A study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas

This thesis is a study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas externally biased with a magnetostatic field. The present study is restricted to the nonlinear phenomena rising from the interaction of electromagnetic waves in the ionized gas. The important effects of nonlinearity are wave-form distortion leads to cross modulation of one wave by a second amplitude-modulated wave.

The nonlinear effects are assumed to be small so that a perturbation method can be used. Boltzmann’s kinetic equation with an appropriate expression for the collision term is solved by expanding the electron distribution function into spherical harmonics in velocity space. In turn, the electron convection current density and the conductivity tensors of the nonlinear ionized gas are found from the distribution function. Finally, the expression for the current density and Maxwell’s equations are employed to investigate the effects of nonlinearity on the propagation of electromagnetic waves in the ionized gas, and also on the reflection of waves from an ionized gas of semi-infinite extent.

Propagação de ondas em teorias alternativas da gravitação

Uma forma de generalizar a teoria de Einstein da gravitação é incorporar na lagrangiana termos que dependem de escalares formados com os tensores de Ricci e Riemann, tais como (Ricci)2, ou (Riemann)2. Estas teorias tem sido estudadas intensamente nos últimos anos, já que elas podem ser usadas para descrever a expansão acelerada do universo no modelo cosmológico standard. Entre os desfios de modificar a teoria de Einstein, se encontra o de limitar a ambiguidade na escolha da dependência da lagrangiana com os escalares antes mencionados. A proposta desta dissertação é a de colocar limites sobre as possíveis lagrangianas impondo que as ondas (isto é, perturbações lineares) se propaguem no vácuo sem que apareça, shocks.

Uma dedução dos critérios de multicriticalidade e o cálculo de pontos tricríticos via otimização global

Uma dedução dos critérios de multicriticalidade para o cálculo de pontos críticos de qualquer ordem representa a formalização de ideias utilizadas para calcular pontos críticos e tricríticos e ainda amplia tais ideias. De posse desta dedução pode-se compreender os critérios de tricriticalidade e, com isso, através de uma abordagem via problema de otimização global pode-se fazer o cálculo de pontos tricríticos utilizando um método numérico adequado de otimização global. Para evitar um excesso de custo computacional com rotinas numéricas utilizou-se aproximações na forma de diferenças finitas dos termos que compõem a função objetivo. Para simular a relação P v - T optou-se pela equação de estado cúbica de Peng-Robinson e pela regra clássica de fluidos de van der Vaals, para modelagem do problema também se calculou os tensores de ordem 2, 3, 4 e 5 da função do teste de estabilidade. Os resultados obtidos foram comparados com dados experimentais e por resultados obtidos com outros autores que utilizaram métodos numéricos, equação de estado ou abordagem diferente das utilizadas neste trabalho.

DT-MRI data visualisation using the dual tree Complex Wavelet transform

In this paper a novel visualisation method for diffusion tensor MRI datasets is introduced. This is based on the use of Complex Wavelets in order to produce "stripy" textures which depict the anisotropic component of the diffusion tensors. Grey-scale pixel intensity is used to show the isotropic component. This paper also discusses enhancements of the technique for 3D visualisation. © 2004 IEEE.

Anisotropy preserving DTI processing

Statistical analysis of diffusion tensor imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of diffusion tensors). Building upon earlier studies exploiting a Riemannian framework to address these challenges, the present paper proposes a novel metric and an accompanying computational framework for DTI data processing. The proposed approach grounds the signal processing operations in interpolating curves. Well-chosen interpolating curves are shown to provide a computational framework that is at the same time tractable and information relevant for DTI processing. In addition, and in contrast to earlier methods, it provides an interpolation method which preserves anisotropy, a central information carried by diffusion tensor data. © 2013 Springer Science+Business Media New York.

Polarized Raman scattering studies of nonpolar a-plane GaN films grown on r-plane sapphire substrates by MOCVD

Nonpolar (1120) a-plane GaN thin films were grown on r-plane (1102) sapphire substrates by low-pressure metal organic chemical vapor deposition (MOCVD). The stress characteristics of the a-plane GaN films were investigated by means of polarized Raman scattering spectra in backscattering configurations. The experimental results show that there are strong anisotropic in-plane stresses within the epitaxial a-plane GaN films by calculating the corresponding stress tensors. The temperature dependence of Raman scattering spectra was studied in the range from 100 K to 550 K. The measurements reveal that the Raman phonon frequencies decrease with increasing temperature. The temperature at which nonpolar a-plane GaN films are strain free is discussed. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Biologically Inspired Tensor Features

According to the research results reported in the past decades, it is well acknowledged that face recognition is not a trivial task. With the development of electronic devices, we are gradually revealing the secret of object recognition in the primate's visual cortex. Therefore, it is time to reconsider face recognition by using biologically inspired features. In this paper, we represent face images by utilizing the C1 units, which correspond to complex cells in the visual cortex, and pool over S1 units by using a maximum operation to reserve only the maximum response of each local area of S1 units. The new representation is termed C1 Face. Because C1 Face is naturally a third-order tensor (or a three dimensional array), we propose three-way discriminative locality alignment (TWDLA), an extension of the discriminative locality alignment, which is a top-level discriminate manifold learning-based subspace learning algorithm. TWDLA has the following advantages: (1) it takes third-order tensors as input directly so the structure information can be well preserved; (2) it models the local geometry over every modality of the input tensors so the spatial relations of input tensors within a class can be preserved; (3) it maximizes the margin between a tensor and tensors from other classes over each modality so it performs well for recognition tasks and (4) it has no under sampling problem. Extensive experiments on YALE and FERET datasets show (1) the proposed C1Face representation can better represent face images than raw pixels and (2) TWDLA can duly preserve both the local geometry and the discriminative information over every modality for recognition.

