A Statistical Model of Current Loops and Magnetic Monopoles

We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we analyse this formula in the infinite volume limit and show that the local monopole density, free energy and entropy can be expressed in terms of well-known elliptic functions. Our technique is a novel determinantal formula for the partition function of a model of isolated vertices and loops for arbitrary graphs.

Beamforming correction for dipole measurement using two-dimensional microphone arrays

In this paper, a beamforming correction for identifying dipole sources by means of phased microphone array measurements is presented and implemented numerically and experimentally. Conventional beamforming techniques, which are developed for monopole sources, can lead to significant errors when applied to reconstruct dipole sources. A previous correction technique to microphone signals is extended to account for both source location and source power for two-dimensional microphone arrays. The new dipole-beamforming algorithm is developed by modifying the basic source definition used for beamforming. This technique improves the previous signal correction method and yields a beamformer applicable to sources which are suspected to be dipole in nature. Numerical simulations are performed, which validate the capability of this beamformer to recover ideal dipole sources. The beamforming correction is applied to the identification of realistic aeolian-tone dipoles and shows an improvement of array performance on estimating dipole source powers. © 2008 Acoustical Society of America.

Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.

Beta and gamma vibrational bands in deformed nuclei

Energies and relative intensities of gamma transitions in ¹⁵²Sm, ¹⁵²Gd, ¹⁵⁴Gd, ¹⁶⁶Er, and ²³²U following radioactive decay have been measured with a Ge(Li) spectrometer. A peak fitting program has been developed to determine gamma ray energies and relative intensities with precision sufficient to give a meaningful test of nuclear models. Several previously unobserved gamma rays were placed in the nuclear level schemes. Particular attention has been paid to transitions from the beta and gamma vibrational bands, since the gamma ray branching ratios are sensitive tests of configuration mixing in the nuclear levels. As the reduced branching ratios depend on the multipolarity of the gamma transitions, experiments were performed to measure multipole mixing ratios for transitions from the gamma vibrational band. In ¹⁵⁴Gd, angular correlation experiments showed that transitions from the gamma band to the ground state band were predominantly electric quadrupole, in agreement with the rotational model. In ²³²U, the internal conversion spectrum has been studied with a Si(Li) spectrometer constructed for electron spectroscopy. The strength of electric monopole transitions and the multipolarity of some gamma transitions have been determined from the measured relative electron intensities.

The results of the experiments have been compared with the rotational model and several microscopic models. Relative B(E2) strengths for transitions from the gamma band in ²³²U and ¹⁶⁶Er are in good agreement with a single parameter band mixing model, with values of z₂= 0.025(10) and 0.046(2), respectively. Neither the beta nor the gamma band transition strengths in ¹⁵²Sm and ¹⁵⁴Gd can be accounted for by a single parameter theory, nor can agreement be found by considering the large mixing found between the beta and gamma bands. The relative B(E2) strength for transitions from the gamma band to the beta band in ²³²U is found to be five times greater than the strength to the ground state band, indicating collective transitions with strength approximately 15 single particle units.

Dinâmica socioeconômica do município de Macaé/RJ: uma análise do mercado de trabalho formal após a quebra do monopólio na exploração do petróleo

Esta tese tem por objetivo analisar as transformações socioeconômicas, com ênfase na dinâmica do mercado de trabalho, que ocorreram no município de Macaé, principalmente após a promulgação da Lei n 9.478, de 06/08/1997. Esta lei acabou com o monopólio da petrobras no que concerne a prospecção de petróleo atraindo para a região inúmeras empresas multinacionais. A importância do estudo deste municípío se deve ao fato de Macaé exercer um importante papel economico na retomada do crescimento da economia do Estado do Rio de Janeiro em funçaõ da indústria petrolífera e seus impactos estarem além de suas fronteiras, repercurtindo em toda a região norte fluminense e municípios da baixada litorãnea. Outro aspecto abordado é a forma como a região norte fluminense sempre esteve ligada aos projetos de desenvolvimento de nosso país, principalmente no que diz respeito a políticas energéticas, como o proálcool e o petróleo. Macaé tornou-se um pólo econômico muito forte para o capital porém, as contradições do sistema capítalista caminham na mesma proporção que o dinheiro do petróleo, logo as desigualdades sociais despontam de maneira muito forte e o mercado de trabalho local reflete esta contradição.

