Flow Instability and Flow Control Scaling Laws
NASA Astrophysics Data System (ADS)
van Ness, Daniel; Corke, Thomas; Morris, Scott
2006-11-01
A flow instability that is receptive to perturbations is present in the tip clearance leakage flow over the tip of a turbine blade. This instability was investigated through the introduction of active flow control in the viscous flow field. Control was implemented in the form of a dielectric barrier discharge created by a weakly-ionized plasma actuation arrangement. The experimental setup consisted of a low-speed linear turbine cascade made up of an array of nine Pratt & Whitney ``PakB'' turbine blades. This idealized cascade configuration was used to examine the tip clearance leakage flow that exists within the low pressure turbine stage of a gas-turbine engine. The center blade of the cascade array had a variable tip clearance up to five percent chord. Reynolds numbers based on axial blade chord varied from 10^4 to 10^5. Multi-port pressure probe measurements, as well as Stereo Particle Image Velocimetry were used to document the dependence of the instability on the frequency and amplitude of flow control perturbations. Scaling laws based on the variation of blade tip clearance height and inflow conditions were investigated. These results permitted an improved understanding of the mechanism of flow instability.
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. PMID:25871063
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.
Experiments on turbulent flows in rough pipes: Spectral scaling laws and the spectral link
NASA Astrophysics Data System (ADS)
Zuniga Zamalloa, Carlo Cesar
Motivated by a recently proposed theory that entails the existence of a "spectral link" between the turbulent energy spectra and the attendant turbulent mean velocity profile in a pipe flow, we establish new scaling laws for the turbulent energy spectra of pipe flows. These new scaling laws--- an inner scaling law and an outer scaling law---differ from the scaling laws that were predicated on Townsend's attached-eddy hypothesis in that they are proper analogues (or spectral counterparts) of the classical scaling properties of the turbulent mean velocity profile. To test the new scaling laws, we have recourse to (1) published computational data from direct numerical simulations and (2) new experimental data from unprecedented measurements, carried out in our laboratory, of the streamwise component of the turbulent energy spectrum on numerous locations along the radii of three rough-walled pipes, for flows spanning a decade in Reynolds number. We show that the new scaling laws are consistent with the turbulent energy spectra of both smooth- and rough- walled flows. In addition, we use the new experimental data to probe the spatial distribution of the streamwise turbulent kinetic energy u 2, the longitudinal integral length scale L 11, and the Kolmogorov length scale eta in turbulent rough-walled pipe flows. We document in our rough- pipe flows a striking phenomenon recently discovered in smooth-pipe flows: the occurrence of an outer peak in u+2 (y+), whose magnitude is an increasing function of the Reynolds number, but the Reynolds number where the outer peak emerges is an order of magnitude smaller than the corresponding Reynolds number in smooth pipes. Last, we carry out a comparative study of the three canonical wall-bounded turbulent flows: pipe flow, channel flow, and boundary layer flow. We are able to trace the similarities and disparities among the turbulent mean velocity profiles of the three canonical flows to corresponding similarities and disparities
Two-phase flow in porous media: power-law scaling of effective permeability
NASA Astrophysics Data System (ADS)
Grøva, Morten; Hansen, Alex
2011-09-01
A recent experiment has reported power-law scaling of effective permeability of two-phase flow with respect to capillary number for a two-dimensional model porous medium. In this paper, we consider the simultaneous flow of two phases through a porous medium under steady-state conditions, fixed total flow-rate and saturation, using a two-dimensional network simulator. We obtain power-law exponents for the scaling of effective permeability with respect to capillary number. The simulations are performed both for viscosity matched fluids and for a high viscosity ratio resembling that of air and water. Good power-law behaviour is found for both cases. Different exponents are found, depending on saturation.
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.
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.
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. PMID:25166542
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. PMID:23554584
Scaling laws and flow structures of double diffusive convection in the finger regime
NASA Astrophysics Data System (ADS)
Yang, Yantao; Verzicco, Roberto; Lohse, Detlef
2016-09-01
Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates, with fluid properties similar to the values of seawater. The DDC flow is driven by an unstable salinity difference and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: The non-dimensional salinity flux $Nu_S$ mainly depends on the salinity Rayleigh number $Ra_S$, which measures the strength of the salinity difference, and exhibits a very weak dependence on the density ratio $\\Lambda$, which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity $Re$ and the non-dimensional heat flux $Nu_T$ are dependent on both $Ra_S$ and $\\Lambda$. However, the rescaled Reynolds number $Re\\Lambda^{\\alpha^{\\rm eff}_u}$ and the rescaled convective heat flux $(Nu_T-1)\\Lambda^{\\alpha^{\\rm eff}_T}$ depend only on $Ra_S$. The two exponents are dependent on the fluid properties and are determined from the numerical results. Moreover, the behaviors of $Nu_S$ and $Re\\Lambda^{\\alpha^{\\rm eff}_u}$ agree with the predictions of the Grossmann-Lohse theory which was originally developed for the Rayleigh-B\\'{e}nard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by $\\Lambda^{\\alpha^{\\rm eff}_u/2}$, collapse and obey a similar power-law scaling relation with $Ra_S$. When $Ra_S$ is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat-copper-ion system~(Hage and Tilgner, Phys. Fluids, 22, 076603, 2010).
Scaling laws of turbulent Couette flow with wall-normal transpiration
NASA Astrophysics Data System (ADS)
Kraheberger, Stephanie; Oberlack, Martin; Hoyas, Sergio
2015-11-01
An extensive DNS study of turbulent plane Couette flows with permeable boundary conditions, i.e. wall-normal transpiration, was conducted at Reτ = 250 , 500 , 1000 and varying transpiration velocities v0 . The discretization employed is speudo-spectral in wall-parallel and compact finite differences in wall-normal direction (see Hoyas et al., Phys. Fluids 2006). We derived a global stress relation for the flow, balancing total shear stresses, with very different friction velocities at lower and upper wall. This, in turn, was used to validate convergence of DNS statistics. Most important, we derived a viscous sublayer velocity scaling for the suction wall employing asymptotic methods. Moreover, using Lie group symmetry analysis applied to the multi-point correlation equation we derived scaling laws for the near-wall region on the blowing wall and the channel center, predicting mean velocity
Innovative scaling laws for aeroelastic and aeroservoelastic problems in compressible flow
NASA Astrophysics Data System (ADS)
Presente, Eyal
Active flutter suppression of a two dimensional wing section in subsonic flow is studied. The equations of motion of a typical cross section are presented in nondimensional form. A two degree of freedom problem, with pitch and plunge dynamics, combined with a trailing-edge control surface is considered. Aerodynamic loads are expressed in the time-domain using Roger's approximation. Augmented aerodynamic states are reconstructed using a Kalman filter, and linear optimal control is used to design a full-state feedback regulator for flutter suppression. Recent advances in the area of adaptive materials, smart structures, have led to the use of such materials as actuators for aeroservoelastic applications. The attractiveness of such materials consists of their potential to introduce continuous structural deformations of the lifting surface that can be exploited to manipulate the unsteady aerodynamic loads and prevent undesirable aeroelastic effects such as flutter. A general formulation of the aerodynamic loads, based on thin airfoil theory, and the deformation of a flat plate wing section are used to calculate the amount of power required to twist a wing along its span with piezoelectric patches. Composite materials enhance bend/twist coupling, which is used to modify the aerodynamic loads for the purpose of flutter suppression. Scaling laws of aeroservoelastic systems are addressed. Scaling parameters required for maintaining similarity between a full-scale system and a model are studied. An innovative two-pronged approach is used to obtain "similarity solutions" of the aeroservoelastic problem. Changes of structural and aerodynamic variables between a full scale configuration and its scaled models facilitate similarity between the systems. Two cases of scaled models are examined, a geometrically scaled model and an aeroelastically scaled one. Flutter suppression of a typical cross section employing a trailing edge control surface is compared with that of a typical
Log-Law scaling of a convective boundary layer in an unstably stratified turbulent channel flow
NASA Astrophysics Data System (ADS)
Scagliarini, Andrea; Einarsson, Halldor; Gylfason, Armann; Toschi, Federico
2014-11-01
Turbulent convection is ubiquitous in a variety of natural and industrial flows. In particular, convective motions may play a role in sheared flows. In this work, we are concerned with the interplay of buoyancy and shear in the dynamical boundary layer structure. The lattice Boltzmann Method (LBM) is applied to study numerically an unstably-stratified, fully developed, turbulent channel flow, driven by a longitudinal pressure gradient and with an imposed transverse wall temperature difference along the direction of gravity. Spanning the friction Reynolds (Retau <= 205) and Rayleigh numbers (Ra <= 1 . 3 ×107) we could systematically study the influence of the convection on the boundary layer structure and mean profiles of flow quantities in the channel. Our focus is on providing physical understanding of the deviations observed from the logarithmic law of the wall due to the buoyant motions as well as providing a model of this behavior, and link with fundamental quantities of heat transfer in the convective channel flow. Our findings show that the introduction of an unstably stratified thermal field results in an effective drag increase in the channel flow, quantified in the logarithmic region by a modified log-law, with model parameters dependent on Ra , Retau .
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.
NASA Technical Reports Server (NTRS)
Holsapple, K. A.
1987-01-01
Impact craters are numerous on planetary bodies and furnish important information about the composition and past histories of those bodies. The interpretation of that information requires knowledge about the fundamental aspects of impact cratering mechanics. Since the typical conditions of impacts are at a size scale and velocity far in excess of experimental capabilities, direct simulations are precluded. Therefore, one must rely on extrapolation from experiments of relatively slow impacts of very small bodies, using physically based scaling laws, or must study the actual cases of interest using numerical code solutions of the fundamental physical laws that govern these processes. A progress report is presented on research on impact cratering scaling laws, on numerical studies that were designed to investigate those laws, and on various applications of the scaling laws developed by the author and his colleagues. These applications are briefly reviewed.
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.
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.
Unified scaling law for earthquakes
Christensen, Kim; Danon, Leon; Scanlon, Tim; Bak, Per
2002-01-01
We propose and verify a unified scaling law that provides a framework for viewing the probability of the occurrence of earthquakes in a given region and for a given cutoff magnitude. The law shows that earthquakes occur in hierarchical correlated clusters, which overlap with other spatially separated correlated clusters for large enough time periods and areas. For a small enough region and time-scale, only a single correlated group can be sampled. The law links together the Gutenberg–Richter Law, the Omori Law of aftershocks, and the fractal dimensions of the faults. The Omori Law is shown to be the short time limit of general hierarchical phenomenon containing the statistics of both “main shocks” and “aftershocks,” indicating that they are created by the same mechanism. PMID:11875203
Allometric scaling laws of metabolism
NASA Astrophysics Data System (ADS)
da Silva, Jafferson Kamphorst Leal; Garcia, Guilherme J. M.; Barbosa, Lauro A.
2006-12-01
One of the most pervasive laws in biology is the allometric scaling, whereby a biological variable Y is related to the mass M of the organism by a power law, Y=YM, where b is the so-called allometric exponent. The origin of these power laws is still a matter of dispute mainly because biological laws, in general, do not follow from physical ones in a simple manner. In this work, we review the interspecific allometry of metabolic rates, where recent progress in the understanding of the interplay between geometrical, physical and biological constraints has been achieved. For many years, it was a universal belief that the basal metabolic rate (BMR) of all organisms is described by Kleiber's law (allometric exponent b=3/4). A few years ago, a theoretical basis for this law was proposed, based on a resource distribution network common to all organisms. Nevertheless, the 3/4-law has been questioned recently. First, there is an ongoing debate as to whether the empirical value of b is 3/4 or 2/3, or even nonuniversal. Second, some mathematical and conceptual errors were found these network models, weakening the proposed theoretical arguments. Another pertinent observation is that the maximal aerobically sustained metabolic rate of endotherms scales with an exponent larger than that of BMR. Here we present a critical discussion of the theoretical models proposed to explain the scaling of metabolic rates, and compare the predicted exponents with a review of the experimental literature. Our main conclusion is that although there is not a universal exponent, it should be possible to develop a unified theory for the common origin of the allometric scaling laws of metabolism.
Constructing cities, deconstructing scaling laws
Arcaute, Elsa; Hatna, Erez; Ferguson, Peter; Youn, Hyejin; Johansson, Anders; Batty, Michael
2015-01-01
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. PMID:25411405
Scaling laws for bubbling bifurcations
NASA Astrophysics Data System (ADS)
González-Tokman, Cecilia; Hunt, Brian R.
2009-11-01
We establish rigorous scaling laws for the average bursting time for bubbling bifurcations of an invariant manifold, assuming the dynamics within the manifold to be uniformly hyperbolic. This type of global bifurcation appears in nearly synchronized systems, and is conjectured to be typical among those breaking the invariance of an asymptotically stable hyperbolic invariant manifold. We consider bubbling precipitated by generic bifurcations of a fixed point in both symmetric and non-symmetric systems with a codimension one invariant manifold, and discuss their extension to bifurcations of periodic points. We also discuss generalizations to invariant manifolds with higher codimension, and to systems with random noise.
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.
Plasma focus ion beam-scaling laws
NASA Astrophysics Data System (ADS)
Saw, S. H.
2014-08-01
Measurements on plasma focus ion beams include various advanced techniques producing a variety of data which has yet to produce benchmark numbers. Recent numerical experiments using an extended version of the Lee Code has produced reference numbers and scaling trends for number and energy fluence of deuteron beams as functions of stored energy E0. At the pinch exit the ion number fluence (ions m-2) and energy fluence (J m-2) computed as 2.4-7.8×1020 and 2.2-33×106 respectively were found to be independent of E0 from 0.4 - 486 kJ. This work was extended to the ion beams for various gases. The results show that, for a given plasma focus, the fluence, flux, ion number and ion current decrease from the lightest to the heaviest gas except for trend-breaking higher values for Ar fluence and flux. The energy fluence, energy flux, power flow and damage factors are relatively constant from H2 to N2 but increase for Ne, Ar, Kr and Xe due to radiative cooling and collapse effects. This paper reviews this work and in a concluding section attempts to put the accumulating large amounts of data into the form of a scaling law of beam energy Ebeam versus storage energy E0 taking the form for deuteron as: {Ebeam} = 18.2{E}01.23; where Ebeam is in J and E0 is in kJ. It is hoped that the establishment of such scaling laws places on a firm footing the reference quantitative ideas for plasma focus ion beams.
Scaling laws for laser-induced filamentation
NASA Astrophysics Data System (ADS)
Zhokhov, P. A.; Zheltikov, A. M.
2014-04-01
Despite all the complexity of the underlying nonlinear physics, the filamentation of ultrashort optical field wave forms is shown to obey a set of physically transparent scaling laws. This scaling is applicable within a remarkably broad range of laser powers, pulse widths, gas pressures, and propagation paths, suggesting specific recipes for the power scaling of filamentation-based pulse compression.
Scaling laws predict global microbial diversity.
Locey, Kenneth J; Lennon, Jay T
2016-05-24
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⋅10(6) 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 (10(12)) microbial species. Microbial biodiversity seems greater than ever anticipated yet predictable from the smallest to the largest microbiome. PMID:27140646
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
Time-dependent corona models - Scaling laws
NASA Technical Reports Server (NTRS)
Korevaar, P.; Martens, P. C. H.
1989-01-01
Scaling laws are derived for the one-dimensional time-dependent Euler equations that describe the evolution of a spherically symmetric stellar atmosphere. With these scaling laws the results of the time-dependent calculations by Korevaar (1989) obtained for one star are applicable over the whole Hertzsprung-Russell diagram and even to elliptic galaxies. The scaling is exact for stars with the same M/R-ratio and a good approximation for stars with a different M/R-ratio. The global relaxation oscillation found by Korevaar (1989) is scaled to main sequence stars, a solar coronal hole, cool giants and elliptic galaxies.
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. PMID:25271781
Predictive scaling laws for spherical rotating dynamos
NASA Astrophysics Data System (ADS)
Oruba, L.; Dormy, E.
2014-08-01
State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth's core. In order to establish a connection between dynamo modelling and the geophysical motivation, it is necessary to use scaling laws. Such scaling laws establish the dependence of essential quantities (such as the magnetic field strength) on measured or controlled quantities. They allow for a direct confrontation of advanced models with geophysical constraints. We combine a numerical approach, based on a multiple linear regression method in the form of power laws, applied to a database of 102 direct numerical simulations (courtesy of U. Christensen), and a physical approach, based on energetics and forces balances. We show that previous empirical scaling laws for the magnetic field strength essentially reflect the statistical balance between energy production and dissipation for saturated dynamos. Such power based scaling laws are thus necessarily valid for any dynamo in statistical equilibrium and applicable to any numerical model, irrespectively of the dynamo mechanism. We show that direct numerical fits can provide contradictory results owing to biases in the parameters space covered in the numerics and to the role of a priori hypothesis on the fraction of ohmic dissipation. We introduce predictive scaling laws, that is relations involving input parameters of the governing equations only. We guide our reasoning on physical considerations. We show that our predictive scaling laws can properly describe the numerical database and reflect the dominant forces balance at work in these numerical simulations. We highlight the dependence of the magnetic field strength on the rotation rate. Finally, our results stress that available numerical models operate in a viscous dynamical regime, which is not relevant to the Earth's core.
Practical scaling law for photoelectron angular distributions
Guo Dongsheng; Zhang Jingtao; Xu Zhizhan; Li Xiaofeng; Fu Panming; Freeman, R.R.
2003-10-01
A practical scaling law that predicts photoelectron angular distributions (PADs) is derived using angular distribution formulas which explicitly contain spontaneous emission. The scaling law is used to analyze recent PAD measurements in above-threshold ionization, and to predict results of future experiments. Our theoretical and numerical studies show that, in the non-relativistic regime and long-wavelength approximation, the shapes of PADs are determined by only three dimensionless numbers: (1) u{sub p}{identical_to}U{sub p}/({Dirac_h}/2{pi}){omega}, the ponderomotive number (ponderomotive energy in units of laser photon energy); (2) {epsilon}{sub b}{identical_to}E{sub b}/({Dirac_h}/2{pi}){omega}, the binding number (atomic binding energy in units of the laser photon energy); (3) j, the absorbed-photon number. The scaling law is shown to be useful in predictions of results from strong-field Kapitza-Dirac effect measurements; specifically, the application of this scaling law to recently reported Kapitza-Dirac diffraction is discussed. Possible experimental tests to verify the scaling law are suggested.
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 in urban supply networks
NASA Astrophysics Data System (ADS)
Kühnert, Christian; Helbing, Dirk; West, Geoffrey B.
2006-04-01
In previous work, it has been proposed that urban structures may be understood as a result of self-organization principles. In particular, researchers have identified fractal structures of public transportation networks and land use patterns. Here, we will study spatial distribution systems for energy, fuel, medical, and food supply. It is found that these systems show power-law scaling as well, when the number of “supply stations” is plotted over the population size. Surprisingly, only some supply systems display a linear scaling with population size. Others show sublinear or superlinear scaling. We suggest an interpretation regarding the kind of scaling law that is expected in dependence of the function and constraints of the respective supply system.
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.
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
Centrifugal fans: Similarity, scaling laws, and fan performance
NASA Astrophysics Data System (ADS)
Sardar, Asad Mohammad
Centrifugal fans are rotodynamic machines used for moving air continuously against moderate pressures through ventilation and air conditioning systems. There are five major topics presented in this thesis: (1) analysis of the fan scaling laws and consequences of dynamic similarity on modelling; (2) detailed flow visualization studies (in water) covering the flow path starting at the fan blade exit to the evaporator core of an actual HVAC fan scroll-diffuser module; (3) mean velocity and turbulence intensity measurements (flow field studies) at the inlet and outlet of large scale blower; (4) fan installation effects on overall fan performance and evaluation of fan testing methods; (5) two point coherence and spectral measurements conducted on an actual HVAC fan module for flow structure identification of possible aeroacoustic noise sources. A major objective of the study was to identity flow structures within the HVAC module that are responsible for noise and in particular "rumble noise" generation. Possible mechanisms for the generation of flow induced noise in the automotive HVAC fan module are also investigated. It is demonstrated that different modes of HVAC operation represent very different internal flow characteristics. This has implications on both fan HVAC airflow performance and noise characteristics. It is demonstrated from principles of complete dynamic similarity that fan scaling laws require that Reynolds, number matching is a necessary condition for developing scale model fans or fan test facilities. The physical basis for the fan scaling laws derived was established from both pure dimensional analysis and also from the fundamental equations of fluid motion. Fan performance was measured in a three times scale model (large scale blower) in air of an actual forward curved automotive HVAC blower. Different fan testing methods (based on AMCA fan test codes) were compared on the basis of static pressure measurements. Also, the flow through an actual HVAC
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.
In Search of Reaction Rate Scaling Law for Supersonic Combustion
NASA Astrophysics Data System (ADS)
Ladeinde, Foluso; Lou, Zhipeng; Li, Wenhai
2015-11-01
As a way of employing the flamelet approach, which was developed essentially for incompressible flows, to model supersonic combustion, the role ascribed to pressure has not been very convincing. That is, the reaction rate is often scaled on the square of the pressure in the finite Mach number flow field relative to the usually atmospheric static pressure field used in the generation of the flamelet library. This scaling assumption is quite simple and will therefore be very attractive if it has a sound theoretical basis and it works for a large selection of high-speed combustion flows. We try to find some justifications for different scaling laws, with the hope of coming up with a more universally-acceptable flamelet procedure for supersonic combustion.
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 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.
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 laws and the modern city
NASA Astrophysics Data System (ADS)
Isalgue, Antonio; Coch, Helena; Serra, Rafael
2007-08-01
The inter-relations and the complexity of modern urban spaces are difficult to analyse in a way that allows improving living conditions or help to ascertain optimal decisions for saving energy or improving sustainability. Carefully designed decisions and guidelines might produce unexpected results because of particularities, or complex sets of reactions from residents or economic counterparts. Complexity tends to increase with size, such as when, for instance, services tend to concentrate in large agglomerations, and transportation needs take on critical importance. Complex systems such as living organisms are known to follow approximate relationships as scaling laws between the variables that describe them. Some of these kinds of relationships are tested in relation to modern developed urban spaces, in which it is possible to find a reasonable continuity with the types of scales seen in living organisms, and some preliminary conclusions are drawn.
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.
Anomalous scaling laws in multifractal objects
NASA Astrophysics Data System (ADS)
Paladin, Giovanni; Vulpiani, Angelo
1987-12-01
Anomalous scaling laws appear in a wide class of phenomena where global dilation invariance fails. In this case, the description of scaling properties requires the introduction of an infinite set of exponents. Numerical and experimental evidence indicates that this description is relevant in the theory of dynamical systems, of fully developed turbulence, in the statistical mechanics of disordered systems, and in some condensed matter problems. We describe anomalous scaling in terms of multifractal objects. They are defined by a measure whose scaling properties are characterized by a family of singularities, which are identified by a scaling exponent. Singularities corresponding to the same exponent are distributed on fractal set. The multifractal object arises as the superposition of these sets, whose fractal dimensions are related to the anomalous scaling exponents via a Legendre transformation. It is thus possible to reconstruct the probability distribution of the singularity exponents. We review the application of this formalism to the description of chaotic attractors in dissipative systems, of the energy dissipating set in fully developed turbulence, of some probability distributions in condensed matter problems. Moreover, a simple extension of the method allows us to treat from the same point of view temporal intermittency in chaotic systems and sample to sample fluctuations in disordered systems. We stress the phenomenological nature of the approach and discuss the few cases in which it was possible to reach a more fundamental understanding of anomalous scaling. We point out the need of a theory which should explain its origin and pave the way to a microscopic calculation of the probability distribution of the singularities.
A Scaling Law of Vascular Volume
Huo, Yunlong; Kassab, Ghassan S.
2009-01-01
Abstract Vascular volume is of fundamental significance to the function of the cardiovascular system. An accurate prediction of blood volume in patients is physiologically and clinically significant. This study proposes what we believe is a novel volume scaling relation of the form: Vc=KvDs2/3Lc, where Vc and Lc are cumulative vessel volume and length, respectively, in the tree, and Ds is the diameter of the vessel segment. The scaling relation is validated in vascular trees of various organs including the heart, lung, mesentery, muscle, and eye of different species. Based on the minimum energy hypothesis and volume scaling relation, four structure-function scaling relations are predicted, including the diameter-length, volume-length, flow-diameter, and volume-diameter relations, with exponent values of 3/7, 127, 2⅓, and 3, respectively. These four relations are validated in the various vascular trees, which further confirm the volume scaling relation. This scaling relation may serve as a control reference to estimate the blood volume in various organs and species. The deviation from the scaling relation may indicate hypovolemia or hypervolemia and aid diagnosis. PMID:19167288
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
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.
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.
Revised scaling laws for asteroid disruptions
NASA Astrophysics Data System (ADS)
Jutzi, M.
2014-07-01
Models for the evolution of small-body populations (e.g., the asteroid main belt) of the solar system compute the time-dependent size and velocity distributions of the objects as a result of both collisional and dynamical processes. A scaling parameter often used in such numerical models is the critical specific impact energy Q^*_D, which results in the escape of half of the target's mass in a collision. The parameter Q^*_D is called the catastrophic impact energy threshold. We present recent improvements of the Smooth Particle Hydrodynamics (SPH) technique (Benz and Asphaug 1995, Jutzi et al. 2008, Jutzi 2014) for the modeling of the disruption of small bodies. Using the improved models, we then systematically study the effects of various target properties (e.g., strength, porosity, and friction) on the outcome of disruptive collisions (Figure), and we compute the corresponding Q^*_D curves as a function of target size. For a given specific impact energy and impact angle, the outcome of a collision in terms of Q^*_D does not only depend on the properties of the bodies involved, but also on the impact velocity and the size ratio of target/impactor. Leinhardt and Stewardt (2012) proposed scaling laws to predict the outcome of collisions with a wide range of impact velocities (m/s to km/s), target sizes and target/impactor mass ratios. These scaling laws are based on a "principal disruption curve" defined for collisions between equal-sized bodies: Q^*_{RD,γ = 1} = c^* 4/5 π ρ G R_{C1}^2, where the parameter c^* is a measure of the dissipation of energy within the target, R_{C1} the radius of a body with the combined mass of target and projectile and a density ρ = 1000 kg/m^3, and γ is the mass ratio. The dissipation parameter c^* is proposed to be 5±2 for bodies with strength and 1.9±0.3 for hydrodynamic bodies (Leinhardt and Stewardt 2012). We will present values for c^* based on our SPH simulations using various target properties and impact conditions. We
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
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.
Scaling laws and vector effects in bandgap-guiding fibres.
Birks, T; Bird, D; Hedley, T; Pottage, J; Russell, P
2004-01-12
Scaling laws for photonic bandgaps in photonic crystal fibres are described. Although only strictly valid for small refractive index contrast, they successfully identify corresponding features in structures with large index contrast. Furthermore, deviations from the scaling laws distinguish features that are vector phenomena unique to electromagnetic waves from those that would be expected for generic scalar waves. PMID:19471512
Dark Halo and Disk Galaxy Scaling Laws
NASA Astrophysics Data System (ADS)
Navarro, J. F.
I highlight recent progress in our understanding of the origin of disk galaxy scaling laws in a hierarchically clustering universe. Numerical simulations of galaxy formation in Cold Dark Matter (CDM) dominated universes indicate that the slope and scatter of the I-band Tully-Fisher (TF) relation are well reproduced in this model, although not, as proposed in recent work, because of the cosmological equivalence between halo mass and circular velocity, but rather as a result of the dynamical response of the halo to the assembly of the luminous component of the galaxy. The zero-point of the TF relation is determined mainly by the stellar mass-to-light ratio (ΥI) as well as by the concentration (c) of the dark halo. For c ~ 10, as is typical of halos formed in the `concordance' ΛCDM model, we find that this requires ΥI ~ 1.5, in reasonable agreement with the mass-to-light ratios expected of stellar populations with colors similar to those of TF galaxies. This conclusion supersedes that of Navarro & Steinmetz (2000a,b), who claimed the ΛCDM halos were too concentrated to be consistent with the observed TF relation. The disagreement can be traced to an incorrect normalization of the power spectrum used in that work. Our new results show that simulated disk galaxies in the ΛCDM scenario are not clearly inconsistent with the observed I-band Tully-Fisher relation. On the other hand, their angular momenta is much lower than observed. Accounting simultaneously for the spin, size and luminosity of disk galaxies remains a challenge for hierarchical models of galaxy formation.
WESTERN WATER LAWS AND IRRIGATION RETURN FLOW
The impact of water law allocation and use of waters within the Western United States is currently recognized as one of the major constraints to adaptation by irrigated agriculture of more efficient operation practices. This project provides a background of the law and evaluation...
A simplified Mach number scaling law for helicopter rotor noise
NASA Technical Reports Server (NTRS)
Aravamudan, K. S.; Lee, A.; Harris, W. L.
1978-01-01
Mach number scaling laws are derived for the rotational and the high-frequency broadband noise from helicopter rotors. The rotational scaling law is obtained directly from the theory of Lowson and Ollerhead (1969) by exploiting the properties of the dominant terms in the expression for the complex Fourier coefficients of sound radiation from a point source. The scaling law for the high-frequency broadband noise is obtained by assuming that the noise sources are acoustically compact and computing the instantaneous pressure due to an element on an airfoil where vortices are shed. Experimental results on the correlation lengths for stationary airfoils are extended to rotating airfoils. On the assumption that the correlation length varies as the boundary layer displacement thickness, it is found that the Mach number scaling law contains a factor of Mach number raised to the exponent 5.8. Both scaling laws were verified by model tests.
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.
The exponential flow law applied to necking and folding of a ductile layer
NASA Astrophysics Data System (ADS)
Schmalholz, Stefan M.; Fletcher, Raymond C.
2011-01-01
The uniaxial exponential law, ?, has been applied to experimental results for steady-state creep, including that of wet and dry olivine, pyroxenite and carbonates, at a deviatoric stress greater than ˜100 MPa. Such stress levels likely occur in the upper-mantle lithosphere and middle crust. In a layered rock, in layer-parallel extension or shortening, high deviatoric stress can occur in the stiffest layers, for example, a dolomite layer in fine-grained marble. Under assumptions of isotropy and incompressibility, the uniaxial law yields ? where J2=sijsij/2 is an invariant of the deviatoric stress tensor, sij. Linearization about a homogeneous basic-state of flow yields equations identical in form to those obtained for the familiar power law. This establishes expressions for an effective viscosity, ? and stress exponent, ?, where ? is an invariant of the basic-state deformation rate, ?. These results allow application of existing analytical folding and necking solutions for a rock layer of power-law fluid to a rock layer with an exponential flow law. The effective stress exponent for the exponential flow law increases with decreasing temperature, through the dependence of C on the latter and, weakly, with increasing deformation rate. For dry olivine, effective stress exponents are between 10 and 30 for temperatures between 400 and 600°C with little dependence on deformation rate. Finite element simulations employing full non-linear forms of the flow laws show that large strain necking is nearly identical for power law and exponential flow laws. The results suggest that the instability in necking and folding in ductile rock layers can be considerably stronger than inferred from results based on flow laws representing diffusion and dislocation creep. The large values of the effective stress exponent, ne > ˜15, that may be attained for exponential flow laws can account for observed outcrop-scale ductile necking.
Scaling laws and coherent structures in the solar wind
NASA Astrophysics Data System (ADS)
Bruno, Roberto; D'Amicis, Raffaella; Bavassano, Bruno; Carbone, Vincenzo; Sorriso-Valvo, Luca
2007-12-01
The interplanetary medium is characterized by a very high Reynolds number and is pervaded by fluctuations providing information on a wide range of scales, from fractions of second up to the solar rotation period. In the past decade or so, turbulence in the solar wind has been used as a large wind tunnel to investigate scaling laws of turbulent fluctuations and multifractal models. Moreover, new interesting insights in the theory of turbulence have been derived from the point of view which considers a turbulent flow as a complex system, a sort of benchmark for the theory of dynamical systems. Important finding like the lack of a strict self-similarity of the fluctuations with the consequent nonapplicability of strict scale invariance, the strong anisotropy of velocity and magnetic field fluctuations, the clear lack of equipartition between magnetic and kinetic fluctuations all contributed to suggest the idea that interplanetary fluctuations could possibly be due to a mixture of propagating waves and static structures convected by the wind. In this paper we further discuss this point and bring new evidence about the fact that the presence of a background magnetic field introduces not only a symmetry breaking in interplanetary space but also organizes fluctuations about its large scale orientation.
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
NASA Astrophysics Data System (ADS)
Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.; Duarte, Lúcia 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.
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 LAW FOR THE IMPACT OF MAGNET FRINGE FIELDS.
WEI,J.; PAPAPHILIPPOU,Y.; TALMAN,R.
