16,469 research outputs found
Application of the Schwinger variational principle to electron scattering
The authors present the results of the first rigorous application of the Schwinger variational principle to electron scattering with the inclusion of exchange. The results of this application to e-He scattering in the static-exchange approximation show that the Schwinger method provides accurate solutions of the scattering problem with small basis set expansions
Accurate Hartree-Fock vibrational branching ratios in 3σg photoionisation of N2
The authors report vibrational branching ratios for resonant photoionisation of N2 leading to the X2 Sigma g+ state of N2+. Their theoretical values are obtained from an accurate solution of the adiabatic-nuclei frozen-core Hartree-Fock model of molecular photoionisation. In contrast to other theoretical results the present results are in very good agreement with experimental measurements. Differences between the present and previous calculations are discussed
A Stochastic Representation of the Local Structure of Turbulence
Based on the mechanics of the Euler equation at short time, we show that a
Recent Fluid Deformation (RFD) closure for the vorticity field, neglecting the
early stage of advection of fluid particles, allows to build a 3D
incompressible velocity field that shares many properties with empirical
turbulence, such as the teardrop shape of the R-Q plane. Unfortunately, non
gaussianity is weak (i.e. no intermittency) and vorticity gets preferentially
aligned with the wrong eigenvector of the deformation. We then show that
slightly modifying the former vectorial field in order to impose the long range
correlated nature of turbulence allows to reproduce the main properties of
stationary flows. Doing so, we end up with a realistic incompressible, skewed
and intermittent velocity field that reproduces the main characteristics of 3D
turbulence in the inertial range, including correct vorticity alignment
properties.Comment: 6 pages, 3 figures, final version, published
Stochastic Gene Expression in Cells: A Point Process Approach
This paper investigates the stochastic fluctuations of the number of copies
of a given protein in a cell. This problem has already been addressed in the
past and closed-form expressions of the mean and variance have been obtained
for a simplified stochastic model of the gene expression. These results have
been obtained under the assumption that the duration of all the protein
production steps are exponentially distributed. In such a case, a Markovian
approach (via Fokker-Planck equations) is used to derive analytic formulas of
the mean and the variance of the number of proteins at equilibrium. This
assumption is however not totally satisfactory from a modeling point of view
since the distribution of the duration of some steps is more likely to be
Gaussian, if not almost deterministic. In such a setting, Markovian methods can
no longer be used. A finer characterization of the fluctuations of the number
of proteins is therefore of primary interest to understand the general economy
of the cell. In this paper, we propose a new approach, based on marked Poisson
point processes, which allows to remove the exponential assumption. This is
applied in the framework of the classical three stages models of the
literature: transcription, translation and degradation. The interest of the
method is shown by recovering the classical results under the assumptions that
all the durations are exponentially distributed but also by deriving new
analytic formulas when some of the distributions are not anymore exponential.
Our results show in particular that the exponential assumption may,
surprisingly, underestimate significantly the variance of the number of
proteins when some steps are in fact not exponentially distributed. This
counter-intuitive result stresses the importance of the statistical assumptions
in the protein production process
Models of protein production along the cell cycle: an investigation of possible sources of noise
In this article, we quantitatively study, through stochastic models, the
efects of several intracellular phenomena, such as cell volume growth, cell
division, gene replication as well as fuctuations of available RNA polymerases
and ribosomes. These phenomena are indeed rarely considered in classic models
of protein production and no relative quantitative comparison among them has
been performed. The parameters for a large and representative class of proteins
are determined using experimental measures. The main important and surprising
conclusion of our study is to show that despite the signifcant fuctuations of
free RNA polymerases and free ribosomes, they bring little variability to
protein production contrary to what has been previously proposed in the
literature. After verifying the robustness of this quite counter-intuitive
result, we discuss its possible origin from a theoretical view, and interpret
it as the result of a mean-feld efect
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