Full Sphere Research Articles

Explicit Relation Between Volume and Lower Bound for Q for Small Dipole Topologies

A rigorous relation is derived between any local change of the volume of an electrically small radiating device and the lower bound of its radiation Q factor. The relation concerns the actual volume and not the circumscribing volume. This means that also (incremental) changes in volume can be studied where the circumscribing volume remains the same. The relation clearly proves that any arbitrary increase in volume decreases the Q, and any arbitrary reduction in volume increases the Q. When directly applied to volumes embedded within a sphere, it is almost trivial to rigorously prove the well-known fact that the full sphere provides the absolute minimal Q. The communication ends with a simple analytical proof of the limit as introduced by Thal for dipole type spherical TM modes. To the knowledge of the author, these explicit relations between Q factor and occupied volume have not been described in literature yet.

A momentum imaging microscope for dissociative electron attachment

We describe an experimental approach to image the three-dimensional (3D) momentum distribution of the negative ions arising from dissociative electron attachment (DEA). The experimental apparatus employs a low energy pulsed electron gun, an effusive gas source and a 4π solid-angle ion momentum imaging spectrometer consisting of a pulsed ion extraction field, an electrostatic lens, and a time- and position-sensitive detector. The time-of-flight and impact position of each negative ion are measured event by event in order to image the full 3D ion momentum sphere. The system performance is tested by measuring the anion momentum distributions from two DEA resonances, namely H(-) from H(2)O(-) ((2)B(1)) and O(-) from O(2)(-) ((2)Π(u)). The results are compared with existing experimental and theoretical data.

First principles simulation of reaction steps in the atomic layer deposition of titania: dependence of growth on Lewis acidity of titanocene precursor

It is a common finding that titanocene-derived precursors do not yield TiO(2) films in atomic layer deposition (ALD) with water. For instance, ALD with Ti(OMe)(4) and water gives 0.5 Å/cycle, while TiCp*(OMe)(3) does not show any growth (Me = CH(3), Cp* = C(5)(CH(3))(5)). From mass spectrometry we found that Ti(OMe)(4) occurs in the gas phase practically exclusively as a monomer. We then used first principles density functional theory (DFT) to model the ALD reaction sequence and find the reason for the difference in growth behaviour. Both precursors adsorb initially via hydrogen-bonding. The simulations reveal that the Cp* ligand of TiCp*(OMe)(3) lowers the Lewis acidity of the Ti centre and prevents its coordination to surface O ('densification') during both of the ALD pulses. The effect of Cp* on Ti seems to be both steric (full coordination sphere) and electronic (lower electrophilicity). This crucial step in the sequence of ALD reactions is therefore not possible in the case of TiCp*(OMe)(3) + H(2)O, which means that there is no deposition of TiO(2) films.

Relay Selection in Distributed Transmission Based on the Golden Code Using ML and Sphere Decoding in Wireless Networks

The implementation of cooperative diversity with relays has advantages over point-to-point multiple-input multiple-output (MIMO) systems, in particular, overcoming correlated paths due to small inter-element spacing. A simple transmitter with one antenna may exploit cooperative diversity or space time coding gain through distributed relays. In this paper, similar distributed transmission is considered with the golden code, and the authors propose a new strategy for relay selection, called the maximum-mean selection policy, for distributed transmission with the full maximum-likelihood (ML) decoding and sphere decoding (SD) based on a wireless relay network. This strategy performs a channel strength tradeoff at every relay node to select the best two relays for transmission. It improves on the established one-sided selection strategy of maximum-minimum policy. Simulation results comparing the bit error rate (BER) based on different detectors and a scheme without relay selection, with the maximum-minimum and maximum-mean selection schemes confirm the performance advantage of relay selection. The proposed strategy yields the best performance of the three methods.

