Nanoparticle Dynamics:  A Multiscale Analysis of the Liouville Equation†

2005 ◽  
Vol 109 (45) ◽  
pp. 21258-21266 ◽  
Author(s):  
Peter J. Ortoleva
Keyword(s):  
Liouville Equation ◽  
Multiscale Analysis ◽  
Nanoparticle Dynamics

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Multiscale analysis to determine the sensitive zones for temperature sensors location in tubular reactors

2021 ◽  
Author(s):  
Jazael G. Moguel-Castañeda ◽  
Juan L. Hernandez-Ayala ◽  
Rafael Gomez-Rodriguez ◽  
Juan-Rodrigo Bastidas-Oyanedel ◽  
Eliseo Hernandez-Martinez
Keyword(s):  
Multiscale Analysis ◽  
Temperature Sensors ◽  
Tubular Reactors

scholarly journals Estimates for Liouville equation with quantized singularities

2021 ◽  
Vol 380 ◽  
pp. 107606
Author(s):  
Juncheng Wei ◽  
Lei Zhang
Keyword(s):  
Liouville Equation
Sign in / Sign up

Export Citation Format

Share Document