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Scaling of the density of state of the weighted Laplacian in the presence of fractal boundaries

Adrover, Alessandra and Garofalo, Fabio LU (2010) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00 81(2).
Abstract

Spectral properties of the weighted Laplace operator in the presence of fractal boundaries are numerically investigated for both Neumann and Dirichlet boundary conditions. This corresponds to the characterization of heat and mass transport in microchannels with irregular and rough surfaces induced by the microfabrication process. The axial velocity field with no-slip boundary conditions, representing the weighting function of the Laplace operator, influences the localization properties of the eigenfunctions and the scaling of the integrated density of state (IDOS) N (λ). The results indicate that N (λ) deviates from the form given by the modified Weyl-Berry-Lapidus conjecture as it shows a correction of ΔN (λ) ∼ λ Df /4 to... (More)

Spectral properties of the weighted Laplace operator in the presence of fractal boundaries are numerically investigated for both Neumann and Dirichlet boundary conditions. This corresponds to the characterization of heat and mass transport in microchannels with irregular and rough surfaces induced by the microfabrication process. The axial velocity field with no-slip boundary conditions, representing the weighting function of the Laplace operator, influences the localization properties of the eigenfunctions and the scaling of the integrated density of state (IDOS) N (λ). The results indicate that N (λ) deviates from the form given by the modified Weyl-Berry-Lapidus conjecture as it shows a correction of ΔN (λ) ∼ λ Df /4 to the leading-order Weil term. Numerical results are presented for Koch and Koch snowflake fractal boundaries. The role of slip or no-slip boundary conditions of the velocity field on the IDOS is also investigated. © 2010 The American Physical Society.

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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00
volume
81
issue
2
publisher
American Physical Society
external identifiers
  • Scopus:77249115795
ISSN
1539-3755
DOI
10.1103/PhysRevE.81.027202
language
English
LU publication?
no
id
f2c5967b-b4fd-4c99-8ffb-92f15c9b998a
date added to LUP
2016-06-27 10:16:31
date last changed
2016-09-20 03:01:33
@misc{f2c5967b-b4fd-4c99-8ffb-92f15c9b998a,
  abstract     = {<p>Spectral properties of the weighted Laplace operator in the presence of fractal boundaries are numerically investigated for both Neumann and Dirichlet boundary conditions. This corresponds to the characterization of heat and mass transport in microchannels with irregular and rough surfaces induced by the microfabrication process. The axial velocity field with no-slip boundary conditions, representing the weighting function of the Laplace operator, influences the localization properties of the eigenfunctions and the scaling of the integrated density of state (IDOS) N (λ). The results indicate that N (λ) deviates from the form given by the modified Weyl-Berry-Lapidus conjecture as it shows a correction of ΔN (λ) ∼ λ Df <sup>/</sup>4 to the leading-order Weil term. Numerical results are presented for Koch and Koch snowflake fractal boundaries. The role of slip or no-slip boundary conditions of the velocity field on the IDOS is also investigated. © 2010 The American Physical Society.</p>},
  author       = {Adrover, Alessandra and Garofalo, Fabio},
  issn         = {1539-3755},
  language     = {eng},
  month        = {02},
  number       = {2},
  publisher    = {ARRAY(0x9ccaf20)},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00},
  title        = {Scaling of the density of state of the weighted Laplacian in the presence of fractal boundaries},
  url          = {http://dx.doi.org/10.1103/PhysRevE.81.027202},
  volume       = {81},
  year         = {2010},
}