2000-06-30
A general scaling law can be derived for the relative momentum deflection produced on a particle beam by fringe fields, to leading order. The formalism is applied to two concrete examples, for magnets having dipole and quadrupole symmetry. During recent years, the impact of magnet fringe fields is becoming increasingly important for rings of relatively small circumference but large acceptance. A few years ago, following some heuristic arguments, a scaling law was proposed [1], for the relative deflection of particles passing through a magnet fringe-field. In fact, after appropriate expansion of the magnetic fields in Cartesian coordinates, which generalizes the expansions of Steffen [2], one can show that this scaling law is true for any multipole magnet, at leading order in the transverse coefficients [3]. This paper intends to provide the scaling law to estimate the impact of fringe fields in the special cases of magnets with dipole and quadrupole symmetry.
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 laws between population and facility densities
Um, Jaegon; Son, Seung-Woo; Lee, Sung-Ik; Jeong, Hawoong; Kim, Beom Jun
2009-01-01
When a new facility like a grocery store, a school, or a fire station is planned, its location should ideally be determined by the necessities of people who live nearby. Empirically, it has been found that there exists a positive correlation between facility and population densities. In the present work, we investigate the ideal relation between the population and the facility densities within the framework of an economic mechanism governing microdynamics. In previous studies based on the global optimization of facility positions in minimizing the overall travel distance between people and facilities, it was shown that the density of facility D and that of population ρ should follow a simple power law D ∼ ρ2/3. In our empirical analysis, on the other hand, the power-law exponent α in D ∼ ρα is not a fixed value but spreads in a broad range depending on facility types. To explain this discrepancy in α, we propose a model based on economic mechanisms that mimic the competitive balance between the profit of the facilities and the social opportunity cost for populations. Through our simple, microscopically driven model, we show that commercial facilities driven by the profit of the facilities have α = 1, whereas public facilities driven by the social opportunity cost have α = 2/3. We simulate this model to find the optimal positions of facilities on a real U.S. map and show that the results are consistent with the empirical data. PMID:19706506
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
2012-01-01
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. PMID:22223802
Numerical Simulations of the Geodynamo and Scaling Laws
NASA Astrophysics Data System (ADS)
Oruba, L.; Dormy, E.
2013-12-01
State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth core. In order to establish a connection between dynamo modeling and the geophysical motivation, it is necessary to use scaling laws. Such laws establish the dependency of essential quantities (such as the magnetic field strength) on measured or controlled quantities. They allow for a direct confrontation of advanced models with geophysical constraints. We will present a detailed analysis of scaling laws based on a wide database of 185 direct numerical simulations (courtesy of U. Christensen) and test various existing scaling laws. Our main concern is to stress the risks of a direct numerical fit free from physical insight. We show that different a priori hypothesis can yield contradictory dependences, in particular concerning the dependence of the magnetic field strength on the rotation rate as well as on the viscosity.
Power law scaling of topographic depressions and their hydrologic connectivity
NASA Astrophysics Data System (ADS)
Le, Phong V. V.; Kumar, Praveen
2014-03-01
Topographic depressions, areas of no lateral surface flow, are ubiquitous characteristics of the land surface that control many ecosystem and biogeochemical processes. High density of depressions increases the surface storage capacity, whereas lower depression density increases runoff, thus influencing soil moisture states, hydrologic connectivity, and the climate-soil-vegetation interactions. With the widespread availability of high-resolution lidar-based digital elevation model (lDEM) data, it is now possible to identify and characterize the structure of the spatial distribution of topographic depressions for incorporation in ecohydrologic and biogeochemical studies. Here we use lDEM data to document the prevalence and patterns of topographic depressions across five different landscapes in the United States and quantitatively characterize the probability distribution of attributes, such as surface area, storage volume, and the distance to the nearest neighbor. Through the use of a depression identification algorithm, we show that these probability distributions of attributes follow scaling laws indicative of a structure in which a large fraction of land surface areas can consist of high number of topographic depressions of all sizes and can account for 4 to 21 mm of depression storage. This implies that the impacts of small-scale topographic depressions in the landscapes on the redistribution of material fluxes, evaporation, and hydrologic connectivity are quite significant.
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.
Scaling laws in chiral hydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2016-06-01
We study the turbulent regime of chiral (magneto)hydrodynamics for charged and neutral matter with chirality imbalance. We find that the chiral magnetohydrodynamics for charged plasmas possesses a unique scaling symmetry, only without fluid helicity under the local charge neutrality. We also find a different type of unique scaling symmetry in the chiral hydrodynamics for neutral matter with fluid helicity in the inertial range. We show that these symmetries dictate the self-similar inverse cascade of the magnetic and kinetic energies. Our results imply the possible inverse energy cascade in core-collapse supernovae due to the chiral transport of neutrinos.
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. 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.
2014-01-01
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
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.
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.
Scaling properties in the production range of shear dominated flows.
Casciola, C M; Gualtieri, P; Jacob, B; Piva, R
2005-07-01
In large Reynolds number turbulence, isotropy is recovered as the scale is reduced and homogeneous-isotropic scalings are eventually observed. This picture is violated in many cases, e.g., wall bounded flows, where, due to the shear, different scaling laws emerge. This effect has been ascribed to the contamination of the inertial range by the larger anisotropic scales. The issue is addressed here by analyzing both numerical and experimental data for a homogeneous shear flow. In fact, under strong shear, the alteration of the scaling exponents is not induced by the contamination from the anisotropic sectors. Actually, the exponents are universal properties of the isotropic component of the structure functions of shear dominated flows. The implications are discussed in the context of turbulence near solid walls, where improved closure models would be advisable. PMID:16090687
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
Triadic closure dynamics drives scaling laws in social multiplex networks
NASA Astrophysics Data System (ADS)
Klimek, Peter; Thurner, Stefan
2013-06-01
Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree. A detailed understanding if and how these scaling laws are inter-related is missing so far, let alone whether they can be understood through a common, dynamical principle. We propose a simple model for stationary network formation and show that the three mentioned scaling relations follow as natural consequences of triadic closure. The validity of the model is tested on multiplex data from a well-studied massive multiplayer online game. We find that the three scaling exponents observed in the multiplex data for the friendship, communication and trading networks can simultaneously be explained by the model. These results suggest that triadic closure could be identified as one of the fundamental dynamical principles in social multiplex network formation.
Energy Scaling Law for the Regular Cone
NASA Astrophysics Data System (ADS)
Olbermann, Heiner
2016-04-01
We consider a thin elastic sheet in the shape of a disk whose reference metric is that of a singular cone. That is, the reference metric is flat away from the center and has a defect there. We define a geometrically fully nonlinear free elastic energy and investigate the scaling behavior of this energy as the thickness h tends to 0. We work with two simplifying assumptions: Firstly, we think of the deformed sheet as an immersed 2-dimensional Riemannian manifold in Euclidean 3-space and assume that the exponential map at the origin (the center of the sheet) supplies a coordinate chart for the whole manifold. Secondly, the energy functional penalizes the difference between the induced metric and the reference metric in L^∞ (instead of, as is usual, in L^2). Under these assumptions, we show that the elastic energy per unit thickness of the regular cone in the leading order of h is given by C^*h^2|log h|, where the value of C^* is given explicitly.
Leidenfrost effect: accurate drop shape modeling and new scaling laws
NASA Astrophysics Data System (ADS)
Sobac, Benjamin; Rednikov, Alexey; Dorbolo, Stéphane; Colinet, Pierre
2014-11-01
In this study, we theoretically investigate the shape of a drop in a Leidenfrost state, focusing on the geometry of the vapor layer. The drop geometry is modeled by numerically matching the solution of the hydrostatic shape of a superhydrophobic drop (for the upper part) with the solution of the lubrication equation of the vapor flow underlying the drop (for the bottom part). The results highlight that the vapor layer, fed by evaporation, forms a concave depression in the drop interface that becomes increasingly marked with the drop size. The vapor layer then consists of a gas pocket in the center and a thin annular neck surrounding it. The film thickness increases with the size of the drop, and the thickness at the neck appears to be of the order of 10--100 μm in the case of water. The model is compared to recent experimental results [Burton et al., Phys. Rev. Lett., 074301 (2012)] and shows an excellent agreement, without any fitting parameter. New scaling laws also emerge from this model. The geometry of the vapor pocket is only weakly dependent on the superheat (and thus on the evaporation rate), this weak dependence being more pronounced in the neck region. In turn, the vapor layer characteristics strongly depend on the drop size.
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
Robust regression on noisy data for fusion scaling laws
NASA Astrophysics Data System (ADS)
Verdoolaege, Geert
2014-11-01
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.
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.
The approximate scaling law of the cochlea box model.
Vetesník, A; Nobili, R
2006-12-01
The hydrodynamic box-model of the cochlea is reconsidered here for the primary purpose of studying in detail the approximate scaling law that governs tonotopic responses in the frequency domain. "Scaling law" here means that any two solutions representing waveforms elicited by tones of equal amplitudes differ only by a complex factor depending on frequency. It is shown that this property holds with excellent approximation almost all along the basilar membrane (BM) length, with the exception of a small region adjacent to the BM base. The analytical expression of the approximate law is explicitly given and compared to numerical solutions carried out on a virtually exact implementation of the model. It differs significantly from that derived by Sondhi in 1978, which suffers from an inaccuracy in the hyperbolic approximation of the exact Green's function. Since the cochleae of mammals do not exhibit the scaling properties of the box model, the subject presented here may appear to be just an academic exercise. The results of our study, however, are significant in that a more general scaling law should hold for real cochleae. To support this hypothesis, an argument related to the problem of cochlear amplifier-gain stabilization is advanced. PMID:17008036
Rate-dependent scaling laws for spall failure
NASA Astrophysics Data System (ADS)
Wilkerson, Justin; Ramesh, Kt
Here we derive simple bounds on the growth rate of voids considering the combined retarding effects of micro-inertia and dislocation kinetics. We make use of these bounds to derive simple scaling laws capable of predicting the strong rate-dependence of spall strength. We show that the rate-sensitivity exponent for spall strength is bounded to below 6/7 when micro-inertia is the dominant retarding effect on void growth. However, under conditions in which the void growth is predominately governed by dislocation kinetics the rate-sensitivity exponent may rise to a maximum value of 1. With these scaling laws in hand, we go on to further explore the role of microstructure on spall strength. Though simple, the derived scaling laws compare well with experimental measurements and prove useful in shedding light on some of the more perplexing observations associated with spall failure. In particular, the scaling laws are helpful in understanding the somewhat anomalous dependence of spall strength on pre-existing microstructure, e.g. grain size and purity content.
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.
Scaling laws in spherical shell dynamos with free-slip boundaries
NASA Astrophysics Data System (ADS)
Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.
2013-07-01
Numerical simulations of convection driven rotating spherical shell dynamos have often been performed with rigid boundary conditions, as is appropriate for the metallic cores of terrestrial planets. Free-slip boundaries are more appropriate for dynamos in other astrophysical objects, such as gas-giants or stars. Using a set of 57 direct numerical simulations, we investigate the effect of free-slip boundary conditions on the scaling properties of heat flow, flow velocity and magnetic field strength and compare it with earlier results for rigid boundaries. We find that the nature of the mechanical boundary condition has only a minor influence on the scaling laws. We also find that although dipolar and multipolar dynamos exhibit approximately the same scaling exponents, there is an offset in the scaling pre-factors for velocity and magnetic field strength. We argue that the offset can be attributed to the differences in the zonal flow contribution between dipolar and multipolar dynamos.
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
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
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).
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. PMID:26230279
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.
Transition in the Flow of Power-Law Fluids through Isotropic Porous Media
NASA Astrophysics Data System (ADS)
Zami-Pierre, F.; de Loubens, R.; Quintard, M.; Davit, Y.
2016-08-01
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.
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. PMID:27563969
NASA Astrophysics Data System (ADS)
Soné, Naomi; Mori, Marie; Okumura, Ko
2012-07-01
Strong materials and a solid method of estimating their toughness are important for manufacturing materials valuable for human life, such as rubber and plastic. Such strong materials often exhibit a complex response to external force, which resists description by simple scaling laws. In addition, even for simple nonlinear materials, no theoretical or experimental reports have been available on a clear scaling law between fracture stress and crack size, which would, if available, provide a solid test for toughness. Here, we perform experiments on thin sheet samples to make important length scales well-separated. This practically suppresses all the finite-size effects so that we succeed in finding a clear scaling law for fracture (that between failure stress and crack size) by studying nonlinear polymer sheets. This leads to plausible estimates of the fracture toughness. Remarkably, we experimentally find the scaling law even though the nonlinearity in force response is not so simple as described by power laws. The fracture scaling can be explained by a theory developed here for simple nonlinear materials and we expect that this theory will be valid for many other materials with a complex nonlinearity, as demonstrated here. This clarifies the advantage of testing thin sheets. The scaling law established here can be regarded as a nonlinear extension of the Griffith's formula and holds also for thick samples: the nonlinear Griffith's formula is also applicable to three-dimensional bulk objects.
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.
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.
Model selection for identifying power-law scaling.
Ton, Robert; Daffertshofer, Andreas
2016-08-01
Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present. PMID:26774613
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.
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
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.
A kinematic conservation law in free surface flow
NASA Astrophysics Data System (ADS)
Gavrilyuk, Sergey; Kalisch, Henrik; Khorsand, Zahra
2015-06-01
The Green-Naghdi system is used to model highly nonlinear weakly dispersive waves propagating at the surface of a shallow layer of a perfect fluid. The system has three associated conservation laws which describe the conservation of mass, momentum, and energy due to the surface wave motion. In addition, the system features a fourth conservation law which is the main focus of this note. It will be shown how this fourth conservation law can be interpreted in terms of a concrete kinematic quantity connected to the evolution of the tangent velocity at the free surface. The equation for the tangent velocity is first derived for the full Euler equations in both two and three dimensional flows, and in both cases, it gives rise to an approximate balance law in the Green-Naghdi theory which turns out to be identical to the fourth conservation law for this system. It is also shown that the conservation equation for the tangent velocity at the free surface appears as an endpoint case of a more general conservation equation for tangent velocities along material surfaces in the body of the fluid.
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
Scaling law for dynamical hysteresis of cavity solitons
NASA Astrophysics Data System (ADS)
Ahmadipanah, Sahar; Kheradmand, Reza; Prati, Franco
2016-02-01
By applying to a cavity soliton a control beam modulated in time, we study numerically the performance of the soliton as a flip-flop memory. The soliton is switched on and off periodically through a hysteresis cycle whose size increases dynamically with the modulation frequency. We show that the phenomenon is ruled by a scaling law with an exponent compatible with the theoretical value 2/3 predicted in much simpler systems in the low-frequency limit.
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.
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
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.
NASA Astrophysics Data System (ADS)
Skaugen, Audun; Angheluta, Luiza
The relationship between vortex dynamics and the turbulent energy spectrum is an active research topic in quantum turbulence of superfluids and Bose-Einstein condensates. The energy spectra in quantum turbulence exhibit a Kolmogorov -5/3 scaling law, analogous to classical turbulence. Recent developments show that in two-dimensional quantum flows, this energy spectrum corresponds to an inverse energy cascade, which is realized by clustering of like-signed quantized vortices. 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 velocity, which also show a similar scaling behavior. The -5/3 scaling law appearing in the power spectrum of the vortex number is consistent with a scenario of isolated vortices passively advected by a turbulent superfluid velocity, which is again generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial correlations, and exhibits a power-law tail with a -5/3 exponent that we can predict analytically from the point vortex model.
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.
A new Reynolds-number-dependent scaling law for turbulent boundary layers
NASA Astrophysics Data System (ADS)
Buschmann, M.; Gad-El-Hak, M.
2002-11-01
There has been considerable controversy during the past few years concerning the validity of the universal logarithmic law that describes the mean velocity profile in the overlap region of a turbulent wall-bounded flow. New ideas follow from Lie-group analysis that considers linear, algebraic, logarithmic and exponential laws for the mean velocity of a stationary, parallel turbulent shear flow. The objective of the present work is to find a compact expression for the mean velocity profile of a canonical turbulent boundary layer, including parts of the buffer layer, the classical overlap region and parts of the wake region. Based on Afzal's extension of the two-layer approach, we propose herein a higher-order solution for the mean velocity profile. The new law depends on the Kármán number (ratio of outer to inner length scale) and the dimensionless wall-normal coordinate. The result is a profile that consists of a logarithmic term plus an exponential one. The logarithmic term includes an additional constant in the log that extends the profile toward the buffer layer. The exponential term is an expression for the wake component. Both terms represent a blending of two results that were derived from first principles by applying the Lie-group theory. For infinite Kármán number, the exponential term becomes constant and a law similar to the classical log law is found. In this case, the only difference between the new law and the classical log law is an additional constant inside the log. Therefore, no straight line will appear in the usual semi-log plot of the mean velocity profile. A comparison with experimental data and DNS results shows that the new law provides a superior fit.
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. PMID:10562643
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. PMID:26232979
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework
NASA Astrophysics Data System (ADS)
Haltas, Ismail; Ulusoy, Suleyman
2015-07-01
Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.
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.
Decay Power Law in, High Intensity, Isotropic Turbulent Flow
NASA Astrophysics Data System (ADS)
Koster, Timothy; Puga, Alejandro; Larue, John
2014-11-01
In the study reported here, isotropy is determined using the measure proposed by George (1992), where isotropy corresponds to those downstream positions where the product of the Taylor Reynolds number and the skewness of the velocity derivative is a constant. Straight forward approach can be used which is based on the observation of Batchelor (1953), that the square of the Talor micorscale is linearly related to downstream distance relative to the virtual origin. The fact that the decay of downstream velocity variance is described by a power law is shown to imply power law behavior for various other parameters such as the dissipation, the integral length scale, the Taylor microscale, the Kolmogorov microscale and the Taylor Reynolds number and that there is an algebraic relationship between the various power law exponents. Results are presented for mean velocities of 6 and 8 m/s for the downstream decay of the parameters listed in the preceding. The corresponding values of the Taylor Reynolds number at the start of the isotropic region are 290 and 400, and the variance decay exponent and virtual origin are found to be respectively -1.707 and -1.298 and -27.95 and -5.757. The exponents in the decay law for the other parameters are found to be within +/- 3% of the expected values. University of California Irvine Research Funds.
On an Unified Scaling Law for Volcanic Eruptions
NASA Astrophysics Data System (ADS)
Cannavo, F.; Nunnari, G.
2014-12-01
Volcanoes constitute dissipative systems with many degrees of freedom. Their eruptions are the result of complex processes that involve interacting chemical-physical systems. At the present, both analytical and numerical models are unable to include all the possible dynamics involved into eruptions. On the other hand, the knowledge of eruption duration can be a key factor for natural hazard estimation. In this work, analyzing a large database with most of all the known volcanic eruptions, we have determined that the duration of eruptions can be described by a unique universal distribution which fully governs eruption duration dynamics. In particular, after the well-known results proposed in literature concerning the seismicity (i.e. the Gutenberg-Richter law), we present an Earth-wise power-law distribution of durations of volcanic eruptions that holds from worldwide to local scales, for different volcanic environments and for all the considered eruption types.
NASA Astrophysics Data System (ADS)
Wang, L.; Cardenas, M.; Slottke, D. T.; Ketcham, R. A.; Sharp, J. M.
2013-12-01
Fundamental understanding of flow and transport processes through single rough-walled fractures remains a challenge to gain insight for interpreting hydrological phenomena at continuum scale. The Generalized Local Cubic Law (GLCL) developed here is based on (1) modifying the aperture field by orienting it with the flow direction accounting for tortuosity, and (2) correcting for roughness changes associated with flow expansion/contraction and inertial effects. We compared its performance in estimating flow rate to results of direct numerical simulations with the Navier-Stokes equations (NSE) and physical flow experiments for real and synthetic three-dimensional rough-walled fractures. We also evaluated the performance of the Local Cubic Law (LCL). The LCL consistently overestimates flow rate with relative error δ ranging from 20% to 100% with arithmetic mean of |δ| (<|δ|>) equal to 45.4% depending on the degree of tortuosity and roughness. However, the GLCL performs well and improves the performance of the LCL, where δ in flow rate range from -3.1% to 11.4% with <|δ|>=4.7%. Furthermore, we generated breakthrough curves (BTCs) through direct numerical simulations based on the advection-diffusion equation with flow field resulting from solving the NSE (which are considered to the true or experimental BTCs). We revisited the applicability of random walk particle tracking (RWPT) to simulate solute transport dynamics through real fractures, where flow fields resulted from the GLCL and LCL, respectively. We found persistent early arrival and heavy tailing in the BTCs from both direct numerical simulations and RWPT, which are the salient characteristics of non-Fickian behavior. The LCL consistently overestimates mean flow velocity; whereas the GLCL improves estimating flow field, and markedly improves fits to the BTCs relative to those fitted with LCL solutions. Therefore, PWPT with flow field resulting from the GLCL is robust in predicting solute transport through
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.
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
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
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 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.
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.
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 between Urban Electrical Consumption and Population in China
NASA Astrophysics Data System (ADS)
Zhu, Xiaowu; Xiong, Aimin; Li, Liangsheng; Liu, Maoxin; Chen, X. S.
The relation between the household electrical consumption Y and population N for Chinese cities in 2006 has been investigated with the power law scaling form Y = A_0 N^{β}. It is found that the Chinese cities should be divided into three categories characterized by different scaling exponent β. The first category, which includes the biggest and coastal cities of China, has the scaling exponent β> 1. The second category, which includes mostly the cities in central China, has the scaling exponent β ≈ 1. The third category, which consists of the cities in northwestern China, has the scaling exponent β< 1 . Using a urban growth equation, different ways of city population evolution can be obtained for different β. For β< 1 , population evolutes always to a fixed point population N f from below or above depending on the initial population. For β> 1, there is also a fixed point population N f . If the initial population N(0) > N f , the population increases very fast with time and diverges within a finite time. If the initial population N(0) < N f , the population decreases with time and collapse finally. The pattern of population evolution in a city is determined by its scaling exponent and initial population.
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.
Experiments and scaling laws for catastrophic collisions. [of asteroids
NASA Technical Reports Server (NTRS)
Fujiwara, A.; Cerroni, P.; Davis, D.; Ryan, E.; Di Martino, M.
1989-01-01
The existing data on shattering impacts are reviewed using natural silicate, ice, and cement-mortar targets. A comprehensive data base containing the most important parameters describing these experiments was prepared. The collisional energy needed to shatter consolidated homogeneous targets and the ensuing fragment size distributions have been well studied experimentally. However, major gaps exist in the data on fragment velocity and rotational distributions, as well as collisional energy partitioning for these targets. Current scaling laws lead to predicted outcomes of asteroid collisions that are inconsistent with interpretations of astronomical data.
Scaling Laws and 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. PMID:27228416
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.
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.
Power-Law Tails from Dynamical Comptonization in Converging Flows
NASA Astrophysics Data System (ADS)
Turolla, Roberto; Zane, Silvia; Titarchuk, Lev
2002-09-01
The effects of bulk motion Comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semianalytical, diffusion approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates when photon diffusion holds. Our semianalytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method, we find that although the power-law tail at extremely large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Γ=3 at large accretion rates, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft seed photons when the accretion rate is either quite low (<~5 in Eddington units) or sufficiently high (>~10). On the other hand, the spatial distribution of source photons controls the photon index at intermediate accretion rates, when Γ switches from the first to the second mode. Our analysis confirms that a hard tail with photon index Γ<3 is produced by the upscattering of primary photons onto infalling electrons if the central object is a black hole.
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
2015-12-01
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=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. PMID:26701881
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
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.
Hierarchical scaling law for the strength of composite fibre bundles
NASA Astrophysics Data System (ADS)
Pimenta, Soraia; Pinho, Silvestre T.
2013-06-01
This paper presents an analytical model for size effects on the longitudinal tensile strength of composite fibre bundles. The strength of individual fibres is modelled by a Weibull distribution, while the matrix (or fibre-matrix interface) is represented through a perfectly plastic shear-lag model. A probabilistic analysis of the failure process in hierarchical bundles (bundles of bundles) is performed, so that a scaling law relating the strength distributions and characteristic lengths of consecutive bundle levels is derived. An efficient numerical scheme (based on asymptotic limits) is proposed, hence coupon-sized bundle strength distributions are obtained almost instantaneously. Parametric studies show that both fibre and matrix properties are critical for bundle strength; model predictions at different scales are validated against experimental results available in the literature.
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.
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
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.
Scaling laws for the upper ocean temperature dissipation rate
NASA Astrophysics Data System (ADS)
Bogucki, Darek J.; Huguenard, K.; Haus, B. K.; Özgökmen, T. M.; Reniers, A.; Laxague, N. J. M.
2015-02-01
Our understanding of temperature dissipation rate χ within the upper ocean boundary layer, which is critical for climate forecasts, is very limited. Near-surface turbulence also affects dispersion of contaminants and biogeochemical tracers. Using high-resolution optical turbulence measurements, scaling laws for χ are investigated under forcing states where either the daytime heat flux or the wind stress forcing is dominant. We find that χ remains constant over 1.5 times the significant wave height, while over a layer below, χ decays based on the local surface forcing. When the heat flux is dominant, traditional scaling based on the Monin-Obukhov similarity theory remains valid; χ ∝ z-1. When the wind stress dominates, we observe the emergence of a new scaling, χ ∝ z-1/2, which is explained by invoking the effect of small-scale coherent structures on vertical heat transport. These results have implications for improved modeling of the ocean's heat and CO2 intake.
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.
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.
Environmental flow by-law developmment for Bosnia and Herzegovina
NASA Astrophysics Data System (ADS)
Vucijak, Branko; Smolar-Zvanut, Natasa; Antonelli, Francesca
2010-05-01
The main aim of this paper is to present the results of the application of several methodologies for environmental flow assessment, in order to find appropriate one(s) to be used in Bosnia and Herzegovina. Several methods were tested, mostly belonging to the category of hydrological environmental flow assessment methods. Additionally, instream ecological values and critical parameters for environmental flow assessment were evaluated. Pilot areas were also assessed in terms of its geography, climate conditions, historic heritage of the river, demography, geology of the river and its tributaries, river hydrology and morphology, ecological characteristics, river pollution, river use and river management. The research highlited very important criteria for environmental flow evaluation are disregarded by the some of these methodologies, i.e. river ecology andr river morphology. As a consequence additional criteria were considered with the aim of preserving the river and riparian ecosystem. In the first phase of the project hydrological EF assessment method GEP (guaranteed ecological flow) was assessed in details and exercise carried out led to the conclusion that the GEP methodology provides some advantages, but also has remarkable disadvantages During next phase 4 selected methods of EF assessment were tested. Large difference was the cause of elimination for three of these methods for EF estimation. Considering the advantages and disadvantages of tested methods, MNQ approach was selected as the most acceptable method to use in BiH, still in need for important methodological improvements that are stressed. In case of protected areas or the presence of endangered and rare species, the holistic approach of EF assessment was proposed too and both of methods are part of drafted By-law on EF.
Physical symmetries of Taylor cone-jets: foundations of scaling laws
NASA Astrophysics Data System (ADS)
Ganan-Calvo, Alfonso M.; Montanero, Jose M.; Rebollo-Munoz, Noelia
2012-11-01
In this work, we aim to establish the scaling laws for the liquid rate of flow naturally ejected by quasi-steady Taylor cone-jets. To this end, we utilize an ample literature in the field reporting precise measurements of the electric current transported and the resulting droplet size as a function of liquid properties and flow rate. The projection of thousands of experimental conditions onto an appropriate non-dimensional parameter space maps a region bounded by the minimum rate of flow attainable in steady state. In this limit, a theoretical model here proposed teaches that a remarkable system of symmetries rises at the geometrical transition from the cone to the jet. This system of symmetries determines an inescapable scaling for the minimum flow rate and related variables. If the flow rate is further decreased, those symmetries break down (the system bifurcates: global instability & dripping). Our model predicts the minimum flow rates reached in experiments reported so far in the literature, including all ranges of liquid properties. The existing literature and a set of new experiments performed for this specific purpose confirms our predictions. The Ministry of Science and Education (Spain) supported this work through Grant No. DPI2010-21103-C04.
Inertial Subrange Spectra in the Log-Law Layer of Turbulent Channel Flow
NASA Astrophysics Data System (ADS)
Kaneda, Yukio; Morishita, Koji; Ishihara, Takashi
2013-11-01
High resolution direct numerical simulations (DNSs) of turbulent channel flows with the friction Reynolds number Reτ up to 5120 show that there exists a layer at y+ being approximately between 200 and 1200, in which the mean velocity profile and the diagonal components of the inertial subrange velocity correlation spectra fit well to the logarithmic law and the k - 5 / 3 law, respectively. Here y+ is the distance from the wall normalized by the wall unit, and k is the wavenumber in the stream wise direction. The DNS data suggest that in the layer (log-law layer), there exists a high wave number range in which the influence of the mean flow on the turbulence statistics may be regarded to be small as compared to that of nonlinear interactions between the small-scale eddies of size ~ 1 / (wave number), so that the former influence may be treated as a perturbation added to the turbulent state determined by the nonlinear turbulence dynamics in the absence of the mean flow. A perturbation analysis on the basis of this idea yields a simple prediction for the anisotropic velocity correlation spectra in the inertial subrange. The DNS data agree fairly well with the prediction.
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
Determining scaling laws from geodynamic simulations using adjoint gradients.
NASA Astrophysics Data System (ADS)
Reuber, Georg; Kaus, Boris; Popov, Anton
2016-04-01
Whereas significant progress has been made in modelling of lithospheric and crustal scale processes in recent years, it often remains a challenge to understand which of the many model parameters is of key importance for a particular simulation. Determining this is usually done by manually changing the model input parameters and performing new simulations. For a few cases, such as for crustal-scale folding instabilities (with viscous rheologies, e.g. [1]) or for Rayleigh-Taylor instabilities, one can use existing scaling laws to obtain such insights. Yet, for a more general case, it is not straightforward to do this (apart from running many simulations). Here, we test a different approach which computes gradients of the model parameters using adjoint based methods, which has the advantage that we can test the influence of an independent number of parameters on the system by computing and analysing the covariance matrix and the gradient of the parameter space. This method might give us the chance to get insights on which parameters affect for example subduction processes and how strong the system depends on their influence. [1] Fernandez, N., & Kaus, B. J. (2014). Fold interaction and wavelength selection in 3D models of multilayer detachment folding. Tectonophysics, 632, 199-217.
Scaling law for topologically ordered systems at finite temperature
Iblisdir, S.; Perez-Garcia, D.; Aguado, M.; Pachos, J.
2009-04-01
Understanding the behavior of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy for T>0, namely, the subleading correction I{sub topo} to the area law for mutual information. Its dependence on T can be written, for Abelian Kitaev models, in terms of information-theoretical functions and readily identifiable scaling behavior, from which the interplay between volume, temperature, and topological order, can be read. These arguments are extended to non-Abelian quantum double models, and numerical results are given for the D(S{sub 3}) model, showing qualitative agreement with the Abelian case.
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
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
Optical Accelerator: Scaling Laws and Figures of Merit
Schachter, L.; Byer, R.L.; Siemann, R.H.; /SLAC
2005-09-27
Indications that solid-state lasers will reach wall-plug to light efficiencies of 30% or more make a laser-driven vacuum-accelerator increasingly appealing. Since at the wavelength of relevant lasers, dielectrics may sustain significantly higher electric field and transmit power with reduced loss comparing to metals, the basic assumption is that laser accelerator structures will be dielectrics. For structures that have typical dimensions of a few microns, present manufacturing constraints entail planar structures that in turn, require re-evaluation of many of the scaling laws that were developed for azimuthally symmetric structures. Moreover, structures that operate at a wavelength of a few centimeters are machined today with an accuracy of microns. In future it will not be possible to maintain 4-5 orders of magnitude difference between operating wavelength and achievable tolerance. An additional difference is, that contrary to present accelerators where the number of electrons in a micro-bunch is of the order of a 10{sup 10}, in an optical structure this number drops to a few thousands. Consequently, the relative impact of individual electrons may be significantly larger. Acceleration structures with higher degree of symmetry, similar to optical fibers, have also some inherent advantages however thermal gradients as well as heat dissipation may become critical impediments. The impact of all these factors on the performance of a laser accelerator structure needs to be determined. Efficiency, wakes and emittance scaling laws that have been developed recently will be presented. It will be shown that there are some inherent advantages in combining the accelerator structure and the laser cavity in one system.
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.
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.
Flow topologies and turbulence scales in a jet-in-cross-flow
NASA Astrophysics Data System (ADS)
Ruiz, A. M.; Lacaze, G.; Oefelein, J. C.
