The effects of the small t properties of hadronic scattering amplitude on the determination its real part

Taking into account the different forms of the Coulomb-hadron interference phase and the possible spin-flip contribution the new analysis of the experimental data of the proton-antiproton elastic scattering at $3.8 < p_L <6.0 \$GeV/c and small momentum transfer is carried out. It is shown that the size of the spin-flip amplitude can be determined from the form of the differential cross sections at small $t$, and the deviation of $\rho(s,t)$ obtained from the examined experimental data of the $p\bar{p}$ scattering from the analysis \cite{Kroll}, based on the dispersion relations, is conserved in all xamined assumptions. The analysis of the proton-proton elastic scattering at $9 < p_L < 70 \$GeV/c also shows the impact of the examined effects on the form of the differential cross sections.Comment: 13 pages, 3 figure

Z2_2 topology and superconductivity from symmetry lowering of a 3D Dirac Metal Au2_2Pb

3D Dirac semi-metals (DSMs) are materials that have massless Dirac electrons and exhibit exotic physical properties It has been suggested that structurally distorting a DSM can create a Topological Insulator (TI), but this has not yet been experimentally verified. Furthermore, quasiparticle excitations known as Majorana Fermions have been theoretically proposed to exist in materials that exhibit superconductivity and topological surface states. Here we show that the cubic Laves phase Au$_2$Pb has a bulk Dirac cone above 100 K that gaps out upon cooling at a structural phase transition to create a topologically non trivial phase that superconducts below 1.2 K. The nontrivial Z$_2$ = -1 invariant in the low temperature phase indicates that Au$_2$Pb in its superconducting state must have topological surface states. These characteristics make Au$_2$Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Measurement of the Electric and Magnetic Polarizabilities of the Proton

The Compton scattering cross section on the proton has been measured at laboratory angles of 90$^\circ$ and 135$^\circ$ using tagged photons in the energy range 70--100 MeV and simultaneously using untagged photons in the range 100--148~MeV. With the aid of dispersion relations, these cross sections were used to extract the electric and magnetic polarizabilities, $\bar{\alpha}$ and $\bar{\beta}$ respectively, of the proton. We find $$\bar{\alpha}+\bar{\beta} = ( 15.0 \pm 2.9 \pm 1.1 \pm 0.4 ) \times 10^{-4} \: {\rm fm}^3,$$ in agreement with a model-independent dispersion sum rule, and $$\bar{\alpha}-\bar{\beta} = ( 10.8 \pm 1.1 \pm 1.4 \pm 1.0 ) \times 10^{-4} \: {\rm fm}^3,$$ where the errors shown are statistical, systematic, and model-dependent, respectively. A comparison with previous experiments is given and global values for the polarizabilities are extracted.Comment: 35 pages, 11 PostScript figures, uses RevTex 3.

Brief for Petitioners

Petitioners Brief written by ACLU and Public Patent Foundation in support of petitioners in AMP v. Myriad Genetics (Supreme Court Case Docket No. 12-398)

Petition for a Writ of Certiorari

Petition for a Writ of Certiorari submitted by petitioners Public Patent Foundation and American Civil Liberties Union (No. 11-725

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Physics of the Riemann Hypothesis

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.Comment: 27 pages, 9 figure

Non-Markovian polymer reaction kinetics

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.Comment: Main text (7 pages, 5 figures) + Supplemantary Information (13 pages, 2 figures