination of existing flow turning and loss models, combined with a compressible flow correction. This approach allows for a steady calculation to capture distortion transfer; as a result, the computational cost is reduced by two orders of magnitude. At peak efficiency, the rotor work coefficient and isentropic efficiency are matched within 1.4% of previously published experimental results. A key finding of this thesis is that, in non-uniform flow, the state-of-the-art loss model employed is unable to capture the impact of variations in local flow coefficient, limiting the analysis of local entropy generation. New insight explains the mechanism governing the interaction between a total temperature distortion and a compressor rotor. A parametric study comprising 16 inlet distortions reveals that for total temperature distortions, upstream flow redistribution and rotor diffusion factor changes are shown to scale linearly with distortion severity. Linear diffusion factor scaling does not hold true for total pressure distortions. For combined total temperature and total pressure distortions, the
Scaling of low-Prandtl-number thermocapillary flows
NASA Technical Reports Server (NTRS)
Rivas, Damian; Ostrach, Simon
1992-01-01
Scaling analysis was used to study thermocapillary flows of low-Prandtl-number fluids in shallow rectangular enclosures under an imposed-heat-flux configuration. Different regimes that appear in the thermo-fluid problem are identified and the proper parameters and reference quantities that define them are obtained. Assuming that the flow is driven by thermocapillary effects and it is concluded that the extent of the region where the thermocapillary driving force is important defines the region of applicability of the scaling results.
Modeling field scale unsaturated flow and transport processes
Gelhar, L.W.; Celia, M.A.; McLaughlin, D.
1994-08-01
The scales of concern in subsurface transport of contaminants from low-level radioactive waste disposal facilities are in the range of 1 to 1,000 m. Natural geologic materials generally show very substantial spatial variability in hydraulic properties over this range of scales. Such heterogeneity can significantly influence the migration of contaminants. It is also envisioned that complex earth structures will be constructed to isolate the waste and minimize infiltration of water into the facility. The flow of water and gases through such facilities must also be a concern. A stochastic theory describing unsaturated flow and contamination transport in naturally heterogeneous soils has been enhanced by adopting a more realistic characterization of soil variability. The enhanced theory is used to predict field-scale effective properties and variances of tension and moisture content. Applications illustrate the important effects of small-scale heterogeneity on large-scale anisotropy and hysteresis and demonstrate the feasibility of simulating two-dimensional flow systems at time and space scales of interest in radioactive waste disposal investigations. Numerical algorithms for predicting field scale unsaturated flow and contaminant transport have been improved by requiring them to respect fundamental physical principles such as mass conservation. These algorithms are able to provide realistic simulations of systems with very dry initial conditions and high degrees of heterogeneity. Numerical simulation of the movement of water and air in unsaturated soils has demonstrated the importance of air pathways for contaminant transport. The stochastic flow and transport theory has been used to develop a systematic approach to performance assessment and site characterization. Hypothesis-testing techniques have been used to determine whether model predictions are consistent with observed data.
Scaling laws of ambush predator ‘waiting’ behaviour are tuned to a common ecology
Wearmouth, Victoria J.; McHugh, Matthew J.; Humphries, Nicolas E.; Naegelen, Aurore; Ahmed, Mohammed Z.; Southall, Emily J.; Reynolds, Andrew M.; Sims, David W.
2014-01-01
The decisions animals make about how long to wait between activities can determine the success of diverse behaviours such as foraging, group formation or risk avoidance. Remarkably, for diverse animal species, including humans, spontaneous patterns of waiting times show random ‘burstiness’ that appears scale-invariant across a broad set of scales. However, a general theory linking this phenomenon across the animal kingdom currently lacks an ecological basis. Here, we demonstrate from tracking the activities of 15 sympatric predator species (cephalopods, sharks, skates and teleosts) under natural and controlled conditions that bursty waiting times are an intrinsic spontaneous behaviour well approximated by heavy-tailed (power-law) models over data ranges up to four orders of magnitude. Scaling exponents quantifying ratios of frequent short to rare very long waits are species-specific, being determined by traits such as foraging mode (active versus ambush predation), body size and prey preference. A stochastic–deterministic decision model reproduced the empirical waiting time scaling and species-specific exponents, indicating that apparently complex scaling can emerge from simple decisions. Results indicate temporal power-law scaling is a behavioural ‘rule of thumb’ that is tuned to species’ ecological traits, implying a common pattern may have naturally evolved that optimizes move–wait decisions in less predictable natural environments. PMID:24619440
An examination of the scaling laws for LWFA in the self-guided nonlinear blowout regime
NASA Astrophysics Data System (ADS)
Davidson, Asher; Tableman, Adam; Yu, Peicheng; An, Weiming; Tsung, Frank; Lu, Wei; Fonseca, Ricardo A.; Mori, Warren B.
2017-03-01
A detailed study of the scaling laws for LWFA in the self-guided, nonlinear blowout regime is presented. The study is enabled through the recent implementation of the quasi-3D algorithm into OSIRIS, which permits particle-in-cell simulations of LWFA at lower densities and higher laser energy. We find that the scaling laws continue to work well when we fix the normalized laser amplitude, pulse-length, and spot size, while reducing the plasma density. We examine parameters for which the self-injected electron energies are between 1 and 10 GeV. Over a wide parameter space, the evolution of the electron energy and laser spot size are similar when plotted in normalized units.
Scaling Laws for Proton Acceleration from the Rear Surface of Laser-Irradiated Thin Foils
NASA Astrophysics Data System (ADS)
Fuchs, J.; Antici, P.; d'Humières, E.; Lefebvre, E.; Borghesi, M.; Brambrink, E.; Cecchetti, C. A.; Kaluza, M.; Malka, V.; Manclossi, M.; Meyroneinc, S.; Mora, P.; Schreiber, J.; Toncian, T.; Pépin, H.; Audebert, P.
2006-04-01
In the last few years, intense research has been conducted on the topic of laser-accelerated ion sources and their applications. Ultra-bright beams of multi-MeV protons are produced by irradiating thin metallic foils with ultra-intense short laser pulses. These sources open new opportunities for ion beam generation and control, and could stimulate development of compact ion accelerators for many applications, in particular proton therapy of deep-seated tumours. Here we show that scaling laws deduced from fluid models reproduce well the acceleration of proton beams for a large range of laser and target parameters. These scaling laws show that, in our regime, there is an optimum in the laser pulse duration of ˜200 fs-1 ps, with a needed laser energy level of 30 to 100 J, in order to achieve e.g. 200 MeV energy protons necessary for proton therapy.