14,097 research outputs found
Flow transitions in two-dimensional foams
For sufficiently slow rates of strain, flowing foam can exhibit inhomogeneous
flows. The nature of these flows is an area of active study in both
two-dimensional model foams and three dimensional foam. Recent work in
three-dimensional foam has identified three distinct regimes of flow [S. Rodts,
J. C. Baudez, and P. Coussot, Europhys. Lett. {\bf 69}, 636 (2005)]. Two of
these regimes are identified with continuum behavior (full flow and
shear-banding), and the third regime is identified as a discrete regime
exhibiting extreme localization. In this paper, the discrete regime is studied
in more detail using a model two dimensional foam: a bubble raft. We
characterize the behavior of the bubble raft subjected to a constant rate of
strain as a function of time, system size, and applied rate of strain. We
observe localized flow that is consistent with the coexistence of a power-law
fluid with rigid body rotation. As a function of applied rate of strain, there
is a transition from a continuum description of the flow to discrete flow when
the thickness of the flow region is approximately 10 bubbles. This occurs at an
applied rotation rate of approximately
Statistics of Bubble Rearrangements in a Slowly Sheared Two-dimensional Foam
Many physical systems exhibit plastic flow when subjected to slow steady
shear. A unified picture of plastic flow is still lacking; however, there is an
emerging theoretical understanding of such flows based on irreversible motions
of the constituent ``particles'' of the material. Depending on the specific
system, various irreversible events have been studied, such as T1 events in
foam and shear transformation zones (STZ's) in amorphous solids. This paper
presents an experimental study of the T1 events in a model, two-dimensional
foam: bubble rafts. In particular, I report on the connection between the
distribution of T1 events and the behavior of the average stress and average
velocity profiles during both the initial elastic response of the bubble raft
and the subsequent plastic flow at sufficiently high strains
Fibrational induction rules for initial algebras
This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set
Supersymmetry solution for finitely extensible dumbbell model
Exact relaxation times and eigenfunctions for a simple mechanical model of
polymer dynamics are obtained using supersymmetry methods of quantum mechanics.
The model includes the finite extensibility of the molecule and does not make
use of the self-consistently averaging approximation. The finite extensibility
reduces the relaxation times when compared to a linear force. The linear
viscoelastic behaviour is obtained in the form of the ``generalized Maxwell
model''. Using these results, a numerical integration scheme is proposed in the
presence of a given flow kinematics.Comment: 5 pages, 2 figure
Thermodynamics of polymer adsorption to a flexible membrane
We analyze the structural behavior of a single polymer chain grafted to an
attractive, flexible surface. Our model is composed of a coarse-grained
bead-and-spring polymer and a tethered membrane. By means of extensive parallel
tempering Monte Carlo simulations it is shown that the system exhibits a rich
phase behavior ranging from highly ordered, compact to extended random coil
structures and from desorbed to completely adsorbed or even partially embedded
conformations. These findings are summarized in a pseudophase diagram
indicating the predominant class of conformations as a function of the external
parameters temperature and polymer-membrane interaction strength. By comparison
with adsorption to a stiff membrane surface it is shown that the flexibility of
the membrane gives rise to qualitatively new behavior such as stretching of
adsorbed conformations
Transition to turbulence in slowly divergent pipe flow
The results of a combined experimental and numerical study of the flow in
slowly diverging pipes are presented. Interestingly, an axisymmetric conical
recirculation cell has been observed. The conditions for its existence and the
length of the cell are simulated for a range of diverging angles and expansion
ratios. There is a critical velocity for the appearance of this state. When the
flow rate increases further, a subcritical transition for localized turbulence
arises. The transition and relaminarization experiments described here quantify
the extent of turbulence. The findings suggest that the transition scenario in
slowly diverging pipes is a combination of stages similar to those observed in
sudden expansions and in straight circular pipe flow.Comment: 8 pages, 5 figure
Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities
We investigate solid-solid and solid-liquid transitions of elastic flexible
off-lattice polymers with Lennard-Jones monomer-monomer interaction and
anharmonic springs by means of sophisticated variants of multicanonical Monte
Carlo methods. We find that the low-temperature behavior depends strongly and
non-monotonically on the system size and exhibits broad similarities to unbound
atomic clusters. Particular emphasis is dedicated to the classification of
icosahedral and non-icosahedral low-energy polymer morphologies.Comment: 9 pages, 17 figure
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
Two-dimensional turbulence of dilute polymer solutions
We investigate theoretically and numerically the effect of polymer additives
on two-dimensional turbulence by means of a viscoelastic model. We provide
compelling evidence that at vanishingly small concentrations, such that the
polymers are passively transported, the probability distribution of polymer
elongation has a power law tail: its slope is related to the statistics of
finite-time Lyapunov exponents of the flow, in quantitative agreement with
theoretical predictions. We show that at finite concentrations and sufficiently
large elasticity the polymers react on the flow with manifold consequences:
velocity fluctuations are drastically depleted, as observed in soap film
experiments; the velocity statistics becomes strongly intermittent; the
distribution of finite-time Lyapunov exponents shifts to lower values,
signalling the reduction of Lagrangian chaos.Comment: 4 pages, 5 figure
Shell Model of Two-dimensional Turbulence in Polymer Solutions
We address the effect of polymer additives on two dimensional turbulence, an
issue that was studied recently in experiments and direct numerical
simulations. We show that the same simple shell model that reproduced drag
reduction in three-dimensional turbulence reproduces all the reported effects
in the two-dimensional case. The simplicity of the model offers a
straightforward understanding of the all the major effects under consideration
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