639 research outputs found
Impact of boundaries on velocity profiles in bubble rafts
Under conditions of sufficiently slow flow, foams, colloids, granular matter,
and various pastes have been observed to exhibit shear localization, i.e.
regions of flow coexisting with regions of solid-like behavior. The details of
such shear localization can vary depending on the system being studied. A
number of the systems of interest are confined so as to be quasi-two
dimensional, and an important issue in these systems is the role of the
confining boundaries. For foams, three basic systems have been studied with
very different boundary conditions: Hele-Shaw cells (bubbles confined between
two solid plates); bubble rafts (a single layer of bubbles freely floating on a
surface of water); and confined bubble rafts (bubbles confined between the
surface of water below and a glass plate on top). Often, it is assumed that the
impact of the boundaries is not significant in the ``quasi-static limit'', i.e.
when externally imposed rates of strain are sufficiently smaller than internal
kinematic relaxation times. In this paper, we directly test this assumption for
rates of strain ranging from to . This
corresponds to the quoted quasi-static limit in a number of previous
experiments. It is found that the top plate dramatically alters both the
velocity profile and the distribution of nonlinear rearrangements, even at
these slow rates of strain.Comment: New figures added, revised version accepted for publication in Phys.
Rev.
Limits of the equivalence of time and ensemble averages in shear flows
In equilibrium systems, time and ensemble averages of physical quantities are
equivalent due to ergodic exploration of phase space. In driven systems, it is
unknown if a similar equivalence of time and ensemble averages exists. We
explore effective limits of such convergence in a sheared bubble raft using
averages of the bubble velocities. In independent experiments, averaging over
time leads to well converged velocity profiles. However, the time-averages from
independent experiments result in distinct velocity averages. Ensemble averages
are approximated by randomly selecting bubble velocities from independent
experiments. Increasingly better approximations of ensemble averages converge
toward a unique velocity profile. Therefore, the experiments establish that in
practical realizations of non-equilibrium systems, temporal averaging and
ensemble averaging can yield convergent (stationary) but distinct
distributions.Comment: accepted to PRL - final figure revision
Bubble kinematics in a sheared foam
We characterize the kinematics of bubbles in a sheared two-dimensional foam
using statistical measures. We consider the distributions of both bubble
velocities and displacements. The results are discussed in the context of the
expected behavior for a thermal system and simulations of the bubble model.
There is general agreement between the experiments and the simulation, but
notable differences in the velocity distributions point to interesting elements
of the sheared foam not captured by prevalent models
An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation
Monotonicity is a simple yet significant qualitative characteristic. We
consider the problem of segmenting a sequence in up to K segments. We want
segments to be as monotonic as possible and to alternate signs. We propose a
quality metric for this problem using the l_inf norm, and we present an optimal
linear time algorithm based on novel formalism. Moreover, given a
precomputation in time O(n log n) consisting of a labeling of all extrema, we
compute any optimal segmentation in constant time. We compare experimentally
its performance to two piecewise linear segmentation heuristics (top-down and
bottom-up). We show that our algorithm is faster and more accurate.
Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142
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