153 research outputs found
First Passage Time for Many Particle Diffusion in Space-Time Random Environments
The first passage time for a single diffusing particle has been studied
extensively, but the first passage time of a system of many diffusing
particles, as is often the case in physical systems, has received little
attention until recently. We consider two models for many particle diffusion --
one treats each particle as independent simple random walkers while the other
treats them as coupled to a common space-time random forcing field that biases
particles nearby in space and time in similar ways. The first passage time of a
single diffusing particle under both of these models show the same statistics
and scaling behavior. However, for many particle diffusions, the first passage
time among all particles (the `extreme first passage time') is very different
between the two models, effected in the latter case by the randomness of the
common forcing field. We develop an asymptotic (in the number of particles and
location where first passage is being probed) theoretical framework to separate
out the impact of the random environment with that of sampling trajectories
within it. We identify a new power-law describing the impact to the extreme
first passage time variance of the environment. Through numerical simulations
we verify that the predictions from this asymptotic theory hold even for
systems with widely varying numbers of particles, all the way down to 100
particles. This shows that measurements of the extreme first passage time for
many-particle diffusions provide an indirect measurement of the underlying
environment in which the diffusion is occurring
Universal microstructure and mechanical stability of jammed packings
Jammed packings' mechanical properties depend sensitively on their detailed
local structure. Here we provide a complete characterization of the pair
correlation close to contact and of the force distribution of jammed
frictionless spheres. In particular we discover a set of new scaling relations
that connect the behavior of particles bearing small forces and those bearing
no force but that are almost in contact. By performing systematic
investigations for spatial dimensions d=3-10, in a wide density range and using
different preparation protocols, we show that these scalings are indeed
universal. We therefore establish clear milestones for the emergence of a
complete microscopic theory of jamming. This description is also crucial for
high-precision force experiments in granular systems.Comment: 11 pages, 7 figure
Universal non-Debye scaling in the density of states of amorphous solids
At the jamming transition, amorphous packings are known to display anomalous
vibrational modes with a density of states (DOS) that remains constant at low
frequency. The scaling of the DOS at higher densities remains, however,
unclear. One might expect to find simple Debye scaling, but recent results from
effective medium theory and the exact solution of mean-field models both
predict an anomalous, non-Debye scaling. Being mean-field solutions, however,
these solutions are only strictly applicable to the limit of infinite spatial
dimension, and it is unclear what value they have for finite-dimensional
systems. Here, we study packings of soft spheres in dimensions 3 through 7 and
find, far from jamming, a universal non-Debye scaling of the DOS that is
consistent with the mean-field predictions. We also consider how the soft mode
participation ratio converges to the mean-field prediction as dimension
increases.Comment: 5 pages, 4 figure
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