4,911 research outputs found
Dirac eigenvalues and total scalar curvature
It has recently been conjectured that the eigenvalues of the Dirac
operator on a closed Riemannian spin manifold of dimension can be
estimated from below by the total scalar curvature: We show by example that such
an estimate is impossible.Comment: 9 pages, LaTeX, uses pstricks macro package. to appear in Journal of
Geometry and Physic
Chiral perturbation theory for lattice QCD including O(a^2)
The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD
with Wilson fermions are constructed. The results are generalized to partially
quenched QCD with Wilson fermions as well as to the "mixed'' lattice theory
with Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 3 pages, Lattice2003 (spectrum
Prescribing eigenvalues of the Dirac operator
In this note we show that every compact spin manifold of dimension
can be given a Riemannian metric for which a finite part of the spectrum of the
Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity
1.Comment: To appear in Manuscripta Mathematic
The first conformal Dirac eigenvalue on 2-dimensional tori
Let M be a compact manifold with a spin structure \chi and a Riemannian
metric g. Let \lambda_g^2 be the smallest eigenvalue of the square of the Dirac
operator with respect to g and \chi. The \tau-invariant is defined as
\tau(M,\chi):= sup inf \sqrt{\lambda_g^2} Vol(M,g)^{1/n} where the supremum
runs over the set of all conformal classes on M, and where the infimum runs
over all metrics in the given class. We show that \tau(T^2,\chi)=2\sqrt{\pi} if
\chi is ``the'' non-trivial spin structure on T^2. In order to calculate this
invariant, we study the infimum as a function on the spin-conformal moduli
space and we show that the infimum converges to 2\sqrt{\pi} at one end of the
spin-conformal moduli space.Comment: published version (typos removed, bibliography updated
Upper bounds for the first eigenvalue of the Dirac operator on surfaces
In this paper we will prove new extrinsic upper bounds for the eigenvalues of
the Dirac operator on an isometrically immersed surface as well as intrinsic bounds for 2-dimensional compact manifolds of
genus zero and genus one. Moreover, we compare the different estimates of the
eigenvalue of the Dirac operator for special families of metrics.Comment: Latex2.09, 23 page
Reentry produced by small-scale heterogeneities in a discrete model of cardiac tissue
Reentries are reexcitations of cardiac tissue after the passing of an excitation wave which can cause
dangerous arrhythmias like tachycardia or life-threatening heart failures like fibrillation. The heart is formed by a
network of cells connected by gap junctions. Under ischemic conditions some of the cells lose their connections,
because gap junctions are blocked and the excitability is decreased. We model a circular region of the tissue where
a fraction of connections among individual cells are removed and substituted by non-conducting material in a twodimensional
(2D) discrete model of a heterogeneous excitable medium with local kinetics based on electrophysiology.
Thus, two neighbouring cells are connected (disconnected) with a probability f (1 - f). Such a region is assumed to be
surrounded by homogeneous tissue. The circular heterogeneous area is shown to act as a source of new waves which
reenter into the tissue and reexcitate the whole domain. We employ the Fenton-Karma equations to model the action potential for the local kinetics of the discrete nodes to study the statistics of the reentries in two dimensional networks
with different topologies. We conclude that the probability of reentry is determined by the proximity of the fraction of
disrupted connections between neighboring nodes (Peer ReviewedPostprint (published version
Double poles in Lattice QCD with mixed actions
We consider effects resulting from the use of different discretizations for
the valence and the sea quarks, considering Wilson and/or Ginsparg--Wilson
fermions. We assume that such effects appear through scaling violations that
can be studied using effective-lagrangian techniques. We show that a double
pole is present in flavor-neutral Goldstone meson propagators, even if the
flavor non-diagonal Goldstone mesons made out of valence or sea quark have
equal masses. We then consider some observables known to be anomalously
sensitive to the presence of a double pole. We find that the double-pole
enhanced scaling violations may turn out to be rather small in practice.Comment: 8 pages; combined writeup of talks given at Lattice 2005 (Dublin) and
the Workshop on Computational Hadron Physics (Cyprus
The Dirac spectrum on manifolds with gradient conformal vector fields
We show that the Dirac operator on a spin manifold does not admit
eigenspinors provided the metric has a certain asymptotic behaviour and is a
warped product near infinity. These conditions on the metric are fulfilled in
particular if the manifold is complete and carries a non-complete vector field
which outside a compact set is gradient conformal and non-vanishing.Comment: 12 page
Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics
Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue
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