Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of 10^5, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing fromthe steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and another is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space rajectories.

Electrical and Optical Phase Transition Properties of Nano Vanadium Dioxide Thin Films

Nano-vanadium dioxide thin films were prepared through thermal annealing vanadium oxide thin films deposited by dual ion beam sputtering. The nano-vanadium dioxide thin films changed its state from semiconductor phase to metal phase through heating by homemade system. Four point probe method and Fourier transform infrared spectrum technology were employed to measure and anaylze the electrical and optical semiconductor-to-metal phase transition properties of nano-vanadium dioxide thin films, respectively. The results show that there is an obvious discrepancy between the semiconductor-to-metal phase transition properties of electrical and optical phase transition. The nano-vanadium dioxide thin films' phase transiton temperature defined by electrical phase transiton property is 63 degrees C, higher than that defined by optical phase transiton property at 5 mu m, 60 degrees C; and the temperature width of electrical phase transition duration is also wider than that of optical phase transiton duration. The semiconductor-to-metal phase transiton temperature defined by optical properties increases with increasing wavelength in the region of infrared wave band, and the occuring temperature of phase transiton from semiconductor to metal also increases with wavelength increasing, but the duration temperature width of transition decreases with wavelength increasing. The phase transition properties of nano-vanadium dioxide thin film has obvious relationship with wavelength in infrared wave band. The phase transition properties can be tuned through wavelength in infrared wave band, and the semiconductor-to-metal phase transition properties of nano vanadiium dioxide thin films can be better characterized by electrical property.

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

A study of velocity fields in the transition region of ε Eri (K2 V)

Analyses of the widths and shifts of optically thin emission lines in the ultraviolet spectrum of the active dwarf e Eri (K2 V) are presented. The spectra were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer. The linewidths are used to find the non-thermal energy density and its variation with temperature from the chromosphere to the upper transition region. The energy fluxes that could be carried by Alfvén and acoustic waves are investigated, to test their possible roles in coronal heating. Acoustic waves do not appear to be a viable means of coronal heating. There is, in principle, ample flux in Alfvén waves, but detailed calculations of wave propagation are required before definite conclusions can be drawn concerning their viability. The high sensitivity and spectral resolution of the above instruments have allowed two-component Gaussian fits to be made to the profiles of the stronger transition region lines. The broad and narrow components that result share some similarities with those observed in the Sun, but in e Eri the broad component is redshifted relative to the narrow component and contributes more to the total line flux. The possible origins of the two components and the energy fluxes implied are discussed. On balance our results support the conclusion of Wood, Linsky & Ayres, that the narrow component is related to Alfvén waves reaching to the corona, but the origin of the broad component is not clear.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Structural and morphological characterization of Pb1-xBaxTiO3 thin films prepared by chemical route: An investigation of phase transition

Detailed room temperature micro-Raman scattering, X-ray diffraction, atomic force microscopy and specular reflectance infrared Fourier transform spectroscopy studies were carried out on soft chemical by processed Pb1-xBaxTiO3 thin films. The micro-Raman spectra pointed the existence of a stable tetragonal ferroelectric phase in the entire composition range (0 < x <= 1). The infrared reflectance spectra showed that the frequency of several peaks decreases as the Ba2+ concentration increases. These features are correlated to a decrease in the tetragonal distortion of the TiO6 octahedra as the Ba2+ concentration increases. Furthermore, as x increases from 0.70 to 1.0, the Raman spectrum shows an evolution towards the well-known Raman spectrum of the tetragonal BaTiO3. Therefore, we demonstrated that the combination of solid solution PbTiO3-BaTiO3 with a grain size in the order of 30-40 nm supports the tetragonal ferroelectric phase at room temperature. (C) 2007 Elsevier B.V. All rights reserved.

Ab-initio determination of x-ray absorption near edge structure (xanes) spectra in an ultrasoft and norm conserving pseudopotentials scheme

X-ray absorption spectroscopy (XAS) is a powerful means of investigation of structural and electronic properties in condensed -matter physics. Analysis of the near edge part of the XAS spectrum, the so – called X-ray Absorption Near Edge Structure (XANES), can typically provide the following information on the photoexcited atom: - Oxidation state and coordination environment. - Speciation of transition metal compounds. - Conduction band DOS projected on the excited atomic species (PDOS). Analysis of XANES spectra is greatly aided by simulations; in the most common scheme the multiple scattering framework is used with the muffin tin approximation for the scattering potential and the spectral simulation is based on a hypothetical, reference structure. This approach has the advantage of requiring relatively little computing power but in many cases the assumed structure is quite different from the actual system measured and the muffin tin approximation is not adequate for low symmetry structures or highly directional bonds. It is therefore very interesting and justified to develop alternative methods. In one approach, the spectral simulation is based on atomic coordinates obtained from a DFT (Density Functional Theory) optimized structure. In another approach, which is the object of this thesis, the XANES spectrum is calculated directly based on an ab – initio DFT calculation of the atomic and electronic structure. This method takes full advantage of the real many-electron final wavefunction that can be computed with DFT algorithms that include a core-hole in the absorbing atom to compute the final cross section. To calculate the many-electron final wavefunction the Projector Augmented Wave method (PAW) is used. In this scheme, the absorption cross section is written in function of several contributions as the many-electrons function of the finale state; it is calculated starting from pseudo-wavefunction and performing a reconstruction of the real-wavefunction by using a transform operator which contains some parameters, called partial waves and projector waves. The aim of my thesis is to apply and test the PAW methodology to the calculation of the XANES cross section. I have focused on iron and silicon structures and on some biological molecules target (myoglobin and cytochrome c). Finally other inorganic and biological systems could be taken into account for future applications of this methodology, which could become an important improvement with respect to the multiscattering approach.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

Turbulent diffusion phase transition is due to singular energy spectrum.

