scholarly journals Predicting observational signatures of coronal heating by Alfvén waves and nanoflares

2007 ◽  
Vol 3 (S247) ◽  
pp. 279-287
Author(s):  
Patrick Antolin ◽  
Kazunari Shibata ◽  
Takahiro Kudoh ◽  
Daiko Shiota ◽  
David Brooks
Keyword(s):  
Power Law ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Power Law Distribution ◽  
Longitudinal Modes ◽  
Heating Mechanism ◽  
Set Up ◽  
Power Law Index ◽  
Power Law Distributions ◽  
Release Processes

AbstractAlfvén waves can dissipate their energy by means of nonlinear mechanisms, and constitute good candidates to heat and maintain the solar corona to the observed few million degrees. Another appealing candidate is the nanoflare-reconnection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power law distribution in frequency whose index may tell us whether small heating events contribute substantially to the heating or not. In this work we show a link between the power law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfvén waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy through shocks; in the second model numerous heating events with nanoflare-like energies are input randomly along the loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-D MHD code. The obtained coronae differ in many aspects, for instance, in the simulated intensity profile that Hinode/XRT would observe. The intensity histograms display power law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.

scholarly journals Reacceleration of Relativistic Electrons by Turbulent Alfvén Waves in Radio Jets

2000 ◽  
Vol 195 ◽  
pp. 439-441
Author(s):  
D.-Y. Wang ◽  
Y. Ma
Keyword(s):  
Electron Energy ◽  
Power Law ◽  
Diffusion Approximation ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Relativistic Electrons ◽  
Radio Jets

Relativistic electrons may be effectively accelerated by turbulent Alfvén waves in radio jets. The acceleration spectrum is a power law with the electron energy as high as γ ~ 106, but the spectrum index is ~ 1.2 in the condition of diffusion approximation, which is less than the observation value.

From the central limit theorem to heavy-tailed distributions

2003 ◽  
Vol 40 (3) ◽  
pp. 803-806 ◽  
Author(s):  
Jinwen Chen
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Power Law ◽  
Power Law Distribution ◽  
The Central Limit Theorem ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Random Indices ◽  
Power Law Distributions

It has been observed that in many practical situations randomly stopped products of random variables have power law distributions. In this note we show that, in order for such a product to have a power law distribution, the only random indices are the exponentially distributed ones. We also consider a more general problem, which is closely related to problems concerning transformation from the central limit theorem to heavy-tailed distributions.

scholarly journals Power-law energy distributions of small-scale impulsive events on the active Sun: results from IRIS

2020 ◽  
Vol 499 (1) ◽  
pp. 1385-1394
Author(s):  
Nived Vilangot Nhalil ◽  
Chris J Nelson ◽  
Mihalis Mathioudakis ◽  
J Gerry Doyle ◽  
Gavin Ramsay
Keyword(s):  
Energy Range ◽  
Power Law ◽  
Coronal Heating ◽  
Radiative Energy ◽  
Small Scale ◽  
Data Sets ◽  
Imaging Data ◽  
Power Law Distribution ◽  
Energy Distributions ◽  
Power Law Index

ABSTRACT Numerous studies have analysed inferred power-law distributions between frequency and energy of impulsive events in the outer solar atmosphere in an attempt to understand the predominant energy supply mechanism in the corona. Here, we apply a burst detection algorithm to high-resolution imaging data obtained by the Interface Region Imaging Spectrograph to further investigate the derived power-law index, γ, of bright impulsive events in the transition region. Applying the algorithm with a constant minimum event lifetime (of either 60 s or 110 s) indicated that the target under investigation, such as Plage and Sunspot, has an influence on the observed power-law index. For regions dominated by sunspots, we always find γ < 2; however, for data sets where the target is a plage region, we often find that γ > 2 in the energy range (∼1023, ∼1026) erg. Applying the algorithm with a minimum event lifetime of three time-steps indicated that cadence was another important factor, with the highest cadence data sets returning γ > 2 values. The estimated total radiative power obtained for the observed energy distributions is typically 10–25 per cent of what would be required to sustain the corona indicating that impulsive events in this energy range are not sufficient to solve coronal heating. If we were to extend the power-law distribution down to an energy of 1021 erg, and assume parity between radiative energy release and the deposition of thermal energy, then such bursts could provide 25–50 per cent of the required energy to account for the coronal heating problem.

