6,563 research outputs found
Spanning trees short or small
We study the problem of finding small trees. Classical network design
problems are considered with the additional constraint that only a specified
number of nodes are required to be connected in the solution. A
prototypical example is the MST problem in which we require a tree of
minimum weight spanning at least nodes in an edge-weighted graph. We show
that the MST problem is NP-hard even for points in the Euclidean plane. We
provide approximation algorithms with performance ratio for the
general edge-weighted case and for the case of points in the
plane. Polynomial-time exact solutions are also presented for the class of
decomposable graphs which includes trees, series-parallel graphs, and bounded
bandwidth graphs, and for points on the boundary of a convex region in the
Euclidean plane. We also investigate the problem of finding short trees, and
more generally, that of finding networks with minimum diameter. A simple
technique is used to provide a polynomial-time solution for finding -trees
of minimum diameter. We identify easy and hard problems arising in finding
short networks using a framework due to T. C. Hu.Comment: 27 page
Significance of thermal fluctuations and hydrodynamic interactions in receptor-ligand mediated adhesive dynamics of a spherical particle in wall bound shear flow
The dynamics of adhesion of a spherical micro-particle to a ligand-coated
wall, in shear flow, is studied using a Langevin equation that accounts for
thermal fluctuations, hydrodynamic interactions and adhesive interactions.
Contrary to the conventional assumption that thermal fluctuations play a
negligible role at high Pclet numbers, we find that for particles
with low surface densities of receptors, rotational diffusion caused by
fluctuations about the flow and gradient directions aids in bond formation,
leading to significantly greater adhesion on average, compared to simulations
where thermal fluctuations are completely ignored. The role of wall
hydrodynamic interactions on the steady state motion of a particle, when the
particle is close to the wall, has also been explored. At high Pclet
numbers, the shear induced force that arises due to the stresslet part of the
Stokes dipole, plays a dominant role, reducing the particle velocity
significantly, and affecting the states of motion of the particle. The coupling
between the translational and rotational degrees of freedom of the particle,
brought about by the presence of hydrodynamic interactions, is found to have no
influence on the binding dynamics. On the other hand, the drag coefficient,
which depends on the distance of the particle from the wall, plays a crucial
role at low rates of bond formation. A significant difference in the effect of
both the shear force and the position dependent drag force, on the states of
motion of the particle, is observed when the Plet number is small.Comment: The manuscript has been accepted as an article in Physical Review E
Journa
Wet and dry internal friction can be measured with the Jarzynski equality
The existence of two types of internal friction wet and dry is revisited, and
a simple protocol is proposed for distinguishing between the two types and
extracting the appropriate internal friction coefficient. The scheme requires
repeatedly stretching a polymer molecule, and measuring the average work
dissipated in the process by applying the Jarzynski equality. The internal
friction coefficient is then estimated from the average dissipated work in the
extrapolated limit of zero solvent viscosity. The validity of the protocol is
established through analytical calculations on a one-dimensional free-draining
Hookean spring-dashpot model for a polymer, and Brownian dynamics simulations
of: (a) a single-mode nonlinear spring-dashpot model for a polymer, and (b) a
finitely extensible bead-spring chain with cohesive intra-chain interactions,
both of which incorporate fluctuating hydrodynamic interactions.
Well-established single-molecule manipulation techniques, such as optical
tweezer-based pulling, can be used to implement the suggested protocol
experimentally.Comment: 27 pages, 17 figure
An exposition on Friedmann Cosmology with Negative Energy Densities
How would negative energy density affect a classic Friedmann cosmology?
Although never measured and possibly unphysical, certain realizations of
quantum field theories leaves the door open for such a possibility. In this
paper we analyze the evolution of a universe comprising varying amounts of
negative energy forms. Negative energy components have negative normalized
energy densities, . They include negative phantom energy with an
equation of state parameter , negative cosmological constant: ,
negative domain walls: , negative cosmic strings: , negative
mass: , negative radiation: and negative ultralight: .
