356 research outputs found
Leaf-wise intersections and Rabinowitz Floer homology
In this article we explain how critical points of a particular perturbation
of the Rabinowitz action functional give rise to leaf-wise intersection points
in hypersurfaces of restricted contact type. This is used to derive existence
and multiplicity results for leaf-wise intersection points in hypersurfaces of
restricted contact type in general exact symplectic manifolds. The notion of
leaf-wise intersection points was introduced by Moser.Comment: 18 pages, 1 figure; v3: completely rewritten, improved result
Quelques plats pour la m\'etrique de Hofer
We show, by an elementary and explicit construction, that the group of
Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with
Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of
arbitrary dimension.Comment: 9 pages, minor change
On the origin of the Boson peak in globular proteins
We study the Boson Peak phenomenology experimentally observed in globular
proteins by means of elastic network models. These models are suitable for an
analytic treatment in the framework of Euclidean Random Matrix theory, whose
predictions can be numerically tested on real proteins structures. We find that
the emergence of the Boson Peak is strictly related to an intrinsic mechanical
instability of the protein, in close similarity to what is thought to happen in
glasses. The biological implications of this conclusion are also discussed by
focusing on a representative case study.Comment: Proceedings of the X International Workshop on Disordered Systems,
Molveno (2006
Open Gromov-Witten invariants in dimension six
Let be a closed orientable Lagrangian submanifold of a closed symplectic
six-manifold . We assume that the first homology group with coefficients in a commutative ring injects into the group and that contains no Maslov zero pseudo-holomorphic disc with
boundary on . Then, we prove that for every generic choice of a tame
almost-complex structure on , every relative homology class and adequate number of incidence conditions in or , the
weighted number of -holomorphic discs with boundary on , homologous to
, and either irreducible or reducible disconnected, which satisfy the
conditions, does not depend on the generic choice of , provided that at
least one incidence condition lies in . These numbers thus define open
Gromov-Witten invariants in dimension six, taking values in the ring .Comment: 19 pages, 1 figur
Twisting gauged non-linear sigma-models
We consider gauged sigma-models from a Riemann surface into a Kaehler and
hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted
to produce a gauged A-model. This model localizes to the moduli space of
solutions of the vortex equations and computes the Hamiltonian Gromov-Witten
invariants. When the target is equivariantly Calabi-Yau, i.e. when its first
G-equivariant Chern class vanishes, the supersymmetric theory can also be
twisted into a gauged B-model. This model localizes to the Kaehler quotient
X//G.Comment: 33 pages; v2: small additions, published versio
Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs
The probability density function (PDF) associated with a given set of samples
is approximated by a piecewise-linear polynomial constructed with respect to a
binning of the sample space. The kernel functions are a compactly supported
basis for the space of such polynomials, i.e. finite element hat functions,
that are centered at the bin nodes rather than at the samples, as is the case
for the standard kernel density estimation approach. This feature naturally
provides an approximation that is scalable with respect to the sample size. On
the other hand, unlike other strategies that use a finite element approach, the
proposed approximation does not require the solution of a linear system. In
addition, a simple rule that relates the bin size to the sample size eliminates
the need for bandwidth selection procedures. The proposed density estimator has
unitary integral, does not require a constraint to enforce positivity, and is
consistent. The proposed approach is validated through numerical examples in
which samples are drawn from known PDFs. The approach is also used to determine
approximations of (unknown) PDFs associated with outputs of interest that
depend on the solution of a stochastic partial differential equation
Quantum dynamics in strong fluctuating fields
A large number of multifaceted quantum transport processes in molecular
systems and physical nanosystems can be treated in terms of quantum relaxation
processes which couple to one or several fluctuating environments. A thermal
equilibrium environment can conveniently be modelled by a thermal bath of
harmonic oscillators. An archetype situation provides a two-state dissipative
quantum dynamics, commonly known under the label of a spin-boson dynamics. An
interesting and nontrivial physical situation emerges, however, when the
quantum dynamics evolves far away from thermal equilibrium. This occurs, for
example, when a charge transferring medium possesses nonequilibrium degrees of
freedom, or when a strong time-dependent control field is applied externally.
Accordingly, certain parameters of underlying quantum subsystem acquire
stochastic character. Herein, we review the general theoretical framework which
is based on the method of projector operators, yielding the quantum master
equations for systems that are exposed to strong external fields. This allows
one to investigate on a common basis the influence of nonequilibrium
fluctuations and periodic electrical fields on quantum transport processes.
Most importantly, such strong fluctuating fields induce a whole variety of
nonlinear and nonequilibrium phenomena. A characteristic feature of such
dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres
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