Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Equation of state for Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This methods is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise the equation of state in the form $p=-\Lambda+w_{1}\rho(a)+w_{2}a^{\beta}+0$ and energy density $\rho=\Lambda+\rho_{01}a^{-3(1+w)}+\rho_{02}a^{\beta}+\rho_{03}a^{-3}$, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data. We showed that the model with scaling fluid fits well to supernovae data. We found that $\Omega_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($\beta = -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $\Omega_{\text{m},0}=0.3$ then the favoured model is close to concordance $\Lambda$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $\Lambda$CDM model, while intermediate distant SNIa should be fainter than in $\Lambda$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $\Lambda$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.Comment: accepted for publication versio

Small, Dense Quark Stars from Perturbative QCD

As a model for nonideal behavior in the equation of state of QCD at high density, we consider cold quark matter in perturbation theory. To second order in the strong coupling constant, $\alpha_s$, the results depend sensitively on the choice of the renormalization mass scale. Certain choices of this scale correspond to a strongly first order chiral transition, and generate quark stars with maximum masses and radii approximately half that of ordinary neutron stars. At the center of these stars, quarks are essentially massless.Comment: ReVTeX, 5 pages, 3 figure

Systematic study of the effect of short range correlations on the form factors and densities of s-p and s-d shell nuclei

Analytical expressions of the one- and two-body terms in the cluster expansion of the charge form factors and densities of the s-p and s-d shell nuclei with N=Z are derived. They depend on the harmonic oscillator parameter b and the parameter $\beta$ which originates from the Jastrow correlation function. These expressions are used for the systematic study of the effect of short range correlations on the form factors and densities and of the mass dependence of the parameters b and $\beta$. These parameters have been determined by fit to the experimental charge form factors. The inclusion of the correlations reproduces the experimental charge form factors at the high momentum transfers ($q\geq 2 1/fm$). It is found that while the parameter $\beta$ is almost constant for the closed shell nuclei, $^4$He, $^{16}$O and $^{40}$Ca, its values are larger (less correlated systems) for the open shell nuclei, indicating a shell effect in the closed shell nuclei.Comment: Latex, 21 pages, 6 figures, 1 tabl

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere

Primordial Nucleosynthesis for the New Cosmology: Determining Uncertainties and Examining Concordance

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) have a long history together in the standard cosmology. The general concordance between the predicted and observed light element abundances provides a direct probe of the universal baryon density. Recent CMB anisotropy measurements, particularly the observations performed by the WMAP satellite, examine this concordance by independently measuring the cosmic baryon density. Key to this test of concordance is a quantitative understanding of the uncertainties in the BBN light element abundance predictions. These uncertainties are dominated by systematic errors in nuclear cross sections. We critically analyze the cross section data, producing representations that describe this data and its uncertainties, taking into account the correlations among data, and explicitly treating the systematic errors between data sets. Using these updated nuclear inputs, we compute the new BBN abundance predictions, and quantitatively examine their concordance with observations. Depending on what deuterium observations are adopted, one gets the following constraints on the baryon density: OmegaBh^2=0.0229\pm0.0013 or OmegaBh^2 = 0.0216^{+0.0020}_{-0.0021} at 68% confidence, fixing N_{\nu,eff}=3.0. Concerns over systematics in helium and lithium observations limit the confidence constraints based on this data provide. With new nuclear cross section data, light element abundance observations and the ever increasing resolution of the CMB anisotropy, tighter constraints can be placed on nuclear and particle astrophysics. ABRIDGEDComment: 54 pages, 20 figures, 5 tables v2: reflects PRD version minor changes to text and reference

Search for H→γγ produced in association with top quarks and constraints on the Yukawa coupling between the top quark and the Higgs boson using data taken at 7 TeV and 8 TeV with the ATLAS detector

A search is performed for Higgs bosons produced in association with top quarks using the diphoton decay mode of the Higgs boson. Selection requirements are optimized separately for leptonic and fully hadronic final states from the top quark decays. The dataset used corresponds to an integrated luminosity of 4.5 fb−14.5 fb−1 of proton–proton collisions at a center-of-mass energy of 7 TeV and 20.3 fb−1 at 8 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. No significant excess over the background prediction is observed and upper limits are set on the tt¯H production cross section. The observed exclusion upper limit at 95% confidence level is 6.7 times the predicted Standard Model cross section value. In addition, limits are set on the strength of the Yukawa coupling between the top quark and the Higgs boson, taking into account the dependence of the tt¯H and tH cross sections as well as the H→γγ branching fraction on the Yukawa coupling. Lower and upper limits at 95% confidence level are set at −1.3 and +8.0 times the Yukawa coupling strength in the Standard Model