542 research outputs found
Generic metrics and the mass endomorphism on spin three-manifolds
Let be a closed Riemannian spin manifold. The constant term in the
expansion of the Green function for the Dirac operator at a fixed point is called the mass endomorphism in associated to the metric due to
an analogy to the mass in the Yamabe problem. We show that the mass
endomorphism of a generic metric on a three-dimensional spin manifold is
nonzero. This implies a strict inequality which can be used to avoid
bubbling-off phenomena in conformal spin geometry.Comment: 8 page
The Dirac operator on untrapped surfaces
We establish a sharp extrinsic lower bound for the first eigenvalue of the
Dirac operator of an untrapped surface in initial data sets without apparent
horizon in terms of the norm of its mean curvature vector. The equality case
leads to rigidity results for the constraint equations with spherical boundary
as well as uniqueness results for constant mean curvature surfaces in Minkowski
space.Comment: 16 page
Alternative mechanisms of structuring biomembranes: Self-assembly vs. self-organization
We study two mechanisms for the formation of protein patterns near membranes
of living cells by mathematical modelling. Self-assembly of protein domains by
electrostatic lipid-protein interactions is contrasted with self-organization
due to a nonequilibrium biochemical reaction cycle of proteins near the
membrane. While both processes lead eventually to quite similar patterns, their
evolution occurs on very different length and time scales. Self-assembly
produces periodic protein patterns on a spatial scale below 0.1 micron in a few
seconds followed by extremely slow coarsening, whereas self-organization
results in a pattern wavelength comparable to the typical cell size of 100
micron within a few minutes suggesting different biological functions for the
two processes.Comment: 4 pages, 5 figure
A characterization of Dirac morphisms
Relating the Dirac operators on the total space and on the base manifold of a
horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps
which pull back (local) harmonic spinor fields onto (local) harmonic spinor
fields.Comment: 18 pages; restricted to the even-dimensional cas
Propagation Failure in Excitable Media
We study a mechanism of pulse propagation failure in excitable media where
stable traveling pulse solutions appear via a subcritical pitchfork
bifurcation. The bifurcation plays a key role in that mechanism. Small
perturbations, externally applied or from internal instabilities, may cause
pulse propagation failure (wave breakup) provided the system is close enough to
the bifurcation point. We derive relations showing how the pitchfork
bifurcation is unfolded by weak curvature or advective field perturbations and
use them to demonstrate wave breakup. We suggest that the recent observations
of wave breakup in the Belousov-Zhabotinsky reaction induced either by an
electric field or a transverse instability are manifestations of this
mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud
Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm
Some Curvature Problems in Semi-Riemannian Geometry
In this survey article we review several results on the curvature of
semi-Riemannian metrics which are motivated by the positive mass theorem. The
main themes are estimates of the Riemann tensor of an asymptotically flat
manifold and the construction of Lorentzian metrics which satisfy the dominant
energy condition.Comment: 25 pages, LaTeX, 4 figure
Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium
The spatiotemporal dynamics of an excitable medium with multiple spiral
defects is shown to vary smoothly with system size from short-lived transients
for small systems to extensive chaos for large systems. A comparison of the
Lyapunov dimension density with the average spiral defect density suggests an
average dimension per spiral defect varying between three and seven. We discuss
some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure
Individual Eigenvalue Distributions for the Wilson Dirac Operator
We derive the distributions of individual eigenvalues for the Hermitian
Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac
Operator DW. The framework we provide is valid in the epsilon regime of chiral
perturbation theory for any number of flavours Nf and for non-zero low energy
constants W6, W7, W8. It is given as a perturbative expansion in terms of the
k-point spectral density correlation functions and integrals thereof, which in
some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at
fixed chirality nu this expansion truncates after at most nu terms for small
lattice spacing "a". Explicit examples for the distribution of the first and
second eigenvalue are given in the microscopic domain as a truncated expansion
of the Fredholm Pfaffian for quenched D5, where all k-point densities are
explicitly known from random matrix theory. For the real eigenvalues of
quenched DW at small "a" we illustrate our method by the finite expansion of
the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion
of W6 and W7 extende
Angular Correlations in Internal Pair Conversion of Aligned Heavy Nuclei
We calculate the spatial correlation of electrons and positrons emitted by
internal pair conversion of Coulomb excited nuclei in heavy ion collisions. The
alignment or polarization of the nucleus results in an anisotropic emission of
the electron-positron pairs which is closely related to the anisotropic
emission of -rays. However, the angular correlation in the case of
internal pair conversion exhibits diverse patterns. This might be relevant when
investigating atomic processes in heavy-ion collisions performed at the Coulomb
barrier.Comment: 27 pages + 6 eps figures, uses revtex.sty and epsf.sty,
tar-compressed and uuencoded with uufile
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