The calculation of acoustic shielding of engine noise by the Silent Aircraft Airframe

The Silent Aircraft airframe has a flying wing design with a large wing planform and a propulsion system embedded in the rear of the airframe with intake on the upper surface of the wing. In the present paper, boundary element calculations are presented to evaluate acoustic shielding at low frequencies. Besides the three-dimensional geometry of the Silent Aircraft airframe, a few two-dimensional problems are considered that provide some physical insight into the shielding calculations. Mean flow refraction effects due to forward flight motion are accounted for by a simple time transformation that decouples the mean-flow and acoustic-field calculations. It is shown that significant amount of shielding can be obtained in the shadow region where there is no direct line of sight between the source and observer. The boundary element solutions are restricted to low frequencies. We have used a simple physically-based model to extend the solution to higher frequencies. Based on this model, using a monopole acoustic source, we predict at least an 18 dBA reduction in the overall sound pressure level of forward-propagating fan noise because of shielding.

Shell-model Hamiltonian from self-consistent mean-field model: N = Z nuclei

We propose a procedure to determine the effective nuclear shell-model Hamiltonian in a truncated space from a self-consistent mean-field model, e.g., the Skyrme model. The parameters of pairing plus quadrupole-quadrupole interaction with monopole force are obtained so that the potential energy surface of the Skyrme Hartree-Fock + BCS calculation is reproduced. We test our method for N = Z nuclei in the fpg- and sd-shell regions. It is shown that the calculated energy spectra with these parameters are in a good agreement with experimental data, in which the importance of the monopole interaction is discussed. This method may represent a practical way of defining the Hamiltonian for general shell-model calculations. (C) 2009 Elsevier B.V. All rights reserved.

Low-lying states of heavy nuclei within the nucleon pair approximation

In this article we perform systematic calculations on low-lying states of 33 nuclei with A=202-212, using the nucleon pair approximation of the shell model. We use a phenomenological shell-model Hamiltonian that includes single-particle energies, monopole and quadrupole pairing interactions, and quadrupole-quadrupole interactions. The building blocks of our model space include one J=4 valence neutron pair, and one J=4,6,8 valence proton pair, in addition to the usual S and D pairs. We calculate binding energies, excitation energies, electric quadrupole and magnetic dipole moments of low-lying states, and E2 transition rates between low-lying states. Our calculated results are reasonably consistent with available experimental data. The calculated quadrupole moments and magnetic moments, many of which have not yet been measured for these nuclei, are useful for future experimental measurements.

Isospin symmetry breaking at high spins in the mirror pair Se-67 and As-67

Recent experimental data have revealed large mirror energy differences (MED) between high-spin states in the mirror nuclei Se-67 and As-67, the heaviest pair where MED have been determined so far. The MED are generally attributed to the isospin symmetry breaking caused by the Coulomb force and by the isospin-nonconserving part of the nucleon-nucleon residual interaction. The different contributions of the various terms have been extensively studied in the fp shell. By employing large-scale shell-model calculations, we show that the inclusion of the g(9/2) orbit causes interference between the electromagnetic spin-orbit and the Coulomb monopole radial terms at high spin. The large MED are attributed to the aligned proton pair excitations from the p(3/2) and f(5/2) orbits to the g(9/2) orbit. The relation of the MED to deformation is discussed.

Medium-spin states in Ge-70 and the role of the g(9/2) orbital

Medium-spin states of Ge-70 have been studied via the Ni-60(C-12,2p gamma)Ge-70 reaction at 45 MeV. The ground-state band and the second 0(+) band have been extended to the 12(+) and 8(+) states, respectively. Two negative-parity bands, one of which has a coupled structure and the other has a decoupled structure, have been observed additionally. Although the latter decoupled structure was known up to the (21(-)) state from a previous experiment, the part of the level scheme up to the 15(-) state has been largely modified by the present experiment. Backbendings observed in the positive- and negative-parity yrast bands have been compared with those of the neighboring even Ge isotopes. The experimental level structure has been compared with the shell-model calculations in the model space (2p(3/2), 1f(5/2), 2(p1/2), 1g(9/2)) employing two kinds of effective interactions, one of which is an extended P + QQ interaction with monopole interactions and the other is developed from a renormalized G matrix. Microscopic structures of the observed bands have been discussed with the help of the shell-model calculations.

Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with an appropriate momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The trajectories lie on ellipses. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and extends to o(4,2). (c) 2010 Elsevier B.V. All rights reserved.

Relativistic Continuum Random Phase Approximation and Applications II. Applications

The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between the misachieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.

Mechanically tunable multiband compact quadrifilar helix antenna with dual mode operation

We show that by introducing a gap at the center of the helical sections (where the current is minimum) of a lambda/2 quadrifilar helix antenna (QHA) and varying the axial length and radial gap between the overlapping volutes, the antenna gives a 28% impedance bandwidth which is nine times the bandwidth of a conventional QHA. A 16% bandwidth with a front to back ratio of >= 14 dB is achievable with 5-14% reduction in the size of the QHA. The structure can yield a monopole radiation pattern suitable for terrestrial applications or a hemispherical pattern suitable for satellite use. The simulation results are validated by measurements at L-band.

