13,542 research outputs found
Bloch-mode analysis for retrieving effective parameters of metamaterials
We introduce a new approach for retrieving effective parameters of
metamaterials based on the Bloch-mode analysis of quasi-periodic composite
structures. We demonstrate that, in the case of single-mode propagation, a
complex effective refractive index can be assigned to the structure, being
restored by our method with a high accuracy. We employ both surface and volume
averaging of the electromagnetic fields of the dominating (fundamental) Bloch
modes to determine the Bloch and wave impedances, respectively. We discuss how
this method works for several characteristic examples, and demonstrate that
this approach can be useful for retrieval of both material and wave effective
parameters of a broad range of metamaterials.Comment: 12 pages, 10 figure
Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces
We introduce the notion of weak commensurabilty of arithmetic subgroups and
relate it to the length equivalence and isospectrality of locally symmetric
spaces. We prove many strong consequences of weak commensurabilty and derive
from these many interesting results about isolength and isospectral locally
symmetric spaces.Comment: 62 page
Turbulence and Particle Heating in Advection-Dominated Accretion Flows
We extend and reconcile recent work on turbulence and particle heating in
advection-dominated accretion flows. For approximately equipartition magnetic
fields, the turbulence primarily heats the electrons. For weaker magnetic
fields, the protons are primarily heated. The division between electron and
proton heating occurs between and (where
is the ratio of the gas to the magnetic pressure), depending on unknown
details of how Alfv\'en waves are converted into whistlers on scales of the
proton Larmor radius. We also discuss the possibility that magnetic
reconnection could be a significant source of electron heating.Comment: 17 pages (Latex), incl. 2 Figures; submitted to Ap
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