1,296 research outputs found
Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples
We study realizations of pseudodifferential operators acting on sections of
vector-bundles on a smooth, compact manifold with boundary, subject to
conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property,
compositions, adjoints and self-adjointness of such realizations are discussed.
We construct regular spectral triples
for manifolds with boundary of arbitrary dimension, where is the
space of square integrable sections. Starting out from Dirac operators with
APS-conditions, these triples are even in case of even dimensional manifolds;
we show that the closure of in
coincides with the continuous functions on the manifold being constant on each
connected component of the boundary.Comment: 27 pages, to appear in Journal of Noncommutative Geometr
Experimental and Numerical Study of the Dispersion and Transport of Automobile Exhaust Gases from Highways
This paper describes examples of modelling and of measurements of the dispersion and transport of exhaust gases from automobiles on a highway. Model runs were performed by a large-eddy-simulation model. The measurements were carried through by the DLR environmental research aircraft lee-side of the highway between MĂŒnchen and Augsburg
Lattice artefacts and the running of the coupling constant
We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in
the two dimensional O(3) nonlinear model. To investigate the continuum
limit we refine the lattice spacing from the value used by LWW up
to . We find that the lattice artefacts are much larger than
estimated by LWW and that most likely the coupling constant runs slower than
predicted by perturbation theory. A precise determination of the running in the
continuum limit would require a controlled ansatz of extrapolation, which, we
argue, is not presently available.Comment: 4 pages, 4 figures. To address the criticism that we are studying a
different quantitiy than Luscher, Weisz and Wolff originally did, we
introduced a new equation (2), a new paragraph discussing this issue and a
new figure comparing the results obtained with our prescription to that
obtained with the original one of Luscher, Weisz and Wolf
Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
We study the universality between a discrete spin model with icosahedral
symmetry and the O(3) model in two dimensions. For this purpose we study
numerically the renormalized two-point functions of the spin field and the four
point coupling constant. We find that those quantities seem to have the same
continuum limits in the two models. This has far reaching consequences, because
the icosahedron model is not asymptotically free in the sense that the coupling
constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in
the short distance limit. By universality this then also applies to the O(3)
model, contrary to the predictions of perturbation theory.Comment: 18 pages, 8 figures Color coding in Fig. 5 changed to improve
visibilit
Universality Class of Models
We point out that existing numerical data on the correlation length and
magnetic susceptibility suggest that the two dimensional model with
standard action has critical exponent , which is inconsistent with
asymptotic freedom. This value of is also different from the one of the
Wess-Zumino-Novikov-Witten model that is supposed to correspond to the
model at .Comment: 8 pages, with 3 figures included, postscript. An error concerning the
errors has been correcte
Intrinsic energy flow in laser-excited 3d ferromagnets
Ultrafast magnetization dynamics are governed by energy flow between electronic, magnetic and lattice degrees of freedom. A quantitative understanding of these dynamics must be based on a model that agrees with experimental results for all three subsystems. However, ultrafast dynamics of the lattice remain largely unexplored experimentally. Here, we combine femtosecond electron diffraction experiments of the lattice dynamics with energy-conserving atomistic spin dynamics (ASD) simulations and ab-initio calculations to study the intrinsic energy flow in the 3d ferromagnets cobalt (Co) and iron (Fe). The simulations yield a good description of experimental data, in particular an excellent description of our experimental results for the lattice dynamics. We find that the lattice dynamics are influenced significantly by the magnetization dynamics due to the energy cost of demagnetization. Our results highlight the role of the spin system as the dominant heat sink in the first hundreds of femtoseconds. Together with previous findings for nickel [1], our work demonstrates that energy-conserving ASD simulations provide a general and consistent description of the laser-induced dynamics in all three elemental 3d ferromagnets
O(N) and RP^{N-1} Models in Two Dimensions
I provide evidence that the 2D model for is equivalent
to the -invariant non-linear -model in the continuum limit. To
this end, I mainly study particular versions of the models, to be called
constraint models. I prove that the constraint and models are
equivalent for sufficiently weak coupling. Numerical results for their
step-scaling function of the running coupling are
presented. The data confirm that the constraint model is in the samei
universality class as the model with standard action. I show that the
differences in the finite size scaling curves of i and models
observed by Caracciolo et al. can be explained as a boundary effect. It is
concluded, in contrast to Caracciolo et al., that and models
share a unique universality class.Comment: 14 pages (latex) + 1 figure (Postscript) ,uuencode
Continuum Limit of Spin Models with Continuous Symmetry and Conformal Quantum Field Theory
According to the standard classification of Conformal Quantum Field Theory
(CQFT) in two dimensions, the massless continuum limit of the model at
the Kosterlitz-Thouless (KT) transition point should be given by the massless
free scalar field; in particular the Noether current of the model should be
proportional to (the dual of) the gradient of the massless free scalar field,
reflecting a symmetry enhanced from to . More
generally, the massless continuum limit of a spin model with a symmetry given
by a Lie group should have an enhanced symmetry . We point out
that the arguments leading to this conclusion contain two serious gaps: i) the
possibility of `nontrivial local cohomology' and ii) the possibility that the
current is an ultralocal field. For the model we give analytic
arguments which rule out the first possibility and use numerical methods to
dispose of the second one. We conclude that the standard CQFT predictions
appear to be borne out in the model, but give an example where they
would fail. We also point out that all our arguments apply equally well to any
symmetric spin model, provided it has a critical point at a finite
temperature.Comment: 19 page
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