A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

On the seasonal variability of eddy kinetic energy in the Gulf Stream region. Geophys

. [1] In the Gulf Stream region, eddy kinetic energy (EKE) peaks in summer while, as measured by the baroclinic eddy growth time scale, the ocean is most baroclinically unstable in late winter. We argue that the seasonally-varying Ekman pumping is unlikely to be responsible for the seasonal variation in growth time, and that the summer peak in EKE results from a reduction in dissipation in summer compared to winter. Citation: Zhai, X., R

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Magnetization reversal of an individual exchange biased permalloy nanotube

We investigate the magnetization reversal mechanism in an individual permalloy (Py) nanotube (NT) using a hybrid magnetometer consisting of a nanometer-scale SQUID (nanoSQUID) and a cantilever torque sensor. The Py NT is affixed to the tip of a Si cantilever and positioned in order to optimally couple its stray flux into a Nb nanoSQUID. We are thus able to measure both the NT's volume magnetization by dynamic cantilever magnetometry and its stray flux using the nanoSQUID. We observe a training effect and temperature dependence in the magnetic hysteresis, suggesting an exchange bias. We find a low blocking temperature $T_B = 18 \pm 2$ K, indicating the presence of a thin antiferromagnetic native oxide, as confirmed by X-ray absorption spectroscopy on similar samples. Furthermore, we measure changes in the shape of the magnetic hysteresis as a function of temperature and increased training. These observations show that the presence of a thin exchange-coupled native oxide modifies the magnetization reversal process at low temperatures. Complementary information obtained via cantilever and nanoSQUID magnetometry allows us to conclude that, in the absence of exchange coupling, this reversal process is nucleated at the NT's ends and propagates along its length as predicted by theory.Comment: 8 pages, 4 figure

Superconducting quantum interference devices with submicron Nb/HfTi/Nb junctions for investigation of small magnetic particles

We investigated, at temperature $4.2\,\mathrm{K}$, electric transport, flux noise and resulting spin sensitivity of miniaturized Nb direct current superconducting quantum interference devices (SQUIDs) based on submicron Josephson junctions with HfTi barriers. The SQUIDs are either of the magnetometer-type or gradiometric in layout. In the white noise regime, for the best magnetometer we obtain a flux noise $S_{\Phi}^{1/2}=250\,\mathrm{n}\Phi_0/\mathrm{Hz}^{1/2}$, corresponding to a spin sensitivity $S^{1/2}_\mu\,\ge\,29\,\mu_B/\mathrm{Hz}^{1/2}$. For the gradiometer we find $S_{\Phi}^{1/2}=300\,\mathrm{n}\Phi_0/\mathrm{Hz}^{1/2}$ and $S^{1/2}_\mu\,\ge\,44\,\mu_B/\mathrm{Hz}^{1/2}$. The devices can still be optimized with respect to flux noise and coupling between a magnetic particle and the SQUID, leaving room for further improvement towards single spin resolution.Comment: 4 pages, 3 figure

Exploring the impact of the inverse Faraday effect on all-optical helicity-dependent magnetization switching

All-optical helicity-dependent magnetization switching (AO-HDS) is the quickest deterministic technique for data storage by solely using ultrashort laser pulses. Granular high data density magnetic storage media developed for heat-assisted magnetic recording (HAMR) provide an ideal playground to investigate the interplay of effects leading to magnetization switching. In the latest perception, we identify two effects, the magnetic circular dichroism (MCD) and the inverse Faraday effect (IFE), as the forces driving the switching process. During photon absorption, which leads to a rapid temperature rise and thus to magnetization quenching, the MCD ensures two distinct electron temperatures due to helicity-dependent absorption. This effect already holds a nonvanishing probability for magnetization switching. At the same time, the IFE induces a magnetic moment within the material, enhancing the switching probability. We present AO-HDS experiments using ultrashort laser pulses ($\lesssim 200\,\mathrm{fs}$) in the near-infrared range from $800\,\mathrm{nm}$ to $1500\,\mathrm{nm}$. The experiments demonstrate a strong dependence of the switching efficiency on the absorbed energy density, elevating the electron temperature in the vicinity of the Curie point, allowing for the IFE to take full effect, inducing a magnetic moment for deterministic switching in the quenched magnetization state. While we do not observe an enhanced switching due to an increased MCD, a higher induced magnetization usually improves the switching rate if the electron temperature reaches the transition temperature vicinity. Therefore, we conclude that the magnetic moment generated by the IFE is crucial for the switching efficiency and the distinct deterministic character of the switching process. Laser pulses with a higher absorption induce a higher magnetic moment and switch magnetization at lower fluences

Search for squarks and gluinos in events with isolated leptons, jets and missing transverse momentum at s√=8 TeV with the ATLAS detector

The results of a search for supersymmetry in final states containing at least one isolated lepton (electron or muon), jets and large missing transverse momentum with the ATLAS detector at the Large Hadron Collider are reported. The search is based on proton-proton collision data at a centre-of-mass energy s√=8 TeV collected in 2012, corresponding to an integrated luminosity of 20 fb−1. No significant excess above the Standard Model expectation is observed. Limits are set on supersymmetric particle masses for various supersymmetric models. Depending on the model, the search excludes gluino masses up to 1.32 TeV and squark masses up to 840 GeV. Limits are also set on the parameters of a minimal universal extra dimension model, excluding a compactification radius of 1/R c = 950 GeV for a cut-off scale times radius (ΛR c) of approximately 30

Measurement of χ c1 and χ c2 production with s√ = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χ c1 and χ c2 charmonium states are measured in pp collisions at s√ = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χ c states are reconstructed through the radiative decay χ c → J/ψγ (with J/ψ → μ + μ −) where photons are reconstructed from γ → e + e − conversions. The production rate of the χ c2 state relative to the χ c1 state is measured for prompt and non-prompt χ c as a function of J/ψ transverse momentum. The prompt χ c cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in b-hadron decays are also measured

Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at s√=8 TeV with ATLAS

Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of s√=8 TeV. The analysis is performed in the H → γγ decay channel using 20.3 fb−1 of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The pp → H → γγ fiducial cross section is measured to be 43.2 ±9.4(stat.) − 2.9 + 3.2 (syst.) ±1.2(lumi)fb for a Higgs boson of mass 125.4GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations