scholarly journals Analytic Properties of the One- and Two-Particle Distribution Functions of Bose Fluids

1969 ◽  
Vol 44 ◽  
pp. 118-143 ◽  
Author(s):  
Hiroaki Hara ◽  
Tohru Morita
Keyword(s):  
Particle Distribution ◽  
Distribution Functions ◽  
The One

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.

MESOSCOPIC SPECTRA IN TWO-DIMENSIONAL DECAYING TURBULENCE

2006 ◽  
Vol 17 (04) ◽  
pp. 531-543 ◽  
Author(s):  
GÁBOR HÁZI
Keyword(s):  
Lattice Boltzmann ◽  
Particle Distribution ◽  
Power Spectra ◽  
Collision Operator ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Two Dimensional ◽  
Decaying Turbulence ◽  
The One ◽  
Boltzmann Model

Two-dimensional decaying turbulence is simulated using a lattice Boltzmann model with the Bhatnagar–Gross–Krook collision operator. Auto-power spectra of the one-velocity particle distribution functions are presented. The relation between the spectrum of the kinetic energy and the spectra of the distribution functions is given. An interpretation of the non-equilibrium spectra as a measure of the dissipation in different scales is given. A peak in the spectrum of the resting particle distribution functions is observed exactly at the ultraviolet cutoff. It is shown that the peak can be associated with enhanced acoustic activity, which might be a numerical artifact or a consequence of the compressibility of the lattice Boltzmann fluid.

KINETIC EQUATION FOR A PLASMA IN A STRONG STATIC MAGNETIC FIELD

1966 ◽  
Vol 44 (1) ◽  
pp. 247-254 ◽  
Author(s):  
M. K. Sundaresan
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Strong Magnetic Field ◽  
Static Magnetic Field ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Collision Term ◽  
The One ◽  
The Magnetic Field ◽  
Complete Account

The present work represents a significant improvement on our earlier work dealing with the formulation of a kinetic equation for a plasma in a "strong" static magnetic field B. Here without making any assumptions concerning the isotropy of the one- and two-particle distribution functions in the plane perpendicular to the magnetic field, a kinetic equation is derived in which the collision term is valid to all orders in 1/B and takes complete account of the effect of the strong magnetic field on the collisions.

IRREVERSIBILITY IN RELATIVISTIC STATISTICAL MECHANICS

1994 ◽  
Vol 08 (29) ◽  
pp. 1847-1860 ◽  
Author(s):  
URI BEN-YA’ACOV
Keyword(s):  
Distribution Function ◽  
Statistical Mechanics ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Distribution Functions ◽  
Relativistic Dynamics ◽  
Direct Computation ◽  
Lagrangian Equations ◽  
The One

Relativistic statistical mechanics should be manifestly Lorentz covariant. In the absence of a Hamiltonian formalism in relativistic dynamics, a different approach which is based on the (Lagrangian) equations of motion is presented. Without any Liouville equation, this approach provides the direct computation of all the reduced n-particle distribution functions. The trajectories in the fully interacting system and ensemble averages are defined with respect to the parameters that fix the trajectories in the interaction-free limit. Irreversibility may emerge from microscopic dynamics due to the choice as to which part of the particles’ history — past or future — contributes to the interaction. Irreversibility is explicitly demonstrated in the evolution of the one-particle distribution function.

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.

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

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