677 research outputs found
The orbifold cohomology of moduli of genus 3 curves
In this work we study the additive orbifold cohomology of the moduli stack of
smooth genus g curves. We show that this problem reduces to investigating the
rational cohomology of moduli spaces of cyclic covers of curves where the genus
of the covering curve is g. Then we work out the case of genus g=3.
Furthermore, we determine the part of the orbifold cohomology of the
Deligne-Mumford compactification of the moduli space of genus 3 curves that
comes from the Zariski closure of the inertia stack of M_3.Comment: 29 pages, 2 figures. Minor changes, to appear in Manuscripta Mat
Quantum multimode model of elastic scattering from Bose Einstein condensates
Mean field approximation treats only coherent aspects of the evolution of a
Bose Einstein condensate. However, in many experiments some atoms scatter out
of the condensate. We study an analytic model of two counter-propagating atomic
Gaussian wavepackets incorporating dynamics of incoherent scattering processes.
Within the model we can treat processes of elastic collision of atoms into the
initially empty modes, and observe how, with growing occupation, the bosonic
enhancement is slowly kicking in. A condition for bosonic enhancement effect is
found in terms of relevant parameters. Scattered atoms form a squeezed state
that can be viewed as a multi-component condensate. Not only are we able to
calculate the dynamics of mode occupation, but also the full statistics of
scattered atoms.Comment: 4 pages, 4 figure
Threshold Effects in Multi-channel Coupling and Spectroscopic Factors in Exotic Nuclei
In the threshold region, the cross section and the associated overlap
integral obey the Wigner threshold law that results in the Wigner-cusp
phenomenon. Due to flux conservation, a cusp anomaly in one channel manifests
itself in other open channels, even if their respective thresholds appear at a
different energy. The shape of a threshold cusp depends on the orbital angular
momentum of a scattered particle; hence, studies of Wigner anomalies in weakly
bound nuclei with several low-lying thresholds can provide valuable
spectroscopic information. In this work, we investigate the threshold behavior
of spectroscopic factors in neutron-rich drip-line nuclei using the Gamow Shell
Model, which takes into account many-body correlations and the continuum
effects. The presence of threshold anomalies is demonstrated and the
implications for spectroscopic factors are discussed.Comment: Accepted in Physical Review C Figure correcte
Invasion success of a Lessepsian symbiont-bearing foraminifera linked to high dispersal ability, preadaptation and suppression of sexual reproduction
Among the most successful Lessepsian invaders is the symbiont-bearing benthic foraminifera Amphistegina lobifera. In its newly conquered habitat, this prolific calcifier and ecosystem engineer is exposed to environmental conditions that exceed the range of its native habitat. To disentangle which processes facilitated the invasion success of A. lobifera into the Mediterranean Sea we analyzed a ~ 1400 bp sequence fragment covering the SSU and ITS gene markers to compare the populations from its native regions and along the invasion gradient. The genetic variability was studied at four levels: intra-genomic, population, regional and geographical. We observed that the invasion is not associated with genetic differentiation, but the invasive populations show a distinct suppression of intra-genomic variability among the multiple copies of the rRNA gene. A reduced genetic diversity compared to the Indopacific is observed already in the Red Sea populations and their high dispersal potential into the Mediterranean appears consistent with a bridgehead effect resulting from the postglacial expansion from the Indian Ocean into the Red Sea. We conclude that the genetic structure of the invasive populations reflects two processes: high dispersal ability of the Red Sea source population pre-adapted to Mediterranean conditions and a likely suppression of sexual reproduction in the invader. This discovery provides a new perspective on the cost of invasion in marine protists: The success of the invasive A. lobifera in the Mediterranean Sea comes at the cost of abandonment of sexual reproduction
Chaotic Phenomenon in Nonlinear Gyrotropic Medium
Nonlinear gyrotropic medium is a medium, whose natural optical activity
depends on the intensity of the incident light wave. The Kuhn's model is used
to study nonlinear gyrotropic medium with great success. The Kuhn's model
presents itself a model of nonlinear coupled oscillators. This article is
devoted to the study of the Kuhn's nonlinear model. In the first paragraph of
the paper we study classical dynamics in case of weak as well as strong
nonlinearity. In case of week nonlinearity we have obtained the analytical
solutions, which are in good agreement with the numerical solutions. In case of
