3,546 research outputs found
Parametric Manifolds I: Extrinsic Approach
A parametric manifold can be viewed as the manifold of orbits of a (regular)
foliation of a manifold by means of a family of curves. If the foliation is
hypersurface orthogonal, the parametric manifold is equivalent to the
1-parameter family of hypersurfaces orthogonal to the curves, each of which
inherits a metric and connection from the original manifold via orthogonal
projections; this is the well-known Gauss-Codazzi formalism. We generalize this
formalism to the case where the foliation is not hypersurface orthogonal.
Crucial to this generalization is the notion of deficiency, which measures the
failure of the orthogonal tangent spaces to be surface-forming, and which
behaves very much like torsion. Some applications to initial value problems in
general relativity will be briefly discussed.Comment: Plain TeX, 21 pages, no figure
Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei
The Dirac structure of the nucleon self-energy in asymmetric nuclear matter
cannot reliably be deduced from the momentum dependence of the single-particle
energies. It is demonstrated that such attempts yield an isospin dependence
with even a wrong sign. Relativistic studies of finite nuclei have been based
on such studies of asymmetric nuclear matter. The effects of these isospin
components on the results for finite nuclei are investigated.Comment: 9 pages, Latex 4 figures include
Seasonal variation in the interactions between piscivorous fish, planktivorous fish and zooplankton in a shallow eutrophic lake
Statistical analysis of the velocity and scalar fields in reacting turbulent wall-jets
The concept of local isotropy in a chemically reacting turbulent wall-jet
flow is addressed using direct numerical simulation (DNS) data. Different DNS
databases with isothermal and exothermic reactions are examined. The chemical
reaction and heat release effects on the turbulent velocity, passive scalar and
reactive species fields are studied using their probability density functions
(PDF) and higher order moments for velocities and scalar fields, as well as
their gradients. With the aid of the anisotropy invariant maps for the Reynolds
stress tensor the heat release effects on the anisotropy level at different
wall-normal locations are evaluated and found to be most accentuated in the
near-wall region. It is observed that the small-scale anisotropies are
persistent both in the near-wall region and inside the jet flame. Two
exothermic cases with different Damkohler number are examined and the
comparison revealed that the Damkohler number effects are most dominant in the
near-wall region, where the wall cooling effects are influential. In addition,
with the aid of PDFs conditioned on the mixture fraction, the significance of
the reactive scalar characteristics in the reaction zone is illustrated. We
argue that the combined effects of strong intermittency and strong persistency
of anisotropy at the small scales in the entire domain can affect mixing and
ultimately the combustion characteristics of the reacting flow
Correlations and the relativistic structure of the nucleon self-energy
A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter
is to decompose the self energy of the nucleons into Lorentz scalar and vector
components. A new method is introduced for this decomposition. It is based on
the dependence of the single-particle energy on the small component in the
Dirac spinors used to calculate the matrix elements of the underlying NN
interaction. The resulting Dirac components of the self-energy depend on the
momentum of the nucleons. At densities around and below the nuclear matter
saturation density this momentum dependence is dominated by the non-locality of
the Brueckner G matrix. At higher densities these correlation effects are
suppressed and the momentum dependence due to the Fock exchange terms is
getting more important. Differences between symmetric nuclear matter and
neutron matter are discussed. Various versions of the Bonn potential are
considered.Comment: 18 pages LaTeX, including 6 figure
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