132 research outputs found
Conformal Mappings and Dispersionless Toda hierarchy
Let be the space consists of pairs , where is a
univalent function on the unit disc with , is a univalent function
on the exterior of the unit disc with and
. In this article, we define the time variables , on which are holomorphic with respect to the natural
complex structure on and can serve as local complex coordinates
for . We show that the evolutions of the pair with
respect to these time coordinates are governed by the dispersionless Toda
hierarchy flows. An explicit tau function is constructed for the dispersionless
Toda hierarchy. By restricting to the subspace consists
of pairs where , we obtain the integrable hierarchy
of conformal mappings considered by Wiegmann and Zabrodin \cite{WZ}. Since
every homeomorphism of the unit circle corresponds uniquely to
an element of under the conformal welding
, the space can be naturally
identified as a subspace of characterized by . We
show that we can naturally define complexified vector fields \pa_n, n\in \Z
on so that the evolutions of on
with respect to \pa_n satisfy the dispersionless Toda
hierarchy. Finally, we show that there is a similar integrable structure for
the Riemann mappings . Moreover, in the latter case, the time
variables are Fourier coefficients of and .Comment: 23 pages. This is to replace the previous preprint arXiv:0808.072
Influence of a classical homogeneous gravitational field on dissipative dynamics of the Jaynes-Cummings model with phase damping
In this paper, we study the dissipative dynamics of the Jaynes-Cummings model
with phase damping in the presence of a classical homogeneous gravitational
field. The model consists of a moving two-level atom simultaneously exposed to
the gravitational field and a single-mode traveling radiation field in the
presence of the phase damping. We present a quantum treatment of the internal
and external dynamics of the atom based on an alternative su(2) dynamical
algebraic structure. By making use of the super-operator technique, we obtain
the solution of the master equation for the density operator of the quantum
system, under the Markovian approximation. Assuming that initially the
radiation field is prepared in a Glauber coherent state and the two-level atom
is in the excited state, we investigate the influence of gravity on the
temporal evolution of collapses and revivals of the atomic population
inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting
statistics and quadrature squeezing of the radiation field in the presence of
phase damping.Comment: 25 pages, 15 figure
Generation of 3 spinocerebellar ataxia type 1 (SCA1) patient-derived induced pluripotent stem cell lines LUMCi002-A, B, and C and 2 unaffected sibling control induced pluripotent stem cell lines LUMCi003-A and B
Spinocerebellar ataxia type 1 (SCA1) is a hereditary neurodegenerative disease caused by a CAG repeat expansion in exon 8 of the ATXN1 gene. We generated induced pluripotent stem cells (hiPSCs) from a SCA1 patient and his non-affected sister by using non-integrating Sendai Viruses (SeV). The resulting hiPSCs are SeVfree, express pluripotency markers, display a normal karyotype, retain the mutation (length of the CAG repeat expansion in the ATXN1 gene) and are able to differentiate into the three germ layers in vitro
Quantum jumps induced by the center-of-mass motion of a trapped atom
We theoretically study the occurrence of quantum jumps in the resonance
fluorescence of a trapped atom. Here, the atom is laser cooled in a
configuration of level such that the occurrence of a quantum jump is associated
to a change of the vibrational center-of-mass motion by one phonon. The
statistics of the occurrence of the dark fluorescence period is studied as a
function of the physical parameters and the corresponding features in the
spectrum of resonance fluorescence are identified. We discuss the information
which can be extracted on the atomic motion from the observation of a quantum
jump in the considered setup
Markov Properties of Electrical Discharge Current Fluctuations in Plasma
Using the Markovian method, we study the stochastic nature of electrical
discharge current fluctuations in the Helium plasma. Sinusoidal trends are
extracted from the data set by the Fourier-Detrended Fluctuation analysis and
consequently cleaned data is retrieved. We determine the Markov time scale of
the detrended data set by using likelihood analysis. We also estimate the
Kramers-Moyal's coefficients of the discharge current fluctuations and derive
the corresponding Fokker-Planck equation. In addition, the obtained Langevin
equation enables us to reconstruct discharge time series with similar
statistical properties compared with the observed in the experiment. We also
provide an exact decomposition of temporal correlation function by using
Kramers-Moyal's coefficients. We show that for the stationary time series, the
two point temporal correlation function has an exponential decaying behavior
with a characteristic correlation time scale. Our results confirm that, there
is no definite relation between correlation and Markov time scales. However
both of them behave as monotonic increasing function of discharge current
intensity. Finally to complete our analysis, the multifractal behavior of
reconstructed time series using its Keramers-Moyal's coefficients and original
data set are investigated. Extended self similarity analysis demonstrates that
fluctuations in our experimental setup deviates from Kolmogorov (K41) theory
for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references,
figures and major correction
Magnetic Field Amplification in Galaxy Clusters and its Simulation
We review the present theoretical and numerical understanding of magnetic
field amplification in cosmic large-scale structure, on length scales of galaxy
clusters and beyond. Structure formation drives compression and turbulence,
which amplify tiny magnetic seed fields to the microGauss values that are
observed in the intracluster medium. This process is intimately connected to
the properties of turbulence and the microphysics of the intra-cluster medium.
Additional roles are played by merger induced shocks that sweep through the
intra-cluster medium and motions induced by sloshing cool cores. The accurate
simulation of magnetic field amplification in clusters still poses a serious
challenge for simulations of cosmological structure formation. We review the
current literature on cosmological simulations that include magnetic fields and
outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure
Fine-mapping of prostate cancer susceptibility loci in a large meta-analysis identifies candidate causal variants
Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. © 2018 The Author(s).Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. © 2018 The Author(s).Peer reviewe
- âŠ