2,259 research outputs found
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 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 , and the deviation of
obtained from the examined experimental data of the 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 GeV/c also shows the impact of the examined effects on the
form of the differential cross sections.Comment: 13 pages, 3 figure
Z topology and superconductivity from symmetry lowering of a 3D Dirac Metal AuPb
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 AuPb 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 = -1 invariant in
the low temperature phase indicates that AuPb in its superconducting state
must have topological surface states. These characteristics make AuPb 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 and 135 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, and
respectively, of the proton. We find
in agreement with a model-independent dispersion sum rule, and
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
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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
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