3,011 research outputs found
Beyond the simple Proximity Force Approximation: geometrical effects on the non-retarded Casimir interaction
We study the geometrical corrections to the simple Proximity Force
Approximation for the non-retarded Casimir force. We present analytical results
for the force between objects of various shapes and substrates, and between
pairs of objects. We compare the results to those from more exact numerical
calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings;
the analytical PFA results together with the geometrical correction factors are
summarized in a table.Comment: 18 pages, 19 figures, 1 tabl
ANCSA and 1991: A Framework for Analysis
We study the geometrical corrections to the simple Proximity Force Approximation (PFA) for the non-retarded Casimir force. We extend traditional PFA in two ways: We take the whole surfaces of the objects facing each other into account, not just the curvatures at the point of closest distance; we take the thickness of the coating of coated objects into account in the formalism. We present analytical and numerical results for a sphere above a substrate, for a spherical shell above a substrate, and for two interacting spheres. We compare the results to those from a multi-polar expansion method, a method based on a more solid foundation.Original Publication: Bo E. Sernelius and C.E. Roman-Velazquez, Test of the proximity force approximation, 2009, Journal of Physics: Conference Series, (161), 012016. http://dx.doi.org/10.1088/1742-6596/161/1/012016 Copyright: Institute of Physics http://journals.iop.org/</p
Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
Burchnall's method to invert the Feldheim-Watson linearization formula for
the Hermite polynomials is extended to all polynomial families in the
Askey-scheme and its -analogue. The resulting expansion formulas are made
explicit for several families corresponding to measures with infinite support,
including the Wilson and Askey-Wilson polynomials. An integrated version gives
the possibility to give alternate expression for orthogonal polynomials with
respect to a modified weight. This gives expansions for polynomials, such as
Hermite, Laguerre, Meixner, Charlier, Meixner-Pollaczek and big -Jacobi
polynomials and big -Laguerre polynomials. We show that one can find
expansions for the orthogonal polynomials corresponding to the
Toda-modification of the weight for the classical polynomials that correspond
to known explicit solutions for the Toda lattice, i.e., for Hermite, Laguerre,
Charlier, Meixner, Meixner-Pollaczek and Krawtchouk polynomials
The role of geometry on dispersive forces
The role of geometry on dispersive forces is investigated by calculating the
energy between different spheroidal particles and planar surfaces, both with
arbitrary dielectric properties. The energy is obtained in the non-retarded
limit using a spectral representation formalism and calculating the interaction
between the surface plasmons of the two macroscopic bodies. The energy is a
power-law function of the separation of the bodies, where the exponent value
depends on the geometrical parameters of the system, like the separation
distance between bodies, and the aspect ratio among minor and major axes of the
spheroid.Comment: Presneted at QFEXT05, Barcelona 2005. Submitted to J. Phys.
Hybrid Organic−Inorganic Solids That Show Shape Selectivity
Hybrid organic−inorganic solids featuring millimolar/gram concentrations of intracrystalline organic moieties and shape-selectivity are synthesized. Pure-silica zeolite beta crystals are coated with zirconia and treated in aqueous sodium hydroxide to create defects and mesoporosity within the crystalline structure. Aminopropyl organic groups are subsequently grafted onto the generated intracrystalline silanol groups. After grafting, characterization data indicate a high organic concentration localized primarily within the intracrystalline voids. Specifically, thermogravimetric analysis shows an organic loading of 0.7 mmol of NH_2/g, ^(29)Si solid-state nuclear magnetic resonance (NMR) spectra display a quantitative decrease in Q^3 silicon atoms with a corresponding resharpening of the Q^4 resonances, and N_2 adsorption data show a decrease in micropore volume to 0.10 cm^3/g. Knoevenagel condensation reactions are catalyzed by the aminopropyl-functionalized materials using differently sized aldehydes and the results show that the zirconia-protected functionalized solid have shape selective properties
Enhancement of entanglement in one-dimensional disordered systems
The pairwise quantum entanglement of sites in disordered electronic
one-dimensional systems (rings) is studied. We focus on the effect of diagonal
and off diagonal disorder on the concurrence between electrons on
neighbor and non neighbor sites as a function of band filling. In the
case of diagonal disorder, increasing the degree of disorder leads to a
decrease of the concurrence with respect to the ordered case. However,
off-diagonal disorder produces a surprisingly strong enhancement of
entanglement. This remarkable effect occurs near half filling, where the
concurrence becomes up to 15% larger than in the ordered system.Comment: 21 pages, 9 figure
Dynamics of the Formation of Bright Solitary Waves of Bose-Einstein Condensates in Optical Lattices
We present a detailed description of the formation of bright solitary waves
in optical lattices. To this end, we have considered a ring lattice geometry
with large radius. In this case, the ring shape does not have a relevant effect
in the local dynamics of the condensate, while offering a realistic set up to
implement experiments with conditions usually not available with linear
lattices (in particular, to study collisions). Our numerical results suggest
that the condensate radiation is the relevant dissipative process in the
relaxation towards a self-trapped solution. We show that the source of
dissipation can be attributed to the presence of higher order dispersion terms
in the effective mass approach. In addition, we demonstrate that the stability
of the solitary solutions is linked with particular values of the width of the
wavepacket in the reciprocal space. Our study suggests that these critical
widths for stability depend on the geometry of the energy band, but are
independent of the condensate parameters (momentum, atom number, etc.).
Finally, the non-solitonic nature of the solitary waves is evidenced showing
their instability under collisions.Comment: 7 pages, 7 figures, to appear in PR
Mechanism of Glucose Isomerization Using a Solid Lewis Acid Catalyst in Water
^1H and ^(13)C NMR spectroscopy on isotopically labeled glucose reveals that in the presence of tin-containing zeolite Sn-Beta, the isomerization reaction of glucose in water proceeds by way of an intramolecular hydride shift (see scheme) rather than proton transfer. This is the first mechanistic demonstration of Sn-Beta acting as a Lewis acid in a purely aqueous environment
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