Seminars & Events

Mathematics and Computer Science Division
"Colored Noise and its Effect On the Solutions to Differential Equations"

DATE: July 6, 2011 to July 6, 2011
TIME: 10:30 AM - 11:30 AM
SPEAKER: Miroslav Stoyanov, LANS Postdoc Interviewee
LOCATION: Building 240 Seminar Room 4301, Argonne National Laboratory
HOST: Emil Constantinescu and Mihai Anitescu

Description:
White noise is a very common way for accounting for randomness in the inputs to partial differential equations, especially in cases where little is know about those inputs. On the other hand, pink noise, or more generally, colored noise having a power spectrum that decays as $1/f^\alpha$, where $f$ denotes the frequency and $\alpha\in(0,2]$, has been found to accurately model many natural, social, economic, and other phenomena. Our goal is to study, the effects of modeling random inputs as $1/f^\alpha$ random fields, including the white noise ($\alpha=0$), pink noise ($\alpha=1$), and brown noise ($\alpha=2$)cases. We show how such random fields can be approximated so that they can be used in computer simulations. We then show that the solutions of the differential equations exhibit a strong dependence on $\alpha$, indicating that further examination of how randomness in partial differential equation is modeled and simulated is warranted.

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