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.

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.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

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