1,569 research outputs found
Data-driven parameterization of the generalized Langevin equation
We present a data-driven approach to determine the memory kernel and random
noise in generalized Langevin equations. To facilitate practical
implementations, we parameterize the kernel function in the Laplace domain by a
rational function, with coefficients directly linked to the equilibrium
statistics of the coarse-grain variables. We show that such an approximation
can be constructed to arbitrarily high order and the resulting generalized
Langevin dynamics can be embedded in an extended stochastic model without
explicit memory. We demonstrate how to introduce the stochastic noise so that
the second fluctuation-dissipation theorem is exactly satisfied. Results from
several numerical tests are presented to demonstrate the effectiveness of the
proposed method
The abundance of high-redshift objects as a probe of non-Gaussian initial conditions
The observed abundance of high-redshift galaxies and clusters contains
precious information about the properties of the initial perturbations. We
present a method to compute analytically the number density of objects as a
function of mass and redshift for a range of physically motivated non-Gaussian
models. In these models the non-Gaussianity can be dialed from zero and is
assumed to be small. We compute the probability density function for the
smoothed dark matter density field and we extend the Press and Schechter
approach to mildly non-Gaussian density fields. The abundance of high-redshift
objects can be directly related to the non-Gaussianity parameter and thus to
the physical processes that generated deviations from the Gaussian behaviour.
Even a skewness parameter of order 0.1 implies a dramatic change in the
predicted abundance of z\gap 1 objects. Observations from NGST and X-ray
satellites (XMM) can be used to accurately measure the amount of
non-Gaussianity in the primordial density field.Comment: Minor changes to match the accepted ApJ version (ApJ, 539
A Process Algebra Software Engineering Environment
In previous work we described how the process algebra based language PSF can
be used in software engineering, using the ToolBus, a coordination architecture
also based on process algebra, as implementation model. In this article we
summarize that work and describe the software development process more formally
by presenting the tools we use in this process in a CASE setting, leading to
the PSF-ToolBus software engineering environment. We generalize the refine step
in this environment towards a process algebra based software engineering
workbench of which several instances can be combined to form an environment
Software (Re-)Engineering with PSF II: from architecture to implementation
This paper presents ongoing research on the application of PSF in the field
of software engineering and reengineering. We build a new implementation for
the simulator of the PSF Toolkit starting from the specification in PSF of the
architecture of a simple simulator and extend it with features to obtain the
architecture of a full simulator. We apply refining and constraining techniques
on the specification of the architecture to obtain a specification low enough
to build an implementation from
Dimension reduction for systems with slow relaxation
We develop reduced, stochastic models for high dimensional, dissipative
dynamical systems that relax very slowly to equilibrium and can encode long
term memory. We present a variety of empirical and first principles approaches
for model reduction, and build a mathematical framework for analyzing the
reduced models. We introduce the notions of universal and asymptotic filters to
characterize `optimal' model reductions for sloppy linear models. We illustrate
our methods by applying them to the practically important problem of modeling
evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof
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