Bi-stability in turbulent, rotating spherical Couette flow

Flow between concentric spheres of radius ratio η=ri/ro=0.35 is studied in a 3 m diameter experiment. We have measured the torques required to maintain constant boundary speeds as well as localized wall shear stress, velocity, and pressure. At low Ekman number E=2.1×10-7 and modest Rossby number 0.07<Ro<3.4, the resulting flow is highly turbulent with a maximum Reynolds number (Re = Ro/E) exceeding 15 million. Several turbulent flow regimes are evident as Ro is varied for fixed E. We focus our attention on one flow transition, in particular, between Ro = 1.8 and Ro = 2.6, where the flow shows bistable behavior. For Ro within this range, the flow undergoes intermittent transitions between the states observed alone at adjacent Ro outside the switching range. The two states are clearly distinguished in all measured flow quantities, including a striking reduction in torque demanded from the inner sphere by the state lying at higher Ro. The reduced angular momentum transport appears to be associated with the development of a fast zonal circulation near the experiment core. The lower torque state exhibits waves, one of which is similar to an inertial mode known for a full sphere and another which appears to be a strongly advected Rossby-type wave. These results represent a new laboratory example of the overlapping existence of distinct flow states in high Reynolds number flow. Turbulent multiple stability and the resilience of transport barriers associated with zonal flows are important topics in geophysical and astrophysical contexts.

A shape memory alloy probe for electrovaporization of renal cell carcinoma.

e15090 Background: We developed a new shape memory alloy (SMA) probe for percutaneous treatment of renal cell carcinoma (RCC) by electro-vaporization, and investigated its efficacy and safety in experimental models. Methods:The SMA electrode can be manipulated to any shape at room temperature and regains its original shape at ≥ 65 °C. By adding a high-frequency electric current to the probe, the electrodes quickly regain their original shape and vaporize tissues into a spherical defect. The performance of this probe was tested using agar, dog kidney and rat RCC models. The treatment effect was evaluated by magnetic resonance imaging (MRI) and histological examination. Results: The vaporizing electrode produces heat due to its own resistance to the high frequency electric current, and vaporizes surrounding agar. In the agar model, the electro-vaporization inside the spherical electrode was successfully achieved in several seconds. The area of ≥ 60 °C extended about 5 mm beyond the periphery of the vaporized part, and corresponded with the histological findings on the dog kidney that an irreversible heat denaturation occurred to the same extent. A tumor model made by transplanting RCC cell line in the subcutaneous tissue of nude rats. After applying the electorical current, the electrode part completely recovered to a full sphere shape. The study on the RCC model also confirmed that about 5 mm extent of heat denaturation was seen in the muscular tissue adjacent to the tumor. In the study using the RCC model, some remaining tissues close to the tumor were observed after vaporization. However, dynamic MRI demonstrated no enhancement in this area and no viable tumor cells were documented by histological examination. Conclusions: This novel tissue ablation system has potential as a viable option for percutaneous treatment of renal tumors.

On the pulse-width statistics in radio pulsars - I. Importance of the interpulse emission

We performed Monte Carlo simulations of different properties of pulsar radio emission, such as: pulsar periods, pulse-widths, inclination angles and rates of occurrence of interpulse emission (IP). We used recently available large data sets of the pulsar periods P, the pulse profile widths W and the magnetic inclination angle alpha. We also compiled the largest ever database of pulsars with interpulse emission, divided into the double-pole (DP-IP) and the single-pole (SP-IP) cases. Their distribution on the P - Pdot diagram strongly suggests a secular alignment of the magnetic axis from the originally random orientation. We derived possible parent distribution functions of important pulsar parameters by means of the Kolmogorov-Smirnov significance test using the available data sets (P, W, alpha and IP), different models of pulsar radio beam rho = rho(P) as well as different trial distribution functions of pulsar period and the inclination angles. The best suited parent period distribution function is the log-normal distribution, although the gamma function distribution cannot be excluded. The strongest constraint on derived model distribution functions was the requirement that the numbers of interpulses were exactly (within 1sigma errors) at the observed level of occurrences. We found that a suitable model distribution function for the inclination angle is the complicated trigonometric function which has two local maxima, one near 0 deg and the other near 90 deg. The former and the latter implies the right rates of IP occurrence. It is very unlikely that the pulsar beam deviates significantly from the circular cross-section. We found that the upper limit for the average beaming factor fb describing a fraction of the full sphere (called also beaming fraction) covered by a pulsar beam is about 10%. This implies that the number of the neutron stars in the Galaxy might be underestimated.

A full-sphere convection-driven dynamo: Implications for the ancient geomagnetic field

The solid inner core of the Earth formed at 2–3 Ga as a result of the gradual cooling of the Earth’s deep interior plays an essential role both energetically and dynamically, in the generation of the Earth’s present magnetic field. In the early stage of the Earth’s evolution, however, the entire core was made of molten liquid. Understanding convection-driven dynamo in a full sphere is hence of importance in elucidating the dynamics of the young Earth and its ancient magnetic field. We present a numerical convection and dynamo model for the full sphere using a finite element method. A large effort is made to efficiently parallelize the dynamo model so that it can take the full advantage of modern massively parallel computers. It is found that sustaining the full sphere dynamo – driven by convective flows in the absence of the tangent cylinder without imposing any boundary conditions at the center – is more difficult than that in spherical shells. Furthermore, the morphology of the magnetic field generated by the full sphere dynamo is largely dominated by non-dipolar components, indicating the structure of the ancient geomagnetic field prior to the onset of inner-core crystallization would be different from the current geomagnetic field.

