On the Equivalence of Quadratic APN Functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.Comment: 13 p

Quasi-one-dimensional Bose gases with large scattering length

Bose gases confined in highly-elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1d model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1d Bose gas become independent of the actual value of the 3d scattering length. In this unitary regime, the energy of the system is well described by a hard rod equation of state. We investigate the stability of quasi-1d Bose gases with positive and negative 3d scattering length.Comment: 5 pages, 3 figure

Fast drift kilometric radio bursts and solar proton events

Initial results of a comparative study of major fast drift kilometric bursts and solar proton events from Sep. 1978 to Feb. 1983 are presented. It was found that only about half of all intense, long duration ( 40 min above 500 sfu) 1 MHz bursts can be associated with F 20 MeV proton events. However, for the subset of such fast drift bursts accompanied by metric Type 2 and/or 4 activity (approximately 40% of the total), the degree of association with 20 MeV events is 80%. For the reverse association, it was found that proton events with J( 20 MeV) 0.01 1 pr cm(-2)s(-1)sr(-1)MeV(-1) were typically (approximately 80% of the time) preceded by intense 1 MHz bursts that exceeded the 500 sfu level for times 20 min (median duration approximately 35 min)

Static and Dynamic Magnetism in Underdoped Superconductor BaFe1.92_{1.92}Co0.08_{0.08}As2_2

We report neutron scattering measurements on single crystals of BaFe$_{1.92}$Co$_{0.08}$As$_2$. The magnetic Bragg peak intensity is reduced by 6 % upon cooling through T$_C$. The spin dynamics exhibit a gap of 8 meV with anisotropic three-dimensional (3d) interactions. Below T$_C$ additional intensity appears at an energy of $\sim$4.5(0.5) meV similar to previous observations of a spin resonance in other Fe-based superconductors. No further gapping of the spin excitations is observed below T$_C$ for energies down to 2 meV. These observations suggest the redistribution of spectral weight from the magnetic Bragg position to a spin resonance demonstrating the direct competition between static magnetic order and superconductivity.Comment: 4 pages, 4 figure

Quantum Monte Carlo study of quasi-one-dimensional Bose gases

We study the behavior of quasi-one-dimensional (quasi-1d) Bose gases by Monte Carlo techniques, i.e., by the variational Monte Carlo, the diffusion Monte Carlo, and the fixed-node diffusion Monte Carlo technique. Our calculations confirm and extend our results of an earlier study [Astrakharchik et al., cond-mat/0308585]. We find that a quasi-1d Bose gas i) is well described by a 1d model Hamiltonian with contact interactions and renormalized coupling constant; ii) reaches the Tonks-Girardeau regime for a critical value of the 3d scattering length a_3d; iii) enters a unitary regime for |a_3d| -> infinity, where the properties of the gas are independent of a_3d and are similar to those of a 1d gas of hard-rods; and iv) becomes unstable against cluster formation for a critical value of the 1d gas parameter. The accuracy and implications of our results are discussed in detail.Comment: 15 pages, 9 figure

Calculation of the photoionization with de-excitation cross sections of He and helium-like ions

We discuss the results of the calculation of the photoionization with de-excitation of excited He and helium-like ions Li$^{+}$ and B$^{3+}$ at high but non-relativistic photon energies $\omega$. Several lower $^{1}S$ and $^{3}S$ states are considered. We present and analyze the ratios $R_{d}^{+\ast}$ of the cross sections of photoionization with de-excitation, $\sigma_{(d)}^{+\ast}(\omega)$, and of the photo-ionization with excitation, $\sigma ^{+\ast}(\omega)$. The dependence of $R_{d}^{+\ast}$ on the excitation of the target object and the charge of its nucleus is presented. Apart to theoretical interest, results obtained can be verified using such long living excited state as $2^{3}S$ of He.Comment: 10 pages, 6 table

High pressure floating zone growth and structural properties of ferrimagnetic quantum paraelectric BaFe12_{12}O19_{19}

High quality single crystals of BaFe$_{12}$O$_{19}$ were grown using the floating zone technique in flowing oxygen pressurized to 100 atm. Single crystal neutron diffraction was used to determine the nuclear and magnetic structure of BaFe$_{12}$O$_{19}$ at 4 K and 295 K. At both temperatures, there exist local electric dipoles formed by the off-mirror-plane displacements of magnetic Fe$^{3+}$ ions at the bipyramidal sites. The displacement at 4 K is about half of that at room temperature. The temperature dependence of the specific heat shows no anomaly associated with long range polar ordering in the temperature range from 1.90-300 K. The inverse dielectric permittivity, $1/\varepsilon$, along the c-axis shows a $T^2$ temperature dependence between 10 K and 20 K, with a significantly reduced temperature dependence displayed below 10 K. Moreover, as the sample is cooled below 1.4 K there is an anomalous sharp upturn in $1/\varepsilon$. These features resemble those of classic quantum paraelectrics such as SrTiO$_3$. The presence of the upturn in $1/\varepsilon$ indicates that BaFe$_{12}$O$_{19}$ is a critical quantum paraelectric system with Fe$^{3+}$ ions involved in both magnetic and electric dipole formation.Comment: 9 pages, 9 figures, submitted to APL Material

The role of science in physical natural hazard assessment : report to the UK Government by the Natural Hazard Working Group

Following the tragic Asian tsunami on 26 December 2004, the Prime Minister asked the Government’s Chief Scientific Adviser, Sir David King, to convene a group of experts (the Natural Hazard Working Group) to advise on the mechanisms that could and should be established for the detection and early warning of global physical natural hazards. 2. The Group was asked to examine physical hazards which have high global or regional impact and for which an appropriate early warning system could be put in place. It was also asked to consider the global natural hazard frameworks currently in place and under development and their effectiveness in using scientific evidence; to consider whether there is an existing appropriate international body to pull together the international science community to advise governments on the systems that need to be put in place, and to advise on research needed to fill current gaps in knowledge. The Group was asked to make recommendations on whether a new body was needed, or whether other arrangements would be more effective