海底金属矿床充水条件及矿坑突水的断层效应研究

The Xinli mine area of Sanshandao mine is adjacent to the Bohai Sea and its main exploitable ore deposit occurs in the undersea rock mass. The mine is the biggest undersea gold mine of China after production. The mine area faces a latent danger of water bursting, even sudden seawater inrush. There is no mature experience in undersea mining in China so far. The vein ore deposit is located in the lower wall of a fault; its possible groundwater sources mainly include bittern, Quaternary pore water and modern seawater. To ensure the safety of undersea mining, to survey the flooding conditions of the ore deposit using proper measures and study the potential seawater inrush pattern are the key technical problems. With the Xinli mine area as a case study, the engineering geological conditions of the Xinli mine area are surveyed in situ, the regional structural pattern and rock mass framework characteristics are found out, the distribution of the structural planes are modeled by a Monte Carlo method and the connectivity coefficients of rock mass structural planes are calculated. The regional hydro-geological conditions are analyzed and the in-situ hydro-geological investigation and sampling are performed in detail, the hydrochemistry and isotopes testing and groundwater dynamic monitoring are conducted, the recharge, runoff, discharge conditions are specified and the sources of flooding are distinguished. Some indices are selected from the testing results to calculate the proportion of each source in some water discharge points and in the whole water discharge of the Xinli mine area. The temporal and spatial variations of each water source of the whole ore deposit flooding are analyzed. According to the special project conditions in the Xinli mine area, the permeability coefficient tensors of the rock mass in Xinli mine area are calculated based on a fracture geometry measurement method, in terms of the connectivity and a few hydraulic testing results, a modified synthetic permeability coefficient are calculated. The hydro-geological conceptual and mathematical model are established，the water yield of mine is predicted using Visual Modflow code. The spreading law of surrounding rock mass deformation and secondary stress are studied by numerical analysis; the intrinsic mechanism of the faults slip caused by the excavation of ore deposit is analyzed. The results show that the development of surrounding rock mass deformation and secondary stress of vein ore deposit in the lower wall of a fault, is different from that in a thick-big ore deposit. The secondary stress caused by the excavation of vein ore deposit in the lower wall of a fault, is mainly distributed in the upper wall of the fault, one surface subsidence center will occur. The influences of fault on the rock mass movement, secondary stress and hydro-geological structures are analyzed; the secondary stress is blocked by the fault and the tensile stress concentration occurs in the rock mass near the fault, the original water blocking structure is destructed and the permeable structure is reconstructed, the primary structural planes begin to expand and newborn fissures occur, so the permeability of the original permeable structure is greatly enhanced, so the water bursting will probably occur. Based on this knowledge, the possible water inrush pattern and position of the Xinli mine area are predicted. Some computer programs are developed using object-oriented design method under the development platform Visual Studio.Net. These programs include a Monte Carlo simulation procedure, a joint diagrammatizing procedure, a structural planes connectivity coefficient calculating procedure, a permeability tensor calculating procedure, a water chemical formula edit and water source fixture conditions calculating procedure. A new computer mapping algorithm of joint iso-density diagram is raised. Based on the powerful spatial data management and icon functions of Geographic Information System, the pit water discharge dynamic monitoring data management information systems are established with ArcView.

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Uniaxial metallo-dielectric metamaterials with scalar positive permeability

The dispersion relation for plane waves in uniaxial metamaterials with indefinite dielectric tensors and scalar positive permeability is theoretically investigated. It is found, that the isofrequency surfaces of the plane extraordinary waves have a hyperbolic shape which allows the propagation of waves with infinitely long wave vectors. As an example a metallodielectric multilayer was considered and the dispersion relations were determined using an effective medium approximation and an analytically exact Bloch wave calculation. The extraordinary waves in this structure are identified as multilayer plasmons and the validity of the effective medium approximation is examined.

