Magnitude and variation of the critical power law exponent and its physical controls

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

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Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

Journal of Fluids ◽

10.1155/2013/405985 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

J. Prakash ◽

S. Gouse Mohiddin ◽

S. Vijaya Kumar Varma

Keyword(s):

Boundary Layer ◽

Power Law ◽

Mass Flux ◽

Numerical Study ◽

Convection Boundary Layer ◽

Vertical Cone ◽

Local Skin ◽

Surface Mass ◽

Flow Past ◽

Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

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Breakdown coefficients and scaling properties of rain fields

Nonlinear Processes in Geophysics ◽

10.5194/npg-5-93-1998 ◽

1998 ◽

Vol 5 (2) ◽

pp. 93-104 ◽

Cited By ~ 22

Author(s):

D. Harris ◽

M. Menabde ◽

A. Seed ◽

G. Austin

Keyword(s):

Time Series ◽

Parameter Estimation ◽

Power Law ◽

Scale Parameter ◽

Probability Distributions ◽

Scaling Analysis ◽

Scaling Properties ◽

Power Law Exponent ◽

Scale Similarity ◽

Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

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Differences in power-law growth over time and indicators of COVID-19 pandemic progression worldwide

10.1101/2020.03.31.20048827 ◽

2020 ◽

Cited By ~ 1

Author(s):

Jack Merrin

Keyword(s):

Error Analysis ◽

Real Time ◽

Power Law ◽

Growth Phase ◽

Exponential Growth ◽

Spreading Rate ◽

Exponential Growth Phase ◽

Power Law Exponent ◽

Disease Spreading ◽

Over Time

1AbstractAn automated statistical and error analysis of 45 countries or regions with more than 1000 cases of COVID-19 as of March 28, 2020, has been performed. This study reveals differences in the rate of disease spreading rate over time in different countries. This survey observes that most countries undergo a beginning exponential growth phase, which transitions into a power-law phase, as recently suggested by Ziff and Ziff. Tracking indicators of growth, such as the power-law exponent, are a good indication of the relative danger different countries are in and show when social measures are effective towards slowing the spread. The data compiled here are usefully synthesizing a global picture, identifying country to country variation in spreading, and identifying countries most at risk. This analysis may factor into how best to track the effectiveness of social distancing policies and quarantines in real-time as data is updated each day.

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Scale-free networks with the power-law exponent between 1 and 3

Acta Physica Sinica ◽

10.7498/aps.56.5635 ◽

2007 ◽

Vol 56 (10) ◽

pp. 5635

Author(s):

Guo Jin-Li ◽

Wang Li-Na

Keyword(s):

Power Law ◽

Scale Free ◽

Power Law Exponent ◽

Scale Free Networks

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Typical Distances in Ultrasmall Random Networks

Advances in Applied Probability ◽

10.1239/aap/1339878725 ◽

2012 ◽

Vol 44 (2) ◽

pp. 583-601 ◽

Cited By ~ 7

Author(s):

Steffen Dereich ◽

Christian Mönch ◽

Peter Mörters

Keyword(s):

Power Law ◽

Preferential Attachment ◽

Shortest Paths ◽

Giant Component ◽

Configuration Model ◽

Random Networks ◽

Power Law Exponent ◽

Extra Factor ◽

Typical Distances

We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 + o(1))log log N / (-log(τ − 2)), where N denotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of typical shortest paths in preferential attachment graphs.

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Similarity Solutions of the MHD Stagnation-Point Flow over a Power-Law Stretching Sheet

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.52-54.1895 ◽

2011 ◽

Vol 52-54 ◽

pp. 1895-1900

Author(s):

Jing Zhu ◽

Lian Cun Zheng ◽

Xue Hui Chen

Keyword(s):

Stagnation Point ◽

Power Law ◽

Stretching Sheet ◽

Velocity Ratio ◽

Similarity Solutions ◽

Stagnation Point Flow ◽

Electrically Conducting ◽

Power Law Exponent ◽

Permeability Parameter ◽

Scaling Group Of Transformations

A similarity analysis is performed for a steady laminar boundary layer stagnation-point flow of an electrically conducting fluid in a porous medium subject to a transverse non-uniform magnetic field past a non-linear stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third order ordinary differential equation corresponding to the momentum is obtained. We show the existence and uniqueness of convex and concave solutions for the power law exponent, according to the values of magnetic parameter, permeability parameter and velocity ratio parameter.

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Joint measurements of optical parameters by irradiance scintillation and angle-of-arrival fluctuations

Open Physics ◽

10.1515/phys-2018-0053 ◽

2018 ◽

Vol 16 (1) ◽

pp. 387-393

Author(s):

Chao Gao ◽

Haodong Liang ◽

Xiaofeng Li

Keyword(s):

Error Analysis ◽

Atmospheric Turbulence ◽

Power Law ◽

Structure Constant ◽

Simultaneous Equations ◽

Scintillation Index ◽

Optical Parameters ◽

Angle Of Arrival ◽

Power Law Exponent

AbstractA method for joint measuring the power law exponent and the structure constant of atmospheric turbulence is proposed and examined. The measurements are equivalent to solve the simultaneous equations formed by the irradiance scintillation index and the angle-of-arrival fluctuations variance, where the measured parameters are regarded as the unknowns. The measured error analysis is also presented. Based on our proposed method, the measured results accord with the daily trend of atmospheric turbulence.

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Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406218796040 ◽

2018 ◽

Vol 233 (8) ◽

pp. 2636-2662 ◽

Cited By ~ 1

Author(s):

Piyush Pratap Singh ◽

Mohammad Sikandar Azam ◽

Vinayak Ranjan

Keyword(s):

Boundary Conditions ◽

Power Law ◽

Functionally Graded Material ◽

Functionally Graded ◽

Pasternak Foundation ◽

Functionally Graded Plate ◽

Material Inhomogeneity ◽

Power Law Exponent ◽

Out Of Plane ◽

Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

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