22,305 research outputs found
Effective conductivity of composites of graded spherical particles
We have employed the first-principles approach to compute the effective
response of composites of graded spherical particles of arbitrary conductivity
profiles. We solve the boundary-value problem for the polarizability of the
graded particles and obtain the dipole moment as well as the multipole moments.
We provide a rigorous proof of an {\em ad hoc} approximate method based on the
differential effective multipole moment approximation (DEMMA) in which the
differential effective dipole approximation (DEDA) is a special case. The
method will be applied to an exactly solvable graded profile. We show that DEDA
and DEMMA are indeed exact for graded spherical particles.Comment: submitted for publication
Multipole polarizability of a graded spherical particle
We have studied the multipole polarizability of a graded spherical particle
in a nonuniform electric field, in which the conductivity can vary radially
inside the particle. The main objective of this work is to access the effects
of multipole interactions at small interparticle separations, which can be
important in non-dilute suspensions of functionally graded materials. The
nonuniform electric field arises either from that applied on the particle or
from the local field of all other particles. We developed a differential
effective multipole moment approximation (DEMMA) to compute the multipole
moment of a graded spherical particle in a nonuniform external field. Moreover,
we compare the DEMMA results with the exact results of the power-law graded
profile and the agreement is excellent. The extension to anisotropic DEMMA will
be studied in an Appendix.Comment: LaTeX format, 2 eps figures, submitted for publication
The leptonic decay using the principle of maximum conformality
In the paper, we study the leptonic decay width
by using the principle of maximum
conformality (PMC) scale-setting approach. The PMC adopts the renormalization
group equation to set the correct momentum flow of the process, whose value is
independent to the choice of the renormalization scale and its prediction thus
avoids the conventional renormalization scale ambiguities. Using the known
next-to-next-to-next-to-leading order perturbative series together with the PMC
single scale-setting approach, we do obtain a renormalization scale independent
decay width, keV,
where the error is squared average of those from
, GeV and the choices of
factorization scales within of their central values. To compare with
the result under conventional scale-setting approach, this decay width agrees
with the experimental value within errors, indicating the importance of a
proper scale-setting approach.Comment: 6 pages, 4 figure
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