Experimental evidence for power‐law wave number spectra of fractal tracer distributions in a complicated surface flow

1996 ◽  
Vol 8 (9) ◽  
pp. 2441-2446 ◽  
Author(s):  
John C. Sommerer
Keyword(s):  
Experimental Evidence ◽  
Power Law ◽  
Surface Flow ◽  
Wave Number ◽  
Complicated Surface

scholarly journals HELICAL MAGNETIC FIELDS FROM INFLATION

2009 ◽  
Vol 18 (09) ◽  
pp. 1395-1411 ◽  
Author(s):  
LEONARDO CAMPANELLI
Keyword(s):  
Magnetic Fields ◽  
Power Law ◽  
Background Field ◽  
Wave Number ◽  
Conformal Time ◽  
De Sitter ◽  
Simple Power ◽  
Dimensionless Constant ◽  
Real Positive Number

We analyze the generation of seed magnetic fields during de Sitter inflation considering a noninvariant conformal term in the electromagnetic Lagrangian of the form [Formula: see text], where I(ϕ) is a pseudoscalar function of a nontrivial background field ϕ. In particular, we consider a toy model that could be realized owing to the coupling between the photon and either a (tachyonic) massive pseudoscalar field or a massless pseudoscalar field nonminimally coupled to gravity, where I follows a simple power law behavior I(k,η) = g/(-kη)β during inflation, while it is negligibly small subsequently. Here, g is a positive dimensionless constant, k the wave number, η the conformal time, and β a real positive number. We find that only when β = 1 and 0.1 ≲ g ≲ 2 can astrophysically interesting fields be produced as excitation of the vacuum, and that they are maximally helical.

Power law wave number spectra of fractal particle distributions advected by flowing fluids

1996 ◽  
Vol 8 (9) ◽  
pp. 2426-2434 ◽  
Author(s):  
Arthur Namenson ◽  
Thomas M. Antonsen ◽  
Edward Ott
Keyword(s):  
Power Law ◽  
Wave Number ◽  
Particle Distributions ◽  
Fractal Particle

Experimental evidence of T/sub BD/ power-law for voltage dependence of oxide breakdown

2002 ◽  
Vol 49 (12) ◽  
pp. 2244-2253 ◽  
Author(s):  
E.Y. Wu ◽  
A. Vayshenker ◽  
E. Nowak ◽  
J. Sune ◽  
R.-P. Vollertsen ◽  
...  
Keyword(s):  
Experimental Evidence ◽  
Power Law ◽  
Voltage Dependence ◽  
Oxide Breakdown

Multi-dimensional complex phase transition model by catastrophe theory developing Kolmogorov turbulence theory

2020 ◽  
Vol 34 (15) ◽  
pp. 2050159
Author(s):  
Zhuo Zhou ◽  
Jiu Hui Wu ◽  
Xiao Liang ◽  
Mei Lin ◽  
Xiao Yang Yuan ◽  
...  
Keyword(s):  
Phase Transition ◽  
Power Law ◽  
Catastrophe Theory ◽  
Equilibrium Phase ◽  
Turbulence Theory ◽  
Wave Number ◽  
Transition Model ◽  
Kolmogorov Turbulence ◽  
Equilibrium Phase Transition ◽  
Non Equilibrium

In this paper, a novel multi-dimensional complex non-equilibrium phase transition model is put forward to describe quantitatively the physical development process of turbulence and develop the Kolmogorov turbulence theory from the catastrophe theory, in which the well-known −5/3 power law is only a special case in this paper proving the accuracy of our methods. Catastrophe theory is a highly generalized mathematical tool that summarizes the laws of non-equilibrium phase transition. Every control variable in catastrophe theory could be skillfully expanded into multi-parameter multiplication with different indices and the relationship among these characteristic indices can be determined by dimensionless analysis. Thus, the state variables can be expressed quantitatively with multiple parameters, and the multi-dimensional non-equilibrium phase transition theory is established. As an example, by adopting the folding catastrophe model, we strictly derive out the quantitative relationship between energy and wave number with respect to a new scale index [Formula: see text] to quantitative study the whole process of the laminar flow to turbulence, in which [Formula: see text] varies from [Formula: see text] to [Formula: see text] corresponding to energy containing range and [Formula: see text] to energy containing scale where [Formula: see text] power law is deduced, and at [Formula: see text] the [Formula: see text] law of Kolmogorov turbulence theory is obtained, and fully developed turbulence phase starts at [Formula: see text] giving [Formula: see text] law. Furthermore, this theory presented is verified by our wind tunnel experiments. This novel non-equilibrium phase transition methods cannot only provide a new insight into the turbulence model, but also be applied to other non-equilibrium phase transitions.