scholarly journals Investigating the damping rate of phase-mixed Alfvén waves

2019 ◽  
Vol 632 ◽  
pp. A93 ◽  
Author(s):  
A. P. K. Prokopyszyn ◽  
A. W. Hood
Keyword(s):  
Wave Energy ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Phase Mixing ◽  
Heating Mechanism ◽  
At Resonance ◽  
Damping Rate ◽  
Field Lines ◽  
The Waves

Context. This paper investigates the effectiveness of phase mixing as a coronal heating mechanism. A key quantity is the wave damping rate, γ, defined as the ratio of the heating rate to the wave energy. Aims. We investigate whether or not laminar phase-mixed Alfvén waves can have a large enough value of γ to heat the corona. We also investigate the degree to which the γ of standing Alfvén waves which have reached steady-state can be approximated with a relatively simple equation. Further foci of this study are the cause of the reduction of γ in response to leakage of waves out of a loop, the quantity of this reduction, and how increasing the number of excited harmonics affects γ. Methods. We calculated an upper bound for γ and compared this with the γ required to heat the corona. Analytic results were verified numerically. Results. We find that at observed frequencies γ is too small to heat the corona by approximately three orders of magnitude. Therefore, we believe that laminar phase mixing is not a viable stand-alone heating mechanism for coronal loops. To arrive at this conclusion, several assumptions were made. The assumptions are discussed in Sect. 2. A key assumption is that we model the waves as strictly laminar. We show that γ is largest at resonance. Equation (37) provides a good estimate for the damping rate (within approximately 10% accuracy) for resonant field lines. However, away from resonance, the equation provides a poor estimate, predicting γ to be orders of magnitude too large. We find that leakage acts to reduce γ but plays a negligible role if γ is of the order required to heat the corona. If the wave energy follows a power spectrum with slope −5/3 then γ grows logarithmically with the number of excited harmonics. If the number of excited harmonics is increased by much more than 100, then the heating is mainly caused by gradients that are parallel to the field rather than perpendicular to it. Therefore, in this case, the system is not heated mainly by phase mixing.

Power Law Distributions and the Size Distribution of Strikes

2017 ◽  
Vol 48 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Michele Campolieti
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Model Fit ◽  
Power Law Distribution ◽  
Policy Perspective ◽  
Methodological Research ◽  
Canadian Data ◽  
Alternative Measures ◽  
Power Law Distributions ◽  
Research And Policy

Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

An analysis of power law distributions and tipping points during the global financial crisis

2018 ◽  
Vol 13 (1) ◽  
pp. 80-91 ◽  
Author(s):  
Yifei Li ◽  
Lei Shi ◽  
Neil Allan ◽  
John Evans
Keyword(s):  
Financial Crisis ◽  
Power Law ◽  
Global Financial Crisis ◽  
Operational Risk ◽  
Tipping Point ◽  
Power Law Distribution ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
The Global Financial Crisis ◽  
Power Law Distributions

AbstractHeavy-tailed distributions have been observed for various financial risks and papers have observed that these heavy-tailed distributions are power law distributions. The breakdown of a power law distribution is also seen as an indicator of a tipping point being reached and a system then moves from stability through instability to a new equilibrium. In this paper, we analyse the distribution of operational risk losses in US banks, credit defaults in US corporates and market risk events in the US during the global financial crisis (GFC). We conclude that market risk and credit risk do not follow a power law distribution, and even though operational risk follows a power law distribution, there is a better distribution fit for operational risk. We also conclude that whilst there is evidence that credit defaults and market risks did reach a tipping point, operational risk losses did not. We conclude that the government intervention in the banking system during the GFC was a possible cause of banks avoiding a tipping point.

scholarly journals Starspot Activity and Superflares on Solar-type Stars

2016 ◽  
Vol 12 (S328) ◽  
pp. 22-29
Author(s):  
Hiroyuki Maehara
Keyword(s):  
Solar Flare ◽  
Power Law ◽  
Magnetic Energy ◽  
Rotation Period ◽  
Occurrence Frequency ◽  
Clear Correlation ◽  
Rotating Stars ◽  
Power Law Distribution ◽  
Solar Type ◽  
Power Law Index

