The Hidden Spatial Geometry of Non-Abelian Gauge Theories

The Gauss law constraint in the Hamiltonian form of the $SU(2)$ gauge theory of gluons is satisfied by any functional of the gauge invariant tensor variable $\phi^{ij} = B^{ia} B^{ja}$. Arguments are given that the tensor $G_{ij} = (\phi^{-1})_{ij}\,\det B$ is a more appropriate variable. When the Hamiltonian is expressed in terms of $\phi$ or $G$, the quantity $\Gamma^i_{jk}$ appears. The gauge field Bianchi and Ricci identities yield a set of partial differential equations for $\Gamma$ in terms of $G$. One can show that $\Gamma$ is a metric-compatible connection for $G$ with torsion, and that the curvature tensor of $\Gamma$ is that of an Einstein space. A curious 3-dimensional spatial geometry thus underlies the gauge-invariant configuration space of the theory, although the Hamiltonian is not invariant under spatial coordinate transformations. Spatial derivative terms in the energy density are singular when $\det G=\det B=0$. These singularities are the analogue of the centrifugal barrier of quantum mechanics, and physical wave-functionals are forced to vanish in a certain manner near $\det B=0$. It is argued that such barriers are an inevitable result of the projection on the gauge-invariant subspace of the Hilbert space, and that the barriers are a conspicuous way in which non-abelian gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223

Communications of the Lunar and Planetary Laboratory, volume 4, part 3 - Ubvrijkl photometry of the bright stars

Multicolor photometric analysis of bright stars - table

Negative index fishnet with nanopillars formed by direct nano-imprint lithography

In this paper we demonstrate the ability to fabricate fishnets by nanoimprinting directly into a pre-deposited three layer metal–dielectric–metal stack, enabling us to pattern large areas in two minutes. We have designed and fabricated two different fishnet structures of varying dimensions using this method and measured their resonant wavelengths in the near-infrared at 1.45 μm and 1.88 μm. An important by-product of directly imprinting into the metal–dielectric stack, without separation from the substrate, is the formation of rectangular nanopillars that sit within the rectangular apertures between the fishnet slabs. Simulations complement our measurements and suggest a negative refractive index real part with a magnitude of 1.6. Further simulations suggest that if the fishnet were to be detached from the supporting substrate a refractive index real part of 5 and FOM of 2.74 could be obtained

Breakdown of QCD factorization at large Feynman x

Recent measurements by the BRAHMS collaboration of high-pT hadron production at forward rapidities at RHIC found the relative production rate(d-Au)/(p-p) to be suppressed, rather than enhanced. Examining other known reactions (forward production of light hadrons, the Drell-Yan process, heavy flavor production, etc.), one notes that all of these display a similar property, namely, their cross sections in nuclei are suppressed at large xF. Since this is the region where x2 is minimal, it is tempting to interpret this as a manifestation of coherence, or of a color glass condensate, whereas it is actually a simple consequence of energy conservation and takes place even at low energies. We demonstrate that in all these reactions there is a common suppression mechanism that can be viewed, alternatively, as a consequence of a reduced survival probability for large rapidity gap processes in nuclei, Sudakov suppression, an enhanced resolution of higher Fock states by nuclei, or an effective energy loss that rises linearly with energy. Our calculations agree with data.Comment: 12 pages Latex, 8 figures (only technical corrections in the replacement

Computation and visualization of photonic quasicrystal spectra via Blochs theorem

Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwells equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Blochs theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.Comment: Published in Physical Review B, 77 104201, 200

Influence of Hydrodynamic Interactions on the Kinetics of Colloidal Particle's Adsorption

The kinetics of irreversible adsorption of spherical particles onto a flat surface is theoretically studied. Previous models, in which hydrodynamic interactions were disregarded, predicted a power-law behavior $t^{-2/3}$ for the time dependence of the coverage of the surface near saturation. Experiments, however, are in agreement with a power-law behavior of the form $t^{-1/2}$. We outline that, when hydrodynamic interactions are considered, the assymptotic behavior is found to be compatible with the experimental results in a wide region near saturation.Comment: 4 pages, 1 figures, Phys. Rev. Lett. (in press

Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods

We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a "localized" coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking a limit in which a coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g. from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a sub-pixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.Comment: 10 page

On-line monitoring of methane in sewer air

Methane is a highly potent greenhouse gas and contributes significantly to climate change. Recent studies have shown significant methane production in sewers. The studies conducted so far have relied on manual sampling followed by off-line laboratory-based chromatography analysis. These methods are labor-intensive when measuring methane emissions from a large number of sewers, and do not capture the dynamic variations in methane production. In this study, we investigated the suitability of infrared spectroscopy-based on-line methane sensors for measuring methane in humid and condensing sewer air. Two such sensors were comprehensively tested in the laboratory. Both sensors displayed high linearity (R2 > 0.999), with a detection limit of 0.023% and 0.110% by volume, respectively. Both sensors were robust against ambient temperature variations in the range of 5 to 35°C. While one sensor was robust against humidity variations, the other was found to be significantly affected by humidity. However, the problem was solved by equipping the sensor with a heating unit to increase the sensor surface temperature to 35°C. Field studies at three sites confirmed the performance and accuracy of the sensors when applied to actual sewer conditions, and revealed substantial and highly dynamic methane concentrations in sewer air

Casimir force between planes as a boundary finite size effect

The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1 dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.Comment: 10 pages, 2 eps figures, LaTeX2e file. v2: A reference is added, some minor modifications made to clarify the text. v3: 9 pages, 3 eps figures, LaTeX2e file, revtex style. Paper throughly restructured and rewritten. Much more details are given, but essential results and conclusions are unchanged. Version accepted for publicatio

High power TiO2 and high capacity Sn-doped TiO2 nanomaterial anodes for lithium-ion batteries

A range of phase-pure anatase TiO2 (∼5 nm) and Sn-doped TiO2 nanoparticles with the formula Ti1-xSnxO2 (where x = 0, 0.06, 0.11 and 0.15) were synthesized using a continuous hydrothermal flow synthesis (CHFS) reactor. Charge/discharge cycling tests were carried out in two different potential ranges of 3 to 1 V and also a wider range of 3 to 0.05 V vs Li/Li+. In the narrower potential range, the undoped TiO2 nanoparticles display superior electrochemical performance to all the Sn-doped titania crystallites. In the wider potential range, the Sn-doped samples perform better than undoped TiO2. The sample with composition Ti0.85Sn0.15O2, shows a capacity of ca. 350 mAh g−1 at an applied constant current of 100 mA g−1 and a capacity of 192.3 mAh g−1 at a current rate of 1500 mA g−1. After 500 charge/discharge cycles (at a high constant current rate of 382 mA g−1), the same nanomaterial anode retains a relatively high specific capacity of 240 mAh g−1. The performance of these nanomaterials is notable, particularly as they are processed into electrodes, directly from the CHFS process (after drying) without any post-synthesis heat-treatment, and they are made without any conductive surface coating