2015-04-01
This paper presents a detailed analysis of the flow topologies and turbulence scales in the jet-in-cross-flow experiment of Su and Mungal ["Simultaneous measurements of scalar and velocity field evolution in turbulent crossflowing jets," J. Fluid Mech. 513(1), 1-45 (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.
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.
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 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.
Constitutive Law and Flow Mechanism in Diamond Deformation
Yu, Xiaohui; Raterron, Paul; Zhang, Jianzhong; Lin, Zhijun; Wang, Liping; Zhao, Yusheng
2012-01-01
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. Here 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. At high temperature the plastic deformation and ductile flow is meditated by the <110>{111} dislocation glide and a very active {111} micro-twinning. PMID:23166859
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.
Shape of gas flow paths causes power law tailing
NASA Astrophysics Data System (ADS)
Kawanishi, T.; Sakami, A.; Hayashi, Y.
2004-12-01
In soil and/or groundwater remediation, we often see prolonged tailings: continuous outflow of low concentration pollutants for very long time, and in many cases power low behavior of late-time time-concentration curves. We considered that this kind of tailing can be caused by the shape of the gaseous flow introduced in saturated/unsaturated porous media. When gas is introduced to porous media, like air-sparging or soil vapor extraction, the shape of the gas flow path would be tree-like, or to some extent "fractal." So, there would be a distribution of the distance that a solute would have to travel by diffusion before getting to a gas/water interface, and we might expect that the distribution of this "diffusion distance" would be power-law-like. In order to see if tailing can be caused by this mechanism, simple column experiments were carried out. A column, 64 mm in inner diameter and 240 mm in height, was prepared and was packed with 1mm diameter glass beads. Nitrogen gas containing 5 % CO2 and 5% He was supplied from the bottom of the column, and after the water in the column is approximately saturated with CO2, the sparging gas was changed to pure nitrogen. The CO2 and He concentrations in the effluent gas was monitored and recorded. As the result, we saw tailing: the double-log plots of the concentration vs. time relationship was practically linear, and the absolute value of the slope in the double-log charts were 1.28, 0.95 and 0.83 according to the gas flow rates of 40, 80 and 120 ml/min, respectively. Slope less than 1.00 showed that these tailings cannot be explained by Freundlich-type adsorption behavior. Model analysis showed that this power low time-concentration behavior with the slope of approximately -1.0 can be explained by the power law distribution of diffusion distance \\textit{a} with PDF p(\\textit{a}) proportional to \\textit{a}^{-1}.
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. PMID:26655146
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.
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.
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
Scaling of Fluid Flow and Seismic Stiffness of Fractures
NASA Astrophysics Data System (ADS)
Petrovitch, C.; Nolte, D.; Pyrak-Nolte, L. J.
2011-12-01
computed using the "cubic law." Fractures were generated at five sizes (1, 0.5, 0.25, 0.125, and 0.0625m) to provide an order of magnitude variation. Each fracture was constructed such that the contact area ranged from approximately 5% to 30%. The rocks were given the properties of granite and stressed to a maximum load of 70MPa. The deformation solver was given 50 steps to reach the final load so that its flow rate could be monitored during each loading step. The results clearly showed a dependence on scale. Under low loads flow-stiffness was in an effective medium regime. However as the load increased, a distinct scale dependence emerged. This occurs because as the load increases there is an overall increase in contact area, which in turn moves the flow dynamics into a critical regime. From this finite size scaling effect, we analyzed how the uncorrelated topologies length scales changed under load to compute the flow exponents for the system. Acknowledgments: Geosciences Research Program, Office of Basic Energy Sciences US Department of Energy (DE-FG02-09ER16022), the Geo-mathematical Imaging Group at Purdue University, and the Purdue Research Foundation.
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 laws of van Hove singularities in twisted bilayer graphene
NASA Astrophysics Data System (ADS)
Jung, Jeil; Dasilva, Ashley; Wang, Yang; Wong, Dillon; Crommie, Michael; Adam, Shaffique; MacDonald, Allan H.
2014-03-01
Van Hove singularities (vHS) appear in twisted coupled bilayer graphene at saddle points in the band structure. The lowest energy vHS can be associated with the overlap between the displaced Dirac cones of the top and bottom layers, resulting in an approximately linear increase of its position in energy with increasing twist angle. This picture, which is applicable in the perturbative regime for moderately large twist angles, sees departures in the small angle limit due to non-perturbative coupling between the layers. Using a theory for twisted bilayer graphene [1] that incorporates all the relevant interlayer coupling compatible with momentum conservation of k-vectors of the top and bottom layers we explore the scaling laws of the vHS for sufficiently small twist angles and long period moire superlattices. We analyze the localization properties of their wave functions through their local density of states (LDOS) paying particular attention to the behavior of the states corresponding to higher energy van Hove singularities. We comment on our results in light of the experimental DOS and LDOS maps obtained through scanning tunneling microscopy. This work is supported by the Singapore National Research Foundation under its Fellowship program (NRF-NRFF2012-01).
Combined Scaling of Fluid Flow and Seismic Stiffness in Single Fractures
NASA Astrophysics Data System (ADS)
Petrovitch, C. L.; Pyrak-Nolte, L. J.; Nolte, D. D.
2014-09-01
The connection between fluid flow and seismic stiffness in single fractures is governed by the geometry of the fracture through the size and spatial distributions of the void and contact areas. Flow and stiffness each exhibit scaling behavior as the scale of observation shifts from local to global sample sizes. The purpose of this study was to explore the joint scaling of both properties using numerical models. Finite-size scaling methods are used to extract critical thresholds and power laws for fluid flow through weakly correlated fractures under increasing load. An important element in the numerical fracture deformation is the use of extended boundary conditions that simulate differences between laboratory cores relative to in situ field studies. The simulated field conditions enable joint scaling of flow and stiffness to emerge with the potential to extrapolate from small laboratory samples to behavior on the field scale.
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. PMID:18517510
A universal scaling law for the evolution of granular gases
NASA Astrophysics Data System (ADS)
Hummel, Mathias; Clewett, James P. D.; Mazza, Marco G.
2016-04-01
Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier-Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of O(1) . Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters.
A universal scaling law for the evolution of granular gases
NASA Astrophysics Data System (ADS)
Hummel, Mathias; Clewett, James; Mazza, Marco G.
Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier-Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of O(1). Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters.
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.
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.
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
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
Modeling of Building Scale Flow and Dispersion
Lee, R L; Calhoun, R J; Chan, S T; Leone, J; Stevens, D E
2001-07-10
Predictions of airflows around buildings and the associated thermal and dispersion phenomena continue to be challenging because of the presence of extremely heterogeneous surface structures within urban areas. Atmospheric conditions can induce local winds to flow around structures rather than over them. Thus pollutants that are released at or near the ground tend to persist at relatively low levels with only minimal ventilation of the airborne material away from the ground surface. While flow and dispersion phenomena can be studied within wind tunnel settings, recent advances in numerical modeling have enabled computational fluid dynamics (CFD) to evolve into an important tool in the simulation of building scale flows. They are developing numerical models to simulate the flow and dispersion of releases around multi-building complexes. These models will be used to assess the transport and fate of releases of hazardous agents within urban areas and to support emergency response activities. There are already a number of models that have been developed to simulate flow and dispersion around urban settings. A recent collection of these papers can be found in the Proceedings of the International Workshop on CFD for Wind Climate in Cities. Most of the simulation studies presented in the literature are based on single buildings with a few of these results compared with wind tunnel experiments. As the applications become more advanced, the influence of multiple buildings, vegetation, surface heating and atmospheric stability on flow and dispersion has begun to be incorporated into recent CFD models. The focus of this paper is to describe LLNL's effort in the development of a high-performance CFD model for simulating transport and diffusion of hazardous releases around buildings and building complexes. A number of new physics features have been implemented in order to customize the CFD model for the urban application. These include surface heating, vegetation canopy, heat
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.
NASA Astrophysics Data System (ADS)
Poggi, D.; Katul, G. G.; Vidakovic, B.
2011-04-01
The scalar concentration fluctuations within a plane parallel-to-the-ground surface were measured inside a model canopy composed of densely arrayed rods using the laser-induced fluorescence technique. Two-dimensional scalar concentration spectra were computed and were shown to exhibit an approximate -3 power-law scaling at wavenumbers larger than those associated with wake production during quiescent instances when von Karman vortex streets dominated the flow. However, during instances when sweeps disrupted the flow, the spectral exponents increased above -3. The -3 power-law for these concentration fluctuation spectra measurements was shown to be consistent with a simplified spectral budget for locally homogeneous and isotropic turbulence augmented with a relaxation time scale similarity argument that assumed a constant enstrophy injection rate and wake generation mechanism. Hence, the origin of this -3 power-law scaling here differs from the well-known -3 power-law result for the so-called inertial diffusive range derived for the scalar concentration spectrum at small Prandtl numbers.
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.
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. PMID:23401536
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.
Navier wall law for nonstationary viscous incompressible flows
NASA Astrophysics Data System (ADS)
Higaki, Mitsuo
2016-05-01
We study the Navier wall law for the two-dimensional initial boundary value problem of the Navier-Stokes equations in a domain with a rough boundary. The Navier wall law is verified for the initial data in C1 class under the natural compatibility condition. Our proof relies on the boundary layer analysis and the L∞ theory of the Navier-Stokes equations in the half space.
Numerical tests of constitutive laws for dense granular flows.
Lois, Gregg; Lemaître, Anaël; Carlson, Jean M
2005-11-01
We numerically and theoretically study the macroscopic properties of dense, sheared granular materials. In this process we first consider an invariance in Newton's equations, explain how it leads to Bagnold's scaling, and discuss how it relates to the dynamics of granular temperature. Next we implement numerical simulations of granular materials in two different geometries--simple shear and flow down an incline--and show that measurements can be extrapolated from one geometry to the other. Then we observe nonaffine rearrangements of clusters of grains in response to shear strain and show that fundamental observations, which served as a basis for the shear transformation zone (STZ) theory of amorphous solids [M. L. Falk and J. S. Langer, Phys. Rev. E. 57, 7192 (1998); M.R.S. Bull 25, 40 (2000)], can be reproduced in granular materials. Finally we present constitutive equations for granular materials as proposed by Lemaître [Phys. Rev. Lett. 89, 064303 (2002)], based on the dynamics of granular temperature and STZ theory, and show that they match remarkably well with our numerical data from both geometries. PMID:16383599
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.
2016-04-01
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). PMID:26800025
Scaling and Hierarchy of Models for Flow Processes in Unsaturated Fractured Rock
NASA Astrophysics Data System (ADS)
Faybishenko, B.; Bodvarsson, G. S.; Witherspoon, P. A.; Hinds, J.
2002-12-01
A key question facing soil scientists and hydrogeologists is whether, in analyzing flow processes within unsaturated fractured rock with geological discontinuities, the same measurements and models can be used regardless of scale. The goal of this presentation is to illustrate scaling concepts and suggest using a hierarchy of scales in describing the spatial-temporal behavior of unsaturated flow and transport in fractured rock. A conventional scaling approach is valid for liquid permeability of saturated media or air permeability of unsaturated fractured media. We will illustrate that multiscale spatial and temporal variations of flow and transport processes in unsaturated fractured rock are caused by a variety of processes (such as preferential and fast flow, funneling and divergence of flow paths, transient flow behavior, nonlinearity, unstable and chaotic flow, and fracture-matrix interaction). Small-scale intrafracture flow processes are neither physically nor geometrically analogous to large-scale fracture-network processes. As a consequence, scaling laws developed for unsaturated flow through porous media may fail for fractured rocks. To study unsaturated fractured rock, we utilize the concept of a hierarchy of scales: elemental, small, intermediate, and large scales. For each scale, the triadic hierarchical approach requires investigations one level above this scale to determine boundary conditions, and one level below to determine parameters of the equations. Thus, different conceptual approaches are needed for characterization and modeling at different scales. These theoretical concepts are illustrated using the results from field investigations of fractured basalt at the Snake River Plain, Idaho, and fractured tuff at Yucca Mountain, Nevada.
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
Capillary-scale polarimetry for flowing streams.
Swinney, K; Nodorft, J; Bornhop, D J
2001-05-01
A micro-polarimeter with a 40 nL probe volume was configured so that it is compatible with capillary-scale flowing stream analysis. The optical configuration consists of two polarizing optics, a capillary, a laser source and a photodetector which is very simple to configure with low cost components. This unique polarimeter is based upon the interaction of a linearly polarized laser beam and a capillary tube, in this case one with an inner diameter of 250 microns. Side illumination of the tube results in a 360 degrees fan of scattered light, which contains a set of interference fringes that change in response to optically active solutes. Solutes that exhibit optical activity are quantifiable and are detected by analyzing the polarization state of the backscattered light. The ability of the instrument to make extremely sensitive optical activity measurements in flowing streams is shown by the determination of (R)-mandelic acid, with a detection limit of 66 x 10(-6) M (507 x 10(-12) g), and the non-optically active control, glycerol. Additionally, the detector was configured to minimize refractive index perturbations. PMID:11394312
Scaling laws and model of words organization in spoken and written language
NASA Astrophysics Data System (ADS)
Bian, Chunhua; Lin, Ruokuang; Zhang, Xiaoyu; Ma, Qianli D. Y.; Ivanov, Plamen Ch.
2016-01-01
A broad range of complex physical and biological systems exhibits scaling laws. The human language is a complex system of words organization. Studies of written texts have revealed intriguing scaling laws that characterize the frequency of words occurrence, rank of words, and growth in the number of distinct words with text length. While studies have predominantly focused on the language system in its written form, such as books, little attention is given to the structure of spoken language. Here we investigate a database of spoken language transcripts and written texts, and we uncover that words organization in both spoken language and written texts exhibits scaling laws, although with different crossover regimes and scaling exponents. We propose a model that provides insight into words organization in spoken language and written texts, and successfully accounts for all scaling laws empirically observed in both language forms.
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.
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. PMID:24229109
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.
A modified Darcy's law . Large eddy simulation of turbulent flows through a fractal model city
NASA Astrophysics Data System (ADS)
Gisinger, Sonja; Dörnbrack, Andreas; Schröttle, Josef
2015-08-01
An approach to describe the turbulent flow through a complex geometry (e.g., urban area) by means of an analogy to flows through porous media is presented. Therefore, a modification of the original Darcy's law is proposed, and its application is tested in a prototype problem with an idealized complex geometry using large eddy simulations. The numerical results indicate the validity of the modified Darcy's law for the chosen setup.
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.
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.
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. PMID:23940525
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. PMID:26172645
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.
The energy-magnitude scaling law for M s ≤ 5.5 earthquakes
NASA Astrophysics Data System (ADS)
Wang, Jeen-Hwa
2015-04-01
The scaling law of seismic radiation energy, E s , versus surface-wave magnitude, M s , proposed by Gutenberg and Richter (1956) was originally based on earthquakes with M s > 5.5. In this review study, we examine if this law is valid for 0 < M s ≤ 5.5 from earthquakes occurring in different regions. A comparison of the data points of log( E s ) versus M s with Gutenberg and Richter's law leads to a conclusion that the law is still valid for earthquakes with 0 < M s ≤ 5.5.
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.
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.
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.
A flow law for ilmenite in dislocation creep: Implications for lunar cumulate mantle overturn
NASA Astrophysics Data System (ADS)
Dygert, Nick; Hirth, Greg; Liang, Yan
2016-01-01
We present results from new deformation experiments and a dislocation creep flow law for synthetic ilmenite. The flow law predicts an effective viscosity more than 3 orders of magnitude lower than dry olivine at mantle stresses and temperatures. Using the flow law, we predict that lunar ilmenite-bearing cumulates (IBC) will be weakened by the presence of low-viscosity ilmenite. Dense, low-viscosity IBC are expected to flow into the lunar interior by a process known as cumulate mantle overturn. Low-viscosity IBC that sink to the core-mantle boundary may be dynamically stable with respect to upwelling. A hot, stable layer of IBC surrounding the lunar core would suppress the development of a core dynamo. A layer of partially molten IBC can also explain the inferred zone of seismic attenuation around the lunar core, as well as a low-viscosity layer suggested by tidal dissipation.
LETTER: Scaling law for effective heat diffusivity in ELMy H-mode plasmas
NASA Astrophysics Data System (ADS)
Becker, G.
2004-11-01
Transport simulations of high density scenarios of ITER and other reactor-grade devices require a scaling law for the effective heat diffusivity, χ, in the ELMy H-mode regime. A comprehensive empirical scaling, χH98, compatible with the ITER reference scaling, ITERH-98P(y, 2), for the thermal energy confinement time has been set up. It follows from a power law ansatz for χ and integration of the single-fluid energy equation and recovers all the exponents of the global confinement law. The dependences on temperature and temperature gradient are consistent with the power degradation of confinement and the experimental χ profiles. The χH98 scaling is validated by JET, DIII-D, ASDEX Upgrade and ASDEX discharges covering a wide parameter range. Simulations of the inductive scenario of ITER with χH98 yield an energy confinement time which agrees with the global scaling prediction.
Scaling laws in turbulent Rayleigh-Benard convection with different geometry
NASA Astrophysics Data System (ADS)
Song, Hao; Tong, Penger
2009-11-01
The discovery of scaling laws in the heat flux, large-scale circulation and temperature statistics in turbulent convection has stimulated considerable experimental and theoretical efforts, aimed at understanding the universal nature of the observed scaling laws. Because of historical reasons, most of the experimental results were obtained in upright cylindrical cells with small aspect ratios. An important question one might ask is: To what extend are these scaling laws universal in that they are independent of the cell geometry? Understanding of this question has important implications to large-scale astro/geophysical convection, such as that in the atmosphere and oceans, in which boundary effects are less important. In this talk, we report an experimental study of turbulent convection in a horizontal cylinder with the bottom 1/3 (curved) surface heated and the top 1/3 surface cooled. The experiment is carried out with varying aspect ratios and Rayleigh numbers. It is found that the measured Nusselt number and Reynolds number obey the same scaling laws as those obtained in the upright cylinder. The local temperature statistics, on the other hand, change with the aspect ratio of the cell and are different from the earlier results. The experiment reveals important geometric effects of the scaling laws in turbulent convection. *Work supported by the Research Grants Council of Hong Kong SAR.
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. PMID:22164718
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
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
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.
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
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.
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)
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.}
EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE
Mason, Joanne; Cattaneo, Fausto; Perez, Jean Carlos; Boldyrev, Stanislav E-mail: cattaneo@flash.uchicago.edu E-mail: boldyrev@wisc.edu
2011-07-10
Magnetized turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the inertial range of scales. Numerical simulations serve to guide and test these theories. However, the computational power that is currently available restricts the simulations to Reynolds numbers that are significantly smaller than those in astrophysical settings. In order to increase computational efficiency and, therefore, probe a larger range of scales, one often takes into account the fundamental anisotropy of field-guided MHD turbulence, with gradients being much slower in the field-parallel direction. The simulations are then optimized by employing the reduced MHD equations and relaxing the field-parallel numerical resolution. In this work we explore a different possibility. We propose that there exist certain quantities that are remarkably stable with respect to the Reynolds number. As an illustration, we study the alignment angle between the magnetic and velocity fluctuations in MHD turbulence, measured as the ratio of two specially constructed structure functions. We find that the scaling of this ratio can be extended surprisingly well into the regime of relatively low Reynolds number. However, the extended scaling easily becomes spoiled when the dissipation range in the simulations is underresolved. Thus, taking the numerical optimization methods too far can lead to spurious numerical effects and erroneous representation of the physics of MHD turbulence, which in turn can affect our ability to identify correctly the physical mechanisms that are operating in astrophysical systems.
Hou, Chen
2016-01-01
Complementary to Gowdy & Krall's comparison between ants and humans, I use economy scaling laws to discuss the similarity and difference between them quantitatively. I hypothesize that individual variations in society result in higher energetic efficiency in larger groups, and that the difference in the sustainability between these species originates from the driving forces of growth with different scaling powers. PMID:27562828
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.
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. PMID:15563403
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.
Stability of a Resonant System of Conservation Laws Modeling Polymer Flow with Gravitation
NASA Astrophysics Data System (ADS)
Klingenberg, Christian; Risebro, Nils Henrik
2001-03-01
We prove L1 uniqueness and stability for a resonant 2×2 system of conservation laws that arise as a model for two phase polymer flow in porous media. The analysis uses the equivalence of the Eulerian and Lagrangian formulation of this system, and the results are first established for an auxiliary scalar equation. Our methods are based on front tracking approximations for the auxiliary equation, and the Kružkov entropy condition for scalar conservation laws.
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
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.
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.
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
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.
Sub-diffusive scaling with power-law trapping times
NASA Astrophysics Data System (ADS)
Luo, Liang; Tang, Lei-Han
2014-07-01
Thermally driven diffusive motion of a particle underlies many physical and biological processes. In the presence of traps and obstacles, the spread of the particle is substantially impeded, leading to subdiffusive scaling at long times. The statistical mechanical treatment of diffusion in a disordered environment is often quite involved. In this short review, we present a simple and unified view of the many quantitative results on anomalous diffusion in the literature, including the scaling of the diffusion front and the mean first-passage time. Various analytic calculations and physical arguments are examined to highlight the role of dimensionality, energy landscape, and rare events in affecting the particle trajectory statistics. The general understanding that emerges will aid the interpretation of relevant experimental and simulation results.
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.
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 Technical Reports Server (NTRS)
Holsapple, K. A.; Housen, K. R.
1986-01-01
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).
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.
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. PMID:26232981
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 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.
An anisotropic flow law for incompressible polycrystalline materials
NASA Astrophysics Data System (ADS)
Placidi, Luca; Hutter, Kolumban
2005-11-01
New and explicit anisotropic constitutive equations between the stretching and deviatoric stress tensors for the two- and three-dimensional cases of incompressible polycrystalline materials are presented. The anisotropy is assumed to be driven by an Orientation Distribution Function (ODF). The polycrystal is composed of transversally isotropic crystallites, the lattice orientation of which can be characterized by a single unit vector. The proposed constitutive equations are valid for any frame of reference and for every state of deformation. The basic assumption of this method is that the principle directions of the stretching and of the stress deviator are the same in the isotropic as well as in the anisotropic case. This means that the proposed constitutive laws are able to model the effects of anisotropy only via a change of the fluidity due to a change of the ODF. Such an assumption is justified to guarantee that, besides knowledge of the parameters involved in the isotropic constitutive equation, the anisotropic material response is completely characterized by only one additional parameter, a type of enhancement factor. Explicit comparisons with experimental data are conducted for Ih ice.
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.
Ising ferromagnet on a fractal family: Thermodynamical functions and scaling laws
NASA Astrophysics Data System (ADS)
Redinz, José Arnaldo; de Magalhães, Aglaé C. N.
1995-02-01
The Ising model with external magnetic field on infinitely ramified fractal lattices is studied. We derive exact expressions for the specific heat, spontaneous magnetization, and susceptibility. The critical exponents α, β, and γ corresponding to these respective thermal functions (at zero field) as well as the correlation length critical exponent ν are obtained. The hyperscaling law extended to fractals and the Rushbrooke scaling law are verified for these fractals.
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
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
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.
Slow-Slip Scaling Laws Inferred from Cascadia Tremor Swarms
NASA Astrophysics Data System (ADS)
Creager, K. C.; Wech, A.; Vidale, J. E.
2010-12-01
Episodic tremor and slip (ETS) events, each with geodetically determined moment magnitudes in the mid-6 range, repeat about every 15 months under the Olympic Peninsula/southern Vancouver Island region. We have applied an automatic waveform envelope cross-correlation and clustering (WECC) algorithm to seven Cascadia-wide subarrays to search for non-volcanic tremor in 5-minute, 50% overlapping, time windows, revealing 70,000 tremor epicenters. The tremor epicenters cluster in time and space into nearly 200 tremor swarms. The number of hours of tremor per swarm ranges from about 1 to 470 hours. The smaller (inter-ETS) tremor swarms generally locate along the downdip side of the larger ETS swarms and occur much more frequently. In northern Washington, which is currently best monitored, the ETS events, as well as the larger inter-ETS tremor swarms initiate downdip and propagate updip. For the large ETS events, tremor swarm duration is proportional to geodetically determined seismic moment. We consider tremor swarms to be a proxy for slow slip for the smaller events as well, even though slip would be below current geodetic detection thresholds. An interpretation of the observed transition from longer duration, less frequent tremor swarms up dip to smaller more frequent tremor swarms down-dip, in terms of fault strength is the subject of a presentation by Wech. The combined inter-ETS and ETS swarms follow a power law relationship such that the number of swarms, N, exceeding duration τ is given by τ -0.66. If we assume that seismic moment is proportional to τ, as proposed by Ide et al. [Nature, 2007], we find that the tremor swarms follow a standard Gutenberg-Richter logarithmic frequency-magnitude relation, log10 N ≈ -bMw, with b = 1.0, which lies in the range for normal earthquake catalogs. Finally, crude estimates of the spatial dimensions of tremor swarms L suggest that L ≈ τ 1/n where n is between 2 and 3. A value of 2 is consistent with slip propagation rates
Power law scaling in synchronization of brain signals depends on cognitive load
Tinker, Jesse; Velazquez, Jose Luis Perez
2014-01-01
As it has several features that optimize information processing, it has been proposed that criticality governs the dynamics of nervous system activity. Indications of such dynamics have been reported for a variety of in vitro and in vivo recordings, ranging from in vitro slice electrophysiology to human functional magnetic resonance imaging. However, there still remains considerable debate as to whether the brain actually operates close to criticality or in another governing state such as stochastic or oscillatory dynamics. A tool used to investigate the criticality of nervous system data is the inspection of power-law distributions. Although the findings are controversial, such power-law scaling has been found in different types of recordings. Here, we studied whether there is a power law scaling in the distribution of the phase synchronization derived from magnetoencephalographic recordings during executive function tasks performed by children with and without autism. Characterizing the brain dynamics that is different between autistic and non-autistic individuals is important in order to find differences that could either aid diagnosis or provide insights as to possible therapeutic interventions in autism. We report in this study that power law scaling in the distributions of a phase synchrony index is not very common and its frequency of occurrence is similar in the control and the autism group. In addition, power law scaling tends to diminish with increased cognitive load (difficulty or engagement in the task). There were indications of changes in the probability distribution functions for the phase synchrony that were associated with a transition from power law scaling to lack of power law (or vice versa), which suggests the presence of phenomenological bifurcations in brain dynamics associated with cognitive load. Hence, brain dynamics may fluctuate between criticality and other regimes depending upon context and behaviors. PMID:24822039
Second law analysis of water flow through smooth microtubes under adiabatic conditions
Parlak, Nezaket; Guer, Mesut; Ari, Vedat; Kuecuek, Hasan; Engin, Tahsin
2011-01-15
In the study, a second law analysis for a steady-laminar flow of water in adiabatic microtubes has been conducted. Smooth microtubes with the diameters between 50 and 150 {mu}m made of fused silica were used in the experiments. Considerable temperature rises due to viscous dissipation and relatively high pressure losses of flow were observed in experiments. To identify irreversibility of flow, rate of entropy generation from the experiments have been determined in the laminar flow range of Re = 20-2200. The second law of thermodynamics was applied to predict the entropy generation. The results of model taken from the literature, proposed to predict the temperature rise caused by viscous heating, correspond well with the experimental data. The second law analysis results showed that the flow characteristics in the smooth microtubes distinguish substantially from the conventional theory for flow in the larger tubes with respect to viscous heating/dissipation (temperature rise of flow) total entropy generation rate and lost work. (author)
Evidence of power-law flow in the Mojave desert mantle.
Freed, Andrew M; Bürgmann, Roland
2004-07-29
Studies of the Earth's response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress-strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine--the most abundant mineral in the upper mantle--and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust. PMID:15282602
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. PMID:25618613
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.
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. PMID:25493885
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.
NASA Astrophysics Data System (ADS)
Luginsland, J. W.; Lau, Y. Y.; Umstattd, R. J.; Watrous, J. J.
2002-05-01
Space-charge-limited (SCL) flows in diodes have been an area of active research since the pioneering work of Child and Langmuir in the early part of the last century. Indeed, the scaling of current density with the voltage to the 3/2's power is one of the best-known limits in the fields of non-neutral plasma physics, accelerator physics, sheath physics, vacuum electronics, and high power microwaves. In the past five years, there has been renewed interest in the physics and characteristics of SCL emission in physically realizable configurations. This research has focused on characterizing the current and current density enhancement possible from two- and three-dimensional geometries, such as field-emitting arrays. In 1996, computational efforts led to the development of a scaling law that described the increased current drawn due to two-dimensional effects. Recently, this scaling has been analytically derived from first principles. In parallel efforts, computational work has characterized the edge enhancement of the current density, leading to a better understanding of the physics of explosive emission cathodes. In this paper, the analytic and computational extensions to the one-dimensional Child-Langmuir law will be reviewed, the accuracy of SCL emission algorithms will be assessed, and the experimental implications of multidimensional SCL flows will be discussed.
Vortex clustering and universal scaling laws in two-dimensional quantum turbulence
NASA Astrophysics Data System (ADS)
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.
A phase-field study of the scaling law in free-standing ferroelectric thin films
NASA Astrophysics Data System (ADS)
Yin, Binglun; Mao, Huina; Qu, Shaoxing
2015-12-01
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.
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. PMID:26580133
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.
Scaling law for the dissolution of phenolic resins in aqueous base
NASA Astrophysics Data System (ADS)
Yeh, Tung-Feng; Reiser, Arnost; Dammel, Ralph R.; Pawlowski, Georg; Roeschert, Horst
1993-09-01
A scaling law derived from percolation theory for the dissolution of phenolic resins in aqueous base is tested and confirmed on seven groups of amphiphilic resins. The scaling law can be presented in the dimensionless form: log(R/R1) equals 2 log[(p - pc)/(1 - pc)]. Here R and R1 are the dissolution rates of the resin and of a standard resin for which p equals 1, the percolation parameter, p, linked to the concentration of hydrophilic sites (OH-groups) in the material, and pc is the percolation threshold below which dissolution no longer occurs. In the group of resins of this study Pc equals 0.20. In its dimensionless form the scaling law provides a single function which applies to all resins of this study and, we believe, to amphiphilic resins in general. This allows the prediction of dissolution rates and the selection of polymer structures which are likely to have specified dissolution kinetics.
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.
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
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.
NASA Astrophysics Data System (ADS)
Krajewska, K.; Kamiński, J. Z.
2014-11-01
The distributions of Compton and Thomson radiation for a shaped laser pulse colliding with a free electron are calculated in the framework of quantum and classical electrodynamics, respectively. We introduce a scaling law for the Compton and the Thomson frequency distributions which universally applies to long and short incident pulses. Thus, we extend the validity of frequency scaling postulated in previous studies comparing nonlinear Compton and Thomson processes. The scaling law introduced in this paper relates the Compton no-spin flipping process to the Thomson process over nearly the entire spectrum of emitted radiation, including its high-energy portion. By applying the frequency scaling, we identify that both spin and polarization effects are responsible for differences between classical and quantum results. The same frequency scaling applies to angular distributions and to temporal power distributions of emitted radiation, which we illustrate numerically.
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
2009-08-01
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. PMID:19792547
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.
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.
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.
Scaling Laws of Lissajous Helicon Plasma Accelerator toward Electric Propulsion in Space
NASA Astrophysics Data System (ADS)
Funaki, Ikkou; Matsuoka, T.; Nakamura, T.; Yokoi, K.; Nishida, H.; Shamrai, K. P.; Tanikawa, T.; Hada, T.; Shinohara, S.
2010-11-01
Scaling law of Lissajous Helicon Plasma Accelerator(LHPA) is derived and tested via PIC simulations with code VORPAL. In the LHPA, rotating transverse electric field in external longitudinal uniform magnetic field drives azimuthal current via ExB drift then thrust is produced due to Lorentz force. An 1D analytical model is developed which includes field penetration and ExB current estimation based on trajectory analysis. Scaling law of thrust as a function of parameters of RF drive frequency, applied RF voltage, plasma density, size of the thruster will be shown.
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.
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|
Scaling law for the Lyapunov spectra in globally coupled tent maps
NASA Astrophysics Data System (ADS)
Morita, Satoru
1998-10-01
The collective motions in globally coupled tent maps are investigated in terms of Lyapunov spectra. The scattered states are separated into two distinct phases by the characteristics of the Lyapunov spectra. In the weak-coupling phase, the Lyapunov spectra obey a scaling law with varying system size. This scaling law holds even in the strong-coupling phase except for the singular property of the largest Lyapunov exponent. The Lyapunov exponents are estimated theoretically by using the random field approximation. These approximate results reveal the relation between the Lyapunov exponents and the distribution of the elements. Furthermore, the features of the band structure in the distribution are explored.
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.
