Diffusion in phase space with molecular friction: A numerical study for undercooled liquids

2001 ◽  
Vol 114 (23) ◽  
pp. 10402-10410 ◽  
Author(s):  
Beatrix M. Schulz ◽  
Steffen Trimper ◽  
Michael Schulz
Keyword(s):  
Phase Space ◽  
Numerical Study ◽  
Molecular Friction

scholarly journals The echo of the bar buckling: Phase-space spirals in Gaia Data Release 2

2019 ◽  
Vol 622 ◽  
pp. L6 ◽  
Author(s):  
Sergey Khoperskov ◽  
Paola Di Matteo ◽  
Ortwin Gerhard ◽  
David Katz ◽  
Misha Haywood ◽  
...  
Keyword(s):  
Phase Space ◽  
Milky Way ◽  
Physical Mechanism ◽  
Galactic Center ◽  
Numerical Study ◽  
Vertical Motion ◽  
Solar Neighborhood ◽  
Vertical Coordinate ◽  
Data Release ◽  
Bar Buckling

We present a high-resolution numerical study of the phase-space diversity in an isolated Milky Way-type galaxy. Using a single N-body simulation (N ≈ 0.14 × 109) we explore the formation, evolution, and spatial variation of the phase-space spirals similar to those recently discovered by Antoja et al. in the Milky Way disk with Gaia Data Release 2 (DR2). For the first time in the literature we use a self-consistent N-body simulation of an isolated Milky Way-type galaxy to show that the phase-space spirals develop naturally from vertical oscillations driven by the buckling of the stellar bar. Thus, we claim that the physical mechanism standing behind the observed incomplete phase-space mixing process can be internal and not necessarily due to the perturbation induced by a massive satellite. In our model, the bending oscillations propagate outward and produce axisymmetric variations of the mean vertical coordinate and vertical velocity component of about 100 − 200 pc and 1 − 2 km s−1, respectively. As a consequence, the phase-space wrapping results in the formation of patterns with various morphologies across the disk, depending on the bar orientation, distance to the galactic center, and time elapsed since the bar buckling. Once bending waves appear, they are supported for a long time via disk self-gravity. Such vertical oscillations trigger the formation of various time-dependent phase-space spirals in the entire disk. The underlying physical mechanism implies the link between in-plane and vertical motion that leads directly to phase-space structures whose amplitude and shape are in remarkable agreement with those of the phase-space spirals observed in the Milky Way disk. In our isolated galaxy simulation, phase-space spirals are still distinguishable at the solar neighborhood 3 Gyr after the buckling phase. The long-lived character of the phase-space spirals generated by the bar buckling instability cast doubts on the timing argument used so far to get back to the time of the onset of the perturbation: phase-space spirals may have been caused by perturbations originated several gigayearrs ago, and not as recent as suggested so far.

scholarly journals Numerical study of ion acceleration and plasma jet formation in the interaction of an intense laser beam normally incident on an overdense plasma

2011 ◽  
Vol 29 (3) ◽  
pp. 315-332 ◽  
Author(s):  
M. Shoucri ◽  
X. Lavocat-Dubuis ◽  
J.-P. Matte ◽  
F. Vidal
Keyword(s):  
Phase Space ◽  
Laser Beam ◽  
Laser Intensity ◽  
Numerical Study ◽  
Plasma Jet ◽  
Space Structures ◽  
Rear Side ◽  
Plasma Surface ◽  
Target Plasma ◽  
Overdense Plasma

AbstractWe present a numerical study of the acceleration of ions in the interaction of a high intensity circularly polarized laser beam normally incident on an overdense plasma target, and the subsequent formation of neutral plasma ejected toward the rear side of the target. We compare the results obtained from two different numerical codes. We use an Eulerian Vlasov code for the numerical solution of the one-dimensional relativistic Vlasov-Maxwell set of equations, for both electrons and ions, and a particle-in-cell code applied to the same problem. We consider the case when the laser free space wavelength λ0 is greater than the scale length of the jump in the plasma density at the target plasma edge Ledge (λ0 ≫ Ledge), and the ratio of the plasma density to the critical density is such that n/ncr ≫ 1. The ponderomotive pressure due to the incident high-intensity laser radiation pushes the electrons at the target plasma surface, producing a sharp density gradient at the plasma surface, which gives rise to a charge separation. The resulting electric field accelerates the ions that reach a free streaming expansion phase, where they are neutralized by the electrons. A neutral plasma jet is thus ejected toward the rear side of the target. Two cases are studied: In the first case, the laser intensity rises to a maximum and then remains constant, and in the second case, the laser intensity is a Gaussian-shaped pulse. The results show substantial differences in the phase-space structure of the ions and the electrons between these two cases. There is good agreement between the quantitative macroscopic results obtained by the two codes, and good qualitative agreement between the results showing the kinetic details of the phase-space structures. The low noise level of the Eulerian Vlasov code allows a more detailed representation of the phase-space structures associated with this system, especially in the low density regions of the phase-space where ions are accelerated.

Almost Invariant Sets in Chua's Circuit

1997 ◽  
Vol 07 (11) ◽  
pp. 2475-2485 ◽  
Author(s):  
Michael Dellnitz ◽  
Oliver Junge
Keyword(s):  
Phase Space ◽  
Numerical Investigation ◽  
Numerical Study ◽  
Dynamical Behavior ◽  
Invariant Sets ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Long Time ◽  
Almost Invariant Sets

Recently multilevel subdivision techniques have been introduced in the numerical investigation of complicated dynamical behavior. We illustrate the applicability and efficiency of these methods by a detailed numerical study of Chua's circuit. In particular we will show that there exist two regions in phase space which are almost invariant in the sense that typical trajectories stay inside each of these sets on average for quite a long time.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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