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

A. Adrover, F. Garofalo

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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(¿). The results indicate that N(¿) deviates from the form given by the modified Weyl-Berry-Lapidus conjecture as it shows a correction of ¿N(¿)~¿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.
Original languageEnglish
Article number027202
Pages (from-to)027202-1/4
Number of pages4
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume81
Issue number2
DOIs
Publication statusPublished - 2010

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Integrated Density of States
Slip Boundary Condition
Laplace Operator
Density of States
Velocity Field
Laplace transformation
Fractal
fractals
slip
Scaling
boundary conditions
scaling
Microfabrication
Heat Transport
Mass Transport
Weighting Function
Rough Surface
Microchannel
velocity distribution
Neumann Boundary Conditions

Cite this

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title = "Scaling of the density of state of the weighted Laplacian in the presence of fractal boundaries",
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(¿). The results indicate that N(¿) deviates from the form given by the modified Weyl-Berry-Lapidus conjecture as it shows a correction of ¿N(¿)~¿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.",
author = "A. Adrover and F. Garofalo",
year = "2010",
doi = "10.1103/PhysRevE.81.027202",
language = "English",
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journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
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Scaling of the density of state of the weighted Laplacian in the presence of fractal boundaries. / Adrover, A.; Garofalo, F.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 81, No. 2, 027202, 2010, p. 027202-1/4.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Scaling of the density of state of the weighted Laplacian in the presence of fractal boundaries

AU - Adrover, A.

AU - Garofalo, F.

PY - 2010

Y1 - 2010

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AB - 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(¿). The results indicate that N(¿) deviates from the form given by the modified Weyl-Berry-Lapidus conjecture as it shows a correction of ¿N(¿)~¿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.

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DO - 10.1103/PhysRevE.81.027202

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