Muliadi, Ariel R; Sojka, Paul E
2012-06-01
Spatially resolved drop size, drop velocity, and spray volume flux measurements for sprays produced by a commonly used pharmaceutical coating nozzle were performed in this study. Results showed three distinctive spray patterns: Gaussian, homogeneous, and dumbbell shaped. We found that transition from a dumbbell-shaped to a homogeneous pattern is related to the shaping air-induced breakup of already formed drops: depending on the drop size upstream of the location where the shaping air flows meet (i.e., the "junction" point), the drop viscosity, and the magnitude of the shaping air velocity, the shaping air can either pinch the spray or cause additional drop breakup. When the former outweighs the latter, the dumbbell-shaped pattern occurs; the homogeneous pattern is present when the opposite occurs. A corollary to this experimental interpretation is that whether additional drop breakup homogenizes the sprays or pinches, it is related to a Weber number (We) that is calculated using drop sizes upstream of the junction point, drop viscosity and surface tension, and the shaping air velocity at the junction point. With this idea in mind, we propose a We-based scaling method for optimizing the uniformity of air-assist spray patterns. PMID:22418943
NASA Astrophysics Data System (ADS)
LEVY, C.; Mangeney, A.; Hibert, C.; Bonilla, F.; Calder, E. S.; Smith, P. J.; Cole, P. D.
2013-12-01
Seismic signals associated with rockfalls can provide important information on the characteristics of the source (volume, duration, location). As such, seismic data from the Piton de la Fournaise volcano were used to evidence a scaling law between the energy dissipated as seismic waves and the duration of granular flows (Hilbert et al., 2011, doi:10.1029/2011JF002038). This study was completed by analytical analysis and numerical simulations showing that a similar scaling law exists between the loss of potential energy of an event and the duration of its propagation phase. Thus, this previous study shows that the coefficient of this scaling law is a strong indicator of the effect of topography on the flow dynamics. Morever, this study was used to estimate the volumes of granular flows using seismic records and to constitute databases of rockfall characteristics (volume, location, and occurrence time) in order to study the relationship between rockfall activity and processes related to volcanic activity. Our study aims to test whether a similar scaling law can be observed at the Soufiere Hills Volcano (Montserrat Island, Lesser Antilles) despite differences of settings: -at Piton de la Fournaise, most rockfalls propagate from one side of the Dolomieu crater to its center, whereas at the Soufière Hills volcano, they spread from the dome to the sea shore. -the properties of constituting rocks is quite different. The Piton de la Fournaise is a shield volcano, whereas the Soufrière is an andesitic volcano. The signal processing developed for the data of Piton de la Fournaise was applied to the seismic data of a 3 days crisis with 200 rockfalls and pyroclastic flows at the Soufière Hills volcano. A similar scaling law between seismic energy and potential energy was found. This result suggests that such study could be relevant at a more general level. Later on, the computation of the seismic energy was enhanced using frequency dependent parameters (anelastic
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.
An exact thermodynamical model of power-law temperature time scaling
NASA Astrophysics Data System (ADS)
Zingales, Massimiliano
2016-02-01
In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t) ∝tβ with β ∈ R shows a different evolution of the temperature time rate T ˙ (t) with respect to the temperature time-dependence T(t) . Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the thermal energy flux as soon as the distance increases. In this paper this idea has been exploited showing that such thermodynamical system is represented by an heterogeneous one-dimensional distributed mass one with power-law spatial scaling of its physical properties. The model yields, exactly a power-law evolution (decay) of the temperature field in terms of a real exponent as T ∝tβ (or T ∝t-β) that is related to the power-law spatial scaling of the thermodynamical property of the system. The obtained relation yields a physical ground to the formulation of fractional-order generalization of the Fourier diffusion equation.
NASA Astrophysics Data System (ADS)
v., V.; Porte-Agel, F.; Heuer, W.; Marusic, I.
2007-05-01
In this study, we analyse simultaneous measurements (at 50 Hz) of velocity at several heights and shear stress at the surface made during the Utah field campaign for the presence of ranges of scales, where distinct scale-to-scale interactions between velocity and shear stress can be identified. We find that our results are similar to those obtained in a previous study [Venugopal et al., 2003] (contrary to the claim in V2003, that the scaling relations might be dependent on Reynolds number) where wind tunnel measurements of velocity and shear stress were analysed. We use a wavelet-based scale-to-scale cross-correlation to detect three ranges of scales of interaction between velocity and shear stress, namely, (a) inertial subrange, where the correlation is negligible; (b) energy production range, where the correlation follows a logarithmic law; and (c) for scales larger than the boundary layer height, the correlation reaches a plateau.
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.).
Non-Cubic Power-law Scaling of Density in Metallic Glasses (Invited)
NASA Astrophysics Data System (ADS)
Zeng, Q. C.; Kono, Y.; Lin, Y.; Zeng, Z.; Wang, J.; Sinogeikin, S. V.; Park, C.; Meng, Y.; Yang, W.; Mao, W. L.
2013-12-01
Understanding structure-property relationships and dimensionality plays a central role in materials science. A cubic power law relationship between the average interatomic distance and the global density is commonly expected in 'disordered' glasses and has been extensively employed in various measurements. However, this relationship has never been rigorously verified which challenges our understanding of glass materials. Here, by using high pressure as a tuning tool, we rigorously demonstrated that the density of metallic glass (MG) varies with the 2.5 power of its fundamental atomic-level length scale (the inverse of the principal diffraction peak position, 1/q1). This falls between the 3-dimensional density and 1-dimensional length instead of the expected cubic power-law relationship. We further demonstrated the 2.5 power-law is universally valid for MGs of different compositions, as well as the same MG at different pressures. This study includes high quality data from multiple techniques which provides compelling evidence of the non-cubic power-law scaling in MGs. It has important implications not only in the practical measurements of density, or any measurement involving a change in length scale under various environments by correcting the extensively employed cubic power-law, but also in understanding the real atomic packing in glasses by providing a critical new constraint on a structure-property relationship.
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. PMID:15600971
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)
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
Kolmogorov spectrum consistent optimization for multi-scale flow decomposition
NASA Astrophysics Data System (ADS)
Mishra, M.; Liu, X.; Skote, M.; Fu, C.-W.
2014-05-01
Multi-scale analysis is widely adopted in turbulence research for studying flow structures corresponding to specific length scales in the Kolmogorov spectrum. In the present work, a new methodology based on novel optimization techniques for scale decomposition is introduced, which leads to a bandpass filter with prescribed properties. With this filter, we can efficiently perform scale decomposition using Fourier transform directly while adequately suppressing Gibbs ringing artifacts. Both 2D and 3D scale decomposition results are presented, together with qualitative and quantitative analysis. The comparison with existing multi-scale analysis technique is conducted to verify the effectiveness of our method. Validation of this decomposition technique is demonstrated both qualitatively and quantitatively. The advantage of the proposed methodology enables a precise specification of continuous length scales while preserving the original structures. These unique features of the proposed methodology may provide future insights into the evolution of turbulent flow structures.
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
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.
Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media
NASA Astrophysics Data System (ADS)
Tan, Xiao-Hua; Li, Xiao-Ping; Zhang, Lie-Hui; Liu, Jian-Yi; Cai, Jianchao
2015-09-01
A transient flow model for power-law fluid in fractal porous media is derived by combining transient flow theory with the fractal properties of tortuous capillaries. Pressure changes of transient flow for power-law fluid in fractal porous media are related to pore fractal dimension, tortuosity fractal dimension and the power-law index. Additionally, the starting pressure gradient model of power-law fluid in fractal porous media is established. Good agreement between the predictions of the present model and that of the traditional empirical model is obtained, the sensitive parameters that influence the starting pressure gradient are specified and their effects on the starting pressure gradient are discussed.
Two-phase power-law modeling of pipe flows displaying shear-thinning phenomena
Ding, Jianmin; Lyczkowski, R.W.; Sha, W.T.
1993-12-31
This paper describes work in modeling concentrated liquid-solids flows in pipes. COMMIX-M, a three-dimensional transient and steady-state computer program developed at Argonne National Laboratory, was used to compute velocities and concentrations. Based on the authors` previous analyses, some concentrated liquid-solids suspension flows display shear-thinning rather than Newtonian phenomena. Therefore, they developed a two-phase non-Newtonian power-law model that includes the effect of solids concentration on solids viscosity. With this new two-phase power-law solids-viscosity model, and with constitutive relationships for interfacial drag, virtual mass effect, shear lift force, and solids partial-slip boundary condition at the pipe walls, COMMIX-M is capable of analyzing concentrated three-dimensional liquid-solids flows.
Are scaling laws on strength of solids related to mechanics or to geometry?
Carpinteri, Alberto; Pugno, Nicola
2005-06-01
One of the largest controversial issues of the materials science community is the interpretation of scaling laws on material strength. In spite of the prevailing view, which considers mechanics as the real cause of such effects, here, we propose a different argument, purely based on geometry. Thus, as happened for relativity, geometry could again hold an unexpected and fundamental role. PMID:15928689
Scaling laws for collisionless laser-plasma interactions of relevance for laboratory astrophysics
Ryutov, D D; Rermington, B A
2006-04-04
Scaling laws for interaction of ultra-intense laser beams with a collisionless plasmas are discussed. Special attention is paid to the problem of the collective ion acceleration. Symmetry arguments in application to the generation of the poloidal magnetic field are presented. A heuristic model for evaluating the magnetic field strength is proposed.
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…
NASA Astrophysics Data System (ADS)
Meheust, Y.; De Dreuzy, J.; Pichot, G.
2011-12-01
Flow channeling and permeability scaling in fractured media have been classically addressed either at the fracture- or at the network- scales. In the latter case they are linked to the topological structure of the network, while at the fracture scale they are controlled by the variability of the local aperture distribution inside individual fractures. In this study we analyze these two combined effects, investigating how flow localization below the scale of individual fractures influences that at the network scale and the resulting medium permeability. This is done by use of a new highly-resolved 3D discrete fracture network model (DFN). The local apertures of individual fractures are distributed according to a truncated Gaussian law, and exhibit self-affine spatial correlations that are bounded by an upper cutoff scale Lc; Lc and the fracture closure, defined as the ratio of the aperture fluctuations at scale Lc to the mean aperture, are considered homogeneous over the DFN. The network topology is controlled by a homogeneous scalar fracture density and a power law fracture length distribution. We have varied these features to investigate a large variety of DFN topologies, from sparse networks with varying degrees of fracture interconnections, flow bottlenecks and dead-ends (Fig. 1a), to dense well-connected networks (Fig. 1b). We have also investigated a large range of fracture closures, performing extensive simulations of about 105 different DFN realizations. At the fracture scale, accounting for local aperture fluctuations leads to a monotical deviation (which can exceed 50%) of the equivalent fracture transmissivity from the parallel plate behavior. At the network scale we observe a complex interaction between flow channeling within fracture planes and flow localization in the network. This interaction is controlled by the location of fracture interactions with respect to that of low local transmissivity zones (particularly the closed zones), in the fracture
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
2014-01-01
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. PMID:25267617
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. PMID:25267617
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.
NASA Astrophysics Data System (ADS)
Festa, Gaetano; Vilotte, Jean-Pierre; Raous, Michel; Henninger, Carole
2010-05-01
Propagation and radiation of an earthquake rupture is commonly considered as a friction dominated process on fault surfaces. Friction laws, such as the slip weakening and the rate-and-state laws are widely used in the modeling of the earthquake rupture process. These laws prescribe the traction evolution versus slip, slip rate and potentially other internal variables. They introduce a finite cohesive length scale over which the fracture energy is released. However faults are finite-width interfaces with complex internal structures, characterized by highly damaged zones embedding a very thin principal slip interface where most of the dynamic slip localizes. Even though the rupture process is generally investigated at wavelengths larger than the fault zone thickness, which should justify a formulation based upon surface energy, a consistent homogeneization, a very challenging problem, is still missing. Such homogeneization is however be required to derive the consistent form of an effective interface law, as well as the appropriate physical variables and length scales, to correctly describe the coarse-grained dissipation resulting from surface and volumetric contributions at the scale of the fault zone. In this study, we investigate a scale-dependent law, introduced by Raous et al. (1999) in the context of adhesive material interfaces, that takes into account the transition between a damage dominated and a friction dominated state. Such a phase-field formalism describes this transition through an order parameter. We first compare this law to standard slip weakening friction law in terms of the rupture nucleation. The problem is analyzed through the representation of the solution of the quasi-static elastic problem onto the Chebyshev polynomial basis, generalizing the Uenishi-Rice solution. The nucleation solutions, at the onset of instability, are then introduced as initial conditions for the study of the dynamic rupture propagation, in the case of in-plane rupture
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
Study on law of negative corona discharge in microparticle-air two-phase flow media
NASA Astrophysics Data System (ADS)
He, Bo; Li, Tianwei; Xiu, Yaping; Zhao, Heng; Peng, Zongren; Meng, Yongpeng
2016-03-01
To study the basic law of negative corona discharge in solid particle-air two-phase flow, corona discharge experiments in a needle-plate electrode system at different voltage levels and different wind speed were carried out in the wind tunnel. In this paper, the change law of average current and current waveform were analyzed, and the observed phenomena were systematically explained from the perspectives of airflow, particle charging, and particle motion with the help of PIV (particle image velocity) measurements and ultraviolet observations.
Conservation laws for steady flow and solitons in a multifluid plasma revisited
Mace, R. L.; McKenzie, J. F.; Webb, G. M.
2007-01-15
The conservation laws used in constructing the governing equations for planar solitons in multifluid plasmas are revisited. In particular, the concept of generalized vorticity facilitates the derivation of some general ''Bernoulli theorems,'' which reduce, in specific instances, to conservation laws previously deduced by other means. These theorems clarify the underlying physical principles that give rise to the conserved quantities. As an example of the usefulness of the techniques, even for relatively simple flows and progressive waves, the equations governing stationary nonlinear whistler waves propagating parallel to an ambient magnetic field are derived using generalized vorticity concepts.
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
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 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.
Analysis of the time scales in time periodic Darcy flows
NASA Astrophysics Data System (ADS)
Zhu, T.; Waluga, C.; Wohlmuth, B.; Manhart, M.
2014-12-01
We investigate unsteady flow in a porous medium under time - periodic (sinusoidal) pressure gradient. DNS were performed to benchmark the analytical solution of the unsteady Darcy equation with two different expressions of the time scale : one given by a consistent volume averaging of the Navier - Stokes equation [1] with a steady state closure for the flow resistance term, another given by volume averaging of the kinetic energy equation [2] with a closure for the dissipation rate . For small and medium frequencies, the analytical solutions with the time scale obtained by the energy approach compare well with the DNS results in terms of amplitude and phase lag. For large frequencies (f > 100 [Hz]) we observe a slightly smaller damping of the amplitude. This study supports the use of the unsteady form of Darcy's equation with constant coefficients to solve time - periodic Darcy flows at low and medium frequencies. Our DNS simulations, however, indicate that the time scale predicted by the VANS approach together with a steady - state closure for the flow resistance term is too small. The one obtained by the energy approach matches the DNS results well. At large frequencies, the amplitudes deviate slightly from the analytical solution of the unsteady Darcy equation. Note that at those high frequencies, the flow amplitudes remain below 1% of those of steady state flow. This result indicates that unsteady porous media flow can approximately be described by the unsteady Darcy equation with constant coefficients for a large range of frequencies, provided, the proper time scale has been found.
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
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.
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
Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows
NASA Astrophysics Data System (ADS)
Wei, Liang; Elsinga, Gerrit E.; Brethouwer, Geert; Schlatter, Philipp; Johansson, Arne V.
2014-03-01
The Reynolds number scaling of flow topology in the eigenframe of the strain-rate tensor is investigated for wall-bounded flows, which is motivated by earlier works showing that such topologies appear to be qualitatively universal across turbulent flows. The databases used in the current study are from direct numerical simulations (DNS) of fully developed turbulent channel flow (TCF) up to friction Reynolds number Reτ ≈ 1500, and a spatially developing, zero-pressure-gradient turbulent boundary layer (TBL) up to Reθ ≈ 4300 (Reτ ≈ 1400). It is found that for TCF and TBL at different Reynolds numbers, the averaged flow patterns in the local strain-rate eigenframe appear the same consisting of a pair of co-rotating vortices embedded in a finite-size shear layer. It is found that the core of the shear layer associated with the intense vorticity region scales on the Kolmogorov length scale, while the overall height of the shear layer and the distance between the vortices scale well with the Taylor micro scale. Moreover, the Taylor micro scale collapses the height of the shear layer in the direction of the vorticity stretching. The outer region of the averaged flow patterns approximately scales with the macro scale, which indicates that the flow patterns outside of the shear layer mainly are determined by large scales. The strength of the shear layer in terms of the peak tangential velocity appears to scale with a mixture of the Kolmogorov velocity and root-mean-square of the streamwise velocity scaling. A quantitative universality in the reported shear layers is observed across both wall-bounded flows for locations above the buffer region.
Extended power-law scaling of heavy-tailed random fields or processes
NASA Astrophysics Data System (ADS)
Guadagnini, A.; Riva, M.; Neuman, S. P.
2012-06-01
We analyze the scaling behaviors of two log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along two horizontal transects on a 21 m long outcrop of lower-shoreface bioturbated sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ (q) of separation scale or lag, s, over limited ranges of s. A procedure known as Extended Self-Similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ (q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm, stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm functions.
LETTER: Empirical scaling law for the effective heat diffusivity in ELMy H mode plasmas
NASA Astrophysics Data System (ADS)
Becker, G.
1996-04-01
Predictive code simulations of high density scenarios of ITER and other reactor-grade devices require an experimentally validated scaling relation for the one-fluid effective heat diffusivity chi in the ELMy H mode regime. A comprehensive empirical chi scaling compatible with the ITERH92-P ELMy H mode scaling of the thermal energy confinement time is presented. It follows from a power law ansatz for chi and integration of the single-fluid energy equation and recovers all the exponents of the global confinement law. The numerical factor of the global scaling is used to calibrate the heat diffusivity. The dependences of chi on the temperature and temperature gradient, connected with the power degradation of confinement, are inferred from profile information of a high density H mode discharge. The scaling law obtained is successfully tested against JET, ASDEX and ASDEX Upgrade H mode discharges covering a wide parameter range. It is found to predict the strong rise of the experimental chi profiles with increasing effective radius
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.
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
Broken scaling laws of the transition probabilities from jj to LS coupling transitions
NASA Astrophysics Data System (ADS)
Gao, Xiang; Han, Xiao-Ying; Zeng, De-Ling; Jin, Rui; Li, Jia-Ming
2014-04-01
Accurate electromagnetic transition rates between the ground electronic configurations are important in diagnostic studies of planetary nebulae. Based on a "quasi-complete basis" set, we present large-scale multi-configuration Dirac-Fock calculations of the forbidden transition rates within the ground electronic configuration along the nitrogen-like isoelectronic sequence. The broken scaling laws of the transition probabilities from jj to LS coupling transitions are elucidated and found to be extensions of the well-known scaling laws discussed in the single electron case. The equivalent oscillator strength is very large for ions in high-Z regions and should play a crucial role in the cooling mechanism in astrophysics.
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).
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.
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.
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. PMID:24988199
Identifying All Moiety Conservation Laws in Genome-Scale Metabolic Networks
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. PMID:24988199
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.
Scaling laws and vortex profiles in two-dimensional decaying turbulence
NASA Astrophysics Data System (ADS)
Laval, Jean-Philippe; Chavanis, Pierre-Henri; Dubrulle, Bérengère; Sire, Clément
2001-06-01
We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, like predicted in Carnevale et al., Phys. Rev. Lett. 66, 2735 (1991), and it is observed that viscous effects spoil this scaling regime. The exponent controlling the decay of the number of vortices shows some trends toward ξ=1, in agreement with a recent theory based on the Kirchhoff model [C. Sire and P. H. Chavanis, Phys. Rev. E 61, 6644 (2000)]. In terms of scaled variables, the vortices have a similar profile with a functional form related to the Fermi-Dirac distribution.
Scaling Laws of Microactuators and Potential Applications of Electroactive Polymers in MEMS
NASA Technical Reports Server (NTRS)
Liu, Chang; Bar-Cohen, Y.
1999-01-01
Besides the scale factor that distinguishes the various species, fundamentally biological muscles changes little between species, indicating a highly optimized system. Electroactive polymer actuators offer the closest resemblance to biological muscles, however besides the large actuation displacement these materials are falling short with regards to the actuation force. As improved materials are emerging it is becoming necessary to address key issues such as the need for effective electromechanical modeling and guiding parameters in scaling the actuators. In this paper, we will review the scaling laws for three major actuation mechanisms that are of relevance to micro electromechanical systems: electrostatic actuation, magnetic actuation, thermal bimetallic actuation, and piezoelectric actuation.
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.
Canopy-scale turbulence under oscillatory flow
NASA Astrophysics Data System (ADS)
Pujol, Dolors; Casamitjana, Xavier; Serra, Teresa; Colomer, Jordi
2013-09-01
The aim of this study is to understand the turbulent flow structure within diverse canopy models dominated by progressive waves. A set of experimental conditions were considered in a laboratory flume: three vegetation models (submerged rigid, submerged flexible and emergent rigid), three canopy densities (128, 640 and 1280 stems/m2) and three wave frequencies (f=0.8, 1 and 1.4 Hz). The canopy morphology through both the plant flexibility and height and the canopy density were the characteristic parameters that exerted a control on wave induced turbulence within the canopy bed. In the flexible canopy model, sheltering at the bed was observed and was associated with the movement of the blades. In contrast, in the rigid canopy model larger TKE was found as compared with the case without canopy. The increase of TKE was associated with the production of the stem-wake turbulence. Sheltering in the submerged rigid canopy model was found at the lower layer for the largest canopy density and highest wave frequency because of a great loss of wave velocity, confined below the top of the canopy. Sweeps and ejections were the predominant events, enhancing the transfer of momentum at the top of the canopy. Therefore, below the top of the submerged rigid canopy was characterized by a vertical energy exchange zone. Unlike the submerged model, sheltering was always found for emergent rigid vegetation, and attributed to the inhibition of the wave energy at all depths.
Magnetohydrodynamic (MHD) stretched flow of nanofluid with power-law velocity and chemical reaction
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Rashid, Madiha; Imtiaz, Maria; Alsaedi, Ahmed
2015-11-01
This paper deals with the boundary layer flow of nanofluid over power-law stretched surface. Analysis has been carried out in the presence of applied magnetic field and chemical reaction. Heat and mass transfer characteristics are studied using heat and mass convective conditions. The governing partial differential equations are transferred to the nonlinear ordinary differential equations. Convergent series solutions are obtained for fluid velocity, temperature and concentrations fields. Influences of pertinent parameters including Hartman number, thermal and concentration Biot numbers and chemical reaction parameters are discussed on the velocity, temperature and concentration profiles. Graphical result are presented and discussed. Computations for local Nusselt and Sherwood numbers are carried out. It is observed that the heat transfer rate is enhanced by increasing power-law index, thermal Biot number and chemical reaction parameter while mass transfer rate increases for power-law index and chemical reaction parameter.
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.
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.
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.
Downstream influence scaling of turbulent flow past expansion corners
NASA Technical Reports Server (NTRS)
Lu, Frank K.; Chung, Kung-Ming
1992-01-01
Previous studies of the high-speed viscous inviscid interaction between a turbulent boundary layer and an expansion at a convex corner have noted that surface pressure decreases toward the downstream inviscid value yielded by a Prandtl-Meyer expansion. A downstream influence on the corner is presently identified which is based on the mean surface pressure distribution; a scaling law is proposed for this distance.
Barenblatt, G. I.; Chorin, A. J.; Prostokishin, V. M.
2000-01-01
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.” PMID:10760253
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.
Large-scale flow generation in turbulent convection
Krishnamurti, Ruby; Howard, Louis N.
1981-01-01
In a horizontal layer of fluid heated from below and cooled from above, cellular convection with horizontal length scale comparable to the layer depth occurs for small enough values of the Rayleigh number. As the Rayleigh number is increased, cellular flow disappears and is replaced by a random array of transient plumes. Upon further increase, these plumes drift in one direction near the bottom and in the opposite direction near the top of the layer with the axes of plumes tilted in such a way that horizontal momentum is transported upward via the Reynolds stress. With the onset of this large-scale flow, the largest scale of motion has increased from that comparable to the layer depth to a scale comparable to the layer width. The conditions for occurrence and determination of the direction of this large-scale circulation are described. Images PMID:16592996
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.
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.
Fingering instability in the flow of a power-law fluid on a rotating disc
NASA Astrophysics Data System (ADS)
Arora, Akash; Doshi, Pankaj
2016-01-01
A computational study of the flow of a non-Newtonian power law fluid on a spinning disc is considered here. The main goal of this work is to examine the effect of non-Newtonian nature of the fluid on the flow development and associated contact line instability. The governing mass and momentum balance equations are simplified using the lubrication theory. The resulting model equation is a fourth order non-linear PDE which describes the spatial and temporal evolutions of film thickness. The movement of the contact line is modeled using a constant angle slip model. To solve this moving boundary problem, a numerical method is developed using a Galerkin/finite element method based approach. The numerical results show that the spreading rate of the fluid strongly depends on power law exponent n. It increases with the increase in the shear thinning character of the fluid (n < 1) and decreases with the increase in shear thickening nature of the fluid (n > 1). It is also observed that the capillary ridge becomes sharper with the value of n. In order to examine the stability of these ridges, a linear stability theory is also developed for these power law fluids. The dispersion relationship depicting the growth rate for a given wave number has been reported and compared for different power-law fluids. It is found that the growth rate of the instability decreases as the fluid becomes more shear thinning in nature, whereas it increases for more shear thickening fluids.
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
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.
Global coseismic deformations, GNSS time series analysis, and earthquake scaling laws
NASA Astrophysics Data System (ADS)
Métivier, Laurent; Collilieux, Xavier; Lercier, Daphné; Altamimi, Zuheir; Beauducel, François
2014-12-01
We investigate how two decades of coseismic deformations affect time series of GPS station coordinates (Global Navigation Satellite System) and what constraints geodetic observations give on earthquake scaling laws. We developed a simple but rapid model for coseismic deformations, assuming different earthquake scaling relations, that we systematically applied on earthquakes with magnitude larger than 4. We found that coseismic displacements accumulated during the last two decades can be larger than 10 m locally and that the cumulative displacement is not only due to large earthquakes but also to the accumulation of many small motions induced by smaller earthquakes. Then, investigating a global network of GPS stations, we demonstrate that a systematic global modeling of coseismic deformations helps greatly to detect discontinuities in GPS coordinate time series, which are still today one of the major sources of error in terrestrial reference frame construction (e.g., the International Terrestrial Reference Frame). We show that numerous discontinuities induced by earthquakes are too small to be visually detected because of seasonal variations and GPS noise that disturb their identification. However, not taking these discontinuities into account has a large impact on the station velocity estimation, considering today's precision requirements. Finally, six groups of earthquake scaling laws were tested. Comparisons with our GPS time series analysis on dedicated earthquakes give insights on the consistency of these scaling laws with geodetic observations and Okada coseismic approach.
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.
Phenomenological Blasius-type friction equation for turbulent power-law fluid flows.
Anbarlooei, H R; Cruz, D O A; Ramos, F; Silva Freire, A P
2015-12-01
We propose a friction formula for turbulent power-law fluid flows, a class of purely viscous non-Newtonian fluids commonly found in applications. Our model is derived through an extension of the friction factor analysis based on Kolmogorov's phenomenology, recently proposed by Gioia and Chakraborty. Tests against classical empirical data show excellent agreement over a significant range of Reynolds number. Limits of the model are also discussed. PMID:26764803
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.
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.
Comparison of generalized Reynolds and Navier Stokes equations for flow of a power law fluid
NASA Technical Reports Server (NTRS)
Mullen, R. L.; Prekwas, A.; Braun, M. J.; Hendricks, R. C.
1987-01-01
This paper compares a finite element solution of a modified Reynolds equation with a finite difference solution of the Navier-Stokes equation for a power law fluid. Both the finite element and finite difference formulation are reviewed. Solutions to spiral flow in parallel and conical geometries are compared. Comparison with experimental results are also given. The effects of the assumptions used in the Reynolds equation are discussed.
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.
Electroosmotic Flow of Power-Law Fluids in a Cylindrical Microcapillary
NASA Astrophysics Data System (ADS)
Saidi, M. H.; Babaie, Ashkan; Sadeghi, Arman; Center of Excellence in Energy Conversion Team
2012-11-01
In biological applications where most fluids are considered to be non-Newtonian, Newtonian law of viscosity looks insufficient for describing the flow characteristics. In the present work, the electroosmotic flow of power-law fluids in a circular micro tube is investigated. The Poisson-Boltzmann equation for electrical potential is solved numerically in the complete form without using the Debye-Hückel approximation. The physical model includes the Joule heating and viscous dissipation effects. Once the momentum and energy equations are solved numerically, a parametric study is done to investigate the effects of different parameters such as flow behavior index, wall zeta potential and the Debye-Hückel parameter on thermal and hydrodynamic characteristics of the flow. Results show that based on the value of viscous dissipation and the Debye-Hückel parameter the non-Newtonian characteristics of the flow can lead to significant changes regarding to Newtonian behaviors. The provided results in this study would lead to accurate prediction of temperature of biofluids in Lab-on-a-chip devices which is vital for retaining samples in a healthy condition.
Scaling law for direct current field emission-driven microscale gas breakdown
Venkattraman, A.; Alexeenko, A. A.
2012-12-15
The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices.
Scaling law for direct current field emission-driven microscale gas breakdown
NASA Astrophysics Data System (ADS)
Venkattraman, A.; Alexeenko, A. A.
2012-12-01
The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices.
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
2014-05-01
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
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.
Relativistic thermal electron scale instabilities in sheared flow plasma
NASA Astrophysics Data System (ADS)
Miller, Evan D.; Rogers, Barrett N.
2016-02-01
> 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.
Scaling Laws for Thin Films near the Superconducting-to-Insulating Transition.
Tao, Yong
2016-01-01
We propose a Lagrangian function, which combines Landau-Ginzburg term and Chern-Simons term, for describing the competition between disorder and superconductivity. To describe the normal-to-superconducting transition in the thin superconducting films, we apply Wilson's renormalization group methods into this Lagrangian function. Finally, we obtain a scaling law between critical temperature (Tc), film thickness (d), sheet resistance of the film at the normal state (Rs), and number density of the electrons at the normal state (N). Such a scaling law is in agreement with recent experimental investigations [Ivry, Y. et al., Physical Review B 90, 214515 (2014)]. Our finding may have potential benefits for improving transition temperature Tc. PMID:27029338
Scaling Laws for Thin Films near the Superconducting-to-Insulating Transition
NASA Astrophysics Data System (ADS)
Tao, Yong
2016-03-01
We propose a Lagrangian function, which combines Landau-Ginzburg term and Chern-Simons term, for describing the competition between disorder and superconductivity. To describe the normal-to-superconducting transition in the thin superconducting films, we apply Wilson’s renormalization group methods into this Lagrangian function. Finally, we obtain a scaling law between critical temperature (Tc), film thickness (d), sheet resistance of the film at the normal state (Rs), and number density of the electrons at the normal state (N). Such a scaling law is in agreement with recent experimental investigations [Ivry, Y. et al., Physical Review B 90, 214515 (2014)]. Our finding may have potential benefits for improving transition temperature Tc.
Scaling Laws for Proton Acceleration from the Rear Surface of Laser-Irradiated Thin Foils
Fuchs, J.; Antici, P.; D'Humieres, E.; Lefebvre, E.; Borghesi, M.; Cecchetti, C. A.; Brambrink, E.; Audebert, P.; Kaluza, M.; Schreiber, J.; Malka, V.; Manclossi, M.; Meyroneinc, S.; Mora, P.; Toncian, T.; Pepin, H.
2006-04-07
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 {approx}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.
Scaling Laws for Thin Films near the Superconducting-to-Insulating Transition
Tao, Yong
2016-01-01
We propose a Lagrangian function, which combines Landau-Ginzburg term and Chern-Simons term, for describing the competition between disorder and superconductivity. To describe the normal-to-superconducting transition in the thin superconducting films, we apply Wilson’s renormalization group methods into this Lagrangian function. Finally, we obtain a scaling law between critical temperature (Tc), film thickness (d), sheet resistance of the film at the normal state (Rs), and number density of the electrons at the normal state (N). Such a scaling law is in agreement with recent experimental investigations [Ivry, Y. et al., Physical Review B 90, 214515 (2014)]. Our finding may have potential benefits for improving transition temperature Tc. PMID:27029338
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.
SCALING LAWS AND TEMPERATURE PROFILES FOR SOLAR AND STELLAR CORONAL LOOPS WITH NON-UNIFORM HEATING
Martens, P. C. H.
