14,134 research outputs found
Jamming in a lattice model of stochastically interacting agents with a field of view
We study the collective dynamics of a lattice model of stochastically
interacting agents with a weighted field of vision. We assume that agents
preferentially interact with neighbours, depending on their relative location,
through velocity alignments and the additional constraint of exclusion. Unlike
in previous models of flocking, here the stochasticity arises intrinsically
from the interactions between agents, and its strength is dependent on the
local density of agents. We find that this system yields a first-order jamming
transition as a consequence of these interactions, even at a very low density.
Furthermore, the critical jamming density is found to strongly depend on the
nature of the field of view.Comment: 5 pages, 3 figures + 3 pages supplementary materia
On the use of Kolmogorov-Landau approach in deriving various correlation functions in 2-D incompressible turbulence
We look at various correlation functions, which include those that involve
both the velocity and the vorticity fields, in 2-D isotropic homogeneous
decaying turbulence.We adopt the more intuitive approach due to Kolmogorov (and
subsequently, Landau in his text on fluid dynamics) and show that how the 2-D
turbulence results, obtainable using other methods, may be established in a
simpler way.Also, some experimentally verifiable correlation functions in the
dissipation range have been derived for the same system.The paper also
showcases the inability of the Kolmogorov-Landau approach to get the
``one-eighth law'' in the enstrophy cascade region.As discussed in the paper,
this may raise the spectre of logarithmic corrections once again in 2-D
turbulence.Comment: A typos-corrected version of the earlier submissio
Landau theory of glassy dynamics
An exact solution of a Landau model of an order-disorder transition with
activated critical dynamics is presented. The model describes a funnel-shaped
topography of the order parameter space in which the number of energy lowering
trajectories rapidly diminishes as the ordered ground-state is approached. This
leads to an asymmetry in the effective transition rates which results in a
non-exponential relaxation of the order-parameter fluctuations and a
Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass
transition. We argue that the Landau model provides a general framework for
studying glassy dynamics in a variety of systems.Comment: 4 pages, 2 figure
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.
Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover
We extend the definition of a global order parameter to the case of a
critical system confined between two infinite parallel plates separated by a
finite distance . For a quench to the critical point we study the
persistence property of the global order parameter and show that there is a
crossover behaviour characterized by a non universal exponent which depends on
the ratio of the system size to a dynamic length scale
- …