Non-power-law-scale properties of rainfall in space and time

2005 ◽  
Vol 41 (8) ◽  
Author(s):  
Marco Marani
Keyword(s):  
Power Law ◽  
Space And Time ◽  
Scale Properties

scholarly journals Scale properties as a basis of power law relaxation processes

2007 ◽  
Vol 228 (2) ◽  
pp. 107-111 ◽  
Author(s):  
A. Fondado ◽  
J. Mira ◽  
J. Rivas
Keyword(s):  
Power Law ◽  
Relaxation Processes ◽  
Scale Properties

scholarly journals Kicked Burgers turbulence

2000 ◽  
Vol 416 ◽  
pp. 239-267 ◽  
Author(s):  
J. BEC ◽  
U. FRISCH ◽  
K. KHANIN
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Large Scale ◽  
Order Term ◽  
Inviscid Limit ◽  
Order Structure ◽  
Legendre Transform ◽  
Leading Order ◽  
Space And Time ◽  
Burgers Turbulence

Burgers turbulence subject to a force f(x, t) = [sum ]jfj(x)δ(t − tj), where tj are 'kicking times' and the 'impulses' fj(x) have arbitrary space dependence, combines features of the purely decaying and the continuously forced cases. With large-scale forcing this ‘kicked’ Burgers turbulence presents many of the regimes proposed by E et al. (1997) for the case of random white-noise-in-time forcing. It is also amenable to efficient numerical simulations in the inviscid limit, using a modification of the fast Legendre transform method developed for decaying Burgers turbulence by Noullez & Vergassola (1994). For the kicked case, concepts such as ‘minimizers’ and ‘main shock’, which play crucial roles in recent developments for forced Burgers turbulence, become elementary since everything can be constructed from simple two-dimensional area-preserving Euler–Lagrange maps.The main results are for the case of identical deterministic kicks which are periodic and analytic in space and are applied periodically in time. When the space integrals of the initial velocity and of the impulses vanish, it is proved and illustrated numerically that a space- and time-periodic solution is achieved exponentially fast. In this regime, probabilities can be defined by averaging over space and time periods. The probability densities of large negative velocity gradients and of (not-too-large) negative velocity increments follow the power law with −7/2 exponent proposed by E et al. (1997) in the inviscid limit, whose existence is still controversial in the case of white-in-time forcing. This power law, which is seen very clearly in the numerical simulations, is the signature of nascent shocks (preshocks) and holds only when at least one new shock is born between successive kicks.It is shown that the third-order structure function over a spatial separation Δx is analytic in Δx although the velocity field is generally only piecewise analytic (i.e. between shocks). Structure functions of order p ≠ 3 are non-analytic at Δx = 0. For even p there is a leading-order term proportional to [mid ]Δx[mid ] and for odd p > 3 the leading-order term ∝Δx has a non-analytic correction ∝Δx[mid ]Δx[mid ] stemming from shock mergers.

scholarly journals Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1489
Author(s):  
Ken Sekimoto ◽  
Takahiko Fujita
Keyword(s):  
Power Law ◽  
Late Stage ◽  
Scaling Function ◽  
Early Stage ◽  
The Self ◽  
Scaling Functions ◽  
Self Similarity ◽  
Simple Diffusion ◽  
Early Stages ◽  
Space And Time

The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we address mainly the self-similarity in the limit of early stage, as opposed to the latter one, and also consider the scaling functions that decay or grow algebraically, as opposed to the rapidly decaying functions such as Gaussian or error function. In particular, in the case of simple diffusion, our symmetry analysis shows a mathematical mechanism by which the rapidly decaying scaling functions are generated by other polynomial scaling functions. While the former is adapted to the self-similarity in the late-stage processes, the latter is adapted to the early stages. This paper sheds some light on the internal structure of the family of self-similarities generated by a simple diffusion equation. Then, we present an example of self-similarity for the late stage whose scaling function has power-law tail, and also several cases of self-similarity for the early stages. These examples show the utility of self-similarity to a wider range of phenomena other than the late stage behaviors with rapidly decaying scaling functions.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

1968 ◽  
Vol 11 (1) ◽  
pp. 169-178 ◽  
Author(s):  
Alan Gill ◽  
Charles I. Berlin
Keyword(s):  
Power Law ◽  
Response Magnitude ◽  
Single Units ◽  
Spectral Content ◽  
Hearing Sensitivity ◽  
Subjective Magnitude ◽  
Orderly Fashion ◽  
Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

Languages in Space and Time

2020 ◽  
Author(s):  
Marco Patriarca ◽  
Els Heinsalu ◽  
Jean Leó Leonard
Keyword(s):  
Space And Time

On Space and Time

2008 ◽  
Author(s):  
Alain Connes ◽  
Michael Heller ◽  
Roger Penrose ◽  
John Polkinghorne ◽  
Andrew Taylor
Keyword(s):  
Space And Time
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