strong nonlinearity we have determined the values of those parameters for which
chaos is formed in the system under study. The second paragraph of the paper
refers to the question of the Kuhn's model integrability. It is shown, that at
the certain values of the interaction potential this model is exactly
integrable and under certain conditions it is reduced to so-called universal
Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical
consideration. It shows the possibility of stochastic absorption of external
field energy by nonlinear gyrotropic medium. The last forth paragraph of the
paper is devoted to generalization of the Kuhn's model for infinite chain of
interacting oscillators
Effective diffusion constant in a two dimensional medium of charged point scatterers
We obtain exact results for the effective diffusion constant of a two
dimensional Langevin tracer particle in the force field generated by charged
point scatterers with quenched positions. We show that if the point scatterers
have a screened Coulomb (Yukawa) potential and are uniformly and independently
distributed then the effective diffusion constant obeys the
Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained
for pure Coulomb scatterers frozen in an equilibrium configuration of the same
temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure
Besov priors for Bayesian inverse problems
We consider the inverse problem of estimating a function from noisy,
possibly nonlinear, observations. We adopt a Bayesian approach to the problem.
This approach has a long history for inversion, dating back to 1970, and has,
over the last decade, gained importance as a practical tool. However most of
the existing theory has been developed for Gaussian prior measures. Recently
Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct
Besov prior measures, based on wavelet expansions with random coefficients, and
used these prior measures to study linear inverse problems. In this paper we
build on this development of Besov priors to include the case of nonlinear
measurements. In doing so a key technical tool, established here, is a
Fernique-like theorem for Besov measures. This theorem enables us to identify
appropriate conditions on the forward solution operator which, when matched to
properties of the prior Besov measure, imply the well-definedness and
well-posedness of the posterior measure. We then consider the application of
these results to the inverse problem of finding the diffusion coefficient of an
elliptic partial differential equation, given noisy measurements of its
solution.Comment: 18 page
Continuum Derrida Approach to Drift and Diffusivity in Random Media
By means of rather general arguments, based on an approach due to Derrida
that makes use of samples of finite size, we analyse the effective diffusivity
and drift tensors in certain types of random medium in which the motion of the
particles is controlled by molecular diffusion and a local flow field with
known statistical properties. The power of the Derrida method is that it uses
the equilibrium probability distribution, that exists for each {\em finite}
sample, to compute asymptotic behaviour at large times in the {\em infinite}
medium. In certain cases, where this equilibrium situation is associated with a
vanishing microcurrent, our results demonstrate the equality of the
renormalization processes for the effective drift and diffusivity tensors. This
establishes, for those cases, a Ward identity previously verified only to
two-loop order in perturbation theory in certain models. The technique can be
applied also to media in which the diffusivity exhibits spatial fluctuations.
We derive a simple relationship between the effective diffusivity in this case
and that for an associated gradient drift problem that provides an interesting
constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8
Integral Grothendieck-Riemann-Roch theorem
We show that, in characteristic zero, the obvious integral version of the
Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the
Todd and Chern characters is true (without having to divide the Chow groups by
their torsion subgroups). The proof introduces an alternative to Grothendieck's
strategy: we use resolution of singularities and the weak factorization theorem
for birational maps.Comment: 24 page
Elliptic curves of large rank and small conductor
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the
smallest conductor known, improving on the previous records by factors ranging
from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search
methods, and tabulate, for each r=5,6,...,11, the five curves of lowest
conductor, and (except for r=11) also the five of lowest absolute discriminant,
that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the
Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after
comments by J.Silverman on the previous draft, and again to get the correct
page break
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