Equatorially asymmetric convection inducing a hemispherical magnetic field in rotating spheres and implications for the past martian dynamo

Abstract The convective instability in a rapidly rotating, self-graviting sphere sets up in the form of equatorially symmetric, non-axisymmetric columnar vortices aligned with the rotation axis, carrying heat away in the cylindrical radial direction. In this study, we present numerical simulations of thermal convection and dynamo action driven by internal heating (intended to model a planetary core subject to uniform secular cooling) in a rotating sphere where, from the classical columnar convection regime, we find a spontaneous transition towards an unexpected and previously unobserved flow regime in which an equatorially antisymmetric, axisymmetric (EAA) mode strongly influences the flow. This EAA mode carries heat away along the rotation axis and is the nonlinear manifestation of the first linearly unstable axisymmetric mode. When the amplitude of the EAA mode reaches high enough values, we obtain hemispherical dynamos with one single hemisphere bearing more than 75% of the total magnetic energy at the surface of the rotating sphere. We perform the linear analysis of the involved convective modes and the nonlinear study of this hydrodynamic transition, with and without dynamo action, to obtain scaling laws for the regime boundaries. As secular cooling in a full sphere (i.e. without inner core) is a configuration which has probably been widespread in the early solar system in planetary cores, including the core of Mars, we discuss the possible implications of our results for the past martian dynamo.

Resonant oscillations of an inhomogeneous gas between concentric spheres

We investigate the effects of nonlinearity, geometry and stratification on the resonant motion of a gas contained between two concentric spheres. The emphasis is on whether the motion is continuous, and on how the inhomogeneity, geometry or nonlinearity can move the motion to a shocked state. Linear undamped theory yields a standing wave of arbitrary amplitude and an eigenvalue equation in which the higher eigenvalues are not integer multiples of the fundamental; the system is said to be dissonant. Higher modes, generated by the nonlinearity, are not resonant and consequently shocks may not form. When the output is shockless, the amplitude is two orders of magnitude greater than that of the input. When the eigenvalues for a homogeneous gas are not sufficiently dissonant and shocks form, the introduction of a stratification in the gas can restore dissonance and allow a continuous output. Similarly, the introduction of an inhomogeneity can change a continuous motion to a shocked one, as can an increase in the input Mach number, or an increase in the geometrical parameter. Various limits of the eigenvalue equation are considered and previous results for simpler geometries are recovered; e.g. a full sphere, a cone and a straight tube.

Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 90° phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1–14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1–4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1–20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a non-uniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface. Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity η′∼10 −8−10 −12 N s than those obtained from theoretical spin diffusion analysis where η′≤10 −18 N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity η′∼10 −8−10 −12 N s with a zero spin-velocity boundary condition at the outer wall predicts measureable flow, while simulations setting spin viscosity to zero ( η′ =0) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity ( η′ =0).

Dominant multipoles in WMAP5 mosaic data correlation maps

The method of correlation mapping on the full sphere is used to study the properties of the ILC map, as well as the dust and synchrotron background components. An anomalous correlation of the components with the ILC map in the main plane and in the poles of the ecliptic and equatorial coordinate systems was discovered. Apart from the bias, a dominant quadrupole contribution in the power spectrum of the mosaic correlation maps was found in the pixel correlation histogram. Various causes of the anomalous signal are discussed.

Reconstruction of the cosmic microwave background lensing forPlanck

<i>Aims. <i/>We prepare real-life cosmic microwave background (CMB) lensing extraction with the forthcoming <i>Planck<i/> satellite data by studying two systematic effects related to the foreground contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and the impact of removing a large contaminated region of the sky.<i>Methods. <i/>We first use the generalized morphological component analysis (GMCA) method to perform a component separation within a simplified framework, which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then restore them with a recently developed inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere.<i>Results. <i/>We find that the foreground residuals from the GMCA method does not significantly alter the lensed signal, which is also true for the mask corrected with the inpainting method, even in the presence of point source residuals.

