scholarly journals Fluctuations of TASEP on a Ring in Relaxation Time Scale

2017 ◽  
Vol 71 (4) ◽  
pp. 747-813 ◽  
Author(s):  
Jinho Baik ◽  
Zhipeng Liu
Keyword(s):  
Relaxation Time ◽  
Time Scale ◽  
Relaxation Time Scale

scholarly journals The Energy Exchange between Different Masses in an Expanding Gravitating System

1996 ◽  
Vol 174 ◽  
pp. 387-388
Author(s):  
Yuan Zhou ◽  
Shoken M. Miyama
Keyword(s):  
Relaxation Time ◽  
Dynamic Equation ◽  
Time Scale ◽  
Characteristic Time ◽  
Energy Exchange ◽  
Mass Ratio ◽  
Expansion Time ◽  
Two Component ◽  
Relaxation Time Scale ◽  
Species Groups

We investigate whether or not the energy exchange occurs between two species groups of particles in an expanding two-component gravitating system, and we derive the relaxation time scale for energy exchange in such a phase. This is accomplished by solving the dynamic equation coupled with Poisson's equation. We derive a characteristic time determined by the various mass and velocity ratios. When the expansion time does not exceed the characteristic time, energy exchange between the two components is possible and depends on the mass ratio. Once the characteristic time is exceeded, there is virtually no relaxation at all in system. When m2 ≫ m1, the transfer of energy becomes inefficient. Therefore, energy exchange between two species of particle in an expanding two-component gravitating system depends not only on the mass ratio but also on the expansion time.

scholarly journals Role of Relaxation Time Scale in Noisy Signal Transduction

PLoS ONE ◽  
2015 ◽  
Vol 10 (5) ◽  
pp. e0123242 ◽  
Author(s):  
Alok Kumar Maity ◽  
Pinaki Chaudhury ◽  
Suman K Banik
Keyword(s):  
Signal Transduction ◽  
Relaxation Time ◽  
Time Scale ◽  
Noisy Signal ◽  
Relaxation Time Scale

scholarly journals Collisional Relaxation: A New Approach

1985 ◽  
Vol 113 ◽  
pp. 339-341
Author(s):  
G. Severne ◽  
M. Luwel
Keyword(s):  
Relaxation Time ◽  
Kinetic Equation ◽  
Time Scale ◽  
Mean Field ◽  
Collisional Relaxation ◽  
New Approach ◽  
Periodic Trajectories ◽  
3 Dimensional ◽  
Relaxation Time Scale ◽  
The Mean

Recent numerical simulations for 1-dimensional systems have shown that the relaxation time due to encounters is far shorter than the generally accepted estimate. To account for this, a new approach to the theory is necessary. The analysis of encounters presented here is characterized by the retention of periodic trajectories in the mean field. The kinetic equation obtained yields a relaxation time scale in qualitative agreement with the simulations. The analysis can be extended to the 3-dimensional case, and preliminary results predict here also a reduction of the relaxation time.

scholarly journals TASEP on a Ring in Sub-relaxation Time Scale

2016 ◽  
Vol 165 (6) ◽  
pp. 1051-1085 ◽  
Author(s):  
Jinho Baik ◽  
Zhipeng Liu
Keyword(s):  
Relaxation Time ◽  
Time Scale ◽  
Relaxation Time Scale

scholarly journals Sensitivity of the simulated precipitation to changes in convective relaxation time scale

2010 ◽  
Vol 28 (10) ◽  
pp. 1827-1846 ◽  
Author(s):  
S. K. Mishra ◽  
J. Srinivasan
Keyword(s):  
Relaxation Time ◽  
Time Scale ◽  
Convective Instability ◽  
Convective Available Potential Energy ◽  
Convective Precipitation ◽  
Characteristic Time Scale ◽  
Similar Response ◽  
Total Precipitation ◽  
Simulated Precipitation ◽  
Relaxation Time Scale

