96 research outputs found
Some ideas about quantitative convergence of collision models to their mean field limit
We consider a stochastic -particle model for the spatially homogeneous
Boltzmann evolution and prove its convergence to the associated Boltzmann
equation when . For any time we bound the distance between
the empirical measure of the particle system and the measure given by the
Boltzmann evolution in some homogeneous negative Sobolev space. The control we
get is Gaussian, i.e. we prove that the distance is bigger than
with a probability of type . The two main ingredients are first a
control of fluctuations due to the discrete nature of collisions, secondly a
Lipschitz continuity for the Boltzmann collision kernel. The latter condition,
in our present setting, is only satisfied for Maxwellian models. Numerical
computations tend to show that our results are useful in practice.Comment: 27 pages, references added and style improve
Amniotic fluid epidermal growth factor levels in normal and abnormal pregnancies
OBJECTIVE: TO determine the concentrations of epidermal growth factor (EGF) in amniotic fluid (AF) from women during late pregnancy, with and without pathophysiologic complications
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