Antennas for over-body-surface communication at 2.45 GHz

In this paper, the on-body performance of a range of wearable antennas was investigated by measuring vertical bar S-21 vertical bar path gain between two devices mounted on tissue-equivalent numerical and experimental phantoms, representative of human muscle tissue at 2.45 GHz. In particular, the study focused on the performance of a compact higher mode microstrip patch antenna (HMMPA) with a profile as low as lambda/20. The 5- and 10-mm-high HMMPA prototypes had an impedance bandwidth of 6.7% and 8.6%, respectively, sufficient for the operating requirements of the 2.45-GHz industrial, scientific, and medical (ISM) band and both antennas offered 11-dB higher path gain compared to a fundamental-mode microstrip patch antenna. It was also dernonstrated that a 7-dB improvement in path gain can be obtained for a fundamental-mode patch through the addition of a shortening wall. Notably, on-body HMMPA performance was comparable to a quarter wave monopole antenna on the same size of ground-plane, mounted normal to the tissue surface, indicating that the low-profile and physically more robust antenna is a promising solution for bodyworn antenna applications.

Lorentz TEM investigation of the switching behavior in artificial spin ice building blocks

Frustration – the inability to simultaneously satisfy all interactions – occurs in a wide range of systems including neural networks, water ice and magnetic systems. An example of the latter is the so called spin-ice in pyrochlore materials [1] which have attracted a lot of interest not least due to the emergence of magnetic monopole defects when the ‘ice rules’ governing the local ordering breaks down [2]. However it is not possible to directly measure the frustrated property – the direction of the magnetic moments – in such spin ice systems with current experimental techniques. This problem can be solved by instead studying artificial spin-ice systems where the molecular magnetic moments are replaced by nanoscale ferromagnetic islands [3-8]. Two different arrangements of the ferromagnetic islands have been shown to exhibit spin ice behaviour: a square lattice maintaining four moments at each vertex [3,8] and the Kagome lattice which has only three moments per vertex but equivalent interactions between them [4-7]. Magnetic monopole defects have been observed in both types of lattices [7-8]. One of the challenges when studying these artificial spin-ice systems is that it is difficult to arrive at the fully demagnetised ground-state [6-8].
Here we present a study of the switching behaviour of building blocks of the Kagome lattice influenced by the termination of the lattice. Ferromagnetic islands of nominal size 1000 nm by 100 nm were fabricated in five island blocks using electron-beam lithography and lift-off techniques of evaporated 18 nm Permalloy (Ni80Fe20) films. Each block consists of a central island with four arms terminated by a different number and placement of ‘injection pads’, see Figure 1. The islands are single domain and magnetised along their long axis. The structures were grown on a 50 nm thick electron transparent silicon nitride membrane to allow TEM observation, which was back-coated with a 5 nm film of Au to prevent charge build-up during the TEM experiments.
To study the switching behaviour the sample was subjected to a magnetic field strong enough to magnetise all the blocks in one direction, see Figure 1. Each block obeys the Kagome lattice ‘ice-rules’ of “2-in, 1-out” or “1-in, 2-out” in this fully magnetised state. Fresnel mode Lorentz TEM images of the sample were then recorded as a magnetic field of increasing magnitude was applied in the opposite direction. While the Fresnel mode is normally used to image magnetic domain structures [9] for these types of samples it is possible to deduce the direction of the magnetisation from the Lorentz contrast [5]. All images were recorded at the same over-focus judged to give good Lorentz contrast.
The magnetisation was found to switch at different magnitudes of the applied field for nominally identical blocks. However, trends could still be identified: all the blocks with any injection pads, regardless of placement and number, switched the direction of the magnetisation of their central island at significantly smaller magnitudes of the applied magnetic field than the blocks without injection pads. It can therefore be concluded that the addition of an injection pad lowers the energy barrier to switching the connected island, acting as a nucleation site for monopole defects. In these five island blocks the defects immediately propagate through to the other side, but in a larger lattice the monopoles could potentially become trapped at a vertex and observed [10].
References

[1] M J Harris et al, Phys Rev Lett 79 (1997) p.2554.
[2] C Castelnovo, R Moessner and S L Sondhi, Nature 451 (2008) p. 42.
[3] R F Wang et al, Nature 439 (2006) 303.
[4] M Tanaka et al, Phys Rev B 73 (2006) 052411.
[5] Y Qi, T Brintlinger and J Cumings, Phys Rev B 77 (2008) 094418.
[6] E Mengotti et al, Phys Rev B 78 (2008) 144402.
[7] S Ladak et al, Nature Phys 6 (2010) 359.
[8] C Phatak et al, Phys Rev B 83 (2011) 174431.
[9] J N Chapman, J Phys D 17 (1984) 623.
[10] The authors gratefully acknowledge funding from the EPSRC under grant number EP/D063329/1.