585 research outputs found
Spectral Zeta Functions for a Cylinder and a Circle
Spectral zeta functions for the massless scalar fields obeying the
Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder
are constructed. These functions are defined explicitly in a finite domain of
the complex plane s containing the closed interval of real axis Re . Proceeding from this the spectral zeta functions for the boundary
conditions given on a circle (boundary value problem on a plane) are obtained
without any additional calculations. The Casimir energy for the relevant field
configurations is deduced.Comment: REVTeX4, 13 pages, no tables and figures; v2 some misprints are
correcte
A thick shell Casimir effect
We consider the Casimir energy of a thick dielectric-diamagnetic shell under
a uniform velocity light condition, as a function of the radii and the
permeabilities. We show that there is a range of parameters in which the stress
on the outer shell is inward, and a range where the stress on the outer shell
is outward. We examine the possibility of obtaining an energetically stable
configuration of a thick shell made of a material with a fixed volume
Casimir energy of a non-uniform string
The Casimir energy of a non-uniform string built up from two pieces with
different speed of sound is calculated. A standard procedure of subtracting the
energy of an infinite uniform string is applied, the subtraction being
interpreted as the renormalization of the string tension. It is shown that in
the case of a homogeneous string this method is completely equivalent to the
zeta renormalization.Comment: 11 pages, REVTeX, no figures and table
Casimir energy of a dilute dielectric ball in the mode summation method
In the --approximation the Casimir energy of a
dilute dielectric ball is derived using a simple and clear method of the mode
summation. The addition theorem for the Bessel functions enables one to present
in a closed form the sum over the angular momentum before the integration over
the imaginary frequencies. The linear in contribution
into the vacuum energy is removed by an appropriate subtraction. The role of
the contact terms used in other approaches to this problem is elucidated.Comment: 14 pages, REVTeX, no figures, no tables; presentation is made better,
new references are adde
Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
Using the mode-by-mode summation technique the zero point energy of the
electromagnetic field is calculated for the boundary conditions given on the
surface of an infinite solid cylinder. It is assumed that the dielectric and
magnetic characteristics of the material which makes up the cylinder
and of that which makes up the surroundings obey the relation . With this
assumption all the divergences cancel. The divergences are regulated by making
use of zeta function techniques. Numerical calculations are carried out for a
dilute dielectric cylinder and for a perfectly conducting cylindrical shell.
The Casimir energy in the first case vanishes, and in the second is in complete
agreement with that obtained by DeRaad and Milton who employed a Green's
function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in
previous version corrected, giving a zero Casimir energy for a tenuous
cylinde
LC nanocomposites: induced optical singularities, managed nano/micro structure, and electrical conductivity
Microstructure, phase transitions, electrical conductivity, and optical and
electrooptical properties of multiwalled carbon nanotubes (NTs), dispersed in
the cholesteric liquid crystal (cholesteryl oleyl carbonate, COC), nematic 5CB
and their mixtures, were studied in the temperature range between 255 K and 363
K. The relative concentration X=COC/(COC+5CB)was varied within 0.0-1.0. The
concentration of NTs was varied within 0.01-5% wt. The value of X
affected agglomeration and stability of NTs inside COC+5CB. High-quality
dispersion, exfoliation, and stabilization of the NTs were observed in COC
solvent ("good" solvent). From the other side, the aggregation of NTs was very
pronounced in nematic 5CB solvent ("bad" solvent). The dispersing quality of
solvent influenced the percolation concentration , corresponding to
transition between the low conductive and high conductive states: e.g.,
percolation was observed at and for pure COC and 5CB,
respectively. The effects of thermal pre-history on the heating-cooling
hysteretic behavior of electrical conductivity were studied. The mechanism of
dispersion of NTs in COC+5CB mixtures is discussed. Utilization of the mixtures
of "good" and "bad" solvents allowed fine regulation of the dispersion,
stability and electrical conductivity of LC+NTs composites. The mixtures of COC
and 5CB were found to be promising for application as functional media with
controllable useful chiral and electrophysical properties.Comment: 10 pages, 9 figure
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