The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion.

Developing the descriptions of landmark teaching styles : a spectrum inventory

Mosston & Ashworth‟s Spectrum of Teaching styles was first published in 1966 and is potentially the longest surviving model of teaching within the field of physical education. Its longevity and influence is surely testament to its value and influence. Many tools have also been developed through the years based on The Spectrum of Teaching Styles. In 2005 as part of a doctoral study, this tool was developed by the author, Dr Edwards and Dr Ashworth for researchers and teachers to identify which teaching styles were being utilised from The Spectrum when teaching physical education. It could also be utilised for self-assessment of the teaching styles and individual uses, or those who work with Physical Education Teacher Education courses. The development of this tool took approximately 4 months, numerous emails and meetings. This presentation will outline this process, along with the reasons why such a tool was developed and the differences between it and others like it.

Thermogravimetric analysis and hot stage Raman spectroscopy of cubic indium hydroxide

The transition of cubic indium hydroxide to cubic indium oxide has been studied by thermogravimetric analysis complimented with hot stage Raman spectroscopy. Thermal analysis shows the transition of In(OH)3 to In2O3 occurs at 219°C. The structure and morphology of In(OH)3 synthesised using a soft chemical route at low temperatures was confirmed by X-ray diffraction and scanning electron microscopy. A topotactical relationship exists between the micro/nano-cubes of In(OH)3 and In2O3. The Raman spectrum of In(OH)3 is characterised by an intense sharp band at 309 cm-1 attributed to ν1 In-O symmetric stretching mode, bands at 1137 and 1155 cm-1 attributed to In-OH δ deformation modes, bands at 3083, 3215, 3123 and 3262 cm-1 assigned to the OH stretching vibrations. Upon thermal treatment of In(OH)3 new Raman bands are observed at 125, 295, 488 and 615 cm-1 attributed to In2O3. Changes in the structure of In(OH)3 with thermal treatment is readily followed by hot stage Raman spectroscopy.

The experience of emotional expression in the context of social relations for people diagnosed with schizophrenia : a phenomenological explication

The experience of emotional expression in the context of social relations is not well understood for people diagnosed with schizophrenia. Early phenomenological research on the experience of people diagnosed with schizophrenia traditionally focussed on self experience in isolation from others, with later research explicating isolated aspects of self experience in relation to others. The current research aimed to focus on the progressive experience of emotional expression of people diagnosed with schizophrenia in relation to others over 12 months, in order to gain a broad spectrum of experience. This study involved unstructured interviews with 7 participants, an average of 4 times each, over a period of 12 months. Due to the unstructured nature of the interviews, a great breadth of experience was explicated. From the interviews there emerged 6 themes grouped together as a transition into, and 5 themes grouped together as a recovery from, symptoms associated with a diagnosis of schizophrenia. Special significance was given to the theme of relational confusion as an experience that provides an understanding of the relationship between social stressors and personal characteristics with responses that are associated with a diagnosis of schizophrenia. It was suggested that participants experienced themselves, including their distancing and isolating responses, as a part of a social system. The breadth of experiences that emerged afforded a framework of experiences within which prior phenomenological research findings on static moments of experience have been located. A more meaningful understanding of the transitioning into and recovery from the experiences associated with a diagnosis of schizophrenia will afford advances in mental health practice.

An application of near-infrared and mid-infrared spectroscopy to the study of natural halotrichites : halotrichite, apjohnite and wupatkiite

Near-infrared (NIR) and Fourier transform infrared (FTIR) spectroscopy have been used to determine the mineralogical character of isomorphic substitutions for Mg2+ by divalent transition metals Fe, Mn, Co and Ni in natural halotrichite series. The minerals are characterised by d-d transitions in NIR region 12000-7500 cm-1. NIR spectrum of halotrichite reveals broad feature from 12000 to 7500 cm-1 with a splitting of two bands resulting from ferrous ion transition 5T2g ® 5Eg. The presence of overtones of OH- fundamentals near 7000 cm-1 confirms molecular water in the mineral structure of the halotrichite series. The appearance of the most intense peak at around 5132 cm-1 is a common feature in the three minerals and is derived from combination of OH- vibrations of water molecules and 2 water bending modes. The influence of cations like Mg2+, Fe2+, Mn2+, Co2+, Ni2+ shows on the spectra of halotrichites. Especially wupatkiite-OH stretching vibrations in which bands are distorted conspicuously to low wave numbers at 3270, 2904 and 2454 cm-1. The observation of high frequency 2 mode in the infrared spectrum at 1640 cm-1 indicates coordination of water molecules is strongly hydrogen bonded in natural halotrichites. The splittings of bands in 3 and 4 (SO4)2- stretching regions may be attributed to the reduction of symmetry from Td to C2v for sulphate ion. This work has shown the usefulness of NIR spectroscopy for the rapid identification and classification of the halotrichite minerals.