2,162 research outputs found
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Water-in-air droplet formation in plasma bonded microchannels fabricated by Shrinky-Dink® lithography
Thesis (M.S.) University of Alaska Fairbanks, 2011This thesis presents the first work on water-in-air droplet microfluidics. Polymeric microchannels were prototyped to illustrate water droplet formation in air by the T-junction meditated design. The first part of the thesis is on the proof of using unfiltered air as the process gas for plasma-assisted bonding of polydimethylsiloxane (PDMS) microchannels. A series of bilayered PDMS prototypes were plasma bonded under various plasma treatment parameters to determine the optimal settings for high-strength bonding. Pressure rupture tests were conducted to measure the bonding interface strength, which were shown to be as high as 135 psi. The second part of the thesis illustrates the formation and dispersion of water droplets in a continuous air flow in microchannels, and discusses the mechanisms of how droplets are formed. The Shrinky Dinks lithography and plasma-assisted bonding were used to prototype leakage-free microcbannels for testing droplet production. Droplets are formed under the competition between the fluid viscosity and surface tension forces. The channel dimensions and the fluid flow rates dictate the mechanism of droplet formation. The major finding is that the droplet length increases and droplet velocity decreases with increasing water flow rates, but some droplets were not formed at the T-Junction. These findings are discussed.Alaska NASA EPSCoR Progra
Casimir effect for a -dimensional sphere
The Casimir force on a -dimensional sphere due to the confinement of a
massless scalar field is computed as a function of , where is a
continuous variable that ranges from to . The dependence of
the force on the dimension is obtained using a simple and straightforward
Green's function technique. We find that the Casimir force vanishes as ( non-even integer) and also vanishes when is a negative even
integer. The force has simple poles at positive even integer values of .Comment: 22 pages, REVTeX, 4 uuencoded figures, OKHEP-94-0
An exactly solvable self-convolutive recurrence
We consider a self-convolutive recurrence whose solution is the sequence of
coefficients in the asymptotic expansion of the logarithmic derivative of the
confluent hypergeometic function . By application of the Hilbert
transform we convert this expression into an explicit, non-recursive solution
in which the th coefficient is expressed as the th moment of a
measure, and also as the trace of the th iterate of a linear operator.
Applications of these sequences, and hence of the explicit solution provided,
are found in quantum field theory as the number of Feynman diagrams of a
certain type and order, in Brownian motion theory, and in combinatorics
Progress in Lunar Laser Ranging Tests of Relativistic Gravity
Analyses of laser ranges to the Moon provide increasingly stringent limits on
any violation of the Equivalence Principle (EP); they also enable several very
accurate tests of relativistic gravity. We report the results of our recent
analysis of Lunar Laser Ranging (LLR) data giving an EP test of \Delta
(M_G/M_I)_{EP} =(-1.0 +/- 1.4) x 10^{-13}. This result yields a Strong
Equivalence Principle (SEP) test of \Delta (M_G/M_I)_{SEP} =(-2.0 +/- 2.0) x
10^{-13}. Also, the corresponding SEP violation parameter \eta is (4.4 +/- 4.5)
x 10^{-4}, where \eta=4\beta-\gamma-3 and both \beta and \gamma are
parametrized post-Newtonian (PPN) parameters. Using the recent Cassini result
for the parameter \gamma, PPN parameter \beta is determined to be \beta-1=(1.2
+/- 1.1) x 10^{-4}. The geodetic precession test, expressed as a relative
deviation from general relativity, is K_{gp}=-0.0019 +/- 0.0064. The search for
a time variation in the gravitational constant results in \dot G/G=(4 +/- 9) x
10^{-13} yr^{-1}, consequently there is no evidence for local (~1AU) scale
expansion of the solar system.Comment: 4 pages, revtex4, minor changes made for publicatio
Phononic Self energy effects and superconductivity in CaC
We study the graphite intercalated compound CaC by means of Eliashberg
theory, focusing on the anisotropy properties. An analysis of the
electron-phonon coupling is performed, and we define a minimal 6-band
anisotropy structure. Comparing with Superconducting Density Functional Theory
(SCDFT) the condition under which Eliashberg theory is able to reproduce the
SCDFT gap structure is determined, and we discuss the role of Coulomb
interactions. The Engelsberg-Schrieffer polaron structure is computed by
solving the Eliashberg equation on the Matsubara axis and analytically
continuing it to the full complex plane. This reveals the polaronic
quasiparticle bands anisotropic features as well as the interplay with
superconductivity
PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials
Version 1: The well known Eckart's singular s-wave potential is
PT-symmetrically regularized and continued to the whole real line. The new
model remains exactly solvable and its bound states remain proportional to
Jacobi polynomials. Its real and discrete spectrum exhibits several unusual
features.
Version 2: Parity times time-reversal symmetry of complex Hamiltonians with
real spectra is usually interpreted as a weaker mathematical substitute for
Hermiticity. Perhaps an equally important role is played by the related
strengthened analyticity assumptions. In a constructive illustration we
complexify a few potentials solvable only in s-wave. Then we continue their
domain from semi-axis to the whole axis and get the new exactly solvable
models. Their energies come out real as expected. The new one-dimensional
spectra themselves differ quite significantly from their s-wave predecessors.Comment: Original 10-page letter ``PT-symmetrized exact solution of the
singular Eckart oscillator" is extended to a full pape
Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model
We present results obtained in the calculation of nuclear ground state
properties in relativistic Hartree approximation using a Lagrangian whose
QCD-scaled coupling constants are all natural (dimensionless and of order 1).
Our model consists of four-, six-, and eight-fermion point couplings (contact
interactions) together with derivative terms representing, respectively, two-,
three-, and four-body forces and the finite ranges of the corresponding mesonic
interactions. The coupling constants have been determined in a self-consistent
procedure that solves the model equations for representative nuclei
simultaneously in a generalized nonlinear least-squares adjustment algorithm.
The extracted coupling constants allow us to predict ground state properties of
a much larger set of even-even nuclei to good accuracy. The fact that the
extracted coupling constants are all natural leads to the conclusion that QCD
scaling and chiral symmetry apply to finite nuclei.Comment: 44 pages, 13 figures, 9 tables, REVTEX, accepted for publication in
Phys. Rev.
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