The stability of Na-doped Bi2(NbCr)O7−x pyrochlores: The non-existence of “(BiNa)(NbCr)O6”

We show that the pyrochlore described as “(BiNa)(NbCr)O₆” is in fact a non-stoichiometric pyrochlore with an approximate composition of (Bi_1.33Na_0.67)(Nb_1.33Cr_0.67)O_7−x. Refinement of this structure using constant wavelength powder neutron diffraction data reveals the presence of vacancies in the anion sites coupled with displacive disorder of the Bi and Na cations. This is necessary to achieve a satisfactory bonding arrangement for both the Bi and Na cations that occupy the pyrochlore A-type sites. Attempts to prepare other pyrochlores in the series Bi_2−xNa_x(NbCr)O₆ were unsuccessful and it appears that the pyrochlore is only stable only over a very narrow composition range. The structure of the pure Bi pyrochlore Bi₂(NbCr)O₇ is also described.     

“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

Scattering of ultrashort laser pulses on “ion‐sphere” in dense plasmas

Scattering of ultrashort electromagnetic pulses on the dense strongly coupled plasma is under consideration in the frame of hard ion sphere model. The electron distribution inside the ion sphere is obtained from self‐consistent solution of the Shrodinger equation for bound electrons and the Poisson equation for free electrons. The electron density distribution is determined by plasma electron temperatures. The ion density of Al plasmas under consideration is of the order of 10²⁰–10²² cm^?3, the electron temperature changes between 54 and 816 eV. Dynamical polarizability of the hard sphere determining the scattering cross sections is calculated using the modified local plasma frequency approximation. The spectrum of scattering cross section has maxima in the vicinity of the mean plasma frequency. Dependencies of scattering probability on carrier frequency and pulse duration are analysed in detail. The transition of the total scattering probabilities from nonlinear time dependence at small times to standard linear ones with the increase of pulse duration is demonstrated.     

A possible identification of x (3.45) with a “time-like” c excitation

We identify the four observed intermediate states between J/ψ and ψ′ with the four j^PC = j⁺⁺P waves of a relativistic bound state model. Assuming a point-like quark photon vertex we calculate bounds on their radiative couplings to J/ψ and ψ′ by the help of four-dimensional dipole sum rules. These bounds also imply upper bounds on the total widths.     

Schlieren “PIV” for turbulent flows

The possibility of using commercial PIV equipment combined with schlieren optics to measure the velocity fields of turbulent flows is explored. Given a sufficiently high Reynolds number and adequate refractive flow differences, turbulent eddies can serve as the PIV “particles” in a schlieren image or shadowgram. The PIV software analyzes motion between consecutive schlieren or shadowgraph frames to obtain velocity fields. Velocimetry examples of an axisymmetric sonic helium jet in air and a 2D turbulent boundary layer at Mach 3 are shown. Due to optical path integration, axisymmetric flows require the inverse Abel transform to extract center-plane velocity data. Conditions for optimum schlieren sensitivity are examined. In its present embodiment, “schlieren PIV” is not useful for laminar flows nor for fully 3D flows. Otherwise it functions much like standard PIV under conditions where individual particles are not resolved and velocimetry is instead based on correlation of the motion of turbulent structures. “Schlieren PIV” shows significant promise for general refractive turbulent flow velocimetry if its integrative nature can be overcome through sharp-focusing optics.     

“Proper Time” Method Calculation of the “One Loop” Thermodynamical Potential for QED in External Electromagnetic Field

The extension of the “proper time” method to the statistical field theory is obtained. The procedure is used to calculate the “one loop” contribution to the thermodynamical potential in electrodynamics, when the electron positron gas is located in a combination of an inhomogeneous electrostatic field and an uniform magnetic one. Also, a “proper time” representation of the temperature Green function for this problem is given.     

Designing the “perfect” projection screen

A perfect diffuser would place 100% of the light leaving the projector in that small region of space where there will be audience eyes to observe it. It would not allow light from sources other than the projector to reach the eyes from the screen. The screen should be affordably priced and cosmetically unremarkable, e.g. seamless. The image seen by any observer should be equally bright over the whole screen. I discuss a way to approximate the perfect projection screen using kinoform diffusers, a Fresnel lens and a mirrored surface.     

