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