2010-05-10
The bulk of solar coronal radiative loss consists of soft X-ray emission from quasi-static loops at the cores of active regions. In order to develop diagnostics for determining the heating mechanism of these loops from observations by coronal imaging instruments, I have developed analytical solutions for the temperature structure and scaling laws of loop strands for a set of temperature- and pressure-dependent heating functions that encompass heating concentrated at the footpoints, uniform heating, and heating concentrated at the loop apex. Key results are that the temperature profile depends only weakly on the heating distribution-not sufficiently to be of significant diagnostic value-and that the scaling laws survive for this wide range of heating distributions, but with the constant of proportionality in the Rosner-Tucker-Vaiana scaling law (P{sub 0} L {approx} T {sup 3}{sub max}) depending on the specific heating function. Furthermore, quasi-static solutions do not exist for an excessive concentration of heating near the loop footpoints, a result in agreement with recent numerical simulations. It is demonstrated that a generalization of the results to a set of solutions for strands with a functionally prescribed variable diameter leads to only relatively small correction factors in the scaling laws and temperature profiles for constant diameter loop strands. A quintet of leading theoretical coronal heating mechanisms is shown to be captured by the formalism of this paper, and the differences in thermal structure between them may be verified through observations. Preliminary results from full numerical simulations demonstrate that, despite the simplifying assumptions, the analytical solutions from this paper are accurate and stable.
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 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.
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.
Tippett, Michael K.; Cohen, Joel E.
2016-01-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from ‘outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954–2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210
A fresh look at crater scaling laws for normal and oblique hypervelocity impacts
NASA Technical Reports Server (NTRS)
Watts, A. J.; Atkinson, D. R.; Rieco, S. R.; Brandvold, J. B.; Lapin, S. L.; Coombs, C. R.
1993-01-01
With the concomitant increase in the amount of man-made debris and an ever increasing use of space satellites, the issue of accidental collisions with particles becomes more severe. While the natural micrometeoroid population is unavoidable and assumed constant, continued launches increase the debris population at a steady rate. Debris currently includes items ranging in size from microns to meters which originated from spent satellites and rocket cases. To understand and model these environments, impact damage in the form of craters and perforations must be analyzed. Returned spacecraft materials such as those from LDEF and Solar Max have provided such a testbed. From these space-aged samples various impact parameters (i.e., particle size, particle and target material, particle shape, relative impact speed, etc.) may be determined. These types of analyses require the use of generic analytic scaling laws which can adequately describe the impact effects. Currently, most existing analytic scaling laws are little more than curve-fits to limited data and are not based on physics, and thus are not generically applicable over a wide range of impact parameters. During this study, a series of physics-based scaling laws for normal and oblique crater and perforation formation has been generated into two types of materials: aluminum and Teflon.
Tippett, Michael K; Cohen, Joel E
2016-01-01
Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times as fast as the mean. The mean and variance of the number of tornadoes per outbreak vary according to Taylor's power law of fluctuation scaling (TL), with parameters that are consistent with multiplicative growth. Tornado-related atmospheric proxies show similar power-law scaling and multiplicative growth. Path-length-integrated tornado outbreak intensity also follows TL, but with parameters consistent with sampling variability. The observed TL power-law scaling of outbreak severity means that extreme outbreaks are more frequent than would be expected if mean and variance were independent or linearly related. PMID:26923210
On the Scaling Law for Broadband Shock Noise Intensity in Supersonic Jets
NASA Technical Reports Server (NTRS)
Kanudula, Max
2009-01-01
A theoretical model for the scaling of broadband shock noise intensity in supersonic jets was formulated on the basis of linear shock-shear wave interaction. An hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process rather than the noise generation contribution from off-peak incident angles. The proposed theory satisfactorily explains the well-known scaling law for the broadband shock -associated noise in supersonic jets.
A Theoretical Basis for the Scaling Law of Broadband Shock Noise Intensity in Supersonic Jets
NASA Technical Reports Server (NTRS)
Kandula, Max
2011-01-01
A theoretical basis for the scaling of broadband shock noise intensity In supersonic jets was formulated considering linear shock-shear wave interaction. Modeling of broadband shock noise with the aid of shock-turbulence interaction with special reference to linear theories is briefly reviewed. An hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process with the noise generation contribution from off-peak incident angles being relatively unimportant. The proposed hypothesis satisfactorily explains the well-known scaling law for the broadband shock-associated noise in supersonic jets.
Interpretation of large-scale deviations from the Hubble flow
NASA Astrophysics Data System (ADS)
Grinstein, B.; Politzer, H. David; Rey, S.-J.; Wise, Mark B.
1987-03-01
The theoretical expectation for large-scale streaming velocities relative to the Hubble flow is expressed in terms of statistical correlation functions. Only for objects that trace the mass would these velocities have a simple cosmological interpretation. If some biasing effects the objects' formation, then nonlinear gravitational evolution is essential to predicting the expected large-scale velocities, which also depend on the nature of the biasing.
The role of freestream turbulence scale in subsonic flow separation
NASA Technical Reports Server (NTRS)
Potter, J. L.; Seebaugh, W. R.; Fisher, C. E.; Barnett, R. J.; Gokhale, R. B.
1985-01-01
The clarification of the role of freestream turbulence scale in determining the location of boundary layer separation is discussed. Modifications to the test facility were completed. Wind tunnel flow characteristics, including turbulence parameters, were determined with two turbulence generating grids, as well as no grid. These results are summarized. Initial results on the role of scale on turbulent boundary layer separation on the upper surface of an airfoil model are also discussed.
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. PMID:26311401
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. PMID:26311401
An empirical scaling law for improved confinement in reversed-field pinch plasmas
NASA Astrophysics Data System (ADS)
Yagi, Y.; Koguchi, H.; Hirano, Y.; Sakakita, H.; Frassinetti, L.
2005-02-01
A database of the confinement properties of the toroidal pinch experiment (TPE) series reversed-field pinch (RFP) devices was established, and an empirical scaling law for the energy confinement time, τE, was deduced for a consistently selected set of the database (Yagi Y. et al 2003 Nucl. Fusion 43 1787). The scaling for τE [TPE-scaling; \\smash{\\tau _E \\sim a^{1.7} I_p^{0.8} (I_p/N)^{0.3} \\Theta ^{3}} ], in particular, is a power law similar to that predicted on the basis of the tearing modes, as a function of the plasma minor radius (a), plasma current (Ip), and Ip/N, where N is the column density. On the other hand, the TPE-scaling has a strong dependence on the pinch parameter, Θ, namely τE ~ Θ3. Recently, we have investigated the database of the improved confinement in the pulsed poloidal current drive (PPCD). We show that the TPE-scaling agrees well with the improved τE in the PPCD database, because of its strong Θ dependence. Namely, Θ3 is a factor of merit for RFP plasmas. We discuss why this agreement is obtained in spite of the general difference between the underlying transport mechanisms of the standard and PPCD discharges. We also show that this improvement, represented by Θ3, is related to the increase in magnetic shear with Θ.
Finite-size scaling law in single-crystalline Fe3O4 hollow nanostructures
NASA Astrophysics Data System (ADS)
Zhang, Xiaoping; Wang, Jun; Gao, Miao
2016-07-01
Single-crystalline Fe3O4 hollow nanostructures (nanoring and nanotube) have been successfully synthesized by a hydrothermal method along with a heat treatment process. The temperature dependences of the magnetization of the hollow nanostructures were measured under a high vacuum ( < 9.5 × 10‑6 Torr) from 300K to 900K. The Curie temperatures of the nanoring and nanotube samples were found to decrease with decreasing the mean wall thickness. The Curie temperatures of the hollow magnetite nanostructures follow a finite-size scaling relation with the scaling exponent ν = 1.04 ± 0.03. By comparison with those of the zero-dimensional Fe3O4 particles and two-dimensional Fe3O4 films, we show that the scaling relation for our hollow nanostructures is in better agreement with the quasi-two-dimensional finite-size scaling law.
Temporal scaling in fatigue life of materials and incorporation of temporal events in Paris's law
NASA Astrophysics Data System (ADS)
Frantziskonis, George N.
2013-04-01
Temporal scaling in mechanical strength of materials is vital for long-term effects such as fatigue. The fatigue crack length α is related to the change in the stress intensity factor ΔK by the omnipresent Paris's law, which works well for cyclic fatigue of specific frequency and amplitude. The paper considers time scaling in fatigue and through it incorporates the effects of temporal events such as unexpected or accidental loads, impact loads, and rare events such as earthquake loads. This is achieved by theoretically incorporating the effects of delta-function type loads into fatigue. Since the time-scale decomposition of such a load contains information at all scales, the theoretical framework is easily extended to include general types of loads.
Fine scale features of stable flows over Greenland
NASA Astrophysics Data System (ADS)
Orr, A.; Hunt, J.; Light, M.; Hanna, E.; Cappelen, J.
2003-04-01
The atmospheric flows and processes over Greenland occur on many length scales. Flow over and around Greenland is affected by (i) the large and very steep elevation change between the coastal margins and the central plateau (3km), (ii) the combination of very rough surfaces (roughness length zo ˜ 1-10m) and jagged mountains around the coasts, (iii) the strong katabatic flows from the plateau down to the coasts (˜ 100km), (iv) the presence of the semi-permanent Icelandic Low (˜ 1000km), and (v) air-sea-ice interaction processes. Here and in other coastal flows there are extremely sharp gradients in roughness and elevation. These result in local scale phenomena that have long been observed, for example, coastal wind jets, but as they occur on kilometer length scales, they are only described by mesoscale models when they are run with fine resolution (e.g. Capon 2002). But these local scale phenomena can have large scale climate effects, e.g. drag, wind waves, upwelling, cyclogenesis, air-sea-ice interaction, etc. Hunt et al. (2002) investigated the low-level flow response of atmospheric westerly winds over southern Greenland using idealised and numerical modelling. To further understand Greenland's critical climate processes the low-level flow response to easterly, southerly, and northerly atmospheric winds, and a fast moving front passing over the southern tip, are investigated. At a horizontal resolution of 12km, certain broad features (e.g. wind-jets) are well captured by the numerical model and consistent with aspects of the idealised 2-layer model (Hunt et al. 2002) for typical mesoscale atmospheric flows with variations in surface roughness, elevation, and heating. Further understanding is enabled by comparison with observations. An important development is to show how katabatic winds can combine with and be deflected by synoptic winds in regions of barrier jets and in wake jets. (This agreed with field data.) Our studies should help define the magnitudes and
Wikipedia Information Flow Analysis Reveals the Scale-Free Architecture of the Semantic Space
Masucci, Adolfo Paolo; Kalampokis, Alkiviadis; Eguíluz, Victor Martínez; Hernández-García, Emilio
2011-01-01
In this paper we extract the topology of the semantic space in its encyclopedic acception, measuring the semantic flow between the different entries of the largest modern encyclopedia, Wikipedia, and thus creating a directed complex network of semantic flows. Notably at the percolation threshold the semantic space is characterised by scale-free behaviour at different levels of complexity and this relates the semantic space to a wide range of biological, social and linguistics phenomena. In particular we find that the cluster size distribution, representing the size of different semantic areas, is scale-free. Moreover the topology of the resulting semantic space is scale-free in the connectivity distribution and displays small-world properties. However its statistical properties do not allow a classical interpretation via a generative model based on a simple multiplicative process. After giving a detailed description and interpretation of the topological properties of the semantic space, we introduce a stochastic model of content-based network, based on a copy and mutation algorithm and on the Heaps' law, that is able to capture the main statistical properties of the analysed semantic space, including the Zipf's law for the word frequency distribution. PMID:21407801
Wikipedia information flow analysis reveals the scale-free architecture of the semantic space.
Masucci, Adolfo Paolo; Kalampokis, Alkiviadis; Eguíluz, Victor Martínez; Hernández-García, Emilio
2011-01-01
In this paper we extract the topology of the semantic space in its encyclopedic acception, measuring the semantic flow between the different entries of the largest modern encyclopedia, Wikipedia, and thus creating a directed complex network of semantic flows. Notably at the percolation threshold the semantic space is characterised by scale-free behaviour at different levels of complexity and this relates the semantic space to a wide range of biological, social and linguistics phenomena. In particular we find that the cluster size distribution, representing the size of different semantic areas, is scale-free. Moreover the topology of the resulting semantic space is scale-free in the connectivity distribution and displays small-world properties. However its statistical properties do not allow a classical interpretation via a generative model based on a simple multiplicative process. After giving a detailed description and interpretation of the topological properties of the semantic space, we introduce a stochastic model of content-based network, based on a copy and mutation algorithm and on the Heaps' law, that is able to capture the main statistical properties of the analysed semantic space, including the Zipf's law for the word frequency distribution. PMID:21407801
Scaling Stream Flow Response to Forest Disturbance: the SID Project
NASA Astrophysics Data System (ADS)
Buttle, J. M.; Beall, F. D.; Creed, I. F.; Gordon, A. M.; Mackereth, R.; McLaughlin, J. W.; Sibley, P. K.
2004-05-01
We do not have a good understanding of the hydrologic implications of forest harvesting in Ontario, either for current or alternative management approaches. Attempts to address these implications face a three-fold problem: data on hydrologic response to forest disturbance in Ontario are lacking; most studies of these responses have been in regions with forest cover and hydrologic conditions that differ from the Ontario context; and these studies have generally been conducted at relatively small scales (<1 km2). It is generally assumed that hydrologic changes induced by forest disturbance should diminish with increasing scale due to the buffering capacity of large drainage basins. Recent modeling exercises and reanalysis of paired-basin results call this widespread applicability of this assumption into question, with important implications for assessing the cumulative impacts of forest disturbance on basin stream flow. The SID (Scalable Indicators of Disturbance) project combines stream flow monitoring across basin scales with the RHESSys modeling framework to identify forest disturbance impacts on stream flow characteristics in Ontario's major forest ecozones. As a precursor to identifying stream flow response to forest disturbance, we are examining the relative control of basin geology, topography, typology and topology on stream flow characteristics under undisturbed conditions. This will assist in identifying the dominant hydrologic processes controlling basin stream flow that must be incorporated into the RHESSys model framework in order to emulate forest disturbance and its hydrologic impacts. We present preliminary results on stream flow characteristics in a low-relief boreal forest landscape, and explore how the dominant processes influencing these characteristics change with basin scale in this landscape under both reference and disturbance conditions.
Large-scale anisotropy in stably stratified rotating flows
Marino, R.; Mininni, P. D.; Rosenberg, D. L.; Pouquet, A.
2014-08-28
We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to $1024^3$ grid points and Reynolds numbers of $\\approx 1000$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $\\sim k_\\perp^{-5/3}$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.
Large-scale anisotropy in stably stratified rotating flows
Marino, R.; Mininni, P. D.; Rosenberg, D. L.; Pouquet, A.
2014-08-28
We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up tomore » $1024^3$ grid points and Reynolds numbers of $$\\approx 1000$$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $$\\sim k_\\perp^{-5/3}$$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.« less
Using composite flow laws to extrapolate lab data on ice to nature
NASA Astrophysics Data System (ADS)
de Bresser, Hans; Diebold, Sabrina; Durham, William
2013-04-01
The progressive evolution of the grain size distribution of deforming and recrystallizing Earth materials directly affects their rheological behaviour in terms of composite grain-size-sensitive (GSS, diffusion/grain boundary sliding) and grain-size-insensitive (GSI, dislocation) creep. After time, such microstructural evolution might result in strain progressing at a steady-state balance of mechanisms of GSS and GSI creep. In order to come to a meaningful rheological description of materials deforming by combined GSS and GSI mechanisms, composite flow laws are required that bring together individual, laboratory derived GSS and GSI flow laws, and that include full grain size distributions rather than single mean values representing the grain size. A composite flow law approach including grain size distributions has proven to be very useful in solving discrepancies between microstructural observations in natural calcite mylonites and extrapolations of relatively simple laboratory flow laws (Herwegh et al., 2005, J. Struct Geol., 27, 503-521). In the current study, we used previous and new laboratory data on the creep behavior of water ice to investigate if a composite flow law approach also results in better extrapolation of lab data to nature for ice. The new lab data resulted from static grain-growth experiments and from deformation experiments performed on samples with a starting grain size of either < 2 microns ("fine grained ice") or of 180-250 microns ("coarse grained ice"). The deformation experiments were performed in a special cryogenic Heard-type deformation apparatus at temperatures 180-240 K, at confining pressures 30-100 MPa, and strain rates between 1E-08/s and 1E-04/s. After the experiments, all samples were studied using cryogenic SEM and image analysis techniques. We also investigated natural microstructures in EPICA drilling ice core samples of Dronning Maud Land in Antartica. The temperature of the core ranges from 228 K at the surface to 272 K
Effect of wettability on scale-up of multiphase flow from core-scale to reservoir fine-grid-scale
Chang, Y.C.; Mani, V.; Mohanty, K.K.
1997-08-01
Typical field simulation grid-blocks are internally heterogeneous. The objective of this work is to study how the wettability of the rock affects its scale-up of multiphase flow properties from core-scale to fine-grid reservoir simulation scale ({approximately} 10{prime} x 10{prime} x 5{prime}). Reservoir models need another level of upscaling to coarse-grid simulation scale, which is not addressed here. Heterogeneity is modeled here as a correlated random field parameterized in terms of its variance and two-point variogram. Variogram models of both finite (spherical) and infinite (fractal) correlation length are included as special cases. Local core-scale porosity, permeability, capillary pressure function, relative permeability functions, and initial water saturation are assumed to be correlated. Water injection is simulated and effective flow properties and flow equations are calculated. For strongly water-wet media, capillarity has a stabilizing/homogenizing effect on multiphase flow. For small variance in permeability, and for small correlation length, effective relative permeability can be described by capillary equilibrium models. At higher variance and moderate correlation length, the average flow can be described by a dynamic relative permeability. As the oil wettability increases, the capillary stabilizing effect decreases and the deviation from this average flow increases. For fractal fields with large variance in permeability, effective relative permeability is not adequate in describing the flow.
Nimmo, J.R.; Rubin, J.; Hammermeister, D.P.
1987-01-01
A method has been developed to establish steady flow of water in unsaturated soil sample spinning in a centrifuge. Theoretical analysis predicts moisture conditions in the sample that depend strongly on soil type and certain operating parameter. For Oakley sand, measurements of flux, water content, and matric potential during and after centrifugation verify that steady state flow can be achieved. Experiments have confirmed the theoretical prediction of a nearly uniform moisture distribution for this medium and have demonstrated that the flow can be effectively one-dimensional. The method was used for steady state measurements of hydraulic conductivity K for relatively dry soil, giving values at low as 7. 6 multiplied by 10** minus **1**1 m/s with data obtained in a few hours. Darcy's law was tested by measuring K for different centrifugal driving forces but with the same water content.
Blood Flow: Multi-scale Modeling and Visualization
2010-01-01
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 developing methods for multi-scale computations, techniques for multi-scale visualizations must be designed. This animation presents early results of joint efforts of teams from Brown University and Argonne National Laboratory to develop a multi-scale visualization methodology. It 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 made of 500 DPD-particles, and small spheres show a sub-set of the DPD particles representing the blood plasma, while instantaneous streamlines and slices represent the ensemble average velocity. Credits: Science: Leopold Grinberg and George Karniadakis, Brown University Visualization: Joseph A. Insley and Michael E. Papka, Argonne National Laboratory This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357. This research was supported in part by the National Science Foundation through the PetaApps program and used TeraGrid resources provided by National Institute for Computational Sciences.
How Large Scales Flows May Influence Solar Activity
NASA Technical Reports Server (NTRS)
Hathaway, D. H.
2004-01-01
Large scale flows within the solar convection zone are the primary drivers of the Sun's magnetic activity cycle and play important roles in shaping the Sun's magnetic field. Differential rotation amplifies the magnetic field through its shearing action and converts poloidal field into toroidal field. Poleward meridional flow near the surface carries magnetic flux that reverses the magnetic poles at about the time of solar maximum. The deeper, equatorward meridional flow can carry magnetic flux back toward the lower latitudes where it erupts through the surface to form tilted active regions that convert toroidal fields into oppositely directed poloidal fields. These axisymmetric flows are themselves driven by large scale convective motions. The effects of the Sun's rotation on convection produce velocity correlations that can maintain both the differential rotation and the meridional circulation. These convective motions can also influence solar activity directly by shaping the magnetic field pattern. While considerable theoretical advances have been made toward understanding these large scale flows, outstanding problems in matching theory to observations still remain.
Gray scale and color flow Doppler characterization of uterine tumors.
Carter, J R; Lau, M; Saltzman, A K; Hartenbach, E M; Chen, M D; Johnson, P R; Fowler, J M; Carlson, J W; Carson, L F; Twiggs, L B
1994-11-01
The aim of this study was to investigate gray scale and color flow characteristics of a group of patients with a suspected uterine pathologic condition. One hundred and twenty-two consecutive patients at the Women's Cancer Center, University of Minnesota, undergoing transvaginal sonography and color flow Doppler imaging for suspected uterine corpus abnormality made up the study group. After gray scale morphologic assessment, color flow Doppler imaging of the tumor and uterus was performed, including the ipsilateral uterine artery. Malignant tumors were confirmed pathologically in all 35 patients who had them. In comparing patients with benign versus malignant tumors, gray scale morphologic assessment confirmed that malignant uterine tumors (31 endometrial cancers and four sarcomas) were more likely to have a thickened echoic endometrium (P = < 0.0001), be enlarged (P = 0.004), to be retroverted (P = 0.02), and to lack a subendometrial halo (P < 0.0001). Patients with four benign and 13 malignant tumors demonstrated increased flow when assessed by CFD. The calculated sensitivity of increased color flow in predicting malignancy was 39%, with a specificity of 92%, a positive predictive value of 77%, and a negative predictive value of 71%. No difference existed between the benign and malignant groups for the systolic, diastolic, and mean velocities and for the calculated pulsatility index and resistive index in both sampled uterine and intramyometrial or tumor vessels.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:7837328
2D VARIABLY SATURATED FLOWS: PHYSICAL SCALING AND BAYESIAN ESTIMATION
A novel dimensionless formulation for water flow in two-dimensional variably saturated media is presented. It shows that scaling physical systems requires conservation of the ratio between capillary forces and gravity forces. A direct result of this finding is that for two phys...
Granular flow in pebble bed reactors: Dust generation and scaling
Rycroft, C. H.; Lind, T.; Guentay, S.; Dehbi, A.
2012-07-01
In experimental prototypes of pebble bed reactors, significant quantities of graphite dust have been observed due to rubbing between pebbles as they flow through the core. At the high temperatures and pressures in these reactors, little data is available to understand the frictional properties of the pebble surfaces, and as a result, the Paul Scherrer Institut (Switzerland) proposes a conceptual design of a scaled-down version of a pebble bed reactor to investigate this issue in detail. In this paper, simulations of granular flow in pebble bed reactors using the discrete-element method are presented. Simulations in the full geometry (using 440,000 pebbles) are compared to those in geometries scaled down by 3:1 and 6:1. The simulations show complex behavior due to discrete pebble packing effects, meaning that pebble flow and dust generation in a scaled-down facility may be significantly different. The differences between velocity profiles, packing geometry, and pebble wear at the different scales are discussed. The results can aid in the design of the prototypical facility to more accurately reproduce the flow in a full-size reactor. (authors)
Length scales and self-organization in dense suspension flows
NASA Astrophysics Data System (ADS)
Düring, Gustavo; Lerner, Edan; Wyart, Matthieu
2014-02-01
Dense non-Brownian suspension flows of hard particles display mystifying properties: As the jamming threshold is approached, the viscosity diverges, as well as a length scale that can be identified from velocity correlations. To unravel the microscopic mechanism governing dissipation and its connection to the observed correlation length, we develop an analogy between suspension flows and the rigidity transition occurring when floppy networks are pulled, a transition believed to be associated with the stress stiffening of certain gels. After deriving the critical properties near the rigidity transition, we show numerically that suspension flows lie close to it. We find that this proximity causes a decoupling between viscosity and the correlation length of velocities ξ, which scales as the length lc characterizing the response to a local perturbation, previously predicted to follow lc˜1/√zc-z ˜p0.18, where p is the dimensionless particle pressure, z is the coordination of the contact network made by the particles, and zc is twice the spatial dimension. We confirm these predictions numerically and predict the existence of a larger length scale lr˜√p with mild effects on velocity correlation and of a vanishing strain scale δγ ˜1/p that characterizes decorrelation in flow.
Sensitivity of Flow and Sediment Transport in Meandering Rivers to Scale Effects and Flow Rate
Shams, Mehrzad; Ahmadi, Goodarz; Smith, Duane H.
2008-06-01
Sensitivity of flow and sediment transport in a meandering river to variations in scaling and flow rate was studied. The FLUENT™ code was used for evaluating the river flow characteristics, including the mean velocity field and the Reynolds stress components, as well as for particle trajectory analysis. Particular attention was given to the sensitivity of the sedimentation patterns of different size particles in the river bend for various scales. Simulation studies were performed for both a model river and a physical river. The physical river was geometrically similar to the model river, with a scaling ratio of 1:100, but with identical Froude number. The flow and particle deposition patterns in the physical and model rivers were compared. It was shown that the mean flow quantities exhibit dynamic similarity, but the turbulence parameters and the particle sedimentation features in the physical river were different from the model. The secondary flows and particle transport patterns were also found to be sensitive to variation in the scale and flow rate.
Large scale modelling of bankfull flow: An example for Europe
NASA Astrophysics Data System (ADS)
Schneider, Christof; Flörke, Martina; Eisner, Stephanie; Voss, Frank
2011-10-01
SummaryBankfull flow is a relevant parameter in the field of large scale modelling especially for the analysis of environmental flows and flood related hydrological processes. In our case, bankfull flow data were required within the SCENES project in order to analyse ecological important inundation events at selected grid cells of a European raster. In practise, the determination of bankfull flow is a complex task even on local scale. Subsequent to a literature survey of bankfull flow studies, this paper describes a method which can be applied to estimate bankfull flow on a global or continental grid cell raster. The method is based on the partial duration series approach taking into account a 40-years time series of daily discharge data modelled by the global water model WaterGAP. An increasing threshold censoring procedure, a declustering scheme and the generalised Pareto distribution are applied. Modelled bankfull flow values are then validated by different efficiency criteria against bankfull flows observed at gauging stations in Europe. Thereby, the impact of (i) the applied distribution function, (ii) the threshold setting in the partial duration series, (iii) the climate input data and (iv) applying the annual maxima series are evaluated and compared to the proposed approach. The results show that bankfull flow can be reasonably estimated with a high model efficiency ( E1 = 0.71) and weighted correlation ( ωr2 = 0.90) as well as a systematic overestimation of 22.8%. Finally it turned out that in our study focusing on hydrological extremes, the appliance of the daily climate input data is a basic requirement. While the choice of the distribution function had no significant impact on the final results, the threshold setting in the partial duration series was crucial.
Flow and evaporation in single micrometer and nanometer scale pipes
Velasco, A. E.; Yang, C.; Siwy, Z. S.; Taborek, P.; Toimil-Molares, M. E.
2014-07-21
We report measurements of pressure driven flow of fluids entering vacuum through a single pipe of micrometer or nanometer scale diameter. Nanopores were fabricated by etching a single ion track in polymer or mica foils. A calibrated mass spectrometer was used to measure the flow rates of nitrogen and helium through pipes with diameter ranging from 10 μm to 31 nm. The flow of gaseous and liquid nitrogen was studied near 77 K, while the flow of helium was studied from the lambda point (2.18 K) to above the critical point (5.2 K). Flow rates were controlled by changing the pressure drop across the pipe in the range 0–31 atm. When the pressure in the pipe reached the saturated vapor pressure, an abrupt flow transition was observed. A simple viscous flow model is used to determine the position of the liquid/vapor interface in the pipe. The observed mass flow rates are consistent with no slip boundary conditions.
Multi-Scale Investigation of Sheared Flows In Magnetized Plasmas
Edward, Jr., Thomas
2014-09-19
Flows parallel and perpendicular to magnetic fields in a plasma are important phenomena in many areas of plasma science research. The presence of these spatially inhomogeneous flows is often associated with the stability of the plasma. In fusion plasmas, these sheared flows can be stabilizing while in space plasmas, these sheared flows can be destabilizing. Because of this, there is broad interest in understanding the coupling between plasma stability and plasma flows. This research project has engaged in a study of the plasma response to spatially inhomogeneous plasma flows using three different experimental devices: the Auburn Linear Experiment for Instability Studies (ALEXIS) and the Compact Toroidal Hybrid (CTH) stellarator devices at Auburn University, and the Space Plasma Simulation Chamber (SPSC) at the Naval Research Laboratory. This work has shown that there is a commonality of the plasma response to sheared flows across a wide range of plasma parameters and magnetic field geometries. The goal of this multi-device, multi-scale project is to understand how sheared flows established by the same underlying physical mechanisms lead to different plasma responses in fusion, laboratory, and space plasmas.
Contact area of rough spheres: Large scale simulations and simple scaling laws
NASA Astrophysics Data System (ADS)
Pastewka, Lars; Robbins, Mark O.
2016-05-01
We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.
Detectability of Large-Scale Solar Subsurface Flows
NASA Astrophysics Data System (ADS)
Woodard, M.
2014-04-01
The accuracy of helioseismic measurement is limited by the stochastic nature of solar oscillations. In this article I use a Gaussian statistical model of the global seismic wave field of the Sun to investigate the noise limitations of direct-modeling analysis of convection-zone-scale flows. The theoretical analysis of noise is based on hypothetical data that cover the entire photosphere, including the portions invisible from the Earth. Noise estimates are derived for measurements of the flow-dependent couplings of global-oscillation modes and for combinations of coupling measurements that isolate vector-spherical-harmonic components of the flow velocity. For current helioseismic observations, which sample only a fraction of the photosphere, the inferred detection limits are best regarded as optimistic limits. The flow-velocity fields considered in this work are assumed to be decomposable into vector-spherical-harmonic functions of degree less than five. The problem of measuring the general velocity field is shown to be similar enough to the well-studied problem of measuring differential rotation to permit rough estimates of flow-detection thresholds to be gleaned from past helioseismic analysis. I estimate that, with existing and anticipated helioseismic datasets, large-scale flow-velocity amplitudes of a few tens of should be detectable near the base of the convection zone.
NASA Astrophysics Data System (ADS)
Renardy, M.
1986-02-01
Steady flows of viscoelastic fluids can not be uniquely determined by imposing boundary conditions only for the velocities as in the Newtonian case. The reason for this is that the fluids have memory, and therefore the flow inside the domain is affected by what happened before the fluid entered the domain. This leads to the need for extra boundary conditions at an inflow boundary. The nature of these inflow boundary conditions has not been analyzed previously, and it is certainly dependent on the constitutive law. In this paper, we look at the special case of differential constitutive relations with a single relaxation mode. We consider steady transverse flows across a strip which are small perturbations of a flow with constant velocity. It turns out that in this case two extra inflow boundary conditions are required in two dimensions, and four in three dimensions. This is what would be expected from an analysis of characteristics, but it contradicts the belief of many rheologists that it is possible to prescribe the extra stress at an inflow boundary. The problem studied here is of potential relevance for numerical simulations of steady flows. Many of the flows currently simulated are on infinite domains. Numerically, these domains are truncated, and on the inflow boundary of the truncated domain people usually prescribe the extra stress. According to the analysis in this paper, this is an overdetermined problem, and therefore errors must be expected from this procedure.
Structural Similitude and Scaling Laws for Plates and Shells: A Review
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Starnes, J. H., Jr.; Rezaeepazhand, J.
2000-01-01
This paper deals with the development and use of scaled-down models in order to predict the structural behavior of large prototypes. The concept is fully described and examples are presented which demonstrate its applicability to beam-plates, plates and cylindrical shells of laminated construction. The concept is based on the use of field equations, which govern the response behavior of both the small model as well as the large prototype. The conditions under which the experimental data of a small model can be used to predict the behavior of a large prototype are called scaling laws or similarity conditions and the term that best describes the process is structural similitude. Moreover, since the term scaling is used to describe the effect of size on strength characteristics of materials, a discussion is included which should clarify the difference between "scaling law" and "size effect". Finally, a historical review of all published work in the broad area of structural similitude is presented for completeness.
