Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.

Dirac type condition and Hamiltonian graphs

2010 Mathematics Subject Classification: 05C38, 05C45.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

Photoionization of Co+ and electron-impact excitation of Co2 + using the Dirac R-matrix method

Modelling of massive stars and supernovae (SNe) plays a crucial role in understanding galaxies. From this modelling we can derive fundamental constraints on stellar evolution, mass-loss processes, mixing, and the products of nucleosynthesis. Proper account must be taken of all important processes that populate and depopulate the levels (collisional excitation, de-excitation, ionization, recombination, photoionization, bound–bound processes). For the analysis of Type Ia SNe and core collapse SNe (Types Ib, Ic and II) Fe group elements are particularly important. Unfortunately little data is currently available and most noticeably absent are the photoionization cross-sections for the Fe-peaks which have high abundances in SNe. Important interactions for both photoionization and electron-impact excitation are calculated using the relativistic Dirac atomic R-matrix codes (DARC) for low-ionization stages of Cobalt. All results are calculated up to photon energies of 45 eV and electron energies up to 20 eV. The wavefunction representation of Co III has been generated using GRASP0 by including the dominant 3d⁷, 3d⁶[4s, 4p], 3p⁴3d⁹ and 3p⁶3d⁹ configurations, resulting in 292 fine structure levels. Electron-impact collision strengths and Maxwellian averaged effective collision strengths across a wide range of astrophysically relevant temperatures are computed for Co III. In addition, statistically weighted level-resolved ground and metastable photoionization cross-sections are presented for Co II and compared directly with existing work.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Eficacia de los métodos de reacondicionamiento de los brackets en relación a su resistencia a la tracción. Estudio in vitro

El reacondicionamiento de los brackets es una alternativa que trae consigo beneficios a la práctica ortodóncica. Por tal motivo el propósito de este estudio fue determinar la resistencia a la fuerza de tracción, de los métodos de reacondicionamiento, para ello se utilizó el Tensómetro Universal de fuerzas Z005 serie 157864 ( Zwick/Roell; BE, Alemania); con el mismo que se realizó el estudio in vitro y se obtuvo resultados que mostraron cual presentó mayor resistencia. La investigación se realizó con un total de 90 muestras, las mismas que se las dividieron en 3 grupos de 30 respectivamente. Los resultados de la prueba de tracción fueron los siguientes: grupo 1 (brackets nuevos) fue el grupo que tuvo mayor resistencia a la fuerza de tracción con una media de 11,32 MPa con una desviación estándar mínima de 10,51MPa y máxima de 12,26MPa, grupo 2 (brackets arenados) tuvo una resistencia a la fuerza de tracción de 8,36 MPa con una desviación estándar mínima de 7,20MPa y máxima de 9,49MPa y el grupo 3 (brackets flameados) tuvo una resistencia menor a la fuerza de tracción de 4,73MPa y una desviación estándar mínima de 3,37MPa y máxima de 5,84MPa. La resistencia a la fuerza de tracción de brackets nuevos y reacondicionados, mostró datos diferentes en cada grupos, los mismos que fueron estadísticamente significativos, teniendo un valor de p ≤ 0,05 y registró que el grupo de brackets arenados es el más resistente a la fuerza de tracción, referente a los dos métodos de reacondicionamiento; pero ninguno de los métodos de reacondicionamiento investigados se asemeja o supera a los valores que reporta los brackets nuevos.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Resistencia al desprendimiento de brackets utilizando peróxido de carbamida 10% antes del adhesivo en una técnica convencional de cementación de brackets

Resistencia al desprendimiento de brackets utilizando peróxido de carbamida 10% antes del adhesivo en una técnica convencional de cementación de brackets.

Cambios corticales en los dientes anteriores superiores e inferiores con Brackets convencionales, Damon y biofuncional QR en pacientes de trece a veinte y cuatro años

En el mercado existen varios sistemas de tratamiento en ortodoncia, los cuales deben ser estudiados para evitar que causen alteraciones en el periodonto, especialmente en los procesos alveolares corticales, por lo que el objetivo de este estudio fue conocer los cambios óseos alveolares, sean reabsorciones, aposiciones o ningún cambio óseo. Para realizar el estudio, se tomó como muestra tres sistemas de tratamiento: Sistema de Autoligado Damon, Sistema Biofuncional QR y Sistemas Convencionales Roth y MBT, estos brackets se aplicaron en 18 pacientes (seis de cada sistema), los cuales fueron sometidos a una tomografía antes del tratamiento y otra después de finalizada la etapa de alineación y nivelación. En los estudios tomográficos se realizaron trazados para medir en milímetros las corticales alveolares vestibulares, palatina y lingual, de los seis dientes anteriores superiores e inferiores, siendo la muestra total de 216 dientes. Para obtener los resultados del estudio, se ingresaron los datos recolectados en una hoja de cálculo Excel y procesados estadísticamente mediante el software SPSS versión 22, con las pruebas ANOVA y Tukey, obteniendo como resultados en el promedio de reabsorción ósea total p= 0,05 y con el Sistema Biofuncional QR una significancia de p= 0,025, en este último se demostró la presencia de aposición en la cortical lingual mandibular. Se concluyó que todos los sistemas de tratamiento causan reabsorciones óseas, siendo el Sistema Damon el de mayor reabsorción, seguido del Sistema convencional y luego el Sistema Biofuncional QR, produciendo este último una aposición estadísticamente significante. En los dientes anterosuperiores no existieron cambios óseos significativos y en los dientes anteroinferiores las mayores reabsorciones fueron en las piezas 42 y 32 y aposición en la pieza 41

Public awareness of “green” and “energy efficient” residential property : an empirical survey based on data from New Zealand

