9,485 research outputs found
Limitation of the Press-Schechter Formalism
The Press-Schechter(PS) formalism for the mass function of the collapsed
objects are reanalyzed. The factor of two in the Press-Schechter formalism is
argued to be correct in the sharp -space filter even when we use the another
approach proposed by Jedamzik(1994) in the cloud-in-cloud problem, which is
different from the previous approach by Peacock & Heavens(1990) and Bond et
al.(1991). The spatial correlation of the density fluctuations, however, had
been neglected in the cloud-in-cloud problem. The effects of this spatial
correlation is analyzed by using the Jedamzik formalism and it is found that
this effect alter the PS mass function especially on larger mass scales.
Furthermore the exact formula of deriving mass function is shown. We also find
that the probability of the overlap of the collapsed objects can be neglected
on very small mass scales while it might not be neglected on other mass scales.Comment: 23 pages, uuencoded compressed Postscrip
On -transforms of one-dimensional diffusions stopped upon hitting zero
For a one-dimensional diffusion on an interval for which 0 is the
regular-reflecting left boundary, three kinds of conditionings to avoid zero
are studied. The limit processes are -transforms of the process stopped
upon hitting zero, where 's are the ground state, the scale function, and
the renormalized zero-resolvent. Several properties of the -transforms are
investigated
A space-time variational approach to hydrodynamic stability theory
We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a spaceātime variational formulation and associated generalized singular value decomposition of the (linearized) NavierāStokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ādataā spaceātime norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a āsolutionā spaceātime norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected spaceātime semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (BrezziāRappazāRaviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613)United States. Office of Naval Research (Grant N00014-11-1-0713
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