Poynting's theorem for planes waves at an interface: a scattering matrix approach

We apply the Poynting theorem to the scattering of monochromatic electromagnetic planes waves with normal incidence to the interface of two different media. We write this energy conservation theorem to introduce a natural definition of the scattering matrix S. For the dielectric-dielectric interface the balance equation lead us to the energy flux conservation which express one of the properties of S: it is a unitary matrix. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses at the conductor. However, the dissipative term appearing in the Poynting theorem can be interpreted as a single absorbing mode at the conductor such that a whole S, satisfying flux conservation and containing this absorbing mode, can be defined. This is a simplest version of a model introduced in the current literature to describe losses in more complex systems.Comment: 5 pages, 3 figures, submitted to Am. J. Phy

Edge phonons in black phosphorus

Exfoliated black phosphorus has recently emerged as a new two-dimensional crystal that, due to its peculiar and anisotropic crystalline and electronic band structures, may have potentially important applications in electronics, optoelectronics and photonics. Despite the fact that the edges of layered crystals host a range of singular properties whose characterization and exploitation are of utmost importance for device development, the edges of black phosphorus remain poorly characterized. In this work, the atomic structure and the behavior of phonons near different black phosphorus edges are experimentally and theoretically studied using Raman spectroscopy and density functional theory calculations. Polarized Raman results show the appearance of new modes at the edges of the sample, and their spectra depend on the atomic structure of the edges (zigzag or armchair). Theoretical simulations confirm that the new modes are due to edge phonon states that are forbidden in the bulk, and originated from the lattice termination rearrangements.Comment: 15 pages, 4 figure

Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry

The field equation with the cosmological constant term is derived and the energy of the general 4-dimensional stationary axisymmetric spacetime is studied in the context of the hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR). We find that, by means of the integral form of the constraints equations of the formalism naturally without any restriction on the metric parameters, the energy for the asymptotically flat/de Sitter/Anti-de Sitter stationary spacetimes in the Boyer-Lindquist coordinate can be expressed as $E=\frac{1}{8\pi}\int_S d\theta d\phi(sin\theta \sqrt{g_{\theta\theta}}+\sqrt{g_{\phi\phi}}-(1/\sqrt{g_{rr}})(\partial{\sqrt{g_ {\theta\theta} g_{\phi\phi}}}/\partial r))$. It is surprised to learn that the energy expression is relevant to the metric components $g_{rr}$, $g_{\theta\theta}$ and $g_{\phi\phi}$ only. As examples, by using this formula we calculate the energies of the Kerr-Newman (KN), Kerr-Newman Anti-de Sitter (KN-AdS), Kaluza-Klein, and Cveti\v{c}-Youm spacetimes.Comment: 12 page

Revisiting Clifford algebras and spinors III: conformal structures and twistors in the paravector model of spacetime

This paper is the third of a series of three, and it is the continuation of math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of the group Spin_+(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$ spacetime. We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose the Clifford algebra over R{4,1} is also used to describe conformal maps, instead of R{2,4}. Although some papers have already described twistors using the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds some new light on the use of the paravector model and generalizations.Comment: 17 page

Non-dissipative anomalous currents in 2D materials: the parity magnetic effect as an analog of the chiral magnetic effect

Anomalous electric currents along a magnetic field, first predicted to emerge during large heavy ion collision experiments, were also observed a few years ago in condensed matter environments, exploring the fact that charge carriers in Dirac/Weyl semi-metals exhibit a relativistic-like behavior. The mechanism through which such currents are generated relies on an imbalance in the chirality of systems immersed in a magnetic background, leading to the so-called chiral magnetic effect (CME). While chiral magnetic currents have been observed in materials in three space dimensions, in this work we propose that an analog of the chiral magnetic effect can be constructed in two space dimensions, corresponding to a novel type of intrinsic half-integer Quantum Hall effect, thereby also offering a topological protection mechanism for the current. While the 3D chiral anomaly underpins the CME, its 2D cousin is emerging from the 2D parity anomaly, we thence call it the parity magnetic effect (PME). It can occur in disturbed honeycomb lattices where both spin degeneracy and time reversal symmetry are broken. These configurations harbor two distinct gap-opening mechanisms that, when occurring simultaneously, drive slightly different gaps in each valley, establishing an analog of the necessary chiral imbalance. Some examples of promising material setups that fulfill the prerequisites of our proposal are also listed.Comment: 11 pages, 5 figure

Exploring Halo Substructure with Giant Stars III: First Results from the Grid Giant Star Survey and Discovery of a Possible Nearby Sagittarius Tidal Structure in Virgo

We describe first results of a spectroscopic probe of selected fields from the Grid Giant Star Survey. Multifiber spectroscopy of several hundred stars in a strip of eleven fields along delta approximately -17^{circ}, in the range 12 <~ alpha <~ 17 hours, reveals a group of 8 giants that have kinematical characteristics differing from the main field population, but that as a group maintain coherent, smoothly varying distances and radial velocities with position across the fields. Moreover, these stars have roughly the same abundance, according to their MgH+Mgb absorption line strengths. Photometric parallaxes place these stars in a semi-loop structure, arcing in a contiguous distribution between 5.7 and 7.9 kpc from the Galactic center. The spatial, kinematical, and abundance coherence of these stars suggests that they are part of a diffuse stream of tidal debris, and one roughly consistent with a wrapped, leading tidal arm of the Sagittarius dwarf spheroidal galaxy.Comment: 8 pages including 4 figures. Accepted for publication in ApJ

Modeling and simulation of fructo-oligosaccharides production

It is foreseen that Systems Biology will have a great impact not only in Metabolic Engineering and Drug Discovery efforts, but also in Bioprocess development and optimization. In fact, the computational tools developed in this area made possible to simulate a biochemical process with a mathematical model comprising dynamical equations based on first principles as well as empirical kinetic equations and parameters that can be estimated from experimental data. Fructo-oligosaccharides (FOS) have become important as healthy food ingredients because of their beneficial characteristics to the health of human (Lee, 1999). They can be obtained biotechnologically using the enzyme Betafructofuranosidase, produced by some fungi. The main purpose of this work was to develop a mathematical model able to simulate the formation of FOS in a bioreactor, in order to perform a faster optimization of the FOS production process, allowing to identify which parameters can influence the final amount of FOS. An empirical model presented by Kow Jen Duan et al (1994) was used to obtain the first set of reactions. Several hydrolysis equations were added in order to achieve a general mathematical model of the occurring enzymatic reactions. After the reformulation of the Kow Jen Duan model, the kinetic parameters were determined from experimental data using the System Biology toolbox [2] with the Simulated Annealing method for curve fitting. Several experiments in bioreactors were performed with two different FOS producing fungi for that purpose. The time evolution of 7 state variables (Sucrose, Glucose, Fructose, 1-Kestose, Nystose, 1-Fructosyl Nystose and Biomass) was considered. After parameter fitting, several simulations were performed in MatLab and the simulation results were compared with experimental data, exhibiting a very satisfactory correlation for both fungal cultures. Correlation coefficients of 0.9980 - 0.9549 between simulated and experimental data were obtained. This model will be used to optimize the production process, using an optimization tool that has been developed in our research group