Abstract. The paper describes the sensitivity of the simulated precipitation to changes in convective relaxation time scale (TAU) of Zhang and McFarlane (ZM) cumulus parameterization, in NCAR-Community Atmosphere Model version 3 (CAM3). In the default configuration of the model, the prescribed value of TAU, a characteristic time scale with which convective available potential energy (CAPE) is removed at an exponential rate by convection, is assumed to be 1 h. However, some recent observational findings suggest that, it is larger by around one order of magnitude. In order to explore the sensitivity of the model simulation to TAU, two model frameworks have been used, namely, aqua-planet and actual-planet configurations. Numerical integrations have been carried out by using different values of TAU, and its effect on simulated precipitation has been analyzed. The aqua-planet simulations reveal that when TAU increases, rate of deep convective precipitation (DCP) decreases and this leads to an accumulation of convective instability in the atmosphere. Consequently, the moisture content in the lower- and mid- troposphere increases. On the other hand, the shallow convective precipitation (SCP) and large-scale precipitation (LSP) intensify, predominantly the SCP, and thus capping the accumulation of convective instability in the atmosphere. The total precipitation (TP) remains approximately constant, but the proportion of the three components changes significantly, which in turn alters the vertical distribution of total precipitation production. The vertical structure of moist heating changes from a vertically extended profile to a bottom heavy profile, with the increase of TAU. Altitude of the maximum vertical velocity shifts from upper troposphere to lower troposphere. Similar response was seen in the actual-planet simulations. With an increase in TAU from 1 h to 8 h, there was a significant improvement in the simulation of the seasonal mean precipitation. The fraction of deep convective precipitation was in much better agreement with satellite observations.

scholarly journals The Stability of Mars’s Annular Polar Vortex

2017 ◽  
Vol 74 (5) ◽  
pp. 1533-1547 ◽  
Author(s):  
William J. M. Seviour ◽  
Darryn W. Waugh ◽  
Richard K. Scott
Keyword(s):  
Relaxation Time ◽  
Time Scales ◽  
Time Scale ◽  
Thermal Relaxation ◽  
Polar Vortex ◽  
Radiative Relaxation ◽  
Equilibrium Profile ◽  
Rotating Shallow Water ◽  
The Stability ◽  
Topographic Forcing

Abstract The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising, since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here the stability of a Mars-like annular vortex is investigated using numerical integrations of the rotating shallow-water equations. The mode of instability and its growth rate is shown to depend upon the latitude and width of the annulus. By introducing thermal relaxation toward an annular equilibrium profile with a time scale similar to that of the instability, a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere can be simulated. This time scale, typically 0.5–2 sols, is similar to radiative relaxation time scales for Mars’s polar atmosphere. The persistence of an annular vortex is also shown to be robust to topographic forcing, as long as it is below a certain amplitude. It is therefore proposed that the persistence of this barotropically unstable annular vortex is permitted owing to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.

The effect of compaction of a porous material confiner on detonation propagation

2017 ◽  
Vol 834 ◽  
pp. 434-463 ◽  
Author(s):  
Mark Short ◽  
James J. Quirk
Keyword(s):  
Relaxation Time ◽  
Porous Material ◽  
Time Scale ◽  
Sound Speed ◽  
Volume Fraction ◽  
Relaxation Rates ◽  
Slab Geometry ◽  
Local Flow ◽  
Detonation Propagation ◽  
Detonation Speed

The fluid mechanics of the interaction between a porous material confiner and a steady propagating high explosive (HE) detonation in a two-dimensional slab geometry is investigated through analytical oblique wave polar analysis and multi-material numerical simulation. Two HE models are considered, broadly representing the properties of either a high- or low-detonation-speed HE, which permits studies of detonation propagating at speeds faster or slower than the confiner sound speed. The HE detonation is responsible for driving the compaction front in the confiner, while, in turn, the high material density generated in the confiner as a result of the compaction process can provide a strong confinement effect on the HE detonation structure. Polar solutions that describe the local flow interaction of the oblique HE detonation shock and equilibrium state behind an oblique compaction wave with rapid compaction relaxation rates are studied for varying initial solid volume fractions of the porous confiner. Multi-material numerical simulations are conducted to study the effect of detonation wave driven compaction in the porous confiner on both the detonation propagation speed and detonation driving zone structure. We perform a parametric study to establish how detonation confinement is influenced both by the initial solid volume fraction of the porous confiner and by the time scale of the dynamic compaction relaxation process relative to the detonation reaction time scale, for both the high- and low-detonation-speed HE models. The compaction relaxation time scale is found to have a significant influence on the confinement dynamics, with slower compaction relaxation time scales resulting in more strongly confined detonations and increased detonation speeds. The dynamics of detonation confinement by porous materials when the detonation is propagating either faster or slower than the confiner sound speed is found to be significantly different from that with solid material confiners.

Sign in / Sign up

Export Citation Format

Share Document