Generic phase diagram of “electron-doped” T′ cuprates

We investigated the generic phase diagram of the electron doped superconductor, Nd_2−xCe_xCuO₄, using films prepared by metal organic decomposition. After careful oxygen reduction treatment to remove interstitial O_ap atoms, we found that the T_c increases monotonically from 24 K to 29 K with decreasing x from 0.15 to 0.00, demonstrating a quite different phase diagram from the previous bulk one. The implication of our results is discussed on the basis of tremendous influence of O_ap “impurities” on superconductivity and also magnetism in T′ cuprates. Then we conclude that our result represents the generic phase diagram for oxygen-stoichiometric Nd_2−xCe_xCuO₄.     

Novel comprehension of “common path” principle

The idea of “common path” has been widely applied in optical instrument design for 30 years and even today. But the meaning of “common path” has not yet been explained clearly and sometimes confusion has been created. In this paper an “adaptive principle” is proposed and recommended on optical instrument system. It suggests that the designer not only arranges the measurement system to obtain measurement signal but also sets a channel to give prediction of noise or disturbance in real time or short term. Such a recommendation is based on the recent studies on nonlinear dynamics and atmospheric disturbance by means of experiments as well as theoretical analysis.     

“BEST” Homonuclear Adiabatic Decoupling for C- and N-Double-Labeled Proteins

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f_1rms as the main decoupling that is required for Bloch–Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch–Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or “BEST” decoupling for short, is constructed, which not only compensates the Bloch–Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.     

Universality of “four-coordinated” correlated percolation and random percolation

We consider a site-correlated percolation problem, recently introduced in connection with the anomalous properties of liquid water. Within a position-space renormalization group approach, this problem is shown to belong to the same universality class as random percolation.     

Optimum excitation of “enhanced” central transition populations

Central transition (CT) sensitivity enhancement schemes that transfer polarization from satellites to the CT through selective saturation or inversion of neighboring satellite transitions have provided a welcome improvement for magic-angle spinning spectra of half-integer quadrupole nuclei. While many researchers have investigated and developed different methods of creating enhanced CT populations, here we investigate the conversion of these enhanced CT populations into observable CT coherence. We show a somewhat unexpected result that a conversion pulse length optimized for maximum sensitivity on equilibrium populations may not be optimum for an enhanced (non-equilibrium) polarization. Furthermore, CT enhancements can be lost if excessive rf field strength is used to convert this enhanced polarization into CT coherence. While a maximally enhanced CT signal is expected when using a perfectly selective CT conversion pulse, we have found that significant sensitivity loss can occur when using surprisingly low rf field strengths, even for sites with relatively large quadrupole coupling constants. We have systematically investigated these issues, and present some general guidelines and expectations when optimizing the conversion of enhanced (non-equilibrium) CT populations into observable CT coherence.     

Relative work function, surface composition and topography of “pedigreed” impregnated tungsten dispenser cathodes

A study has been made of the variation in work function, surface composition, and topography of 5:3:2 impregnated tungsten dispenser cathodes made under carefully controlled conditions (pedigreed cathodes). Despite these conditions several cathodes had unexpected deposits on their emitting surfaces, and one showed a variation in work function and composition across the surface during activation.     

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays an important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is well known that the case of energy and time principally differs from more familiar examples of two non‐commuting observables. Since quantum theory was originated, many approaches to energy–time uncertainties have been proposed. Entropic way to formulate the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, uncertainty relations of the “energy–time” type are obtained in terms of Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state‐dependent and state‐independent formulations are of interest. Some of the derived state‐independent bounds are similar to the results obtained within a more general approach on the basis of sandwiched relative entropies. The developed method allows us to address the case of detection inefficiencies.     

Cluster Expansion for Ideal Fermi Systems in the “Fixed Node Approximation”

Results of the direct path integral Monte Carlo simulation (DPIMCS) have shown that the “fixed node approximation” (FNA) rather well describes thermodynamic properties of the strongly coupled fermions at “weak and moderate” degeneracy. To explain the increasing difference for highly degenerate fermions it is rigorously proved that the exact Fermi function with index 5/2 in grand ensemble can not be reproduced in FNA, so FNA has not the correct limit to ideal fermions.