scholarly journals Bubble-mediated transfer of dilute gas in turbulence

2021 ◽  
Vol 920 ◽  
Author(s):  
Palas Kumar Farsoiya ◽  
Stéphane Popinet ◽  
Luc Deike
Keyword(s):  
Dilute Gas

Abstract

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Hydrodynamic analysis of dilute gas—solids flow in a vertical pipe

1990 ◽  
Vol 62 (2) ◽  
pp. 163-170 ◽  
Author(s):  
H. Arastoopour ◽  
P. Pakdel ◽  
M. Adewumi
Keyword(s):  
Vertical Pipe ◽  
Hydrodynamic Analysis ◽  
Dilute Gas

EXPECTED AND UNEXPECTED SOLUTIONS TO THE STATIONARY ONE-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1663-1667
Author(s):  
LINCOLN D. CARR ◽  
CHARLES W. CLARK ◽  
WILLIAM P. REINHARDT
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein Condensate ◽  
Dilute Gas

We present all stationary solutions to the nonlinear Schrödinger equation in one dimension for box and periodic boundary conditions. For both repulsive and attractive nonlinearity we find expected and unexpected solutions. Expected solutions are those that are in direct analogy with those of the linear Schödinger equation under the same boundary conditions. Unexpected solutions are those that have no such analogy. We give a physical interpretation for the unexpected solutions. We discuss the properties of all solution types and briefly relate them to experiments on the dilute-gas Bose-Einstein condensate.

scholarly journals D-BRANE RECOIL MISLAYS INFORMATION

1998 ◽  
Vol 13 (07) ◽  
pp. 1059-1089 ◽  
Author(s):  
JOHN ELLIS ◽  
N. E. MAVROMATOS ◽  
D. V. NANOPOULOS
Keyword(s):  
Evolution Equations ◽  
Zero Mode ◽  
External Source ◽  
Closed String ◽  
The Other ◽  
Light Particle ◽  
World Sheet ◽  
Liouville Type ◽  
Dilute Gas ◽  
String State

We discuss the scattering of a light closed-string state off a D-brane, taking into account quantum recoil effects on the latter, which are described by a pair of logarithmic operators. The light particle and D-brane subsystems may each be described by a world sheet with an external source due to the interaction between them. This perturbs each subsystem away from criticality, which is compensated by dressing with a Liouville field whose zero mode we interpret as time. The resulting evolution equations for the D-brane and the closed string are of Fokker–Planck and modified quantum Liouville type, respectively. The apparent entropy of each subsystem increases as a result of the interaction between them, which we interpret as the loss of information resulting from nonobservation of the other entangled subsystem. We speculate on the possible implications of these results for the propagation of closed strings through a dilute gas of virtual D-branes.

Application of stochastic theory to dilute gas reactions

1976 ◽  
Vol 14 (3) ◽  
pp. 271-289 ◽  
Author(s):  
Paul D. Fleming ◽  
Julian H. Gibbs
Keyword(s):  
Stochastic Theory ◽  
Dilute Gas ◽  
Gas Reactions

Electrostatic effect on the flow behavior of a dilute gas/cohesive particle flow system

AIChE Journal ◽  
1996 ◽  
Vol 42 (6) ◽  
pp. 1590-1599 ◽  
Author(s):  
Yu-Feng Zhang ◽  
Yi Yang ◽  
Hamid Arastoopour
Keyword(s):  
Flow System ◽  
Flow Behavior ◽  
Particle Flow ◽  
Dilute Gas ◽  
Electrostatic Effect
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