scholarly journals Theoretical bounds for the exponent in the empirical power-law advance-time curve for surface flow

2018 ◽  
Vol 210 ◽  
pp. 208-216 ◽  
Author(s):  
Behzad Ghanbarian ◽  
Hamed Ebrahimian ◽  
Allen G. Hunt ◽  
M. Th. van Genuchten
Keyword(s):  
Power Law ◽  
Surface Flow ◽  
Empirical Power ◽  
Time Curve ◽  
Advance Time

scholarly journals Experimental evidence for a power law in electroencephalographic -wave dynamics

1999 ◽  
Vol 12 (2) ◽  
pp. 303-307 ◽  
Author(s):  
Y. Georgelin ◽  
L. Poupard ◽  
R. Sartène ◽  
J.C. Wallet
Keyword(s):  
Experimental Evidence ◽  
Power Law ◽  
Wave Dynamics

scholarly journals On the spectral distribution of kinetic energy in large-scale atmospheric flow

1998 ◽  
Vol 5 (3) ◽  
pp. 187-192
Author(s):  
A. Wiin-Nielsen
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Power Law ◽  
Spectral Distribution ◽  
Large Scale ◽  
Wave Number ◽  
Initial State ◽  
Atmospheric Flow ◽  
Linear Interaction ◽  
Spectral Components

Abstract. A one-dimensional form of the equation of motion with forcing and dissipation is formulated in the spectral domain and used to make long term integrations from which the spectral distribution of the kinetic energy is determined The forcing in the wave number domain is determined in advance and kept constant for the duration of the time integrations. The dissipation is proportional to the second derivative of the velocity. The applied equation is made non-dimensional by selecting a length scale from which the time scale and the velocity scale may be determined. The resulting equation contains no parameters apart from the forcing. The integrations use a large number of spectral components and no approximation is made with respect to the non-linear interaction among the spectral components. Starting from an initial state in which all the velocity components are set to zero the equation is integrated for a long time to see if it reaches a steady state. The spectral distribution of the kinetic energy is determined in the steady state, and it is found that the distribution, in agreement with observational studies, may be approximated by a power law of the form n-3 within certain wave number regions. The wave numbers for which the -3 power law applies is found between the region of maximum forcing and the dissipation range. The intensity of the maximum forcing is varied to see how the resulting steady state varies. In addition, the maximum number of spectral components is varied. However, the available computing power sets an upper limit to the number of components.

scholarly journals Formation of quasi-power law weak Langmuir turbulence spectrum by harmonic generation

2004 ◽  
Vol 11 (2) ◽  
pp. 267-274
Author(s):  
P. H. Yoon
Keyword(s):  
Power Law ◽  
Langmuir Wave ◽  
Wave Number ◽  
Wave Turbulence ◽  
Langmuir Turbulence ◽  
Turbulence Spectrum ◽  
Langmuir Waves ◽  
Multi Scale ◽  
History Of ◽  
Simulation Results

Abstract. Langmuir wave turbulence generated by a beam-plasma interaction has been studied since the early days of plasma physics research. Despite a long history of investigation on this subject, among the outstanding issues is the generation of harmonic Langmuir waves observed in both laboratory and computer-simulated experiments. However, the phenomenon has not been adequately explained in terms of theory, nor has it been fully characterized by means of numerical simulations. In this paper, a theory of harmonic Langmuir wave generation is put forth and tested against the Vlasov simulation results. It is found that the harmonic Langmuir mode spectra exhibit quasi power-law feature implying a multi-scale structure in both frequency and wave number space spanning several orders of magnitude.

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