226 research outputs found
Models of discretized moduli spaces, cohomological field theories, and Gaussian means
We prove combinatorially the explicit relation between genus filtrated
-loop means of the Gaussian matrix model and terms of the genus expansion of
the Kontsevich--Penner matrix model (KPMM). The latter is the generating
function for volumes of discretized (open) moduli spaces
given by for
. This generating function therefore enjoys
the topological recursion, and we prove that it is simultaneously the
generating function for ancestor invariants of a cohomological field theory
thus enjoying the Givental decomposition. We use another Givental-type
decomposition obtained for this model by the second authors in 1995 in terms of
special times related to the discretisation of moduli spaces thus representing
its asymptotic expansion terms (and therefore those of the Gaussian means) as
finite sums over graphs weighted by lower-order monomials in times thus giving
another proof of (quasi)polynomiality of the discrete volumes. As an
application, we find the coefficients in the first subleading order for
in two ways: using the refined Harer--Zagier recursion and
by exploiting the above Givental-type transformation. We put forward the
conjecture that the above graph expansions can be used for probing the
reduction structure of the Delgne--Mumford compactification of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure
Topological recursion for Gaussian means and cohomological field theories
We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M_(g,s)^(disc) (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M_(g,1) for all g in three ways: using the refined Harer–Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly
Haematologic and Clinical Chemical values in 3 and 6 months old Göttingen minipigs
Blood samples were collected from sixty healthy Göttingen minipigs. fifteen males and fifteen females at the age of three months and fifteen males and fifteen females at the age of six months. The samples were taken at the breeder’s facilities. The samples were analysed for nineteen haematological and twenty~six clinical chemical parameters. Means, standard deviations and lowest and highest values are presented. In general the parameters were comparable with those reponed for other breeds of miniature and domestic swine. The white blood cell count, the percentages of neutrophils and monocytes and serum globulin levels were lower in these microbiologically defined minipigs compared with conventionally rearedpigs and minipigs. Three litter mates had a complex of abnormally high serum creatine kinase, lactate dehydrogenase, uspartate aminotransterase and alanine aminotmnsferase levels
Gaussian random waves in elastic media
Similar to the Berry conjecture of quantum chaos we consider elastic analogue
which incorporates longitudinal and transverse elastic displacements with
corresponding wave vectors. Based on that we derive the correlation functions
for amplitudes and intensities of elastic displacements. Comparison to numerics
in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure
Energy level statistics of the two-dimensional Hubbard model at low filling
The energy level statistics of the Hubbard model for square
lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for
a wide range of the coupling strength. All known symmetries of the model
(space, spin and pseudospin symmetry) have been taken into account explicitly
from the beginning of the calculation by projecting into symmetry invariant
subspaces. The details of this group theoretical treatment are presented with
special attention to the nongeneric case of L=4, where a particular complicated
space group appears. For all the lattices studied, a significant amount of
levels within each symmetry invariant subspaces remains degenerated, but except
for L=4 the ground state is nondegenerate. We explain the remaining
degeneracies, which occur only for very specific interaction independent
states, and we disregard these states in the statistical spectral analysis. The
intricate structure of the Hubbard spectra necessitates a careful unfolding
procedure, which is thoroughly discussed. Finally, we present our results for
the level spacing distribution, the number variance , and the
spectral rigidity , which essentially all are close to the
corresponding statistics for random matrices of the Gaussian ensemble
independent of the lattice size and the coupling strength. Even very small
coupling strengths approaching the integrable zero coupling limit lead to the
Gaussian ensemble statistics stressing the nonperturbative nature of the
Hubbard model.Comment: 31 pages (1 Revtex file and 10 postscript figures
Morphological Instabilities in a growing Yeast Colony: Experiment and Theory
We study the growth of colonies of the yeast Pichia membranaefaciens on
agarose film. The growth conditions are controlled in a setup where nutrients
are supplied through an agarose film suspended over a solution of nutrients. As
the thickness of the agarose film is varied, the morphology of the front of the
colony changes. The growth of the front is modeled by coupling it to a
diffusive field of inhibitory metabolites. Qualitative agreement with
experiments suggests that such a coupling is responsible for the observed
instability of the front.Comment: RevTex, 4 pages and 3 figure
Coherent pion production in neutrino nucleus collision in the 1 GeV region
We calculate cross sections for coherent pion production in nuclei induced by
neutrinos and antineutrinos of the electron and muon type. The analogies and
differences between this process and the related ones of coherent pion
production induced by photons, or the (p,n) and reactions are
discussed. The process is one of the several ones occurring for intermediate
energy neutrinos, to be considered when detecting atmospheric neutrinos. For
this purpose the results shown here can be easily extrapolated to other
energies and other nuclei.Comment: 13 pages, LaTex, 8 post-script figures available at
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