An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere

The kinematic dynamo approximation describes the generation of magnetic field in a prescribed flow of electrically-conducting liquid. One of its main uses is as a proof-of-concept tool to test hypotheses about self-exciting dynamo action. Indeed, it provided the very first quantitative evidence for the possibility of the geodynamo. Despite its utility, due to the requirement of resolving fine structures, historically, numerical work has proven difficult and reported solutions were often plagued by poor convergence. In this paper, we demonstrate the numerical superiority of a Galerkin scheme in solving the kinematic dynamo eigenvalue problem in a full sphere. After adopting a poloidal–toroidal decomposition and expanding in spherical harmonics, we express the radial dependence in terms of a basis of exponentially convergent orthogonal polynomials. Each basis function is constructed from a terse sum of one-sided Jacobi polynomials that not only satisfies the boundary conditions of matching to an electrically insulating exterior, but is everywhere infinitely differentiable, including at the origin. This Galerkin method exhibits more rapid convergence, for a given problem size, than any other scheme hitherto reported, as demonstrated by a benchmark of the magnetic diffusion problem and by comparison to numerous kinematic dynamos from the literature. In the axisymmetric flows we consider in this paper, at a magnetic Reynolds number of O(100), a convergence of 9 significant figures in the most unstable eigenvalue requires only 40 radial basis functions; alternatively, 4 significant figures requires 20 radial functions. The terse radial discretization becomes particularly advantageous when considering flows whose associated numerical solution requires a large number of coupled spherical harmonics. We exploit this new method to confirm the tentatively proposed positive growth rate of the planar flow of Bachtiar et al. [4], thereby verifying a counter-example to the Zel’dovich anti-dynamo theorem in a spherical geometry.

Electrocatalysis at Microelectrodes: Geometrical Considerations

The influence of the shape of individual electrocatalytically active, axisymmetric particles supported on an inactive substrate, on the current associated with heterogeneous redox reactions involving solution-phase species has been examined theoretically. In agreement with previous work, the diffusion-limited currents, ilim, for a disk and supported truncated spheres of the same area including a full sphere are very similar (within ca. 10%). Large enhancements in the predicted values of ilim were found, however, for spheroids of the prolate type, as the aspect ratio was increased. Analyses of arrays of electrocatalytically active disks embedded in a planar inactive support in the presence of a diffusion boundary layer of well-defined thickness, for example, a rotating disk electrode, revealed that values of ilim very close to those expected for fully catalytic surfaces could be achieved for disk coverages on the order of 1%. Similar conclusions were made for corresponding arrays of small disks embedded in microdisks or spherical inactive supports in quiescent media. This effect might explain observations made for iron porphyrins adsorbed on graphite surfaces in aqueous electrolytes, for which the experimentally determined onset for oxygen reduction is found to be at potentials well ahead of the onset of the voltammetric wave associated with the conversion of the inactive (ferric) to the active (ferrous) form of the macrocycle.

Expanding the envelope: linking invertebrate bioturbators with micro-evolutionary change

Research on the influence of bioturbators has advanced considerably over the last decade. Their link to evolutionary change, especially their hypothesized role in the Cambrian explo- sion, has generated particular interest. This macro-evolutionary link, however, only partially reveals the role of bioturbators in evolution. A closer inspection of the literature shows that bioturbators may potentially play a greater role in this regard, especially at the micro-evolutionary scale, in which they indirectly influence the selective pressure on co-occurring species and, consequently, the evolution of novel morphologies, behavioural and social interactions. Such effects are absent in current think- ing, but need to be integrated in order to reveal the full sphere of influence of bioturbators.

Electrochemical treatment of tumors using a one-probe two-electrode device

We have recently shown that in the classical electrochemical treatment (EChT) of tumors, i.e., the passage of a direct electric current through two electrodes inserted locally in the tumor tissue, from an initial uniform condition two pH fronts evolve, expanding towards each other, inducing extreme pH changes and tumor destruction, mainly by necrosis. Here we extend these results introducing a one-probe two-electrode device (OPTED) containing the cathode and the anode very close to each other (1 mm). Experiments show that upon application of the OPTED-EChT, two half-spherical pH fronts, one basic and the other acid (from cathode and anode, respectively), expand towards the periphery configuring a distorted full sphere. Tracking of the pH front advance reveals a time scaling close to t 1/2, signature of a diffusion-controlled process. An analytic model presented allows the estimation of the time needed for total tumor destruction with a minimum compromise of healthy tissue. Main advantages of the OPTED are the insertion of one applicator rather than two or more (thus minimizing tissue intrusion, for instance, in the nervous system), the ability to reach tumors beyond capabilities of conventional surgery and the minimization of electric current circulation through the treated organ. We propose here this new design which could have significant implications in EChT optimal operative conditions, in particular, in the way in which the evolving pH spherical fronts can cover and destroy a cancer cell spherical casket.

