573 research outputs found
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
Diffusion approximation for self-similarity of stochastic advection in Burgers' equation
Self-similarity of Burgers' equation with some stochastic advection is
studied. In self-similar variables a stationary solution is constructed which
establishes the existence of a stochastically self-similar solution for the
stochastic Burgers' equation. The analysis assumes that the stochastic
coefficient of advection is transformed to a white noise in the self-similar
variables. Furthermore, by a diffusion approximation, the long time convergence
to the self-similar solution is proved in the sense of distribution.Comment: 37 pages, Comm. Math. Phys., to appear, 201
A conceptual framework for using Doppler radar acquired atmospheric data for flight simulation
A concept is presented which can permit turbulence simulation in the vicinity of microbursts. The method involves a large data base, but should be fast enough for use with flight simulators. The model permits any pilot to simulate any flight maneuver in any aircraft. The model simulates a wind field with three-component mean winds and three-component turbulent gusts, and gust variation over the body of an aircraft so that all aerodynamic loads and moments can be calculated. The time and space variation of mean winds and turbulent intensities associated with a particular atmospheric phenomenon such as a microburst is used in the model. In fact, Doppler radar data such as provided by JAWS is uniquely suited for use with the proposed model. The concept is completely general and is not restricted to microburst studies. Reentry and flight in terrestrial or planetary atmospheres could be realistically simulated if supporting data of sufficient resolution were available
Probabilistic description of extreme events in intermittently unstable systems excited by correlated stochastic processes
In this work, we consider systems that are subjected to intermittent
instabilities due to external stochastic excitation. These intermittent
instabilities, though rare, have a large impact on the probabilistic response
of the system and give rise to heavy-tailed probability distributions. By
making appropriate assumptions on the form of these instabilities, which are
valid for a broad range of systems, we formulate a method for the analytical
approximation of the probability distribution function (pdf) of the system
response (both the main probability mass and the heavy-tail structure). In
particular, this method relies on conditioning the probability density of the
response on the occurrence of an instability and the separate analysis of the
two states of the system, the unstable and stable state. In the stable regime
we employ steady state assumptions, which lead to the derivation of the
conditional response pdf using standard methods for random dynamical systems.
The unstable regime is inherently transient and in order to analyze this regime
we characterize the statistics under the assumption of an exponential growth
phase and a subsequent decay phase until the system is brought back to the
stable attractor. The method we present allows us to capture the statistics
associated with the dynamics that give rise to heavy-tails in the system
response and the analytical approximations compare favorably with direct Monte
Carlo simulations, which we illustrate for two prototype intermittent systems:
an intermittently unstable mechanical oscillator excited by correlated
multiplicative noise and a complex mode in a turbulent signal with fixed
frequency, where multiplicative stochastic damping and additive noise model
interactions between various modes.Comment: 29 pages, 15 figure
Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations
In melt-blowing very thin liquid fiber jets are spun due to high-velocity air
streams. In literature there is a clear, unsolved discrepancy between the
measured and computed jet attenuation. In this paper we will verify numerically
that the turbulent velocity fluctuations causing a random aerodynamic drag on
the fiber jets -- that has been neglected so far -- are the crucial effect to
close this gap. For this purpose, we model the velocity fluctuations as vector
Gaussian random fields on top of a k-epsilon turbulence description and develop
an efficient sampling procedure. Taking advantage of the special covariance
structure the effort of the sampling is linear in the discretization and makes
the realization possible
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