AbstractRecent high-precision photometry from space (e.g., Kepler) enables us to investigate the nature of “superflares” on solar-type stars. The bolometric energy of superflares detected by Kepler ranges from 1033 erg to 1036 erg which is 10-10,000 times larger than that released by a typical X10 class solar flare. The occurrence frequency (dN/dE) of superflares as a function of flare energy (E) shows the power-law distribution with the power-law index of ~−1.8 for 1034 < E < 1036 erg. Most of superflare stars show quasi-periodic light variations which suggest the presence of large starspots. The bolometric energy released by flares is consistent with the magnetic energy stored near the starspots. The occurrence frequency of superflares increases as the rotation period decreases. However, the energy of the largest flares observed in a given period bin does not show any clear correlation with the rotation period. These results suggest that superflares would occur on the slowly-rotating stars.

Comparing Three Environmental Particle Size Distributions: Power Law (FED-STD-209D), Lognormal, Approximate Lognormal (MIL-STD-1246B)

1991 ◽  
Vol 34 (1) ◽  
pp. 21-24
Author(s):  
Douglas Cooper
Keyword(s):  
Particle Size ◽  
Power Law ◽  
Lognormal Distribution ◽  
Cumulative Distribution ◽  
Size Distributions ◽  
Power Law Distribution ◽  
Particle Size Distributions ◽  
Contamination Control ◽  
Control Programs ◽  
Power Law Distributions

Particle size strongly influences particle behavior. To summarize the distribution of particle sizes, a distribution function can be used. The characteristics of the particle size distributions chosen are important for two specification documents currently under revision: (1) FED-STD-209D, concerning air-cleanliness in manufacturing, which uses cumulative particle size distributions that are linear when plotted on log-log axes; these are power law distributions. (2) MIL-STD-1246B, "Product Cleanliness Levels and Contamination Control Programs," primarily concerning surface cleanliness, which uses cumulative particle size distributions that are linear when plotted as the logarithm of the cumulative distribution versus the square of the logarithm of the particle size, log2x, A third distribution, the lognormal, is commonly found in aerosol science, especially where there is a single particle source. The distributions are compared and discussed. The FED-STD-209D power law distribution can approximate a lognormal distribution over only a limited size range. The MIL-STD-1246B distribution is an asymptotic approximation to the lognormal distribution.

scholarly journals On the reflection of Alfvén waves in an ideal magnetoatmosphere

1998 ◽  
Vol 21 (2) ◽  
pp. 381-386
Author(s):  
Hadi Yahya Alkahby ◽  
M. A. Mahrous
Keyword(s):  
Magnetic Field ◽  
Reflection Coefficient ◽  
Linear Combination ◽  
Alfven Waves ◽  
Magnetic Pressure ◽  
Critical Layer ◽  
Alfvén Waves ◽  
Heating Mechanism ◽  
Restoring Forces ◽  
The Magnetic Field

A lineafized theory ofmagnetoatmospheric waves is developed where the restoring forces are those of compressibility and magnetic pressure. An equation for resonance is derived. Reflection and tunneling of upward propagating Alfvén waves in an ideal Magnetoatmosphere are considered. It is shown that the magnetic field produces a reflecting nonabsorbing critical layer. Below the critical layer, the solution of the problem can be written as a linear combination of an upward and a downward propagating wave and above it the solution decays exponentially with the altitude. The location of the critical layer and the magnitude of the reflection coefficient are determined and the conclusions are discussed in cormeetion with the heating mechanism of the solar atmosphere

scholarly journals TRANSITION FROM EXPONENTIAL TO POWER LAW INCOME DISTRIBUTIONS IN A CHAOTIC MARKET

2011 ◽  
Vol 22 (01) ◽  
pp. 21-33 ◽  
Author(s):  
CARMEN PELLICER-LOSTAO ◽  
RICARDO LOPEZ-RUIZ
Keyword(s):  
Power Law ◽  
Chaotic Dynamics ◽  
Pairing Symmetry ◽  
Power Law Distribution ◽  
Closed Economies ◽  
Income Distributions ◽  
Chaotic Model ◽  
New Models ◽  
Micro Level ◽  
Power Law Distributions

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

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