5,133 research outputs found
On uniqueness of end sums and 1-handles at infinity
For oriented manifolds of dimension at least 4 that are simply connected at
infinity, it is known that end summing is a uniquely defined operation. Calcut
and Haggerty showed that more complicated fundamental group behavior at
infinity can lead to nonuniqueness. The present paper examines how and when
uniqueness fails. Examples are given, in the categories TOP, PL and DIFF, of
nonuniqueness that cannot be detected in a weaker category (including the
homotopy category). In contrast, uniqueness is proved for Mittag-Leffler ends,
and generalized to allow slides and cancellation of (possibly infinite)
collections of 0- and 1-handles at infinity. Various applications are
presented, including an analysis of how the monoid of smooth manifolds
homeomorphic to R^4 acts on the smoothings of any noncompact 4-manifold.Comment: 25 pages, 8 figures. v2: Minor expository improvement
Subdiffusive motion in kinetically constrained models
We discuss a kinetically constrained model in which real-valued local
densities fluctuate in time, as introduced recently by Bertin, Bouchaud and
Lequeux. We show how the phenomenology of this model can be reproduced by an
effective theory of mobility excitations propagating in a disordered
environment. Both excitations and probe particles have subdiffusive motion,
characterised by different exponents and operating on different time scales. We
derive these exponents, showing that they depend continuously on one of the
parameters of the model.Comment: 12 pages, 5 figure
Structure and dynamics in glass-formers: predictability at large length scales
Dynamic heterogeneity in glass-formers has been related to their static
structure using the concept of dynamic propensity. We re-examine this
relationship by analyzing dynamical fluctuations in two atomistic glass-formers
and two theoretical models. We introduce quantitative statistical indicators
which show that the dynamics of individual particles cannot be predicted on the
basis of the propensity, nor by any structural indicator. However, the spatial
structure of the propensity field does have predictive power for the spatial
correlations associated with dynamic heterogeneity. Our results suggest that
the quest for a connection between static and dynamic properties of
glass-formers at the particle level is vain, but they demonstrate that such
connection does exist on larger length scales.Comment: 7 pages; 4 figs - Extended, clarified versio
On fundamental groups of quotient spaces
In classical covering space theory, a covering map induces an injection of
fundamental groups. This paper reveals a dual property for certain quotient
maps having connected fibers, with applications to orbit spaces of vector
fields and leaf spaces in general.Comment: 12 pages, 4 figures; added references, keywords, and Remark 1.2;
accepted at Topology and its Application
Orbit Spaces of Gradient Vector Fields
We study orbit spaces of generalized gradient vector fields for Morse
functions. Typically, these orbit spaces are non-Hausdorff. Nevertheless, they
are quite structured topologically and are amenable to study. We show that
these orbit spaces are locally contractible. We also show that the quotient map
associated to each such orbit space is a weak homotopy equivalence and has the
path lifting property.Comment: 16 pages, 4 figures; strengthened a main result (Corollary 3.5) and
updated the introduction and the conclusio
Dissipation and Tunnelling in Quantum Hall Bilayers
We discuss the interplay between transport and intrinsic dissipation in
quantum Hall bilayers, within the framework of a simple thought experiment. We
compute, for the first time, quantum corrections to the semiclassical dynamics
of this system. This allows us to re-interpret tunnelling measurements on these
systems. We find a strong peak in the zero-temperature tunnelling current that
arises from the decay of Josephson-like oscillations into incoherent charge
fluctuations. In the presence of an in-plane field, resonances in the
tunnelling current develop an asymmetric lineshape.Comment: 4 pages, 3 figure
Mechanisms of kinetic trapping in self-assembly and phase transformation
In self-assembly processes, kinetic trapping effects often hinder the
formation of thermodynamically stable ordered states. In a model of viral
capsid assembly and in the phase transformation of a lattice gas, we show how
simulations in a self-assembling steady state can be used to identify two
distinct mechanisms of kinetic trapping. We argue that one of these mechanisms
can be adequately captured by kinetic rate equations, while the other involves
a breakdown of theories that rely on cluster size as a reaction coordinate. We
discuss how these observations might be useful in designing and optimising
self-assembly reactions
Fluctuation-dissipation ratios in the dynamics of self-assembly
We consider two seemingly very different self-assembly processes: formation
of viral capsids, and crystallization of sticky discs. At low temperatures,
assembly is ineffective, since there are many metastable disordered states,
which are a source of kinetic frustration. We use fluctuation-dissipation
ratios to extract information about the degree of this frustration. We show
that our analysis is a useful indicator of the long term fate of the system,
based on the early stages of assembly.Comment: 8 pages, 6 figure
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