Abstract
| Original language | English |
|---|---|
| Article number | 027202 |
| Pages (from-to) | 027202-1/4 |
| Number of pages | 4 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 81 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2010 |
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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 journal › Article › Academic › peer-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
N2 - 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.
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.
U2 - 10.1103/PhysRevE.81.027202
DO - 10.1103/PhysRevE.81.027202
M3 - Article
C2 - 20365679
VL - 81
SP - 027202-1/4
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 2
M1 - 027202
ER -