Single-particle distribution functions in nanoscale particles at finite temperature: Some rigorous results

2006 ◽  
Vol 74 (19) ◽  
Author(s):  
Hyun-Chul Yong ◽  
Kai-Hua Yang ◽  
Guang-Shan Tian
Keyword(s):  
Single Particle ◽  
Finite Temperature ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Rigorous Results ◽  
Nanoscale Particles

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

A perturbation method for the Vlasov–Poisson system

1998 ◽  
Vol 60 (1) ◽  
pp. 181-192 ◽  
Author(s):  
JONAS LUNDBERG ◽  
TOR FLÅ
Keyword(s):  
Perturbation Method ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Poisson System ◽  
Nonlinear Wave Propagation ◽  
Starting Point ◽  
Self Consistent ◽  
Good Starting Point ◽  
New Perturbation ◽  
Lie Transformations

A perturbation method for the Vlasov–Poisson system is presented. It is self-consistent and entirely based on Lie transformations, which are considered as active transformations, generating the dynamics of the particle distribution function in the space of distribution functions. The main result is a set of three equations that forms a good starting point for a wide variety of problems concerning nonlinear wave propagation. Besides being efficient, the new perturbation method is systematic and therefore also suited for the use of computer algebra.

Elastic Constants of Binary Liquid Crystalline Mixtures

1998 ◽  
Vol 53 (12) ◽  
pp. 963-976
Author(s):  
A. Kapanowski ◽  
K. Sokalski
Keyword(s):  
Phase Diagram ◽  
Elastic Constants ◽  
Short Range ◽  
Liquid Crystalline ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Binary Liquid ◽  
Small Density ◽  
Nematic Phases ◽  
The One

Abstract Microscopic expressions for the elastic constants of binary liquid crystalline mixtures composed of short rigid uniaxial molecules are derived in the thermodynamic limit at small distorsions and a small density. Uniaxial and biaxial nematic phases are considered. The expressions involve the one-particle distribution functions and the potential energy of two-body short-range interactions. The theory is used to calculate the phase diagram of a mixture of rigid prolate and oblate molecules. The concentration dependence of the order parameters and the elastic constants are obtained. The possibility of phase separation is not investigated.

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