Reply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion ''

We show here that the model Hamiltonian used in our paper for ion vibrating in a q-analog harmonic oscillator trap and interacting with a classical single-mode light field is indeed obtained by replacing the usual bosonic creation and annihilation operators of the harmonic trap model by their q-deformed counterparts. The approximations made in our paper amount to using for the ion-laser interaction in a q-analog harmonic oscillator trap, the operator F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon A}, which is analogous to the corresponding operator for ion in a harmonic oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger }}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states |g,m> and |e,m> are not analytic vectors.Comment: Revtex, 4pages. To be Published in Physical Review A59, NO.4(April 99

Composition dependent magnetic properties of iron oxide - polyaniline nanoclusters

Gamma - Iron Oxide prepared by sol -gel process was used to produce nanocomposites with polyaniline of varying aniline concentrations. TEM shows the presence of chain like structure for lower polyaniline concentration. The room temperature hysteresis curves show finite coercivity of 160 Oe for all the composites while the saturation magnetization was found to decrease with increasing polymer content. ZFC - FC magnetisation measurements indicate high blocking temperatures. It is believed that this indicates a strongly interacting system, which is also shown by our TEM results. Monte Carlo simulations performed on a random anisotropy model with dipolar and exchange inteactions match well with experimental results.Comment: 9 (nine) pages, 6 figures (jpeg and eps

GALAH Survey: Chemically Tagging the Thick Disk

The GALAH survey targets one million stars in the southern hemisphere down to a limiting magnitude of V = 14 at the Anglo- Australian Telescope. The project aims to measure up to 30 elemental abundances and radial velocities (~1 km/s accuracy) for each star at a resolution of R = 28000. These elements fall into 8 independent groups (e.g. alpha, Fe peak, r-process). For all stars, Gaia will provide distances to 1% and transverse velocities to 1 km/s or better, giving us a 14D set of parameters for each star, i.e. 6D phase space and 8D abundance space. There are many scientic applications but here we focus on the prospect of chemically tagging the thick disk and making a direct measurement of how stellar migration evolves with cosmic time.Comment: Barcelona conference (Dec 1-5, 2014): The Milky Way Unravelled by Gaia, eds. Soubiran, Figueras, Walton; 8 page

Low temperature hopping magnetotransport in paramagnetic single crystals of cobalt doped ZnO

Long needle-shaped single crystals of Zn1-xCoxO were grown at low temperatures using a molten salt solvent technique, up to x=0.10. The conduction process at low temperatures is determined to be by Mott variable range hopping. Both pristine and cobalt doped crystals clearly exhibit a crossover from negative to positive magnetoresistance as the temperature is decreased. The positive magnetoresistance of the Zn1-xCoxO single crystals increases with increased Co concentration and reaches up to 20% at low temperatures (2.5 K) and high fields (>1 T). SQUID magnetometry confirms that the Zn1-xCoxO crystals are predominantly paramagnetic in nature and the magnetic response is independent of Co concentration. The results indicate that cobalt doping of single crystalline ZnO introduces localized electronic states and isolated Co2+ ions into the host matrix, but that the magnetotransport and magnetic properties are decoupled.Comment: 7 pages, 9 figures, submitted to Physical Review

A critical layer model for turbulent pipe flow

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating modes, permitting comparison of our results to experimental data, and identify the steady component of the velocity field that varies only in the wall-normal direction as the turbulent mean profile. The "optimal" forcing shape, that gives the largest velocity response, is assumed to lead to modes that will be dominant and hence observed in turbulent pipe flow. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely a wall layer that scales with $R^{+1/2}$ and a critical layer, where the propagation velocity is equal to the local mean velocity, that scales with $R^{+2/3}$ in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall.Comment: Submitted to the Journal of Fluid Mechanics and currently under revie

On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

The relationship between Koopman mode decomposition, resolvent mode decomposition and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalised to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatio-temporal Koopman operator, which has a travelling wave interpretation. The relationship leads to a generalisation of dynamic mode decomposition, in which symmetry operations are applied to restrict the dynamic modes to span a subspace subject to those symmetries. The resolvent is interpreted as the mapping between the Koopman modes of the Reynolds stress divergence and the velocity field. It is shown that the singular vectors of the resolvent (the resolvent modes) are the optimal basis in which to express the velocity field Koopman modes where the latter are not a priori known