Calibration of the Site-Scale Saturated Zone Flow Model
G. A. Zyvoloski
2001-06-28
The purpose of the flow calibration analysis work is to provide Performance Assessment (PA) with the calibrated site-scale saturated zone (SZ) flow model that will be used to make radionuclide transport calculations. As such, it is one of the most important models developed in the Yucca Mountain project. This model will be a culmination of much of our knowledge of the SZ flow system. The objective of this study is to provide a defensible site-scale SZ flow and transport model that can be used for assessing total system performance. A defensible model would include geologic and hydrologic data that are used to form the hydrogeologic framework model; also, it would include hydrochemical information to infer transport pathways, in-situ permeability measurements, and water level and head measurements. In addition, the model should include information on major model sensitivities. Especially important are those that affect calibration, the direction of transport pathways, and travel times. Finally, if warranted, alternative calibrations representing different conceptual models should be included. To obtain a defensible model, all available data should be used (or at least considered) to obtain a calibrated model. The site-scale SZ model was calibrated using measured and model-generated water levels and hydraulic head data, specific discharge calculations, and flux comparisons along several of the boundaries. Model validity was established by comparing model-generated permeabilities with the permeability data from field and laboratory tests; by comparing fluid pathlines obtained from the SZ flow model with those inferred from hydrochemical data; and by comparing the upward gradient generated with the model with that observed in the field. This analysis is governed by the Office of Civilian Radioactive Waste Management (OCRWM) Analysis and Modeling Report (AMR) Development Plan ''Calibration of the Site-Scale Saturated Zone Flow Model'' (CRWMS M&O 1999a).
Benford's law gives better scaling exponents in phase transitions of quantum XY models
NASA Astrophysics Data System (ADS)
Rane, Ameya Deepak; Mishra, Utkarsh; Biswas, Anindya; SenDe, Aditi; Sen, Ujjwal
2014-08-01
Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.
Benford's law gives better scaling exponents in phase transitions of quantum XY models.
Rane, Ameya Deepak; Mishra, Utkarsh; Biswas, Anindya; Sen De, Aditi; Sen, Ujjwal
2014-08-01
Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data. PMID:25215725
Scaling laws of impact induced shock pressure and particle velocity in planetary mantle
NASA Astrophysics Data System (ADS)
Monteux, J.; Arkani-Hamed, J.
2016-01-01
While major impacting bodies during accretion of a Mars type planet have very low velocities (<10 km/s), the characteristics of the shockwave propagation and, hence, the derived scaling laws are poorly known for these low velocity impacts. Here, we use iSALE-2D hydrocode simulations to calculate shock pressure and particle velocity in a Mars type body for impact velocities ranging from 4 to 10 km/s. Large impactors of 100-400 km in diameter, comparable to those impacted on Mars and created giant impact basins, are examined. To better represent the power law distribution of shock pressure and particle velocity as functions of distance from the impact site at the surface, we propose three distinct regions in the mantle: a near field regime, which extends to 1-3 times the projectile radius into the target, where the peak shock pressure and particle velocity decay very slowly with increasing distance, a mid field region, which extends to ∼4.5 times the impactor radius, where the pressure and particle velocity decay exponentially but moderately, and a more distant far field region where the pressure and particle velocity decay strongly with distance. These scaling laws are useful to determine impact heating of a growing proto-planet by numerous accreting bodies.
Power-law scaling in daily rainfall patterns and consequences in urban stream discharges
NASA Astrophysics Data System (ADS)
Park, Jeryang; Krueger, Elisabeth H.; Kim, Dongkyun; Rao, Suresh C.
2016-04-01
Poissonian rainfall has been frequently used for modelling stream discharge in a catchment at the daily scale. Generally, it is assumed that the daily rainfall depth is described by memoryless exponential distribution which is transformed to stream discharge, resulting in an analytical pdf for discharge [Gamma distribution]. While it is true that catchment hydrological filtering processes (censored by constant rate ET losses, and first-order recession) increases "memory", reflected in 1/f noise in discharge time series. Here, we show that for urban watersheds in South Korea: (1) the observation of daily rainfall depths follow power-law pdfs, and spectral slopes range between 0.2 ~ 0.4; and (2) the stream discharge pdfs have power-law tails. These observation results suggest that multiple hydro-climatic factors (e.g., non-stationarity of rainfall patterns) and hydrologic filtering (increasing impervious area; more complex urban drainage networks) influence the catchment hydrologic responses. We test the role of such factors using a parsimonious model, using different types of daily rainfall patterns (e.g., power-law distributed rainfall depth with Poisson distribution in its frequency) and urban settings to reproduce patterns similar to those observed in empirical records. Our results indicate that fractality in temporally up-scaled rainfall, and the consequences of large extreme events are preserved as high discharge events in urbanizing catchments. Implications of these results to modeling urban hydrologic responses and impacts on receiving waters are discussed.
NASA Astrophysics Data System (ADS)
Makinde, O. D.
2014-12-01
In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.
Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws
El Jarroudi, M.; Brillard, A.
2008-06-15
We consider a new way of establishing Navier wall laws. Considering a bounded domain {omega} of R{sup N}, N=2,3, surrounded by a thin layer {sigma}{sub {epsilon}}, along a part {gamma}{sub 2} of its boundary {partial_derivative}{omega}, we consider a Navier-Stokes flow in {omega} union {partial_derivative}{omega} union {sigma}{sub {epsilon}} with Reynolds' number of order 1/{epsilon} in {sigma}{sub {epsilon}}. Using {gamma}-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface {gamma}{sub 2}. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context.
Flow structure for Power-Law fluids in lid-driven arc-shape cavities
NASA Astrophysics Data System (ADS)
Mercan, Hatice; Atalik, Kunt
2011-06-01
In this paper the lid-driven flow of a Power-Law fluid in arc-shape cavities is studied. Two different arc cavity cross sections are considered with arc angle ratios r = 1/2 and r = 1/3. The unsteady streamfunction-vorticity formulation is adopted together with a Power-Law constitutive relation. Body-fitted coordinate transformation is applied to generate orthogonal computational grids. The equations are discretized in space using a second order finite difference numerical method. Time integration is performed using fourth order Runge-Kutta explicit scheme. The combined effects of inertia, shear thinning/shear thickening and curved geometry on the vortical structure and velocity profiles are shown. The results are compared to Newtonian fluid case. It is found that under inertia, shear thinning effects lead to the early formation and growth of secondary vortices in the curved cavity, however shear thickening has an opposite effect.
Pore-scale simulation of laminar flow through porous media
NASA Astrophysics Data System (ADS)
Piller, M.; Casagrande, D.; Schena, G.; Santini, M.
2014-04-01
The experimental investigation of flow through porous media is inherently difficult due to the lack of optical access. The recent developments in the fields of X-ray micro-tomography (micro-CT hereafter), digital sample reconstruction by image-processing techniques and fluid-dynamics simulation, together with the increasing power of super-computers, allow to carry out pore-scale simulations through digitally-reconstructed porous samples. The scientific relevance of pore-scale simulations lies in the possibility of upscaling the pore-level data, yielding volume-averaged quantities useful for practical purposes. One of the best-known examples of upscaling is the calculation of absolute and relative permeability of reservoir rocks. This contribution presents a complete work-flow for setting up pore-scale simulations, starting from the micro-CT of a (in general small) porous sample. Relevant applications are discussed in order to reveal the potential of the proposed methodology.
Scaling laws in emotion-associated words and corresponding network topology.
Takehara, Takuma; Ochiai, Fumio; Suzuki, Naoto
2015-05-01
We investigated whether scaling laws were present in the appearance-frequency distribution of emotion-associated words and determined whether the network constructed from those words had small-world or scale-free properties. Over 1,400 participants were asked to write down the first single noun that came to mind in response to nine emotional cue words, resulting in a total of 12,556 responses. We identified Zipf's law in the distribution of the data, as the slopes of the regression lines reached approximately -1.0 in the appearance frequencies for each emotional cue word. This suggested that the emotion-associated words had a clear regularity, were not randomly generated, were scale-invariant, and were influenced by unification/diversification forces. Thus, we predicted that the emotional intensity of the words might play an important role for a Zipf's law. Moreover, we also found that the 1-mode network of emotion-associated words clearly had small-world properties in terms of the network topologies of clustering, average distance, and small-worldness value, indicating that all nodes (words) were highly interconnected with each other and were only a few short steps apart. Furthermore, the data suggested the possibility of a scale-free property. Interestingly, we were able to identify hub words with neutral emotional content, such as 'dog', 'woman', and 'face', indicating that these neutral words might be an intermediary between words with conflicting emotional valence. Additionally, efficiency and optimal navigation in terms of complex networks were discussed. PMID:25399403
Segmentation of genomic DNA through entropic divergence: Power laws and scaling
NASA Astrophysics Data System (ADS)
Azad, Rajeev K.; Bernaola-Galván, Pedro; Ramaswamy, Ramakrishna; Rao, J. Subba
2002-05-01
Genomic DNA is fragmented into segments using the Jensen-Shannon divergence. Use of this criterion results in the fragments being entropically homogeneous to within a predefined level of statistical significance. Application of this procedure is made to complete genomes of organisms from archaebacteria, eubacteria, and eukaryotes. The distribution of fragment lengths in bacterial and primitive eukaryotic DNAs shows two distinct regimes of power-law scaling. The characteristic length separating these two regimes appears to be an intrinsic property of the sequence rather than a finite-size artifact, and is independent of the significance level used in segmenting a given genome. Fragment length distributions obtained in the segmentation of the genomes of more highly evolved eukaryotes do not have such distinct regimes of power-law behavior.
Scaling law characterizing the dynamics of the transition of HIV-1 to error catastrophe
NASA Astrophysics Data System (ADS)
Gupta, Vipul; Dixit, Narendra M.
2015-10-01
Increasing the mutation rate, μ , of viruses above a threshold, {μ }c, has been predicted to trigger a catastrophic loss of viral genetic information and is being explored as a novel intervention strategy. Here, we examine the dynamics of this transition using stochastic simulations mimicking within-host HIV-1 evolution. We find a scaling law governing the characteristic time of the transition: τ ≈ 0.6/≤ft(μ -{μ }c\\right). The law is robust to variations in underlying evolutionary forces and presents guidelines for treatment of HIV-1 infection with mutagens. We estimate that many years of treatment would be required before HIV-1 can suffer an error catastrophe.
Applicability of Macroscopic Wear and Friction Laws on the Atomic Length Scale
NASA Astrophysics Data System (ADS)
Eder, S. J.; Feldbauer, G.; Bianchi, D.; Cihak-Bayr, U.; Betz, G.; Vernes, A.
2015-07-01
Using molecular dynamics, we simulate the abrasion process of an atomically rough Fe surface with multiple hard abrasive particles. By quantifying the nanoscopic wear depth in a time-resolved fashion, we show that Barwell's macroscopic wear law can be applied at the atomic scale. We find that in this multiasperity contact system, the Bowden-Tabor term, which describes the friction force as a function of the real nanoscopic contact area, can predict the kinetic friction even when wear is involved. From this the Derjaguin-Amontons-Coulomb friction law can be recovered, since we observe a linear dependence of the contact area on the applied load in accordance with Greenwood-Williamson contact mechanics.
Validation data for models of contaminant dispersal : scaling laws and data needs.
O'Hern, Timothy John; Ceccio, Steven Louis
2004-09-01
Contaminant dispersal models for use at scales ranging from meters to miles are widely used for planning sensor locations, first-responder actions for release scenarios, etc. and are constantly being improved. Applications range from urban contaminant dispersal to locating buried targets from an exhaust signature. However, these models need detailed data for model improvement and validation. A small Sandia National Laboratories Laboratory Directed Research and Development (LDRD) program was funded in FY04 to examine the feasibility and usefulness of a scale-model capability for quantitative characterization of flow and contaminant dispersal in complex environments. This report summarizes the work performed in that LDRD. The basics of atmospheric dispersion and dispersion modeling are reviewed. We examine the need for model scale data, and the capability of existing model test methods. Currently, both full-scale and model scale experiments are performed in order to collect validation data for numerical models. Full-scale experiments are expensive, are difficult to repeat, and usually produce relatively sparse data fields. Model scale tests often employ wind tunnels, and the data collected is, in many cases, derived from single point measurements. We review the scaling assumptions and methods that are used to relate model and full scale flows. In particular, we examine how liquid flows may be used to examine the process of atmospheric dispersion. The scaling between liquid and gas flows is presented. Use of liquid as the test fluid has some advantages in terms of achieving fully turbulent Reynolds numbers and in seeding the flow with neutrally buoyant tracer particles. In general, using a liquid flow instead of a gas flow somewhat simplifies the use of full field diagnostics, such as Particle Image Velocimetry and Laser Induced Fluorescence. It is also possible to create stratified flows through mixtures of fluids (e.g., water, alcohol, and brine). Lastly, we
Simulation of Multiphase FLOW at the Pore Scale: Doable, Useful?
NASA Astrophysics Data System (ADS)
Tchelepi, H.; Abu AlSaud, M.; Soulaine, C.
2014-12-01
We discuss the shotcomings of Darcy-scale formulations and constitutive relations for (unstable) immiscible multiphase flow in natural porous media, and we argue for a more rigorous connection between the Darcy-scale representation and the pore-scale dynamics. We then discuss the challenges associated with so-called Direct Numerical Simulation (DNS) at the pore scale. The emphasis is on contact-line dynamics for non-zero contact angles. We argue that accurate description of the (1) fluid-fluid and (2) fluid-fluid-solid contact lines, as well as, (3) the hysteretic behavior of immiscible displacement processes are needed before claims that Direct Numerical Simulation (DNS) of pore-scale physics is doable. Then, we describe our early attempts to devise a hybrid level-set and volume-of-fluid approach to model the evolution of sharp immiscible interfaces in natural porous media. We also discuss the challenges associated with the translation of two-phase flow dynamics to "Darcy" scales.
Effects of small scale energy injection on large scales in turbulent reaction flows
NASA Astrophysics Data System (ADS)
Xuan, Yuan
2014-11-01
Turbulence causes the generation of eddies of various length scales. In turbulent non-reacting flows, most of the kinetic energy is contained in large scale turbulent structures and dissipated at small scales. This energy cascade process from large scales to small scales provides the foundation of a lot of turbulence models, especially for Large Eddy Simulations. However, in turbulent reacting flows, chemical energy is converted locally to heat and therefore deploys energy at the smallest scales. As such, effects of small scale energy injection due to combustion on large scale turbulent motion may become important. These effects are investigated in the case of auto-ignition under homogeneous isotropic turbulence. Impact of small scale heat release is examined by comparing various turbulent statistics (e.g. energy spectrum, two-point correlation functions, and structure functions) in the reacting case to the non-reacting case. Emphasis is placed on the identification of the most relevant turbulent quantities in reflecting such small-large scale interactions.
On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces
NASA Astrophysics Data System (ADS)
Seo, Jongmin; Mani, Ali
2016-02-01
Superhydrophobic surfaces can significantly reduce hydrodynamic skin drag by accommodating large slip velocity near the surface due to entrapment of air bubbles within their micro-scale roughness elements. While there are many Stokes flow solutions for flows near superhydrophobic surfaces that describe the relation between effective slip length and surface geometry, such relations are not fully known in the turbulent flow limit. In this work, we present a phenomenological model for the kinematics of flow near a superhydrophobic surface with periodic post-patterns at high Reynolds numbers. The model predicts an inverse square root scaling with solid fraction, and a cube root scaling of the slip length with pattern size, which is different from the reported scaling in the Stokes flow limit. A mixed model is then proposed that recovers both Stokes flow solution and the presented scaling, respectively, in the small and large texture size limits. This model is validated using direct numerical simulations of turbulent flows over superhydrophobic posts over a wide range of texture sizes from L+ ≈ 6 to 310 and solid fractions from ϕs = 1/9 to 1/64. Our report also embarks on the extension of friction laws of turbulent wall-bounded flows to superhydrophobic surfaces. To this end, we present a review of a simplified model for the mean velocity profile, which we call the shifted-turbulent boundary layer model, and address two previous shortcomings regarding the closure and accuracy of this model. Furthermore, we address the process of homogenization of the texture effect to an effective slip length by investigating correlations between slip velocity and shear over pattern-averaged data for streamwise and spanwise directions. For L+ of up to O(10), shear stress and slip velocity are perfectly correlated and well described by a homogenized slip length consistent with Stokes flow solutions. In contrast, in the limit of large L+, the pattern-averaged shear stress and slip
Large-scale flow experiments for managing river systems
Konrad, C.P.; Olden, J.D.; Lytle, D.A.; Melis, T.S.; Schmidt, J.C.; Bray, E.N.; Freeman, Mary C.; Gido, K.B.; Hemphill, N.P.; Kennard, M.J.; McMullen, L.E.; Mims, M.C.; Pyron, M.; Robinson, C.T.; Williams, J.G.
2011-01-01
Experimental manipulations of streamflow have been used globally in recent decades to mitigate the impacts of dam operations on river systems. Rivers are challenging subjects for experimentation, because they are open systems that cannot be isolated from their social context. We identify principles to address the challenges of conducting effective large-scale flow experiments. Flow experiments have both scientific and social value when they help to resolve specific questions about the ecological action of flow with a clear nexus to water policies and decisions. Water managers must integrate new information into operating policies for large-scale experiments to be effective. Modeling and monitoring can be integrated with experiments to analyze long-term ecological responses. Experimental design should include spatially extensive observations and well-defined, repeated treatments. Large-scale flow manipulations are only a part of dam operations that affect river systems. Scientists can ensure that experimental manipulations continue to be a valuable approach for the scientifically based management of river systems. ?? 2011 by American Institute of Biological Sciences. All rights reserved.
Large-scale flow experiments for managing river systems
Konrad, Christopher P.; Olden, Julian D.; Lytle, David A.; Melis, Theodore S.; Schmidt, John C.; Bray, Erin N.; Freeman, Mary C.; Gido, Keith B.; Hemphill, Nina P.; Kennard, Mark J.; McMullen, Laura E.; Mims, Meryl C.; Pyron, Mark; Robinson, Christopher T.; Williams, John G.
2011-01-01
Experimental manipulations of streamflow have been used globally in recent decades to mitigate the impacts of dam operations on river systems. Rivers are challenging subjects for experimentation, because they are open systems that cannot be isolated from their social context. We identify principles to address the challenges of conducting effective large-scale flow experiments. Flow experiments have both scientific and social value when they help to resolve specific questions about the ecological action of flow with a clear nexus to water policies and decisions. Water managers must integrate new information into operating policies for large-scale experiments to be effective. Modeling and monitoring can be integrated with experiments to analyze long-term ecological responses. Experimental design should include spatially extensive observations and well-defined, repeated treatments. Large-scale flow manipulations are only a part of dam operations that affect river systems. Scientists can ensure that experimental manipulations continue to be a valuable approach for the scientifically based management of river systems.
Large-scale flow generation by inhomogeneous helicity
NASA Astrophysics Data System (ADS)
Yokoi, N.; Brandenburg, A.
2016-03-01
The effect of kinetic helicity (velocity-vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters the Reynolds stress (mirror-symmetric tensor) expression in the form of a helicity gradient as the coupling coefficient for the mean vorticity and/or the angular velocity (axial vector), which suggests the possibility of mean-flow generation in the presence of inhomogeneous helicity. This inhomogeneous helicity effect, which was previously confirmed at the level of a turbulence- or closure-model simulation, is examined with the aid of direct numerical simulations of rotating turbulence with nonuniform helicity sustained by an external forcing. The numerical simulations show that the spatial distribution of the Reynolds stress is in agreement with the helicity-related term coupled with the angular velocity, and that a large-scale flow is generated in the direction of angular velocity. Such a large-scale flow is not induced in the case of homogeneous turbulent helicity. This result confirms the validity of the inhomogeneous helicity effect in large-scale flow generation and suggests that a vortex dynamo is possible even in incompressible turbulence where there is no baroclinicity effect.
Forces acting on a stationary sphere in power-law fluid flow near the wall
NASA Astrophysics Data System (ADS)
Bocharov, O. B.; Kushnir, D. Yu.
2016-01-01
The analysis and evaluation of the forces acting on the particle in a linear shear flow of power-law fluid (PLF) in the presence of the wall were performed. Using the results of a series of computations for a model problem with a spherical particle near a flat wall in the Reynolds number range of 0-200 and the distance to the wall from 0 to 20 particle diameters, the correlation formulas for calculating the coefficients of drag force and lift force were obtained. Special attention was paid to the behavior of the forces acting on the particle approaching the wall.
Viscous singular shock profiles for a system of conservation laws modeling two-phase flow
NASA Astrophysics Data System (ADS)
Hsu, Ting-Hao
2016-08-01
This paper is concerned with singular shocks for a system of conservation laws via the Dafermos regularization ut + f(u)x = ɛtuxx. For a system modeling incompressible two-phase fluid flow, the existence of viscous profiles is proved using Geometric Singular Perturbation Theory. The weak convergence and the growth rate of the viscous solution are also derived; the weak limit is the sum of a piecewise constant function and a δ-measure supported on a shock line, and the maximum value of the viscous solution is of order exp (1 / ɛ).
A second-law investigation of heat exchanger wall-thickness on flow energy
Wold, S.K.; Maveety, J.G.; Peterson, E.; Olson, D.
1996-03-01
There has been a growing interest in enhancing the performance of space power systems, and quantifying the subsequent optimal operating conditions. In any thermal storage system, the thermodynamic irreversibilities decrease the net power (or exit flow energy) available to do work. Entropy production is closely related to the thermal efficiency of a thermal storage system, and isolating and reducing components of irreversibility will result in increased performance. This paper investigates second-law aspects of four single pass spiral heat exchangers in which helium is the working fluid. {copyright} {ital 1996 American Institute of Physics.}
Suliman, F; French, H; Haugen, L E; Kløve, B; Jenssen, P
2005-01-01
Horizontal subsurface flow constructed wetlands have proven their efficiency in treating wastewater and removing the pollutants of concern. Treatment efficiency depends on the wastewater residence time, which is a function of the hydraulic loading and the physical conditions of the constructed filter system, which can be described with effective parameters such as: hydraulic conductivity, porosity, dispersivity etc. Because spatial variability is often scale dependent, these effective parameters may be affected by the scale of the system being studied. In this paper the results of tracer experiments in constructed filters using saturated horizontal flow at three scales (small and medium lab scales and full-scale system) using the same filter media is reported. Light-weight aggregate (filter media termed Filtralite-P) was used at all scales. Increasing the scale was associated with increasing dispersivity, meanwhile hydraulic conductivity experienced dramatic reduction and variation by increasing the examined scale. Observed changes in the hydraulic parameters indicate that heterogeneity at different scales should be taken into account when the performance of LWA filters are evaluated from small-scale experiments. PMID:16042266
Simple scaling laws for influenza A rise time, duration, and severity.
Chang, David B; Young, Carl S
2007-06-21
Simple scaling laws are developed for the severity and characteristic time scales of influenza A infection in man. The scaling laws are based on a model of the infection described by six coupled ordinary differential equations that describe the time courses of the numbers of infectious viral particles, activated cytotoxic T-lymphocytes, interferon molecules, infected cells, uninfected cells, and the subset of uninfected cells that are protected by interferon from viral infection. Computer simulations show that the disease can be regarded approximately as a two-stage process. In the first stage, the growth in the number of infected cells is determined primarily by the interferon-enhanced limitation in the available number of target cells. In the second stage, the bulk of the duration of the infection is determined mainly by the destruction of the infected cells by the cytotoxic T-lymphocytes. The severity and characteristic times of the infection are found to depend simply on the logarithm of the initial number of viruses. PMID:17379249
Scaling laws for the transmission of random binary dielectric multilayered structures
NASA Astrophysics Data System (ADS)
Nascimento, E. M.; de Moura, F. A. B. F.; Lyra, M. L.
2007-09-01
We investigate several scaling aspects of the transmission spectrum of disordered one-dimensional dielectric structures. We consider a binary stratified medium composed of a random sequence of N slabs with refraction indices satisfying the Bragg condition. The mode for which the optical thickness corresponds to half wavelength is insensitive to disorder and fully transparent. The average transmission in a frequency range around this resonance decays as 1/N1/2 , and the localization length diverges quadratically as this resonance mode is approached. In the vicinity of the quarter-wavelength mode, the localization length diverges logarithmically and the frequency averaged transmission exhibits an stretched exponential dependence on the total thickness. At the quarter-wavelength resonance, the Lyapunov exponent for different realizations of disorder has a Gaussian distribution leading to distinct scaling laws for the geometric and arithmetic averages of the transmission. The scaling laws for the half- and quarter-wavelength modes are analogous to those found in electronic one-dimensional Anderson models with random dimers and pure off-diagonal disorder, respectively, which are known to display similar violations of the usual exponential Anderson localization.
Scaling and saturation laws for the expansion of concrete exposed to sulfate attack
Monteiro, Paulo J. M.
2006-01-01
Reinforced concrete structures exposed to aggressive environments often require repair or retrofit even though they were designed to last >50 years. This statement is especially true for structures subjected to sulfate attack. It is critical that fundamental models of life prediction be developed for durability of concrete. Based on experimental results obtained over a 40-year period, scaling and saturation laws were formulated for concrete exposed to sulfate solution. These features have not been considered in current models used to predict life cycle of concrete exposed to aggressive environment. The mathematical analysis shows that porous concrete made with high and moderate water-to-cement ratios develops a definite scaling law after an initiation time. The scaling coefficient depends on the cement composition but does not depend on the original water-to-cement ratio. Dense concrete made with low water-to-cement ratios develops a cyclic saturation curve. An index for “potential of damage” is created to allow engineers to design concrete structures with better precision and cement chemists to develop portland cements with optimized composition. PMID:16864774
Scaling and saturation laws for the expansion of concrete exposed to sulfate attack.
Monteiro, Paulo J M
2006-08-01
Reinforced concrete structures exposed to aggressive environments often require repair or retrofit even though they were designed to last >50 years. This statement is especially true for structures subjected to sulfate attack. It is critical that fundamental models of life prediction be developed for durability of concrete. Based on experimental results obtained over a 40-year period, scaling and saturation laws were formulated for concrete exposed to sulfate solution. These features have not been considered in current models used to predict life cycle of concrete exposed to aggressive environment. The mathematical analysis shows that porous concrete made with high and moderate water-to-cement ratios develops a definite scaling law after an initiation time. The scaling coefficient depends on the cement composition but does not depend on the original water-to-cement ratio. Dense concrete made with low water-to-cement ratios develops a cyclic saturation curve. An index for "potential of damage" is created to allow engineers to design concrete structures with better precision and cement chemists to develop portland cements with optimized composition. PMID:16864774
A simple model for determining photoelectron-generated radiation scaling laws
Dipp, T.M. |
1993-12-01
The generation of radiation via photoelectrons induced off of a conducting surface was explored using a simple model to determine fundamental scaling laws. The model is one-dimensional (small-spot) and uses monoenergetic, nonrelativistic photoelectrons emitted normal to the illuminated conducting surface. Simple steady-state radiation, frequency, and maximum orbital distance equations were derived using small-spot radiation equations, a sin{sup 2} type modulation function, and simple photoelectron dynamics. The result is a system of equations for various scaling laws, which, along with model and user constraints, are simultaneously solved using techniques similar to linear programming. Typical conductors illuminated by low-power sources producing photons with energies less than 5.0 eV are readily modeled by this small-spot, steady-state analysis, which shows they generally produce low efficiency ({eta}{sub rsL}<10{sup {minus}10.5}) pure photoelectron-induced radiation. However, the small-spot theory predicts that the total conversion efficiency for incident photon power to photoelectron-induced radiated power can go higher than 10{sup {minus}5.5} for typical real conductors if photons having energies of 15 eV and higher are used, and should go even higher still if the small-spot limit of this theory is exceeded as well. Overall, the simple theory equations, model constraint equations, and solution techniques presented provide a foundation for understanding, predicting, and optimizing the generated radiation, and the simple theory equations provide scaling laws to compare with computational and laboratory experimental data.
NASA Astrophysics Data System (ADS)
Chen, Du-Xing; Li, Shuo; Fang, Jin
2015-12-01
Transport ac loss Q of a superconducting rectangular thin strip obeying a power-law relation E∝Jn as a function of current amplitude Im may be, following Norris, expressed by normalized quantities as q(im). A scaling law is deduced that if Icf, Ic and f being the critical current and frequency, is multiplied by a positive constant C, then im and qm are multiplied by C 1 /(n - 1)and C 2 /(n - 1) , respectively. Based on this scaling law and the well-known Norris formula, the general function of q(im, n, f) is obtained graphically or analytically for any practical purpose, after accurate numerical computations on a set of q(im) at several values of n and a fixed value of f.
A wavelet analysis of scaling laws and long-memory in stock market volatility
NASA Astrophysics Data System (ADS)
Vuorenmaa, Tommi A.
2005-05-01
This paper studies the time-varying behavior of scaling laws and long-memory. This is motivated by the earlier finding that in the FX markets a single scaling factor might not always be sufficient across all relevant timescales: a different region may exist for intradaily time-scales and for larger time-scales. In specific, this paper investigates (i) if different scaling regions appear in stock market as well, (ii) if the scaling factor systematically differs from the Brownian, (iii) if the scaling factor is constant in time, and (iv) if the behavior can be explained by the heterogenuity of the players in the market and/or by intraday volatility periodicity. Wavelet method is used because it delivers a multiresolution decomposition and has excellent local adaptiviness properties. As a consequence, a wavelet-based OLS method allows for consistent estimation of long-memory. Thus issues (i)-(iv) shed light on the magnitude and behavior of a long-memory parameter, as well. The data are the 5-minute volatility series of Nokia Oyj at the Helsinki Stock Exchange around the burst of the IT-bubble. Period one represents the era of "irrational exuberance" and another the time after it. The results show that different scaling regions (i.e. multiscaling) may appear in the stock markets and not only in the FX markets, the scaling factor and the long-memory parameter are systematically different from the Brownian and they do not have to be constant in time, and that the behavior can be explained for a significant part by an intraday volatility periodicity called the New York effect. This effect was magnified by the frenzy trading of short-term speculators in the bubble period. The found stronger long-memory is also attributable to irrational exuberance.
Scale-to-scale energy transfer in mixing flow induced by the Richtmyer-Meshkov instability
NASA Astrophysics Data System (ADS)
Liu, Han; Xiao, Zuoli
2016-05-01
The Richtmyer-Meshkov instability (RMI) mixing flow induced by a planar shock wave of Mach 1.6 is investigated using direct numerical simulation method. Interfacial perturbations of different scales between air and sulfur hexafluoride are introduced to study the effect of the initial conditions. Focus is placed on the analysis of the scale-to-scale transfer of kinetic energy in both Fourier and physical spaces. The kinetic energy injected from the perturbation scales is transferred to both larger and smaller scales in an average sense within the inner mixing zone (IMZ) at early times and is mainly passed down into smaller scales at the late stage. The physical-space energy flux due to the subgrid-scale (SGS) stress is studied using a filtering approach in order to shed light on the physical origin of the scale-to-scale kinetic energy transfer. It is found that the pointwise SGS energy flux is highly correlated with the local spike and bubble structures in the IMZ. Moreover, it turns out that the mean SGS energy flux is mainly ascribed to the component in the direction of shock wave propagation. An analysis using the method of conditional averaging manifests that the generation of local SGS energy flux is associated with the property of the surrounding flow induced by quadrupolar or dipolar vortex structures.
Chaube, M. K.; Tripathi, D.; Bég, O. Anwar; Sharma, Shashi; Pandey, V. S.
2015-01-01
A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth. PMID:27057132
Density scaling and quasiuniversality of flow-event statistics for athermal plastic flows.
Lerner, Edan; Bailey, Nicholas P; Dyre, Jeppe C
2014-11-01
Athermal steady-state plastic flows were simulated for the Kob-Andersen binary Lennard-Jones system and its repulsive version in which the sign of the attractive terms is changed to a plus. Properties evaluated include the distributions of energy drops, stress drops, and strain intervals between the flow events. We show that simulations at a single density in conjunction with an equilibrium-liquid simulation at the same density allow one to predict the plastic flow-event statistics at other densities. This is done by applying the recently established "hidden scale invariance" of simple liquids to the glass phase. The resulting scaling of flow-event properties reveals quasiuniversality, i.e., that the probability distributions of energy drops, stress drops, and strain intervals in properly reduced units are virtually independent of the microscopic pair potentials. PMID:25493793
Density scaling and quasiuniversality of flow-event statistics for athermal plastic flows
NASA Astrophysics Data System (ADS)
Lerner, Edan; Bailey, Nicholas P.; Dyre, Jeppe C.
2014-11-01
Athermal steady-state plastic flows were simulated for the Kob-Andersen binary Lennard-Jones system and its repulsive version in which the sign of the attractive terms is changed to a plus. Properties evaluated include the distributions of energy drops, stress drops, and strain intervals between the flow events. We show that simulations at a single density in conjunction with an equilibrium-liquid simulation at the same density allow one to predict the plastic flow-event statistics at other densities. This is done by applying the recently established "hidden scale invariance" of simple liquids to the glass phase. The resulting scaling of flow-event properties reveals quasiuniversality, i.e., that the probability distributions of energy drops, stress drops, and strain intervals in properly reduced units are virtually independent of the microscopic pair potentials.
