1,481 research outputs found
Dirac-harmonic maps from index theory
We prove existence results for Dirac-harmonic maps using index theoretical
tools. They are mainly interesting if the source manifold has dimension 1 or 2
modulo 8. Our solutions are uncoupled in the sense that the underlying map
between the source and target manifolds is a harmonic map.Comment: 26 pages, no figur
Manifolds with small Dirac eigenvalues are nilmanifolds
Consider the class of n-dimensional Riemannian spin manifolds with bounded
sectional curvatures and diameter, and almost non-negative scalar curvature.
Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of
the Dirac operator on such a manifold has small eigenvalues, then the
manifold is diffeomorphic to a nilmanifold and has trivial spin structure.
Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a
non-trivial spin structure, then there exists a uniform lower bound on the r-th
eigenvalue of the square of the Dirac operator. If a manifold with almost
nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume
is not too small, then we show that the metric is close to a Ricci-flat metric
on M with a parallel spinor. In dimension 4 this implies that M is either a
torus or a K3-surface
A remark on the space of metrics having non-trivial harmonic spinors
Let M be a closed spin manifold of dimension congruent to 3 modulo 4. We give a simple proof of the fact that the space of metrics on M with invertible Dirac operator is either empty or it has infinitely many path components
Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations
Pattern formation often occurs in spatially extended physical, biological and
chemical systems due to an instability of the homogeneous steady state. The
type of the instability usually prescribes the resulting spatio-temporal
patterns and their characteristic length scales. However, patterns resulting
from the simultaneous occurrence of instabilities cannot be expected to be
simple superposition of the patterns associated with the considered
instabilities. To address this issue we design two simple models composed by
two asymmetrically coupled equations of non-conserved (Swift-Hohenberg
equations) or conserved (Cahn-Hilliard equations) order parameters with
different characteristic wave lengths. The patterns arising in these systems
range from coexisting static patterns of different wavelengths to traveling
waves. A linear stability analysis allows to derive a two parameter phase
diagram for the studied models, in particular revealing for the Swift-Hohenberg
equations a co-dimension two bifurcation point of Turing and wave instability
and a region of coexistence of stationary and traveling patterns. The nonlinear
dynamics of the coupled evolution equations is investigated by performing
accurate numerical simulations. These reveal more complex patterns, ranging
from traveling waves with embedded Turing patterns domains to spatio-temporal
chaos, and a wide hysteretic region, where waves or Turing patterns coexist.
For the coupled Cahn-Hilliard equations the presence of an weak coupling is
sufficient to arrest the coarsening process and to lead to the emergence of
purely periodic patterns. The final states are characterized by domains with a
characteristic length, which diverges logarithmically with the coupling
amplitude.Comment: 9 pages, 10 figures, submitted to Chao
General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String Theory
We derive conditions for the existence of four-dimensional \N=1
supersymmetric flux vacua of massive type IIA string theory with general
supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show
that such flux vacua exist only when the internal geometry is nearly-K\"ahler.
The geometry is not warped, all the allowed fluxes are proportional to the mass
parameter and the dilaton is fixed by a ratio of (quantized) fluxes. The
four-dimensional cosmological constant, while negative, becomes small in the
vacuum with the weak string coupling.Comment: 4 page
Nonexistence of Generalized Apparent Horizons in Minkowski Space
We establish a Positive Mass Theorem for initial data sets of the Einstein
equations having generalized trapped surface boundary. In particular we answer
a question posed by R. Wald concerning the existence of generalized apparent
horizons in Minkowski space
Spiral waves in a surface reaction: Model calculations
A systematic study of spiral waves in a realistic reactionâdiffusion model describing the isothermal CO oxidation on Pt(110) is carried out. Spirals exist under oscillatory, excitable, and bistable (doubly metastable) conditions. In the excitable region, two separate meandering transitions occur, both when the time scales become strongly different and when they become comparable. By the assumption of surface defects of the order of 10 ÎŒm, to which the spirals can be pinned, the continuous distribution of wavelengths observed experimentally can be explained. An external periodic perturbation generally causes a meandering motion of a free spiral, while a straight drift results, if the period of the perturbation divided by the rotation period is a natural number
Local electronic structure of the peptide bond probed by resonant inelastic soft X-ray scattering.
The local valence orbital structure of solid glycine, diglycine, and triglycine is studied using soft X-ray emission spectroscopy (XES), resonant inelastic soft X-ray scattering (RIXS) maps, and spectra calculations based on density-functional theory. Using a building block approach, the contributions of the different functional groups of the peptides are separated. Cuts through the RIXS maps furthermore allow monitoring selective excitations of the amino and peptide functional units, leading to a modification of the currently established assignment of spectral contributions. The results thus paint a new-and-improved picture of the peptide bond, enhance the understanding of larger molecules with peptide bonds, and simplify the investigation of such molecules in aqueous environment
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
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