scholarly journals Diffusion phenomena in a mixed phase space

2020 ◽  
Vol 30 (1) ◽  
pp. 013108 ◽  
Author(s):  
Matheus S. Palmero ◽  
Gabriel I. Díaz ◽  
Peter V. E. McClintock ◽  
Edson D. Leonel
Keyword(s):  
Phase Space ◽  
Mixed Phase ◽  
Diffusion Phenomena

scholarly journals Illustration of microphysical processes in Amazonian deep convective clouds in the Gamma phase space: Introduction and potential applications

2017 ◽  
Author(s):  
Micael A. Cecchini ◽  
Luiz A. T. Machado ◽  
Manfred Wendisch ◽  
Anja Costa ◽  
Martina Krämer ◽  
...  
Keyword(s):  
Phase Space ◽  
Cloud Droplet ◽  
Mixed Phase ◽  
Relative Dispersion ◽  
Gamma Phase ◽  
Liquid Droplets ◽  
Phase Layer ◽  
Cloud Properties ◽  
Common Framework ◽  
Space Approach

Abstract. The behavior of tropical clouds remains a major open scientific question, given that the associated phys-ics is not well represented by models. One challenge is to realistically reproduce cloud droplet size dis-tributions (DSD) and their evolution over time and space. Many applications, not limited to models, use the Gamma function to represent DSDs. However, there is almost no study dedicated to understanding the phase space of this function, which is given by the three parameters that define the DSD intercept, shape, and curvature. Gamma phase space may provide a common framework for parameterizations and inter-comparisons. Here, we introduce the phase-space approach and its characteristics, focusing on warm-phase microphysical cloud properties and the transition to the mixed-phase layer. We show that trajectories in this phase space can represent DSD evolution and can be related to growth processes. Condensational and collisional growth may be interpreted as pseudo-forces that induce displacements in opposite directions within the phase space. The actually observed movements in the phase space are a result of the combination of such pseudo-forces. Additionally, aerosol effects can be evaluated given their significant impact on DSDs. The DSDs associated with liquid droplets that favor cloud glaciation can be delimited in the phase space, which can help models to adequately predict the transition to the mixed phase. We also consider possible ways to constrain the DSD in two-moment bulk microphysics schemes, where the relative dispersion parameter of the DSD can play a significant role. Overall, the Gamma phase-space approach can be an invaluable tool for studying cloud microphysical evolution and can be readily applied in many scenarios that rely on Gamma DSDs.

Quantum chaotic scattering with a mixed phase space: The three-disk billiard in a magnetic field

2000 ◽  
Vol 61 (1) ◽  
pp. 382-389 ◽  
Author(s):  
Markus Eichengrün ◽  
Walter Schirmacher ◽  
Wolfgang Bregmann
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Mixed Phase ◽  
Chaotic Scattering

scholarly journals Semiclassical Spectra from Periodic-Orbit Clusters in a Mixed Phase Space

1997 ◽  
Vol 79 (6) ◽  
pp. 1022-1025 ◽  
Author(s):  
Henning Schomerus ◽  
Fritz Haake
Keyword(s):  
Phase Space ◽  
Periodic Orbit ◽  
Mixed Phase

scholarly journals Effective dynamics in Hamiltonian systems with mixed phase space

2005 ◽  
Vol 71 (3) ◽  
Author(s):  
Adilson E. Motter ◽  
Alessandro P. S. de Moura ◽  
Celso Grebogi ◽  
Holger Kantz
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Mixed Phase ◽  
Effective Dynamics

Tilted-hat mushroom billiards: Web-like hierarchical mixed phase space

2020 ◽  
Vol 91 ◽  
pp. 105440
Author(s):  
Diogo Ricardo da Costa ◽  
Matheus S. Palmero ◽  
J.A. Méndez-Bermúdez ◽  
Kelly C. Iarosz ◽  
José D. Szezech Jr ◽  
...  
Keyword(s):  
Phase Space ◽  
Mixed Phase

Semi-focusing billiards: ergodicity

2008 ◽  
Vol 28 (5) ◽  
pp. 1377-1417 ◽  
Author(s):  
LEONID A. BUNIMOVICH ◽  
GIANLUIGI DEL MAGNO
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Mixed Phase ◽  
Convex Domains ◽  
Math Phys ◽  
Standing Question

AbstractIn Bunimovich and Del Magno [Semi-focusing billiards: hyperbolicity. Comm. Math. Phys.262 (2006), 17–32], we proved that billiards in certain three-dimensional convex domains are hyperbolic. In this paper, we continue the study of these systems, and prove that they enjoy the Bernoulli property. This result answers affirmatively a long-standing question on the existence of ergodic billiards in convex domains in dimensions greater than two. Besides, it shows that the chaotic components of the first rigorously investigated three-dimensional billiards with mixed phase space (mushroom billiards), introduced in Bunimovich and Del Magno, are in fact Bernoulli.

Probing quantal dynamics of mixed phase space systems with noise

1993 ◽  
Vol 71 (18) ◽  
pp. 2895-2898 ◽  
Author(s):  
L. Sirko ◽  
M. R. W. Bellermann ◽  
A. Haffmans ◽  
P. M. Koch ◽  
D. Richards
Keyword(s):  
Phase Space ◽  
Mixed Phase ◽  
Space Systems

Semiclassical calculation and analysis of dynamical systems with mixed phase space

1994 ◽  
Vol 101 (9) ◽  
pp. 8004-8015 ◽  
Author(s):  
Miguel Angel Sepúlveda ◽  
Eric J. Heller
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Mixed Phase

scholarly journals Quantized invariant tori in Andreev billiards of mixed phase space

2006 ◽  
Vol 73 (21) ◽  
Author(s):  
Z. Kaufmann ◽  
A. Kormányos ◽  
J. Cserti ◽  
C. J. Lambert
Keyword(s):  
Phase Space ◽  
Invariant Tori ◽  
Mixed Phase ◽  
Andreev Billiards
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