(e,2e) Reactions for He+ and Li2+ Ions from their Excited States. Scaling Law
NASA Astrophysics Data System (ADS)
Stia, C. R.; Fojón, O. A.; Rivarola, R. D.
In this work, theoretical triply differential cross sections for ionization of several hydrogenic atoms from excited states by fast electron impact are computed'in the case of asymmetric coplanar geometry. The final wavefunction is chosen as an approximate solution to the three-body scattering problem with correct asymptotic conditions. The initial wavefunction also satisfies correct boundary conditions. Results for Li2+ ions in their 2s and 2p excited states are presented. In addition, it is shown that a simple scaling law for the triply differential cross sections obtained for ionization of hydrogenic targets from their ground state is also satisfied by excited hydrogenic targets.
High speed transport cruise drag. [scaling laws using Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Roberts, Leonard
1992-01-01
This report provides scaling laws for the cruise aerodynamics of high speed transport wings based on the results of Navier-Stokes computations. Expressions for the various drag components are found, together with the corresponding values (L/D)(sub m) for various values of the geometric parameter s/l which allow for simple optimization of the wing configurations with respect to the span. It is found that linear theory expressions can be used for this purpose provided the coefficients of these experiments for C(sub D) and (L/D)(sub m) are available using Navier-Stokes results.
Scaling laws and simulation results for the self-organized critical forest-fire model
NASA Astrophysics Data System (ADS)
Clar, S.; Drossel, B.; Schwabl, F.
1994-08-01
We discuss the properties of a self-organized critical forest-fire model which has been introduced recently [B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992)]. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer simulations in one to eight dimensions. The simulations suggest a critical dimension dc=6 above which the critical exponents assume their mean-field values. Changing the lattice symmetry and allowing trees to be immune against fire, we show that the critical exponents are universal.
Scaling-law equilibria for calcium in canopy-type models of the solar chromosphere
NASA Technical Reports Server (NTRS)
Jones, H. P.
1982-01-01
Scaling laws for resonance line formation are used to obtain approximate excitation and ionization equilibria for a three-level model of singly ionized calcium. The method has been developed for and is applied to the study of magnetograph response in the 8542 A infrared triplet line to magnetostatic canopies which schematically model diffuse, nearly horizontal fields in the low solar chromosphere. For this application, the method is shown to be efficient and semi-quantitative, and the results indicate the type and range of effects on calcium-line radiation which result from reduced gas pressure inside the magnetic regions.
Scaling laws of strategic behavior and size heterogeneity in agent dynamics
NASA Astrophysics Data System (ADS)
Vaglica, Gabriella; Lillo, Fabrizio; Moro, Esteban; Mantegna, Rosario N.
2008-03-01
We consider the financial market as a model system and study empirically how agents strategically adjust the properties of large orders in order to meet their preference and minimize their impact. We quantify this strategic behavior by detecting scaling relations between the variables characterizing the trading activity of different institutions. We also observe power-law distributions in the investment time horizon, in the number of transactions needed to execute a large order, and in the traded value exchanged by large institutions, and we show that heterogeneity of agents is a key ingredient for the emergence of some aggregate properties characterizing this complex system.
Scaling Laws for the Response of Nonlinear Elastic Media with Implications for Cell Mechanics
NASA Astrophysics Data System (ADS)
Shokef, Yair; Safran, Samuel A.
2012-04-01
We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.
Laboratory study of sonic booms and their scaling laws. [ballistic range simulation
NASA Technical Reports Server (NTRS)
Toong, T. Y.
1974-01-01
This program undertook to seek a basic understanding of non-linear effects associated with caustics, through laboratory simulation experiments of sonic booms in a ballistic range and a coordinated theoretical study of scaling laws. Two cases of superbooms or enhanced sonic booms at caustics have been studied. The first case, referred to as acceleration superbooms, is related to the enhanced sonic booms generated during the acceleration maneuvers of supersonic aircrafts. The second case, referred to as refraction superbooms, involves the superbooms that are generated as a result of atmospheric refraction. Important theoretical and experimental results are briefly reported.
Transverse electron-scale instability in relativistic shear flows
NASA Astrophysics Data System (ADS)
Alves, E. P.; Grismayer, T.; Fonseca, R. A.; Silva, L. O.
2015-08-01
Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic (≫c /ωp e ) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales.
Transverse electron-scale instability in relativistic shear flows.
Alves, E P; Grismayer, T; Fonseca, R A; Silva, L O
2015-08-01
Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic (≫c/ωpe) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales. PMID:26382337
Multi-scale analysis for environmental dispersion in wetland flow
NASA Astrophysics Data System (ADS)
Wu, Zi; Li, Z.; Chen, G. Q.
2011-08-01
Presented in this work is a multi-scale analysis for longitudinal evolution of contaminant concentration in a fully developed flow through a shallow wetland channel. An environmental dispersion model for the mean concentration is devised as an extension of Taylor's classical formulation by a multi-scale analysis. Corresponding environmental dispersivity is found identical to that determined by the method of concentration moments. For typical contaminant constituents of chemical oxygen demand, biochemical oxygen demand, total phosphorus, total nitrogen and heavy metal, the evolution of contaminant cloud is illustrated with the critical length and duration of the contaminant cloud with constituent concentration beyond some given environmental standard level.
Instability of Stratified Shear Flow: Intermittency and Length Scales
NASA Astrophysics Data System (ADS)
Ecke, Robert; Odier, Philippe
2015-11-01
The stability of stratified shear flows which occur in oceanic overflows, wind-driven thermoclines, and atmospheric inversion layers is governed by the Richardson Number Ri , a non-dimensional balance between stabilizing stratification and destabilizing shear. For a shear flow with velocity difference U, density difference Δρ and characteristic length H, one has Ri = g (Δρ / ρ) H /U2 . A more precise definition is the gradient Richardson Number Rig =N2 /S2 where the buoyancy frequency N =√{ (g / ρ) ∂ρ / ∂z } , the mean strain S = ∂U / ∂z with z parallel to gravity and with ensemble or time averages defining the gradients. We explore the stability and mixing properties of a wall-bounded shear flow for 0 . 1 < Rig < 1 using simultaneous measurements of density and velocity fields. The flow, confined from the top by a horizontal boundary, is a lighter alcohol-water mixture injected from a nozzle into quiescent heavier salt-water fluid. The injected flow is turbulent with Taylor Reynolds number about 75. We compare a set of length scales that characterize the mixing properties of our turbulent stratified shear flow including Thorpe Length LT, Ozmidov Length LO, and Ellison Length LE.
Large-scale behavior and statistical equilibria in rotating flows
NASA Astrophysics Data System (ADS)
Mininni, P. D.; Dmitruk, P.; Matthaeus, W. H.; Pouquet, A.
2011-01-01
We examine long-time properties of the ideal dynamics of three-dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases, the results agree with the isotropic predictions stemming from statistical mechanics. No accumulation of excitation occurs in the large scales, although, in the dissipative rotating case, anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two dimensionalization of the flow undergoing strong rotation as advocated by several authors.
Debris flow grain size scales with sea surface temperature over glacial-interglacial timescales
NASA Astrophysics Data System (ADS)
D'Arcy, Mitch; Roda Boluda, Duna C.; Whittaker, Alexander C.; Araújo, João Paulo C.
2015-04-01
Debris flows are common erosional processes responsible for a large volume of sediment transfer across a range of landscapes from arid settings to the tropics. They are also significant natural hazards in populated areas. However, we lack a clear set of debris flow transport laws, meaning that: (i) debris flows remain largely neglected by landscape evolution models; (ii) we do not understand the sensitivity of debris flow systems to past or future climate changes; and (iii) it remains unclear how to interpret debris flow stratigraphy and sedimentology, for example whether their deposits record information about past tectonics or palaeoclimate. Here, we take a grain size approach to characterising debris flow deposits from 35 well-dated alluvial fan surfaces in Owens Valley, California. We show that the average grain sizes of these granitic debris flow sediments precisely scales with sea surface temperature throughout the entire last glacial-interglacial cycle, increasing by ~ 7 % per 1 ° C of climate warming. We compare these data with similar debris flow systems in the Mediterranean (southern Italy) and the tropics (Rio de Janeiro, Brazil), and find equivalent signals over a total temperature range of ~ 14 ° C. In each area, debris flows are largely governed by rainfall intensity during triggering storms, which is known to increase exponentially with temperature. Therefore, we suggest that these debris flow systems are transporting predictably coarser-grained sediment in warmer, stormier conditions. This implies that debris flow sedimentology is governed by discharge thresholds and may be a sensitive proxy for past changes in rainfall intensity. Our findings show that debris flows are sensitive to climate changes over short timescales (≤ 104 years) and therefore highlight the importance of integrating hillslope processes into landscape evolution models, as well as providing new observational constraints to guide this. Finally, we comment on what grain size
A High-strain Flow Law for Olivine: Grain-size Sensitivity and Crystallographic Fabric
NASA Astrophysics Data System (ADS)
Hansen, L. N.; Zimmerman, M. E.; Kohlstedt, D. L.
2011-12-01
The dislocation-accommodated grain-boundary sliding regime, which has recently been recognized in deformation experiments on olivine aggregates, has important implications for the rheological characteristics of the upper mantle and for the interpretation of microstructures in naturally deformed rocks. However, previous experimental studies suffer from both the difficulty in synthesizing samples with a desired mean grain size and the limitation that crystallographic fabrics have not fully developed at low strains. We alleviate these difficulties in a series of innovative deformation experiments. Aggregates of iron-bearing olivine, hot pressed as hollow cylinders, were deformed in torsion at 1200°C in a gas-medium apparatus at constant strain rate until a steady-state shear stress was reached, which occurred by a shear strain of ~5. Since recrystallized grain size is a function of shear stress, we were able to systematically vary the mean grain size among samples by changing the controlling shear-strain rate. Above a shear strain of ~5, strain rate stepping tests were performed to determine the stress exponent. Between each strain-rate step, the strain rate was returned to the original strain rate to reset the microstructure. Experiments were stopped when the total shear strain reached ~11. Our results yield a stress exponent of ~4 and a grain size exponent of ~1, both of which agree with previous small-strain compression experiments on olivine in the dislocation-accommodated grain-boundary sliding regime. If the dependence of strain rate on grain size in the power-law flow law is removed by inserting the grain-size piezometer, the apparent stress exponent in the resulting grain size independent flow law increases to 5.2. Microstructural analyses indicate that very strong crystallographic-preferred orientation (CPO) fabrics are developed with M-indices of ~0.6. The CPO fabrics have [100] maxima sub-parallel to the shear direction and [010] maxima sub
NASA Astrophysics Data System (ADS)
Ayalew, Tibebu B.; Krajewski, Witold F.; Mantilla, Ricardo
2014-09-01
We have conducted extensive hydrologic simulation experiments in order to investigate how the flood scaling parameters in the power-law relationship Q(A)=αAθ, between peak-discharges resulting from a single rainfall-runoff event Q(A) and upstream area A, change as a function of rainfall, runoff coefficient (Cr) that we use as a proxy for catchment antecedent moisture state, hillslope overland flow velocity (vh), and channel flow velocity (vc), all of which are variable in space. We use a physically-based distributed numerical framework that is based on an accurate representation of the drainage network and apply it to the Cedar River basin (A=16,861 km), which is located in Eastern Iowa, USA. Our work is motivated by seminal empirical studies that show that the flood scaling parameters α and θ change from event to event. Uncovering the underlying physical mechanism behind the event-to-event variability of α and θ in terms of catchment physical processes and rainfall properties would significantly improve our ability to predict peak-discharge in ungauged basins (PUB). The simulation results demonstrate how both α and θ are systematically controlled by the interplay among rainfall duration T, spatially averaged rainfall intensity E[I], as well as E[Cr], E[vh], and vc. Specifically, we found that the value of θ generally decreases with increasing values of E[I], E[Cr], and E[vh], whereas its value generally increases with increasing T. Moreover, while α is primarily controlled by E[I], it increases with increasing E[Cr] and E[vh]. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly.
Cross correlation and length scales in turbulent flows near surfaces
NASA Technical Reports Server (NTRS)
Hunt, J. C. R.; Moin, P.; Lee, M.; Moser, R. D.; Spalart, P.; Mansour, N. N.; Kaimal, J. C.; Gaynor, E.
1989-01-01
Two kinds of length scales are used in turbulent flows; 'functional length scales' such as mixing length, dissipation length L(sub epsilon), etc., and 'flow-field length scales' derived from cross correlations of velocity, pressure, etc. in the flow. Some connection between these scales are derived here. We first consider the cross correlation R(sub vv)(y,y(sub 1)) of the normal components u at two heights y, y(sub 1) above a rigid surface, normalized by the velocity y(sub 1) (greater than y). For shear-free boundary layers it is found theoretically, and in field and numerical experiments that R(sub vv) approximately equals y/y(sub 1). For shear layers it is also found that R(sub vv) approximately equals f(y/y(sub 1)) less than or equal to y,y(sub 1). This function f differs slightly between low Reynolds number numerical simulations and field experiments. The lateral structure defined by R(sub vv)(y,r(sub 3); y(sub 1),0) is also self similar and shows that the eddies centered at about y(sub 1) appear to have constant lateral width a(sub 3) above and below y(sub 1), where a(sub 3, sup +) approximately equals 7+1/(1.4dU(sup +)/dy(sup +)), when normalized on u(sub *) and v, where U is the mean velocity. Results for L(sub epsilon, sup -1) from direct numerical simulation are found to compare well with the formula L(sub epsilon, sup -1) = A(sub B)/y + A(sub S)dU/dy/v, for unidirectional and reversing turbulent boundary layers and channel flow, except near where dU/dy approximately equals 0. The conclusion is that the large-scale eddy structure and length scales in these flows are determined by a combination of shear and blocking, and that the vertical component of turbulence has a self-similar structure in both kinds of boundary layer.
Double-loop flows and bidirectional Hebb's law in neural networks
NASA Astrophysics Data System (ADS)
Lecerf, Christophe
1999-03-01
This paper presents the double loop feedback model, which is used for structure and data flow modeling through reinforcement learning in an artificial neural network. We first consider physiological arguments suggesting that loops and double loops are widely spread in the exchange flows of the central nervous system. We then demonstrate that the double loop pattern, named a mental object, works as a functional memory unit and we describe the main properties of a double loop resonator built with the classical Hebb's law learning principle in a feedforward basis. In this model, we show how some mental objects aggregate themselves in building blocks, then what are the properties of such blocks. We propose the mental objects block as the representing structure of a concept in a neural network. We show how the local application of Hebb's law at the cell level leads to the concept of functional organization cost at the network level (upward effect), which explains spontaneous reorganization of mental blocks (downward effect). In this model, the simple hebbian learning paradigm appears to have emergent effects in both upward and downward directions.
Scale modeling flow-induced vibrations of reactor components
Mulcahy, T M
1982-06-01
Similitude relationships currently employed in the design of flow-induced vibration scale-model tests of nuclear reactor components are reviewed. Emphasis is given to understanding the origins of the similitude parameters as a basis for discussion of the inevitable distortions which occur in design verification testing of entire reactor systems and in feature testing of individual component designs for the existence of detrimental flow-induced vibration mechanisms. Distortions of similitude parameters made in current test practice are enumerated and selected example tests are described. Also, limitations in the use of specific distortions in model designs are evaluated based on the current understanding of flow-induced vibration mechanisms and structural response.
Excitation of flow instabilities due to nonlinear scale invariance
Prasad Datta, Dhurjati; Sen, Sudip
2014-05-15
A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in conventional treatments. The present approach is based on a scale invariant nonlinear analytic formalism developed to address irregular motions on a chaotic attractor or in turbulence in a more coherent manner. We have studied two specific applications of this turbulence generating mechanism. The warm plasma Langmuir wave dispersion relation is shown to become unstable in the presence of these multifractal measures. In the second application, these multifractal measures are shown to induce naturally non-Gaussian, i.e., a stretched, Gaussian distribution and anomalous transport for tracer particles from the turbulent advection-diffusion transport equation in a Vlasov plasma flow.
Scaling Laws for the Distribution of Gold, Geothermal, and Gas Resources
NASA Astrophysics Data System (ADS)
Blenkinsop, Thomas
2015-07-01
Mass dimensions of natural resources have important implications for ore-forming processes and resource estimation and exploration. The mass dimension is established from a power law scaling relationship between numbers of resources and distance from an origin. The relation between the total quantity of resource and distance, measured by the mass-radius scaling exponent, may be even more useful. Lode gold deposits, geothermal wells and volcanoes, and conventional and unconventional gas wells are examined in this study. Mass dimensions and scaling exponents generally increase from the lode gold through geothermal wells to gas data sets, reflecting decreasing degrees of clustering. Mass dimensions are similar to or slightly less than the mass-radius scaling exponents, and could be used as estimates of the minimum scaling exponent in the common case that data are not available for the latter. All the resources in this study are formed by fluid fluxes in the crust, and, therefore, percolation theory is an appropriate unifying framework to understand their significance. The mass dimensions indicate that none of the percolation networks that formed the deposits reached the percolation threshold.
Adiabatic shear banding and scaling laws in chip formation with application to cutting of Ti-6Al-4V
NASA Astrophysics Data System (ADS)
Molinari, A.; Soldani, X.; Miguélez, M. H.
2013-11-01
The phenomenon of adiabatic shear banding is analyzed theoretically in the context of metal cutting. The mechanisms of material weakening that are accounted for are (i) thermal softening and (ii) material failure related to a critical value of the accumulated plastic strain. Orthogonal cutting is viewed as a unique configuration where adiabatic shear bands can be experimentally produced under well controlled loading conditions by individually tuning the cutting speed, the feed (uncut chip thickness) and the tool geometry. The role of cutting conditions on adiabatic shear banding and chip serration is investigated by combining finite element calculations and analytical modeling. This leads to the characterization and classification of different regimes of shear banding and the determination of scaling laws which involve dimensionless parameters representative of thermal and inertia effects. The analysis gives new insights into the physical aspects of plastic flow instability in chip formation. The originality with respect to classical works on adiabatic shear banding stems from the various facets of cutting conditions that influence shear banding and from the specific role exercised by convective flow on the evolution of shear bands. Shear bands are generated at the tool tip and propagate towards the chip free surface. They grow within the chip formation region while being convected away by chip flow. It is shown that important changes in the mechanism of shear banding take place when the characteristic time of shear band propagation becomes equal to a characteristic convection time. Application to Ti-6Al-4V titanium are considered and theoretical predictions are compared to available experimental data in a wide range of cutting speeds and feeds. The fundamental knowledge developed in this work is thought to be useful not only for the understanding of metal cutting processes but also, by analogy, to similar problems where convective flow is also interfering with
NASA Astrophysics Data System (ADS)
Frishman, A. M.; Lo, C. C. H.; Shen, Y.; Nakagawa, N.
2009-03-01
Shot peening is frequently used to improve mechanical characteristics of metallic components' surfaces. The physical properties of shot peened surfaces exhibit deviations from their bulk values. This paper shows that there exists a scaling law (universality) among seemingly unrelated material property deviations and among different peening conditions. We present examples and support for scaling behaviors based on experimental data on Almen strip deflection, cold work and residual stress profiles of a shot peened nickel-base superalloy (Waspaloy), and swept frequency eddy current signals used for NDE studies of another shot peened nickel-base superalloy (Inconel 718). In addition, a fast impedance calculation formula for a coil placed on a metal with small, continuous conductivity deviation is presented and used for analytical and numerical study of eddy current signals.
Scaling laws to quantify tidal dissipation in star-planet systems
NASA Astrophysics Data System (ADS)
Auclair-Desrotour, P.; Mathis, S.; Le Poncin-Lafitte, C.
2015-12-01
Planetary systems evolve over secular time scales. One of the key mechanisms that drive this evolution is tidal dissipation. Submitted to tides, stellar and planetary fluid layers do not behave like rocky ones. Indeed, they are the place of resonant gravito-inertial waves. Therefore, tidal dissipation in fluid bodies strongly depends on the excitation frequency while this dependence is smooth in solid ones. Thus, the impact of the internal structure of celestial bodies must be taken into account when studying tidal dynamics. The purpose of this work is to present a local model of tidal gravito-inertial waves allowing us to quantify analytically the internal dissipation due to viscous friction and thermal diffusion, and to study the properties of the resonant frequency spectrum of the dissipated energy. We derive from this model scaling laws characterizing tidal dissipation as a function of fluid parameters (rotation, stratification, diffusivities) and discuss them in the context of star-planet systems.
Unification of Small and Large Time Scales for Biological Evolution: Deviations from Power Law
NASA Astrophysics Data System (ADS)
Chowdhury, Debashish; Stauffer, Dietrich; Kunwar, Ambarish
2003-02-01
We develop a unified model that describes both “micro” and “macro” evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the “microevolution” over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the “macroevolution” over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.
Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves
2014-01-01
Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221
Goh, Segun; Lee, Keumsook; Choi, MooYoung; Fortin, Jean-Yves
2014-01-01
Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) “block stop” and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221
Analysis of the scaling laws for the turbulence driven panel responses
NASA Astrophysics Data System (ADS)
Ciappi, E.; Magionesi, F.; De Rosa, S.; Franco, F.
2012-07-01
The high computational costs, associated to the numerical solution of the fluctuating pressure field generated at the wall by the turbulent boundary layer and of the induced structural response, push for the exploration of alternative methodologies of analysis. Wall pressure fluctuations spectra are often modeled using semi-empirical expressions based on the experimental evidence and on the identification of universal scaling laws. In this work the possibility to adopt a dimensionless representation, able to provide a universal expression for the structural response of plates under turbulent boundary layer excitations, is investigated with the help of pressure fluctuations and acceleration experimental data sets. The test article is a plane thin plate wetted by a fluid over one face, the boundary layer is fully developed and pressure gradient effects are negligible. The attention is devoted to the investigation and the definition of a normalization of the required axes: the excitation frequency and the power spectral density of the structural response. The analysis is initially based on analytical models for the structural response under turbulent boundary layer excitations. The proposed scaling laws are successively and successfully applied to four data sets measured in different conditions both in wind tunnels and in a towing tank.
Constraints on plate tectonics initiation from scaling laws for single-cell convection
NASA Astrophysics Data System (ADS)
Wong, Teresa; Solomatov, Viatcheslav S.
2016-08-01
The Earth is the only planet known to have plate tectonics, while other planets are covered with a stagnant lid. On the Earth, the initiation of subduction, which is thought to be the fundamental process for plate tectonics initiation, is caused not only by the negative buoyancy of the lithosphere but also by the forces from plate motions. However, for planets which do not have plate tectonics, the very first episode of lithospheric failure has to be caused by forces other than plate motions. Sublithospheric convection has been proposed as a possible mechanism that provides lithospheric instability through inducing stresses in the lithosphere, and lithospheric failure can occur when the yield stress is below a critical value. We test the applicability of scaling laws for the critical yield stress obtained in single-cell convection simulations to strongly time-dependent multi-cell systems. We show that with an appropriate choice of characteristic aspect ratio for the convective system, the scaling laws from single-cell simulations can be used to evaluate the conditions on the terrestrial planets in the inner Solar System for plate tectonics to exist. In agreement with previous studies, the estimated values for critical yield stress and coefficient of friction are much lower than the expected values for the Earth's lithosphere.
Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media.
Combe, Gaël; Richefeu, Vincent; Stasiak, Marta; Atman, Allbens P F
2015-12-01
In this Letter, we address the relationship between the statistical fluctuations of grain displacements for a full quasistatic plane shear experiment, and the corresponding anomalous diffusion exponent α. We experimentally validate a particular case of the Tsallis-Bukman scaling law, α=2/(3-q), where q is obtained by fitting the probability density function (PDF) of the displacement fluctuations with a q-Gaussian distribution, and the diffusion exponent is measured independently during the experiment. Applying an original technique, we are able to evince a transition from an anomalous diffusion regime to a Brownian behavior as a function of the length of the strain window used to calculate the displacements of the grains. The outstanding conformity of fitting curves to a massive amount of experimental data shows a clear broadening of the fluctuation PDFs as the length of the strain window decreases, and an increment in the value of the diffusion exponent-anomalous diffusion. Regardless of the size of the strain window considered in the measurements, we show that the Tsallis-Bukman scaling law remains valid, which is the first experimental verification of this relationship for a classical system at different diffusion regimes. We also note that the spatial correlations show marked similarities to the turbulence in fluids, a promising indication that this type of analysis can be used to explore the origins of the macroscopic friction in confined granular materials. PMID:26684145
Spherule layers, crater scaling laws, and the population of ancient terrestrial impactors
NASA Astrophysics Data System (ADS)
Johnson, Brandon C.; Collins, Gareth S.; Minton, David A.; Bowling, Timothy J.; Simonson, Bruce M.; Zuber, Maria T.
2016-06-01
Ancient layers of impact spherules provide a record of Earth's early bombardment history. Here, we compare different bombardment histories to the spherule layer record and show that 3.2-3.5 Ga the flux of large impactors (10-100 km in diameter) was likely 20-40 times higher than today. The E-belt model of early Solar System dynamics suggests that an increased impactor flux during the Archean is the result of the destabilization of an inward extension of the main asteroid belt (Bottke et al., 2012). Here, we find that the nominal flux predicted by the E-belt model is 7-19 times too low to explain the spherule layer record. Moreover, rather than making most lunar basins younger than 4.1 Gyr old, the nominal E-belt model, coupled with a corrected crater diameter scaling law, only produces two lunar basins larger than 300 km in diameter. We also show that the spherule layer record when coupled with the lunar cratering record and careful consideration of crater scaling laws can constrain the size distribution of ancient terrestrial impactors. The preferred population is main-belt-like up to ∼50 km in diameter transitioning to a steep distribution going to larger sizes.
Scaling and pedotransfer in numerical simulations of flow and transport in soils
Technology Transfer Automated Retrieval System (TEKTRAN)
Flow and transport parameters of soils in numerical simulations need to be defined at the support scale of computational grid cells. Such support scale can substantially differ from the support scale in laboratory or field measurements of flow and transport parameters. The scale-dependence of flow a...
Gradient Flow and Scale Setting on MILC HISQ Ensembles
Bazavov, A.; Bernard, C.; Brown, N.; Komijani, J.; DeTar, C.; Foley, J.; Levkova, L.; Gottlieb, Steven; Heller, U. M.; Laiho, J.; et al
2016-05-25
We report on a scale determination with gradient-flow techniques on the Nf = 2 + 1 + 1 HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales p √t0/a and w0/a and their tree-level improvements,√t0;imp and w0;imp, are computed on each ensemble using Symanzik ow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolatedmore » to the continuum and interpolated to physical quark masses. We also determine the scales p t0 = 0:1416(+8-5) fm and w0 = 0:1717(+12-11) fm, where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of w0 and √t0 is comparable to or more precise than the best previous estimates, respectively. We also find the continuum mass-dependence of w0 that will be useful for estimating the scales of other ensembles. Furthermore, we estimate the integrated autocorrelation length of . For long flow times, the autocorrelation length of appears to be comparable to or smaller than that of the topological charge.« less
Pore scale imaging of transport in unsaturated flows
NASA Astrophysics Data System (ADS)
Jimenez-Martinez, J.; De Anna, P.; Turuban, R.; Tabuteau, H.; Le Borgne, T.; Meheust, Y.
2013-12-01
The unsaturated zone plays a key role in the transfer of chemical elements from the surface to the subsurface. Predicting the transport of chemical species through unsaturated porous media poses several challenges. The spatial distribution of wetting (water) and non-wetting (air) clusters focuses the water flow onto narrow and complex flow paths. The resulting velocity distribution is wider than that of saturated flow, and is controlled by the saturation degree. As saturation decreases, very low velocity zones in regions of trapped fluid coexist with connected fluid clusters with relatively high velocities. As a consequence, the dispersion of solute elements strongly depends on the saturation degree. We use a novel experimental setup to study the dependence on saturation of the longitudinal dispersion coefficient. The two-dimensional (2d) horizontal medium consists of cylindrical grains and is built using soft lithography. The joint injection of the two phases (wetting and non-wetting) provides a controlled homogeneous saturation in the medium. The simultaneous precise measurement of the flow field, the spatial distribution of wetting and non-wetting phases, and the 2d tracer concentration field, as well as breakthrough curves at different locations, are used to investigate the relationship between the flow field complexity and dispersion properties. The experimental results show a non-Fickian transport behavior, characterized by heavy tailed breakthrough curves and a longitudinal plume variance that does not scale linearly with time. We document and discuss the dependence of these transport properties on the saturation degree.
Small scale flow processes in aqueous heterogeneous porous media
Rashidi, M.; Dickenson, E.
1996-04-01
Small scale flow processes in aqueous heterogeneous porous systems have been studied experimentally via novel nonintrusive fluorescence imaging techniques. The techniques involve 3D visualization and quantification of flow fields within a refractive index-matched transparent porous column. The refractive index-matching yields a transparent porous medium, free from any scattering and refraction at the solid-liquid interfaces, as a result allowing direct optical probing at any point within the porous system. By illuminating the porous regions within the column with a planar sheet of laser beam, flow processes through the porous medium can be observed microscopically, and qualitative and quantitative in-pore transport information can be obtained at a good resolution and a good accuracy. A CCD camera is used to record the fluorescent images at every vertical plane location while sweeping back and forth across the column. These digitized flow images are then analyzed and accumulated over a 3D volume within the column. Series of flow experiments in aqueous, refractive index-matched, porous systems packed with natural mineral particles have been performed successfully in these laboratories.
Scaling of the flow-stiffness relationship in weakly correlated single fractures
NASA Astrophysics Data System (ADS)
Petrovitch, Christopher L.
The remote characterization of the hydraulic properties of fractures in rocks is important in many subsurface projects. Fractures create uncertainty in the hydraulic properties of the subsurface in that their topology controls the amount of flow that can occur in addition to that from the matrix. In turn, the fracture topology is also affected by stress which alters the topology as the stress changes directly. This alteration of fracture topology with stress is captured by fracture specific stiffness. The specific stiffness of a single fracture can be remotely probed from the attenuation and velocity of seismic waves. The hydromechanical coupling of single fractures, i.e. the relationship between flow and stiffness, holds the key to finding a method to remotely characterize a fractures hydraulic properties. This thesis is separated into two parts: (1) a description of the hydromechanical coupling of fractures based on numerical models used to generate synthetic fractures, compute the flow through a fracture, and deform fracture topologies to unravel the scaling function that is fundamental to the hydromechanical coupling of single fractures; (2) a Discontinuous Galerkin (DG) method was developed to accurately simulate the scattered seismic waves from realistic fracture topologies. The scaling regimes of fluid flow and specific stiffness in weakly correlated fractures are identified by using techniques from Percolation Theory and initially treating the two processes separately. The fixed points associated with fluid flow were found to display critical scaling while the fixed points for specific stiffness were trivial. The two processes could be indirectly related because the trivial scaling of the mechanical properties allowed the specific stiffness to be used as surrogate to the void area fraction. The dynamic transport exponent was extracted at threshold by deforming fracture geometries within the effective medium regime (near the ``cubic law'' regime) to the
Local dynamic subgrid-scale models in channel flow
NASA Technical Reports Server (NTRS)
Cabot, William H.
1994-01-01
The dynamic subgrid-scale (SGS) model has given good results in the large-eddy simulation (LES) of homogeneous isotropic or shear flow, and in the LES of channel flow, using averaging in two or three homogeneous directions (the DA model). In order to simulate flows in general, complex geometries (with few or no homogeneous directions), the dynamic SGS model needs to be applied at a local level in a numerically stable way. Channel flow, which is inhomogeneous and wall-bounded flow in only one direction, provides a good initial test for local SGS models. Tests of the dynamic localization model were performed previously in channel flow using a pseudospectral code and good results were obtained. Numerical instability due to persistently negative eddy viscosity was avoided by either constraining the eddy viscosity to be positive or by limiting the time that eddy viscosities could remain negative by co-evolving the SGS kinetic energy (the DLk model). The DLk model, however, was too expensive to run in the pseudospectral code due to a large near-wall term in the auxiliary SGS kinetic energy (k) equation. One objective was then to implement the DLk model in a second-order central finite difference channel code, in which the auxiliary k equation could be integrated implicitly in time at great reduction in cost, and to assess its performance in comparison with the plane-averaged dynamic model or with no model at all, and with direct numerical simulation (DNS) and/or experimental data. Other local dynamic SGS models have been proposed recently, e.g., constrained dynamic models with random backscatter, and with eddy viscosity terms that are averaged in time over material path lines rather than in space. Another objective was to incorporate and test these models in channel flow.
Local dynamic subgrid-scale models in channel flow
NASA Astrophysics Data System (ADS)
Cabot, William H.