Purpose – The purpose of this paper is to examine the buyer awareness and acceptance of environmental and energy efficiency measures in the New Zealand residential property markets. This study aims to provide a greater understanding of consumer behaviour in the residential property market in relation to green housing issues ---------- Design/methodology/approach – The paper is based on an extensive survey of Christchurch real estate offices and was designed to gather data on the factors that were considered important by buyers in the residential property market. The survey was designed to allow these factors to be analysed on a socio-economic basis and to compare buyer behaviour based on property values. ---------- Findings – The results show that regardless of income levels, buyers still consider that the most important factor in the house purchase decision is the location of the property and price. Although the awareness of green housing issues and energy efficiency in housing is growing in the residential property market, it is only a major consideration for young and older buyers in the high income brackets and is only of some importance for all other buyer sectors of the residential property market. Many of the voluntary measures introduced by Governments to improve the energy efficiency of residential housing are still not considered important by buyers, indicating that a more mandatory approach may have to be undertaken to improve energy efficiency in the established housing market, as these measures are not valued by the buyer. ---------- Originality/value – The paper confirms the variations in real estate buyer behaviour across the full range of residential property markets and the acceptance and awareness of green housing issues and measures. These results would be applicable to most established and transparent residential property markets.

Development of the response coefficient-root function method for the transient vibration serviceability design of flat concrete floors

The vibration serviceability limit state is an important design consideration for two-way, suspended concrete floors that is not always well understood by many practicing structural engineers. Although the field of floor vibration has been extensively developed, at present there are no convenient design tools that deal with this problem. Results from this research have enabled the development of a much-needed, new method for assessing the vibration serviceability of flat, suspended concrete floors in buildings. This new method has been named, the Response Coefficient-Root Function (RCRF) method. Full-scale, laboratory tests have been conducted on a post-tensioned floor specimen at Queensland University of Technology’s structural laboratory. Special support brackets were fabricated to perform as frictionless, pinned connections at the corners of the specimen. A series of static and dynamic tests were performed in the laboratory to obtain basic material and dynamic properties of the specimen. Finite-element-models have been calibrated against data collected from laboratory experiments. Computational finite-element-analysis has been extended to investigate a variety of floor configurations. Field measurements of floors in existing buildings are in good agreement with computational studies. Results from this parametric investigation have led to the development of new approach for predicting the design frequencies and accelerations of flat, concrete floor structures. The RCRF method is convenient tool to assist structural engineers in the design for the vibration serviceability limit-state of in-situ concrete floor systems.

Performance load testing and structural adequacy evaluation of road bridge decks

Many ageing road bridges, particularly timber bridges, require urgent improvement due to the demand imposed by the recent version of the Australian bridge loading code, AS 5100. As traffic volume plays a key role in the decision of budget allocations for bridge refurbishment/ replacement, many bridges in low volume traffic network remain in poor condition with axle load and/ or speed restrictions, thus disadvantaging many rural communities. This thesis examines an economical and environmentally sensible option of incorporating disused flat rail wagons (FRW) in the construction of bridges in low volume, high axle load road network. The constructability, economy and structural adequacy of the FRW road bridge is reported in the thesis with particular focus of a demonstration bridge commissioned in regional Queensland. The demonstration bridge comprises of a reinforced concrete slab (RCS) pavement resting on two FRWs with custom designed connection brackets at regular intervals along the span of the bridge. The FRW-RC bridge deck assembly is supported on elastomeric rubber pads resting on the abutment. As this type of bridge replacement technology is new and its structural design is not covered in the design standards, the in-service structural performance of the FRW bridge subjected to the high axle loadings prescribed in AS 5100 is examined through performance load testing. Both the static and the moving load tests are carried out using a fully laden commonly available three-axle tandem truck. The bridge deck is extensively strain gauged and displacement at several key locations is measured using linear variable displacement transducers (LVDTs). A high speed camera is used in the performance test and the digital image data are analysed using proprietary software to capture the locations of the wheel positions on the bridge span accurately. The wheel location is thus synchronised with the displacement and strain time series to infer the structural response of the FRW bridge. Field test data are used to calibrate a grillage model, developed for further analysis of the FRW bridge to various sets of high axle loads stipulated in the bridge design standard. Bridge behaviour predicted by the grillage model has exemplified that the live load stresses of the FRW bridge is significantly lower than the yield strength of steel and the deflections are well below the serviceability limit state set out in AS 5100. Based on the results reported in this thesis, it is concluded that the disused FRWs are competent to resist high axle loading prescribed in AS 5100 and are a viable alternative structural solution of bridge deck in the context of the low volume road networks.

Sulfate intercalated layered double hydroxides prepared by the reformation effect

The removal of the sulfate anion from water using synthetic hydrotalcite (Mg/Al LDH) was investigated using powder x-ray diffraction (XRD) and thermogravimetric analysis (TG). Synthetic hydrotalcite Mg6Al2(OH)16(CO3)∙4H2O was prepared by the co-precipitation method from aluminum and magnesium chloride salts. The synthetic hydrotalcite was thermally activated to a maximum temperature of 380°C. Samples of thermally activated hydrotalcite where then treated with aliquots of 1000ppm sulfate solution. The resulting products where dried and characterized by XRD and TG. Powder XRD revealed that hydrotalcite had been successfully prepared and that the product obtained after treatment with sulfate solution also conformed well to the reference pattern of hydrotalcite. The d(003) spacing of all samples was found to be within the acceptable region for a LDH structure. TG revealed all products underwent a similar decomposition to that of hydrotalcite. It was possible to propose a reasonable mechanism for the thermal decomposition of a sulfate containing Mg/Al LDH. The similarities in the results may indicate that the reformed hydrotalcite may contain carbonate anion as well as sulfate. Further investigation is required to confirm this.