scholarly journals Hypothetical Control of Fatal Quarrel Variability

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1693
Author(s):  
Bruce J. West
Keyword(s):  
Social Network ◽  
Steady State ◽  
Probability Density Function ◽  
Control Process ◽  
Planck Equation ◽  
Power Laws ◽  
Steady State Solution ◽  
Terrorist Attacks ◽  
Natural Catastrophes ◽  
Probability Density Function Pdf

Wars, terrorist attacks, as well as natural catastrophes typically result in a large number of casualties, whose distributions have been shown to belong to the class of Pareto’s inverse power laws (IPLs). The number of deaths resulting from terrorist attacks are herein fit by a double Pareto probability density function (PDF). We use the fractional probability calculus to frame our arguments and to parameterize a hypothetical control process to temper a Lévy process through a collective-induced potential. Thus, the PDF is shown to be a consequence of the complexity of the underlying social network. The analytic steady-state solution to the fractional Fokker-Planck equation (FFPE) is fit to a forty-year fatal quarrel (FQ) dataset.

A resonant test-field model of gravity waves

1983 ◽  
Vol 132 ◽  
pp. 417-430 ◽  
Author(s):  
Bruce J. West
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Planck Equation ◽  
Steady State Solution ◽  
Test Field ◽  
Statistical Fluctuations ◽  
Resonant Interactions ◽  
Energy Spectral Density ◽  
Non Gaussian ◽  
Turbulent Wind Field

In this paper we propose an ‘irreversible’ resonant test-field (RTF) model to describe the statistical fluctuations of gravity waves on deep water driven by a turbulent wind field. The non-resonant interactions in the gravity-wave Hamiltonian are replaced by a Markov process in the equation of motion for the resonantly interacting gravity waves, i.e. Hamilton's equations are replaced by a Langevin equation for the RTF waves. The RTF models the irreversible energy-transfer process by a Fokker-Planck equation for the phase-space probability density, the exact steady-state solution of which is determined to be non-Gaussian. An H-theorem for the RTF predicts the monotonic approach to the asymptotic steady state near which the transport properties of the field are studied. The steady-state energy-spectral density is calculated (in some approximation) to be k−4.

scholarly journals The Study of a Wealth Distribution Model with a Linear Collision Kernel

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xia Zhou ◽  
Kaili Xiang ◽  
Rongmei Sun
Keyword(s):  
Steady State ◽  
Boltzmann Equation ◽  
Substitution Rate ◽  
Wealth Distribution ◽  
Planck Equation ◽  
Steady State Solution ◽  
State Solution ◽  
Distribution Model ◽  
Collision Kernel ◽  
Continuous Trading

The wealth substitution rate, which describes the substitution relationship between agents’ investment in wealth, is introduced into the collision kernel of the Boltzmann equation to study wealth distribution. Using the continuous trading limit, the Fokker–Planck equation is derived and the steady-state solution is obtained. The results show that the inequality of wealth distribution decreases as the wealth substitution rate increases under certain assumptions. The wealth distribution has a bimodal shape if the wealth substitution rate does not equal one.

BOLTZMANN–ARRHENIUS–ZHURKOV (BAZ) MODEL IN PHYSICS-OF-MATERIALS PROBLEMS

2013 ◽  
Vol 27 (13) ◽  
pp. 1330009 ◽  
Author(s):  
E. SUHIR ◽  
S.-M. KANG
Keyword(s):  
Steady State ◽  
Planck Equation ◽  
Steady State Solution ◽  
Degradation Process ◽  
Material Degradation ◽  
Fokker Planck Equation ◽  
Markovian Processes ◽  
Transient Period ◽  
The Given ◽  
Fokker Planck

Boltzmann–Arrhenius–Zhurkov (BAZ) model enables one to obtain a simple, easy-to-use and physically meaningful formula for the evaluation of the probability of failure (PoF) of a material after the given time in operation at the given temperature and under the given stress (not necessarily mechanical). It is shown that the material degradation (aging, damage accumulation, flaw propagation, etc.) can be viewed, when BAZ model is considered, as a Markovian process, and that the BAZ model can be obtained as the steady-state solution to the Fokker–Planck equation in the theory of Markovian processes. It is shown also that the BAZ model addresses the worst and a reasonably conservative situation, when the highest PoF is expected. It is suggested therefore that the transient period preceding the condition addressed by the steady-state BAZ model need not be accounted for in engineering evaluations. However, when there is an interest in understanding the physics of the transient degradation process, the obtained solution to the Fokker–Planck equation can be used for this purpose.

scholarly journals Infinite product expansion of the Fokker–Planck equation with steady-state solution

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150084 ◽  
Author(s):  
R. J. Martin ◽  
R. V. Craster ◽  
M. J. Kearney
Keyword(s):  
Steady State ◽  
Infinite Product ◽  
Planck Equation ◽  
Steady State Solution ◽  
State Solution ◽  
Analytical Technique ◽  
Short And Long Term ◽  
Fokker Planck Equations ◽  
Fokker Planck

We present an analytical technique for solving Fokker–Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples.

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