1994-12-01
The dynamic subgrid-scale (SGS) model has given good results in the large-eddy simulation (LES) of homogeneous isotropic or shear flow, and in the LES of channel flow, using averaging in two or three homogeneous directions (the DA model). In order to simulate flows in general, complex geometries (with few or no homogeneous directions), the dynamic SGS model needs to be applied at a local level in a numerically stable way. Channel flow, which is inhomogeneous and wall-bounded flow in only one direction, provides a good initial test for local SGS models. Tests of the dynamic localization model were performed previously in channel flow using a pseudospectral code and good results were obtained. Numerical instability due to persistently negative eddy viscosity was avoided by either constraining the eddy viscosity to be positive or by limiting the time that eddy viscosities could remain negative by co-evolving the SGS kinetic energy (the DLk model). The DLk model, however, was too expensive to run in the pseudospectral code due to a large near-wall term in the auxiliary SGS kinetic energy (k) equation. One objective was then to implement the DLk model in a second-order central finite difference channel code, in which the auxiliary k equation could be integrated implicitly in time at great reduction in cost, and to assess its performance in comparison with the plane-averaged dynamic model or with no model at all, and with direct numerical simulation (DNS) and/or experimental data. Other local dynamic SGS models have been proposed recently, e.g., constrained dynamic models with random backscatter, and with eddy viscosity terms that are averaged in time over material path lines rather than in space. Another objective was to incorporate and test these models in channel flow.
NASA Astrophysics Data System (ADS)
Chajęcki, Zbigniew; Lisa, Mike
2009-11-01
Collective, explosive flow in central heavy ion collisions manifests itself in the mass dependence of p distributions and femtoscopic length scales, measured in the soft sector (p≲1GeV/c). Measured p distributions from proton-proton collisions differ significantly from those from heavy ion collisions. This has been taken as evidence that p+p collisions generate little collective flow, a conclusion in line with naive expectations. We point out possible hazards of ignoring phase-space restrictions due to conservation laws when comparing high- and low-multiplicity final states. Already in two-particle correlation functions, we see clear signals of such phase-space restrictions in low-multiplicity collisions at RHIC. We discuss how these same effects, then, must appear in the single particle spectra. We argue that the effects of energy and momentum conservation actually dominate the observed systematics, and that p+p collisions may be much more similar to heavy ion collisions than generally thought.
Turbulent flow within vegetated areas: interaction of spatial scales
NASA Astrophysics Data System (ADS)
Ricardo, A.; Franca, M. J.; Schleiss, A.; Ferreira, R. M.
2010-12-01
River engineering works procure, in a sustainable society, not only flood protection but also the promotion of high standards of water quality and habitat diversity within good landscape design practices. Rivers are often subjected to re-design, in the scope of restoration or hazard mitigation works. Special care must be devoted to marginal wetlands as they constitute the interface between terrestrial and aquatic systems; herein, the flow controls the fluxes of sediment, nutrients and contaminants. The characteristics of the flow, namely turbulent velocities, stresses and fluxes, are strongly dependent on the density and resistance of the vegetation. To understand the flow resistance phenomena in vegetated streams, similar conditions to those found in nature were reproduced in laboratory where vegetation were simulated by dense arrays of vertical emergent stems. One key feature is the heterogeneity in the spatial distribution of the stems. In general, stems are not uniformly distributed but arranged in alternating patches of lower and higher stem densities. Within the multiply-averaged paradigm for flow characterization, effects of patchiness are formally expressed as interaction of different spatial scales. This work is aimed at characterizing the interaction of spatial scales, represented by different stem densities, on the structure of the turbulent flow in the inter-stem space. The objectives are i) to quantify the flow structure in terms of instantaneous velocities and spectra, ii) to quantify the mean (double-averaged) flow at the scale of inter-stem space and iii) to characterize qualitatively the influence of different wavelengths in the spatial modulation of the flow. To meet the proposed objectives, two experimental tests were carried out in a 12.5 m long and 40.8 cm wide tilting recirculation flume of the Laboratory of Hydraulics of IST featuring i) a uniform stem density of 400 stems/m2 and ii) a varying stem density with a fixed wavelength of 0.5 m
Viewing inside Pyroclastic Flows - Large-scale Experiments on hot pyroclast-gas mixture flows
NASA Astrophysics Data System (ADS)
Breard, E. C.; Lube, G.; Cronin, S. J.; Jones, J.
2014-12-01
Pyroclastic density currents are the largest threat from volcanoes. Direct observations of natural flows are persistently prevented because of their violence and remain limited to broad estimates of bulk flow behaviour. The Pyroclastic Flow Generator - a large-scale experimental facility to synthesize hot gas-particle mixture flows scaled to pyroclastic flows and surges - allows investigating the physical processes behind PDC behaviour in safety. The ability to simulate natural eruption conditions and to view and measure inside the hot flows allows deriving validation and calibration data sets for existing numerical models, and to improve the constitutive relationships necessary for their effective use as powerful tools in hazard assessment. We here report on a systematic series of large-scale experiments on up to 30 ms-1 fast, 2-4.5 m thick, 20-35 m long flows of natural pyroclastic material and gas. We will show high-speed movies and non-invasive sensor data that detail the internal structure of the analogue pyroclastic flows. The experimental PDCs are synthesized by the controlled 'eruption column collapse' of variably diluted suspensions into an instrumented channel. Experiments show four flow phases: mixture acceleration and dilution during free fall; impact and lateral blasting; PDC runout; and co-ignimbrite cloud formation. The fully turbulent flows reach Reynolds number up to 107 and depositional facies similar to natural deposits. In the PDC runout phase, the shear flows develop a four-partite structure from top to base: a fully turbulent, strongly density-stratified ash cloud with average particle concentrations <<1vol%; a transient, turbulent dense suspension region with particle concentrations between 1 and 10 vol%; a non-turbulent, aerated and highly mobile dense underflows with particle concentrations between 40 and 50 vol%; and a vertically aggrading bed of static material. We characterise these regions and the exchanges of energy and momentum
Gradient flow and scale setting on MILC HISQ ensembles
NASA Astrophysics Data System (ADS)
Bazavov, A.; Bernard, C.; Brown, N.; Komijani, J.; DeTar, C.; Foley, J.; Levkova, L.; Gottlieb, Steven; Heller, U. M.; Laiho, J.; Sugar, R. L.; Toussaint, D.; Van de Water, R. S.; MILC Collaboration
2016-05-01
We report on a scale determination with gradient-flow techniques on the Nf=2 +1 +1 highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales √{t0}/a and w0/a and their tree-level improvements, √{t0 ,imp} and w0 ,imp, are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density E . Using a combination of continuum chiral-perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales √{t0 }=0.1416 (+8/-5) fm and w0=0.1714 (+15/-12) fm , where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of w0 and √{t0} is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass dependence of √{t0} and w0, which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of ⟨E (t )⟩. For long flow times, the autocorrelation length of ⟨E ⟩ appears to be comparable to that of the topological charge.
Bubble motion through a generalized power-law fluid flowing in a vertical tube.
Mukundakrishnan, Karthik; Eckmann, David M; Ayyaswamy, P S
2009-04-01
Intravascular gas embolism may occur with decompression in space flight, as well as during cardiac and vascular surgery. Intravascular bubbles may be deposited into any end organ, such as the heart or the brain. Surface interactions between the bubble and the endothelial cells lining the vasculature result in serious impairment of blood flow and can lead to heart attack, stroke, or even death. To develop effective therapeutic strategies, there is a need for understanding the dynamics of bubble motion through blood and its interaction with the vessel wall through which it moves. Toward this goal, we numerically investigate the axisymmetric motion of a bubble moving through a vertical circular tube in a shear-thinning generalized power-law fluid, using a front-tracking method. The formulation is characterized by the inlet Reynolds number, capillary number, Weber number, and Froude number. The flow dynamics and the associated wall shear stresses are documented for a combination of two different inlet flow conditions (inlet Reynolds numbers) and three different effective bubble radii (ratio of the undeformed bubble radii to the tube radii). The results of the non-Newtonian model are then compared with that of the model assuming a Newtonian blood viscosity. Specifically, for an almost occluding bubble (effective bubble radius = 0.9), the wall shear stress and the bubble residence time are compared for both Newtonian and non-Newtonian cases. Results show that at low shear rates, for a given pressure gradient the residence time for a non-Newtonian flow is higher than that for a Newtonian flow. PMID:19426324
The multi-scale modelling of coronary blood flow.
Lee, Jack; Smith, Nicolas P
2012-11-01
Coronary flow is governed by a number of determinants including network anatomy, systemic afterload and the mechanical interaction with the myocardium throughout the cardiac cycle. The range of spatial scales and multi-physics nature of coronary perfusion highlights a need for a multiscale framework that captures the relevant details at each level of the network. The goal of this review is to provide a compact and accessible introduction to the methodology and current state of the art application of the modelling frameworks that have been used to study the coronary circulation. We begin with a brief description of the seminal experimental observations that have motivated the development of mechanistic frameworks for understanding how myocardial mechanics influences coronary flow. These concepts are then linked to an overview of the lumped parameter models employed to test these hypotheses. We then outline the full and reduced-order (3D and 1D) continuum mechanics models based on the Navier-Stokes equations and highlight, with examples, their application regimes. At the smaller spatial scales the case for the importance of addressing the microcirculation is presented, with an emphasis on the poroelastic approach that is well-suited to bridge an existing gap in the development of an integrated whole heart model. Finally, the recent accomplishments of the wave intensity analysis and related approaches are presented and the clinical outlook for coronary flow modelling discussed. PMID:22565815
Hydrogen-Bromine Flow Battery: Hydrogen Bromine Flow Batteries for Grid Scale Energy Storage
2010-10-01
GRIDS Project: LBNL is designing a flow battery for grid storage that relies on a hydrogen-bromine chemistry which could be more efficient, last longer and cost less than today’s lead-acid batteries. Flow batteries are fundamentally different from traditional lead-acid batteries because the chemical reactants that provide their energy are stored in external tanks instead of inside the battery. A flow battery can provide more energy because all that is required to increase its storage capacity is to increase the size of the external tanks. The hydrogen-bromine reactants used by LBNL in its flow battery are inexpensive, long lasting, and provide power quickly. The cost of the design could be well below $100 per kilowatt hour, which would rival conventional grid-scale battery technologies.
Dynamically Scaled Glottal Flow Through Symmetrically Oscillating Vocal Fold Models
NASA Astrophysics Data System (ADS)
Halvorson, Lori; Baitinger, Andrew; Sherman, Erica; Krane, Michael; Zhang, Lucy; Wei, Timothy
2011-11-01
Experimental results derived from DPIV measurements in a scaled up dynamic human vocal fold model are presented. The 10x scale vocal fold model is a new design that incorporates key features of vocal fold oscillatory motion. This includes coupling of down/upstream rocking as well as the oscillatory open/close motions. Experiments were dynamically scaled to examine a range of frequencies, 100 - 200 Hz, corresponding to the male and female voice. By using water as the working fluid, very high resolution, both spatial and temporal resolution, was achieved. Time resolved movies of flow through symmetrically oscillating vocal folds will be presented. Both individual realizations as well as phase-averaged data will be shown. Key features, such as randomness and development time of the Coanda effect, vortex shedding, and volume flow rate data will be shown. In this talk, effects associated with paralysis of one vocal fold will be discussed. This talk provides the baseline fluid dynamics for the vocal fold paralysis study presented in Sherman, et al. Supported by the NIH.
Very large-scale motions in a turbulent pipe flow
NASA Astrophysics Data System (ADS)
Lee, Jae Hwa; Jang, Seong Jae; Sung, Hyung Jin
2011-11-01
Direct numerical simulation of a turbulent pipe flow with ReD=35000 was performed to investigate the spatially coherent structures associated with very large-scale motions. The corresponding friction Reynolds number, based on pipe radius R, is R+=934, and the computational domain length is 30 R. The computed mean flow statistics agree well with previous DNS data at ReD=44000 and 24000. Inspection of the instantaneous fields and two-point correlation of the streamwise velocity fluctuations showed that the very long meandering motions exceeding 25R exist in logarithmic and wake regions, and the streamwise length scale is almost linearly increased up to y/R ~0.3, while the structures in the turbulent boundary layer only reach up to the edge of the log-layer. Time-resolved instantaneous fields revealed that the hairpin packet-like structures grow with continuous stretching along the streamwise direction and create the very large-scale structures with meandering in the spanwise direction, consistent with the previous conceptual model of Kim & Adrian (1999). This work was supported by the Creative Research Initiatives of NRF/MEST of Korea (No. 2011-0000423).
Modeling of Multi-Scale Channeling Phenomena in Porous Flow
NASA Astrophysics Data System (ADS)
Räss, Ludovic; Omlin, Samuel; Yarushina, Viktoriya; Simon, Nina; Podladchikov, Yuri
2015-04-01
Predictive modeling of fluid percolation through tight porous rocks is critical to evaluate environmental risks associated with waste storage and reservoir operations. To understand the evolution of two-phase mixtures of fluid and solid it is insufficient to only combine single-phase fluid flow methods and solid mechanics. A proper coupling of these two different multi-scales physical processes is required to describe the complex evolution of permeability and porosity in space and in time. We conduct numerical modeling experiments in geometrically simple but physically complex systems of stressed rocks containing self-focusing porous flow. Our model is physically and thermodynamically consistent and describes the formation and evolution of fluid pathways. The model consists of a system of coupled equations describing poro-elasto-viscous deformation and flow. Nonlinearity of the solid rheology is also taken into account. We have developed a numerical application based on an iterative finite difference scheme that runs on mutli-GPUs cluster in parallel. In order to validate these models, we consider the largest CO2 sequestration project in operation at the Sleipner field in the Norwegian North Sea. Attempts to match the observations at Sleipner using conventional reservoir simulations fail to capture first order observations, such as the seemingly effortless vertical flow of CO2 through low permeability shale layers and the formation of focused flow channels or chimneys. Conducted high-resolution three-dimensional numerical simulations predict the formation of dynamically evolving high porosity and permeability pathways as a natural outcome of porous flow nonlinearly coupled with rock deformation, which may trigger leakage through low permeability barriers.
Space-scale unfolding mechanism in canonical multi-scale flows
NASA Astrophysics Data System (ADS)
Baj, Pawel; Bruce, Paul J. K.; Buxton, Oliver R. H.
2015-11-01
Some recent studies on fractal generated turbulence revealed a highly increased transverse turbulent scalar flux downstream of fractal grids compared to regular grids. The complexity of these flows makes it impossible to track the origins of this phenomenon, often referred to as the space-scale unfolding mechanism (SSU). Thus research on flows past canonical examples of single and multi-scale obstacles, which are arrays of bars of the same and different thicknesses, was undertaken in order to investigate the SSU's roots. The velocity field and the scalar concentration field were measured simultaneously downstream of the obstacles by means of particle image velocimetry and laser induced fluorescence techniques. It is observed that the concentration field behind the multi-scale obstacle undergoes intense quasi-periodic transverse scalar bursts, which are believed to be the manifestation of the SSU, whereas such events are either weak or absent in the single scale configuration. Investigation of the velocity field reveals a phase locking between wakes of different scale objects in terms of the phase-conditioned transverse integral length scale. Both phenomena are observed to be triggered at the downstream position corresponding to the wakes' intersection point. The authors acknowledge support form the EU through the FP7 Marie Curie MULTISOLVE project (grant agreement No. 317269).
Dynamic coupling of pore-scale and reservoir-scale models for multiphase flow
NASA Astrophysics Data System (ADS)
Sheng, Qiang; Thompson, Karsten
2013-09-01
The concept of coupling pore-scale and continuum-scale models for subsurface flow has long been viewed as beneficial, but implementation has been slow. In this paper, we present an algorithm for direct coupling of a dynamic pore-network model for multiphase flow with a traditional continuum-scale simulator. The ability to run the two models concurrently (exchanging parameters and boundary conditions in real numerical time) is made possible by a new dynamic pore-network model that allows simultaneous injection of immiscible fluids under either transient-state or steady-state conditions. Allowing the pore-scale model to evolve to steady state during each time step provides a unique method for reconciling the dramatically different time and length scales across the coupled models. The model is implemented by embedding networks in selected gridblocks in the reservoir model. The network model predicts continuum-scale parameters such as relative permeability or average capillary pressure from first principles, which are used in the continuum model. In turn, the continuum reservoir simulator provides boundary conditions from the current time step back to the network model to complete the coupling process. The model is tested for variable-rate immiscible displacements under conditions in which relative permeability depends on flow rate, thus demonstrating a situation that cannot be modeled using a traditional approach. The paper discusses numerical challenges with this approach, including the fact that there is not a way to explicitly force pore-scale phase saturation to equal the continuum saturation in the host gridblock without an artificial constraint. Hurdles to implementing this type of modeling in practice are also discussed.
Instream water use in the United States: water laws and methods for determining flow requirements
Lamb, Berton L.; Doerksen, Harvey R.
1987-01-01
the conterminous United States consists of about 12,000 miles of maintained waterways, over which about 500 million tons of cargo is carried each year (U.S. Army Corps of Engineers, 1988, p. 16). Although not so widely practiced in recent years, streams have been used to dispose of raw waste products from homes, communities, and factories. This use has been discouraged by law and public policy because of public health concerns and the damage it causes to the environment. Beginning in the mid-1960's, other instream uses gained new prominence in the water-resources arena-the assertion of a legal right to a free-flowing stream for biological, recreational, and esthetic purposes. These uses themselves, however, are not new. Riverine habitat always has produced fish, and the beauty of flowing water always has evoked a strong sense of esthetic appreciation. What is new is the emerging legitimacy and awareness of these noneconomic uses under State and Federal laws and regulations. In the past, environmental uses of flowing water were ignored, for the most part, under a long-standing legal tradition that favored offstream uses and certain instream uses that had a strong economic basis. The history of instream-flow policy debate really concerns those recently recognized types of interim uses. Although the more transitional water uses have been protected by law, the recognition of other in stream uses has resulted in substantial changes in State water laws. Although methods for determining the volume of water needed for most traditional water uses are relatively straight-forward and well-established, methods for determining water requirements for the in stream uses have been developed only recently and are continuing to evolve. Water laws that have favored the more traditional water uses, the inherent nature of conflict between instream and offstream water uses, and the special kinds of technological and philosophical problems posed by the "newer" types of instream uses are
Resolving electron scale turbulence in spherical tokamaks with flow shear
Guttenfelder, W.; Candy, J.
2011-02-15
This paper presents nonlinear gyrokinetic simulations of electron temperature gradient (ETG) turbulence based on spherical tokamak (ST) parameters. Most significantly the simulations include the strong toroidal flow and flow shear present in STs that suppress ion-scale turbulence while using kinetic ions at full mass ratio (m{sub i}/m{sub e}=3600). The flow shear provides a physical long-wavelength cutoff mechanism that aids saturation of the simulations, which has previously been demonstrated to be problematic depending on magnetic shear. As magnetic shear varies widely in STs we systematically demonstrate saturation and convergence of the ETG simulations with respect to grid resolution, physical domain size, and boundary conditions. While using reduced ion mass or adiabatic ions can lessen computational expense they do not always provide reliable results. The resulting spectra from converged simulations are anisotropic everywhere in contrast to previous ETG simulations without flow shear. These results have implications for interpreting turbulence measurements, and represent an important step in determining when and where ETG turbulence is expected to be relevant in ST plasmas. They are also important in the context of validating simulations with both experimental transport analysis and turbulence measurements.
Couette flow of non-Newtonian power-law fluids in narrow eccentric annuli
Yang, L.; Chukwu, G.A.
1995-03-01
The analysis of the steady laminar Couette flow of non-Newtonian power-law fluids in a narrow eccentric cannulus is employed in this study to compute the surge or swab pressure encountered when running or pulling tubular goods in a liquid-filled borehole, respectively. Excessive surge pressure can fracture the formation, while uncontrolled swab pressure can result in well blowout. In this study, the eqs of motion are analytically solved and the solution of these eqs is presented in both dimensionless and graphical forms for a more general application to computing the surge or swab pressure. The family of curves is presented for different pipe/borehole eccentricity ratios and power-law fluid index values which span the range of typical drilling fluids. By employing the computed surge pressures, in combination with the family of curves, the maximum velocity at which the casing can be run in the hole without the danger of fracturing the formation can be obtained. The expected error in surge computation for a narrow concentric annulus represented by a slot, as a result of eccentricity, is evaluated. The results obtained from the these analyses will aid in proper design and optimization of drilling programs, especially in deviated holes.
Finite element modeling of cracked bodies using the Bodner-Partom flow law
NASA Technical Reports Server (NTRS)
Nicholas, T.; Bohun, M.
1985-01-01
The Bodner-Partom flow law which models viscoplastic material behavior has been used to represent two nickel-base superalloys, Gatorized IN100 and Inconel 718 at elevated temperature. Procedures for the determination of the material parameters are presented along with a discussion of the physical significance of each parameter. The material model is then used in finite element computations to evaluate the response of cracked bodies to monotonic, sustained, or cyclic loading. Geometries investigated include the center cracked panel, the compact tension specimen, and the single cracked ring under tension. A Hybrid Experimental Numerical (HEN) procedure has been used to deduce crack growth rates from experimental displacement measurements which are input into finite element computations. The results of several studies conducted over the last several years are summarized.
Stewart, Charles W.; Meyer, Perry A.; Kurath, Dean E.; Barnes, Steven M.
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 performed to establish the methodology to perform reduced-scale gas retention and release tests with PJM systems in non-Newtonian fluids with gas generation. The technical basis for scaled testing with unsteady jet mixing systems in gas-generating non-Newtonian fluids is presented in the form of a bubble migration model that accounts for the gas generation rate, the average bubble rise velocity, and the geometry of the vessel. Scaling laws developed from the model were validated with gas holdup and release tests conducted at three scales: large scale, 1/4 scale, and 1/9 scale. Experiments were conducted with two non-Newtonian simulants with in-situ gas generation by decomposition of hydrogen peroxide. The data were compared non-dimensionally, and the important scale laws were examined. From these results, scaling laws are developed which allow the design of mixing systems at a reduced scale.
NASA Astrophysics Data System (ADS)
Lube, G.; Breard, E. C. P.; Cronin, S. J.; Jones, J.
2015-03-01
Pyroclastic flow eruption large-scale experiment (PELE) is a large-scale facility for experimental studies of pyroclastic density currents (PDCs). It is used to generate high-energy currents involving 500-6500 m3 natural volcanic material and air that achieve velocities of 7-30 m s-1, flow thicknesses of 2-4.5 m, and runouts of >35 m. The experimental PDCs are synthesized by a controlled "eruption column collapse" of ash-lapilli suspensions onto an instrumented channel. The first set of experiments are documented here and used to elucidate the main flow regimes that influence PDC dynamic structure. Four phases are identified: (1) mixture acceleration during eruption column collapse, (2) column-slope impact, (3) PDC generation, and (4) ash cloud diffusion. The currents produced are fully turbulent flows and scale well to natural PDCs including small to large scales of turbulent transport. PELE is capable of generating short, pulsed, and sustained currents over periods of several tens of seconds, and dilute surge-like PDCs through to highly concentrated pyroclastic flow-like currents. The surge-like variants develop a basal <0.05 m thick regime of saltating/rolling particles and shifting sand waves, capped by a 2.5-4.5 m thick, turbulent suspension that grades upward to lower particle concentrations. Resulting deposits include stratified dunes, wavy and planar laminated beds, and thin ash cloud fall layers. Concentrated currents segregate into a dense basal underflow of <0.6 m thickness that remains aerated. This is capped by an upper ash cloud surge (1.5-3 m thick) with 100 to 10-4 vol % particles. Their deposits include stratified, massive, normally and reversely graded beds, lobate fronts, and laterally extensive veneer facies beyond channel margins.
Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales
NASA Technical Reports Server (NTRS)
Podesta, J. J.; Roberts, D. A.; Goldstein, M. L.
2006-01-01
The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.
Growth patterns and scaling laws governing AIDS epidemic in Brazilian cities.
Antonio, Fernando Jose; de Picoli, Sergio; Teixeira, Jorge Juarez Vieira; Mendes, Renio dos Santos
2014-01-01
Brazil holds approximately 1/3 of population living infected with AIDS (acquired immunodeficiency syndrome) in Central and South Americas, and it was also the first developing country to implement a large-scale control and intervention program against AIDS epidemic. In this scenario, we investigate the temporal evolution and current status of the AIDS epidemic in Brazil. Specifically, we analyze records of annual absolute frequency of cases for more than 5000 cities for the first 33 years of the infection in Brazil. We found that (i) the annual absolute frequencies exhibit a logistic-type growth with an exponential regime in the first few years of the AIDS spreading; (ii) the actual reproduction number decaying as a power law; (iii) the distribution of the annual absolute frequencies among cities decays with a power law behavior; (iv) the annual absolute frequencies and the number of inhabitants have an allometric relationship; (v) the temporal evolution of the annual absolute frequencies have different profile depending on the average annual absolute frequencies in the cities. These findings yield a general quantitative description of the AIDS infection dynamics in Brazil since the beginning. They also provide clues about the effectiveness of treatment and control programs against the infection, that has had a different impact depending on the number of inhabitants of cities. In this framework, our results give insights into the overall dynamics of AIDS epidemic, which may contribute to select empirically accurate models. PMID:25340796
Power law scaling and ``Dragon-Kings'' in distributions of intraday financial drawdowns
NASA Astrophysics Data System (ADS)
Filimonov, Vladimir; Sornette, Didier
2015-05-01
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which investors are arguably the most concerned with. Similarly to the distribution of returns, we find that the distributions of epsilon-drawdowns and epsilon-drawups exhibit power law tails, albeit with exponents significantly larger than those for the return distributions. This paradoxical result can be attributed to (i) the existence of significant transient dependence between returns and (ii) the presence of large outliers (dragon-kings) characterizing the extreme tail of the drawdown/drawup distributions deviating from the power law. The study of the tail dependence between the sizes, speeds and durations of drawdown/drawup indicates a clear relationship between size and speed but none between size and duration. This implies that the most extreme drawdown/drawup tend to occur fast and are dominated by a few very large returns. We discuss both the endogenous and exogenous origins of these extreme events.
Lifetimes of metastable ion clouds in a Paul trap: Power-law scaling
NASA Astrophysics Data System (ADS)
Weiss, D. K.; Nam, Y. S.; Blümel, R.
2016-04-01
It is well known that ions stored in a Paul trap, one of the most versatile tools in atomic, molecular, and optical (AMO) physics, may undergo a transition from a disordered cloud state to a geometrically well-ordered crystalline state, the Wigner crystal. In this paper we predict that close to the transition, the average lifetime τ¯m of the metastable cloud follows a power law, τ¯m˜(γ-γc) -β , where γc is the value of the damping constant at which the transition occurs. The exponent β depends on the trap control parameter q , but is independent of both the number of particles N stored in the trap and the trap control parameter a , which determines the shape (oblate, prolate, or spherical) of the ion cloud. In addition, we find that for given a and q , γc scales approximately like γc=C ln[ln(N ) ] +D as a function of N , where C and D are constants. Our predictions may be tested experimentally with equipment already available at many AMO laboratories. In addition to their importance in AMO trap physics, we also discuss possible applications of our results to other periodically driven many-particle systems, such as, e.g., particle accelerator beams, and, based on our trap results, conjecture that power laws characterize the phase transition to the Wigner crystal in all such systems.
The US business cycle: power law scaling for interacting units with complex internal structure
NASA Astrophysics Data System (ADS)
Ormerod, Paul
2002-11-01
In the social sciences, there is increasing evidence of the existence of power law distributions. The distribution of recessions in capitalist economies has recently been shown to follow such a distribution. The preferred explanation for this is self-organised criticality. Gene Stanley and colleagues propose an alternative, namely that power law scaling can arise from the interplay between random multiplicative growth and the complex structure of the units composing the system. This paper offers a parsimonious model of the US business cycle based on similar principles. The business cycle, along with long-term growth, is one of the two features which distinguishes capitalism from all previously existing societies. Yet, economics lacks a satisfactory theory of the cycle. The source of cycles is posited in economic theory to be a series of random shocks which are external to the system. In this model, the cycle is an internal feature of the system, arising from the level of industrial concentration of the agents and the interactions between them. The model-in contrast to existing economic theories of the cycle-accounts for the key features of output growth in the US business cycle in the 20th century.
Scaling laws governing stochastic growth and division of single bacterial cells
Iyer-Biswas, Srividya; Wright, Charles S.; Henry, Jonathan T.; Lo, Klevin; Burov, Stanislav; Lin, Yihan; Crooks, Gavin E.; Crosson, Sean; Dinner, Aaron R.; Scherer, Norbert F.
2014-01-01
Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions. PMID:25349411
Scaling laws governing stochastic growth and division of single bacterial cells.
Iyer-Biswas, Srividya; Wright, Charles S; Henry, Jonathan T; Lo, Klevin; Burov, Stanislav; Lin, Yihan; Crooks, Gavin E; Crosson, Sean; Dinner, Aaron R; Scherer, Norbert F
2014-11-11
Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈ 1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions. PMID:25349411
Wright, Christopher K
2010-07-01
Although habitat networks show promise for conservation planning at regional scales, their spatiotemporal dynamics have not been well studied, especially in climate-sensitive landscapes. Here I use satellite remote sensing to compile wetland habitat networks from the Prairie Pothole Region (PPR) of North America. An ensemble of networks assembled across a hydrologic gradient from deluge to drought and a range of representative dispersal distances exhibits power-law scaling of important topological parameters. Prairie wetland networks are "meso-worlds" with mean topological distance increasing faster with network size than small-world networks, but slower than a regular lattice (or "large world"). This scaling implies rapid dispersal through wetland networks without some of the risks associated with "small worlds" (e.g., extremely rapid propagation of disease or disturbance). Retrospective analysis of wetland networks establishes a climatic envelope for landscape connectivity in the PPR, where I show that a changing climate might severely impact metapopulation viability and restrict long-distance dispersal and range shifts. More generally, this study demonstrates an efficient approach to conservation planning at a level of abstraction addressing key drivers of the global biodiversity crisis: habitat fragmentation and climatic change. PMID:20715611
Comparison of RAGE Hydrocode Mars Impact Model Results to Scaling Law Predictions
NASA Astrophysics Data System (ADS)
Plesko, Catherine S.; Wohletz, K. H.; Coker, R. F.; Asphaug, E.; Gittings, M. L.
2007-10-01
Impact devolatilization has been proposed by Segura et al. (2002) and Carr (1996) as a mechanism for triggering sporadic, intense precipitation on Mars. We seek to examine this hypothesis, specifically to determine the lower bound on possible energy/size scales, and thus an upper bound on the frequency of such events. To do this, we employ various analytical and numerical modeling techniques including the RAGE hydrocode. RAGE (Baltrusaitis et al. 1996) is an Eulerian Hydrocode that runs in up to three dimensions and incorporates a variety of detailed equations of state including the temperature-based SESAME tables maintained by LANL. In order to validate RAGE hydrocode results at the scale of moderate to large asteroid impacts, we compare simplified models of vertical impacts of objects of diameter 10 -100 km into homogeneous basalt targets under Martian conditions to pressure scaling law predictions (Holsapple 1993, e.g. Tables 3-4) for the same scenario. Peak pressures are important to the volatile mobilization question (Stewart and Ahrens, 2005), thus it is of primary importance for planned future modeling efforts to confirm that pressures in RAGE are well behaved. Knowledge of the final crater geometry and the fate of ejecta are not required to understand our main question: to what depth and radius are subsurface volatiles are mobilized, for a given impact and target? This effort is supported by LANL/IGPP (CSP, RFC, KHW, MLG) and by NASA PG&G "Small Bodies and Planetary Collisions" (EA).
NASA Astrophysics Data System (ADS)
Liu, Hsing; Chen, Ying-Hsing; Lih, Jiann-Shing
2015-05-01
Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution.
On the Uses of Full-Scale Schlieren Flow Visualization
NASA Astrophysics Data System (ADS)
Settles, G. S.; Miller, J. D.; Dodson-Dreibelbis, L. J.
2000-11-01
A lens-and-grid-type schlieren system using a very large grid as a light source was described at earlier APS/DFD meetings. With a field-of-view of 2.3x2.9 m (7.5x9.5 feet), it is the largest indoor schlieren system in the world. Still and video examples of several full-scale airflows and heat-transfer problems visualized thus far will be shown. These include: heating and ventilation airflows, flows due to appliances and equipment, the thermal plumes of people, the aerodynamics of an explosive trace detection portal, gas leak detection, shock wave motion associated with aviation security problems, and heat transfer from live crops. Planned future projects include visualizing fume-hood and grocery display freezer airflows and studying the dispersion of insect repellent plumes at full scale.