A General Theorem on Angular-Momentum Changes due to Potential Vorticity Mixing and on Potential-Energy Changes due to Buoyancy Mixing

Abstract An initial zonally symmetric quasigeostrophic potential vorticity (PV) distribution qi(y) is subjected to complete or partial mixing within some finite zone |y| &amp;lt; L, where y is latitude. The change in M, the total absolute angular momentum, between the initial and any later time is considered. For standard quasigeostrophic shallow-water beta-channel dynamics it is proved that, for any qi(y) such that dqi/dy &amp;gt; 0 throughout |y| &amp;lt; L, the change in M is always negative. This theorem holds even when “mixing” is understood in the most general possible sense. Arbitrary stirring or advective rearrangement is included, combined to an arbitrary extent with spatially inhomogeneous diffusion. The theorem holds whether or not the PV distribution is zonally symmetric at the later time. The same theorem governs Boussinesq potential-energy changes due to buoyancy mixing in the vertical. For the standard quasigeostrophic beta-channel dynamics to be valid the Rossby deformation length LD ≫ εL where ε is the Rossby number; when LD = ∞ the theorem applies not only to the beta channel but also to a single barotropic layer on the full sphere, as considered in the recent work of Dunkerton and Scott on “PV staircases.” It follows that the M-conserving PV reconfigurations studied by those authors must involve processes describable as PV unmixing, or antidiffusion, in the sense of time-reversed diffusion. Ordinary jet self-sharpening and jet-core acceleration do not, by contrast, require unmixing, as is shown here by detailed analysis. Mixing in the jet flanks suffices. The theorem extends to multiple layers and continuous stratification. A least upper bound and greatest lower bound for the change in M is obtained for cases in which qi is neither monotonic nor zonally symmetric. A corollary is a new nonlinear stability theorem for shear flows.

Optimal loudspeaker placement for sound field reconstruction in geometrically constrained environments.

The design of loudspeaker arrays for holographic sound reproduction systems involves sampling a given aperture by a set of loudspeakers. For full sphere apertures it can be proven that there are only five equidistant sampling methods (given by the five regular polyhedrons) which only allows for arrays with up to 20 elements. For larger arrays, non-equidistant design methods such as t-design and Gaussian sampling have been proposed. However, in realistic environments it is generally not possible to place loudspeakers on the floor or on walls at certain locations. Furthermore, it is not desirable to have the loudspeakers constrained to spherical radii. This work shows a method for loudspeaker array design that allows for consideration of these special cases. The method relies on the decomposition of the sound field into a spatially orthonormal basis of spherical harmonics. A heuristic method is used to minimize the eigenvalue spread of the spherical harmonic matrix. The loudspeaker weights are found by calculating the generalized inverse of this matrix. Constraints on the speaker positions, highest reproduction mode, and number of loudspeakers are imposed in the minimization. The results of a design for a 16 speaker array in our acoustics laboratory are discussed.

A new Legendre-type polynomial and its application to geostrophic flow in rotating fluid spheres

In rapidly rotating spheres, the whole fluid column, extending from the southern to northern spherical boundary along the rotation axis, moves like a single fluid element, which is usually referred to as geostrophic flow. A new Legendre-type polynomial is discovered in undertaking the asymptotic analysis of geostrophic flow in spherical geometry. Three essential properties characterize the new polynomial: (i) it is a function of r and θ but takes a single argument , which is restricted by 0≤ r ≤1 and 0≤ θ ≤ π , where ( r , θ , ϕ ) denote spherical polar coordinates with θ =0 at the rotation axis; (ii) it is odd and vanishes at the axis of rotation θ =0, and (iii) it is defined within—and orthogonal over—the full sphere. As an example of its application, we employ the new polynomial in the asymptotic analysis of forced geostrophic flows in rotating fluid spheres for small Ekman and Rossby numbers. Fully numerical analysis of the same problem is also carried out, showing satisfactory agreement between the asymptotic solution and the numerical solution.