Homogenization driven by a fractional brownian motion: The shear layer case

Tomasz Komorowski; Alexei Novikov; Lenya Ryzhik

doi:10.1137/13092068X

Homogenization driven by a fractional brownian motion: The shear layer case

Tomasz Komorowski, Alexei Novikov, Lenya Ryzhik

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4 Scopus citations

Abstract

We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ε (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ε (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ε (1/2, 1). The proof is based on an auxiliary limit theorem for an additive functional of a fractional Brownian motion.

Original language	English (US)
Pages (from-to)	440-457
Number of pages	18
Journal	Multiscale Modeling and Simulation
Volume	12
Issue number	2
DOIs	https://doi.org/10.1137/13092068X
State	Published - 2014

All Science Journal Classification (ASJC) codes

General Chemistry
Modeling and Simulation
Ecological Modeling
General Physics and Astronomy
Computer Science Applications

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10.1137/13092068X

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title = "Homogenization driven by a fractional brownian motion: The shear layer case",

abstract = "We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ε (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ε (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ε (1/2, 1). The proof is based on an auxiliary limit theorem for an additive functional of a fractional Brownian motion.",

author = "Tomasz Komorowski and Alexei Novikov and Lenya Ryzhik",

year = "2014",

doi = "10.1137/13092068X",

language = "English (US)",

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issn = "1540-3459",

publisher = "Society for Industrial and Applied Mathematics Publications",

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TY - JOUR

T1 - Homogenization driven by a fractional brownian motion

T2 - The shear layer case

AU - Komorowski, Tomasz

AU - Novikov, Alexei

AU - Ryzhik, Lenya

PY - 2014

Y1 - 2014

N2 - We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ε (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ε (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ε (1/2, 1). The proof is based on an auxiliary limit theorem for an additive functional of a fractional Brownian motion.

AB - We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ε (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ε (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ε (1/2, 1). The proof is based on an auxiliary limit theorem for an additive functional of a fractional Brownian motion.

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U2 - 10.1137/13092068X

DO - 10.1137/13092068X

M3 - Article

AN - SCOPUS:84903997355

SN - 1540-3459

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JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

IS - 2

ER -

Homogenization driven by a fractional brownian motion: The shear layer case

Abstract

All Science Journal Classification (ASJC) codes

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