Physical Regions in Invariant Variables fornParticles and the Phase-Space Volume Element

1964 ◽  
Vol 36 (2) ◽  
pp. 595-609 ◽  
Author(s):  
N. BYERS ◽  
C. N. YANG
Keyword(s):  
Phase Space ◽  
Volume Element ◽  
Phase Space Volume ◽  
Space Volume

scholarly journals Relativistic transformation of phase-space distributions

2011 ◽  
Vol 29 (7) ◽  
pp. 1259-1265 ◽  
Author(s):  
R. A. Treumann ◽  
R. Nakamura ◽  
W. Baumjohann
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Volume Element ◽  
Plasma Parameters ◽  
Astrophysical Plasmas ◽  
Relativistic Case ◽  
Phase Space Volume ◽  
Radiation Theory ◽  
High Mach ◽  
Space Volume

Abstract. We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the electron-cyclotron maser radiation theory, in the vicinity of high-Mach number shocks where particles are accelerated to high speeds, and generally in solar and astrophysical plasmas. We show that the phase-space volume element is a Lorentz constant and construct the general particle distribution function from first principles. Application to thermal equilibrium lets us derive a modified version of the isotropic relativistic thermal distribution, the modified Jüttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters.

Phase-space volume based control of semibatch reactors

2010 ◽  
Vol 88 (3) ◽  
pp. 320-330 ◽  
Author(s):  
José-Manuel Zaldívar ◽  
Fernanda Strozzi
Keyword(s):  
Phase Space ◽  
Phase Space Volume ◽  
Space Volume

scholarly journals Almost additive entropy

2014 ◽  
Vol 11 (05) ◽  
pp. 1450040 ◽  
Author(s):  
Nikos Kalogeropoulos
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Power Law ◽  
Physical Significance ◽  
Small Deviations ◽  
Phase Space Volume ◽  
Composition Property ◽  
Flat Manifolds ◽  
Special Case ◽  
Space Volume

We explore consequences of a hyperbolic metric induced by the composition property of the Harvda–Charvat/Daróczy/Cressie–Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter q ≈ 1 from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.

scholarly journals SHARP SPECTRAL ESTIMATES IN DOMAINS OF INFINITE VOLUME

2011 ◽  
Vol 23 (06) ◽  
pp. 615-641 ◽  
Author(s):  
LEANDER GEISINGER ◽  
TIMO WEIDL
Keyword(s):  
Phase Space ◽  
Dirichlet Boundary ◽  
Semiclassical Limit ◽  
Dirichlet Boundary Conditions ◽  
Bounded Domains ◽  
Infinite Volume ◽  
Uniform Bounds ◽  
Phase Space Volume ◽  
Spectral Estimates ◽  
Space Volume

We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume — and therefore on the volume of the domain — must fail. Here we present a method on how one can nevertheless prove uniform bounds on eigenvalues and eigenvalue means which are sharp in the semiclassical limit.We give examples in horn-shaped regions and so-called spiny urchins. Some results are extended to Schrödinger operators defined on quasi-bounded domains with Dirichlet boundary conditions.

scholarly journals A Family of Hierarchical Symplectic Maps for N-body Simulations with Post-Newtonian Corrections

2017 ◽  
Vol 45 ◽  
pp. 1760021
Author(s):  
Guilherme Gonçalves Ferrari
Keyword(s):  
Phase Space ◽  
Body Problem ◽  
Hamiltonian Dynamics ◽  
Symplectic Maps ◽  
Time Step ◽  
Phase Space Volume ◽  
Time Stepping ◽  
Adaptive Time ◽  
The Individual ◽  
Space Volume

Symplectic maps are well known for preserving the phase-space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times, such as the [Formula: see text]-body problem. However, when combined with a varying time-step scheme, they end up losing its symplecticity and become numerically inefficient. We address this problem by using a recursive Hamiltonian splitting based on the time-symmetric value of the individual time-steps required by the particles in the system. We present a family of 48 quasi-symplectic maps with different orders of convergence (2nd-, 4th- & 6th-order) and three time-stepping schemes: i) 16 using constant time-steps, ii) 16 using shared adaptive time-steps, and iii) 16 using hierarchical (individual) time-steps. All maps include post-Newtonian corrections up to order 3.5PN. We describe the method and present some details of the implementation.

scholarly journals A high energy, small phase-space volume muon beam

1969 ◽  
Vol 69 (1) ◽  
pp. 77-88 ◽  
Author(s):  
J. Cox ◽  
F. Martin ◽  
M.L. Perl ◽  
T.H. Tan ◽  
W.T. Toner ◽  
...  
Keyword(s):  
Phase Space ◽  
High Energy ◽  
Muon Beam ◽  
Phase Space Volume ◽  
Small Phase ◽  
Space Volume

scholarly journals Phase Space and Dynamical Fluctuations of Kaon-to-Pion Ratios

2011 ◽  
Vol 126 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Abdel Tawfik
Keyword(s):  
Phase Space ◽  
Center Of Mass ◽  
Gluon Plasma ◽  
Canonical Partition Function ◽  
Phase Space Volume ◽  
Grand Canonical Partition Function ◽  
Wide Range ◽  
Dynamical Fluctuations ◽  
Space Occupation ◽  
Space Volume

Abstract The dynamical fluctuations of kaon-to-pion ratios have been studied over a wide range of center-of-mass energies √s. On the basis of changing phase space volume which apparently is the consequence of phase transition from hadrons to quark-gluon plasma at large √s, the single-particle distribution function f is assumed to be rather modified. Varying f and phase space volume are implemented in the grand-canonical partition function, especially at large √s, so that the hadron resonance gas model, when taking into account the experimental acceptance and quark phase space occupation factor, turns to be able to reproduce the dynamical fluctuations of kaon-to-pion ratios over the entire range of √s.

Sign in / Sign up

Export Citation Format

Share Document