16,046 research outputs found
Time correlations and persistence probability of a Brownian particle in a shear flow
In this article, results have been presented for the two-time correlation
functions for a free and a harmonically confined Brownian particle in a simple
shear flow. For a free Brownian particle, the motion along the direction of
shear exhibit two distinct dynamics, with the mean-square-displacement being
diffusive at short times while at late times scales as . In contrast the
cross-correlation \la x(t) y(t) \ra scales quadratically for all times. In
the case of a harmonically trapped Brownian particle, the
mean-square-displacement exhibits a plateau determined by the strength of the
confinement and the shear. Further, the analysis is extended to a chain of
Brownian particles interacting via a harmonic and a bending potential. Finally,
the persistence probability is constructed from the two-time correlation
functions.Comment: 8 pages, 4 figure
The ACTS propagation program
The success or failure of the ACTS experiment will depend on how accurately the rain-fade statistics and fade dynamics can be predicted in order to derive an appropriate algorithm that will combat weather vagaries, specifically for links with small terminals, such as very small aperture terminals (VSAT's) where the power margin is a premium. The planning process and hardware development program that will comply with the recommendations of the ACTS propagation study groups are described
Persistence of a Brownian particle in a Time Dependent Potential
We investigate the persistence probability of a Brownian particle in a
harmonic potential, which decays to zero at long times -- leading to an
unbounded motion of the Brownian particle. We consider two functional forms for
the decay of the confinement, an exponential and an algebraic decay. Analytical
calculations and numerical simulations show, that for the case of the
exponential relaxation, the dynamics of Brownian particle at short and long
times are independent of the parameters of the relaxation. On the contrary, for
the algebraic decay of the confinement, the dynamics at long times is
determined by the exponent of the decay. Finally, using the two-time
correlation function for the position of the Brownian particle, we construct
the persistence probability for the Brownian walker in such a scenario.Comment: 7 pages, 5 figures, Accepted for publication in Phys. Rev.
Stability and Equilibrium Analysis of Laneless Traffic with Local Control Laws
In this paper, a new model for traffic on roads with multiple lanes is
developed, where the vehicles do not adhere to a lane discipline. Assuming
identical vehicles, the dynamics is split along two independent directions: the
Y-axis representing the direction of motion and the X-axis representing the
lateral or the direction perpendicular to the direction of motion. Different
influence graphs are used to model the interaction between the vehicles in
these two directions. The instantaneous accelerations of each car, in both X
and Y directions, are functions of the measurements from the neighbouring cars
according to these influence graphs. The stability and equilibrium spacings of
the car formation is analyzed for usual traffic situations such as steady flow,
obstacles, lane changing and rogue drivers arbitrarily changing positions
inside the formation. Conditions are derived under which the formation
maintains stability and the desired intercar spacing for each of these traffic
events. Simulations for some of these scenarios are included.Comment: 8 page
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