Assuming that such energy forms generate pressure like perfect fluids, the
attractive or repulsive nature of negative energy components are reviewed. The
Friedmann equation is satisfied only when negative energy forms are coupled to
a greater magnitude of positive energy forms or positive curvature. We show
that the solutions exhibit cyclic evolution with bounces and turnovers.The
future and fate of such universes in terms of curvature, temperature,
acceleration, and energy density are reviewed. The end states are dubbed Big
Crunch, Big Void, or Big Rip and further qualified as "Warped", "Curved", or
"Flat", "Hot" versus "Cold", "Accelerating" versus "Decelerating" versus
"Coasting". A universe that ends by contracting to zero energy density is
termed "Big Poof." Which contracting universes "bounce" in expansion and which
expanding universes "turnover" into contraction are also reviewed.Comment: Abridged version with minor correction
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
Analysis of radial segregation of granular mixtures in a rotating drum
This paper considers the segregation of a granular mixture in a rotating
drum. Extending a recent kinematic model for grain transport on sandpile
surfaces to the case of rotating drums, an analysis is presented for radial
segregation in the rolling regime, where a thin layer is avalanching down while
the rest of the material follows rigid body rotation. We argue that segregation
is driven not just by differences in the angle of repose of the species, as has
been assumed in earlier investigations, but also by differences in the size and
surface properties of the grains. The cases of grains differing only in size
(slightly or widely) and only in surface properties are considered, and the
predictions are in qualitative agreement with observations. The model yields
results inconsistent with the assumptions for more general cases, and we
speculate on how this may be corrected.Comment: 12 pages inclusive of 10 PostScript (*.eps) figures, uses svjour,
psfrag and graphicx. Submitted for publication to Euro. Phys. J.
Universality of the collapse transition of sticky polymers
The universality of the swelling of the radius of gyration of a homopolymer
relative to its value in the state, independent of polymer-solvent
chemistry, in the crossover regime between and athermal solvent
conditions, is well known. Here we study, by Brownian dynamics, a polymer model
where a subset of monomers is labelled as "stickers". The mutual interaction of
the stickers is more attractive than those of the other ("backbone") monomers,
and has the additional important characteristic of "functionality" ,
i.e., the maximum number of stickers that can locally bind to a given sticker.
A saturated bond formed in this manner remains bound until it breaks due to
thermal fluctuations, a requirement which can be viewed as an additional
Boolean degree of freedom that describes the bonding. This, in turn, makes the
question of the order of the collapse transition a non-trivial one.
Nevertheless, for the parameters that we have studied (in particular,
), we find a standard second-order collapse, using a
renormalised solvent quality parameter that takes into account the increased
average attraction due to the presence of stickers. We examine the swelling of
the radius of gyration of such a sticky polymer relative to its value in the
altered state, using a novel potential to model the various excluded
volume interactions that occur between the monomers on the chain. We find that
the swelling of such sticky polymers is identical to the universal swelling of
homopolymers in the thermal crossover regime. Additionally, for our model, the
Kuhn segment length under conditions is found to be the same for
chains with and without stickers.Comment: 13 pages, 10 figures, supplementary material (see ancillary
directory), to appear in Soft Matte
Thresholded Covering Algorithms for Robust and Max-Min Optimization
The general problem of robust optimization is this: one of several possible
scenarios will appear tomorrow, but things are more expensive tomorrow than
they are today. What should you anticipatorily buy today, so that the
worst-case cost (summed over both days) is minimized? Feige et al. and
Khandekar et al. considered the k-robust model where the possible outcomes
tomorrow are given by all demand-subsets of size k, and gave algorithms for the
set cover problem, and the Steiner tree and facility location problems in this
model, respectively.
In this paper, we give the following simple and intuitive template for
k-robust problems: "having built some anticipatory solution, if there exists a
single demand whose augmentation cost is larger than some threshold, augment
the anticipatory solution to cover this demand as well, and repeat". In this
paper we show that this template gives us improved approximation algorithms for
k-robust Steiner tree and set cover, and the first approximation algorithms for
k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios
(except for multicut) are almost best possible.
As a by-product of our techniques, we also get algorithms for max-min
problems of the form: "given a covering problem instance, which k of the
elements are costliest to cover?".Comment: 24 page
Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction
The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys.,
90 (1) : 463-473, 1989] to account for the influence of fluctuations in
hydrodynamic interactions in Rouse chains, is adapted here to derive a new
mean-field approximation for the FENE spring force. This "FENE-PG" force law
approximately accounts for spring-force fluctuations, which are neglected in
the widely used FENE-P approximation. The Gaussian Approximation for
hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force
approximations to obtain approximate models for finitely-extensible bead-spring
chains with hydrodynamic interactions. The closed set of ODE's governing the
evolution of the second-moments of the configurational probability distribution
in the approximate models are used to generate predictions of rheological
properties in steady and unsteady shear and uniaxial extensional flows, which
are found to be in good agreement with the exact results obtained with Brownian
dynamics simulations. In particular, predictions of coil-stretch hysteresis are
in quantitative agreement with simulations' results. Additional simplifying
diagonalization-of-normal-modes assumptions are found to lead to considerable
savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix
with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200
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