257 research outputs found
Constant Approximation for -Median and -Means with Outliers via Iterative Rounding
In this paper, we present a new iterative rounding framework for many
clustering problems. Using this, we obtain an -approximation algorithm for -median with outliers, greatly
improving upon the large implicit constant approximation ratio of Chen [Chen,
SODA 2018]. For -means with outliers, we give an -approximation, which is the first -approximation for
this problem. The iterative algorithm framework is very versatile; we show how
it can be used to give - and -approximation
algorithms for matroid and knapsack median problems respectively, improving
upon the previous best approximations ratios of [Swamy, ACM Trans.
Algorithms] and [Byrka et al, ESA 2015].
The natural LP relaxation for the -median/-means with outliers problem
has an unbounded integrality gap. In spite of this negative result, our
iterative rounding framework shows that we can round an LP solution to an
almost-integral solution of small cost, in which we have at most two
fractionally open facilities. Thus, the LP integrality gap arises due to the
gap between almost-integral and fully-integral solutions. Then, using a
pre-processing procedure, we show how to convert an almost-integral solution to
a fully-integral solution losing only a constant-factor in the approximation
ratio. By further using a sparsification technique, the additive factor loss
incurred by the conversion can be reduced to any
Tensorial Constitutive Models for Disordered Foams, Dense Emulsions, and other Soft Nonergodic Materials
In recent years, the paradigm of `soft glassy matter' has been used to
describe diverse nonergodic materials exhibiting strong local disorder and slow
mesoscopic rearrangement. As so far formulated, however, the resulting `soft
glassy rheology' (SGR) model treats the shear stress in isolation, effectively
`scalarizing' the stress and strain rate tensors. Here we offer generalizations
of the SGR model that combine its nontrivial aging and yield properties with a
tensorial structure that can be specifically adapted, for example, to the
description of fluid film assemblies or disordered foams.Comment: 18 pages, 4 figure
Impact of earthworm activity on the chemical fertility of irrigated soil with urban effluents
The reuse of urban effluents to irrigate the soils of peri-urban grasslands in the vicinity of the town of Setif (northeastern Algeria) is an old and widespread practice. In this context, the present study was conducted to evaluate the effect of the irrigation with urban effluents on the biological and chemical behavior of soils. Effluents analysis showed significant organic and particulate pollution, the latter contributed to earthworm abundance and increased the richness of irrigated soils with nutrients. The analysis of turricules revealed the role of earthworms through the activity of bioturbation in the increase of the rate of organic matter as well as in the bioavailability of the nutrients of the irrigated soils. In space, permanent vegetation cover has played an important role as a biofilter. This was confirmed by the inter-site differences recorded through the measured variables particularly organic ones.Keywords: Natural grasslands, urban effluents, earthworm activity, turricles, organic matte
Non-Equilibrium in Adsorbed Polymer Layers
High molecular weight polymer solutions have a powerful tendency to deposit
adsorbed layers when exposed to even mildly attractive surfaces. The
equilibrium properties of these dense interfacial layers have been extensively
studied theoretically. A large body of experimental evidence, however,
indicates that non-equilibrium effects are dominant whenever monomer-surface
sticking energies are somewhat larger than kT, a common case. Polymer
relaxation kinetics within the layer are then severely retarded, leading to
non-equilibrium layers whose structure and dynamics depend on adsorption
kinetics and layer ageing. Here we review experimental and theoretical work
exploring these non-equilibrium effects, with emphasis on recent developments.
The discussion addresses the structure and dynamics in non-equilibrium polymer
layers adsorbed from dilute polymer solutions and from polymer melts and more
concentrated solutions. Two distinct classes of behaviour arise, depending on
whether physisorption or chemisorption is involved. A given adsorbed chain
belonging to the layer has a certain fraction of its monomers bound to the
surface, f, and the remainder belonging to loops making bulk excursions. A
natural classification scheme for layers adsorbed from solution is the
distribution of single chain f values, P(f), which may hold the key to
quantifying the degree of irreversibility in adsorbed polymer layers. Here we
calculate P(f) for equilibrium layers; we find its form is very different to
the theoretical P(f) for non-equilibrium layers which are predicted to have
infinitely many statistical classes of chain. Experimental measurements of P(f)
are compared to these theoretical predictions.Comment: 29 pages, Submitted to J. Phys.: Condens. Matte
Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate
We analyze in details the atomistic response of a model amorphous material
submitted to plastic shear in the athermal, quasistatic limit. After a linear
stress-strain behavior, the system undergoes a noisy plastic flow. We show that
the plastic flow is spatially heterogeneous. Two kinds of plastic events occur
in the system: quadrupolar localized rearrangements, and shear bands. The
analysis of the individual motion of a particle shows also two regimes: a
hyper-diffusive regime followed by a diffusive regime, even at zero
temperature
Aqueous foams in microgravity, measuring bubble sizes
The paper describes a study of wet foams in microgravity whose bubble size
distribution evolves due to diffusive gas exchange. We focus on the comparison
between the size of bubbles determined from images of the foam surface and the
size of bubbles in the bulk foam, determined from Diffuse Transmission
Spectroscopy (DTS). Extracting the bubble size distribution from images of a
foam surface is difficult so we have used three different procedures : manual
analysis, automatic analysis with a customized Python script and machine
learning analysis. Once various pitfalls were identified and taken into
account, all the three procedures yield identical results within error bars.
DTS only allows the determination of an average bubble radius which is
proportional to the photon transport mean free path . The relation
between the measured diffuse transmitted light intensity and {}
previously derived for slab-shaped samples of infinite lateral extent does not
apply to the cuboid geometry of the cells used in the microgravity experiment.
A new more general expression of the diffuse intensity transmitted with
specific optical boundary conditions has been derived and applied to determine
the average bubble radius. The temporal evolution of the average bubble radii
deduced from DTS and of the same average radii of the bubbles measured at the
sample surface are in very good agreement throughout the coarsening. Finally,
ground experiments were performed to compare bubble size distributions in a
bulk wet foam and at its surface at times so short that diffusive gas exchange
is insignificant. They were found to be similar, confirming that bubbles seen
at the surface are representative of the bulk foam bubbles
Characterization of elastomer sliding behavior across silica and polydimethylsiloxane grafted surfaces
Soft Dynamics simulation: 2. Elastic spheres undergoing a T1 process in a viscous fluid
Robust empirical constitutive laws for granular materials in air or in a
viscous fluid have been expressed in terms of timescales based on the dynamics
of a single particle. However, some behaviours such as viscosity bifurcation or
shear localization, observed also in foams, emulsions, and block copolymer
cubic phases, seem to involve other micro-timescales which may be related to
the dynamics of local particle reorganizations. In the present work, we
consider a T1 process as an example of a rearrangement. Using the Soft dynamics
simulation method introduced in the first paper of this series, we describe
theoretically and numerically the motion of four elastic spheres in a viscous
fluid. Hydrodynamic interactions are described at the level of lubrication
(Poiseuille squeezing and Couette shear flow) and the elastic deflection of the
particle surface is modeled as Hertzian. The duration of the simulated T1
process can vary substantially as a consequence of minute changes in the
initial separations, consistently with predictions. For the first time, a
collective behaviour is thus found to depend on another parameter than the
typical volume fraction in particles.Comment: 11 pages - 5 figure
- …