Experimental characterization of the nonlinear optical and magneto-optical properties of interfaces

An effective ellipsometric technique to determine parameters that characterize second-harmonic optical and magneto-optical effects in centrosymmetric media within the electric-dipole approximation is proposed and outlined in detail. The parameters, which are ratios of components of the nonlinear-surface-susceptibility tensors, are obtained from experimental data related to the state of polarization of the second-harmonic-generated radiation as a function of the angle between the plane of incidence and the polarization plane of the incident, linearly polarized, fundamental radiation. Experimental details of the technique are described. A corresponding theoretical model is given as an example for a single isotropic surface assuming polycrystalline samples. The surfaces of air-Au and air-Ni (in magnetized and demagnetized states) have been investigated ex situ in ambient air, and the results are presented. A nonlinear, least-squares-minimization fitting procedure between experimental data and theoretical formulas has been shown to yield realistic, unambiguous results for the ratios corresponding to each of the above materials. Independent methods for verifying the validity of the fitting parameters are also presented. The influence of temporal variations at the surfaces on the state of polarization (due to adsorption, contamination, or oxidation) is also illustrated for the demagnetized air-Ni surface. (C) 2005 Optical Society of America

Spin-Based Diagnostic of Nanostructure in Copper Phthalocyanine-C-60 Solar Cell Blends

Nanostructure and molecular orientation play a crucial role in determining the functionality of organic thin films. In practical devices, such as organic solar cells consisting of donor-acceptor mixtures, crystallinity is poor and these qualities cannot be readily determined by conventional diffraction techniques, while common microscopy only reveals surface morphology. Using a simple nondestructive technique, namely, continuous-wave electron paramagnetic resonance spectroscopy, which exploits the well-understood angular dependence of the g-factor and hyperfine tensors, we show that in the solar cell blend of C-60 and copper phthalocyanine (CuPc)-for which X-ray diffraction gives no information-the CuPc, and by implication the C-60, molecules form nanoclusters, with the planes of the CuPc molecules oriented perpendicular to the film surface. This information demonstrates that the current nanostructure in CuPc:C-60 solar cells is far from optimal and suggests that their efficiency could be considerably increased by alternative film growth algorithms.

On the anharmonic, multi-phonon, Debye-Waller contributions to the phonon-limited resistivity of metals : applications to Na and K

The anharmonic, multi-phonon (MP), and Oebye-Waller factor (OW) contributions to the phonon limited resistivity (;0) of metals derived by Shukla and Muller (1979) by the doubletime temperature dependent Green function method have been numerically evaluated for Na and K in the high temperature limit. The anharmonic contributions arise from the cubic and quartic shift of phonons (CS, QS), and phonon width (W) and the interference term (1). The QS, MP and OW contributions to I' are also derived by the matrix element method and the results are in agreement with those of Shukla and Muller (1979). In the high temperature limit, the contributions to;O from each of the above mentioned terms are of the type BT2 For numerical calculations suitable expressions are derived for the anharmonic contributions to ~ in terms of the third and fourth rank tensors obtained by the Ewald procedure. The numerical calculation of the contributions to;O from the OW, MP term and the QS have been done exactly and from the CS, Wand I terms only approximately in the partial and total Einstein approximations (PEA, TEA), using a first principle approach (Shukla and Taylor (1976)). The results obtained indicate that there is a strong pairwise cancellation between the: OW and MP terms, the QS and CS and the Wand I terms. The sum total of these contributions to;O for Na and K amounts to 4 to 11% and 2 to 7%, respectively, in the PEA while in the TEA they amount to 3 to 7% and 1 to 4%, respectively, in the temperature range.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

Geodynamics of the Andaman - Sumatra - Java Trench - Arc System Based on Gravity and Seismotectonic Study

This work aims to study the variation in subduction zone geometry along and across the arc and the fault pattern within the subducting plate. Depth of penetration as well as the dip of the Benioff zone varies considerably along the arc which corresponds to the curvature of the fold- thrust belt which varies from concave to convex in different sectors of the arc. The entire arc is divided into 27 segments and depth sections thus prepared are utilized to investigate the average dip of the Benioff zone in the different parts of the entire arc, penetration depth of the subducting lithosphere, the subduction zone geometry underlying the trench, the arctrench gap, etc.The study also describes how different seismogenic sources are identified in the region, estimation of moment release rate and deformation pattern. The region is divided into broad seismogenic belts. Based on these previous studies and seismicity Pattern, we identified several broad distinct seismogenic belts/sources. These are l) the Outer arc region consisting of Andaman-Nicobar islands 2) the back-arc Andaman Sea 3)The Sumatran fault zone(SFZ)4)Java onshore region termed as Jave Fault Zone(JFZ)5)Sumatran fore arc silver plate consisting of Mentawai fault(MFZ)6) The offshore java fore arc region 7)The Sunda Strait region.As the Seismicity is variable,it is difficult to demarcate individual seismogenic sources.Hence, we employed a moving window method having a window length of 3—4° and with 50% overlapping starting from one end to the other. We succeeded in defining 4 sources each in the Andaman fore arc and Back arc region, 9 such sources (moving windows) in the Sumatran Fault zone (SFZ), 9 sources in the offshore SFZ region and 7 sources in the offshore Java region. Because of the low seismicity along JFZ, it is separated into three seismogenic sources namely West Java, Central Java and East Java. The Sunda strait is considered as a single seismogenic source.The deformation rates for each of the seismogenic zones have been computed. A detailed error analysis of velocity tensors using Monte—Carlo simulation method has been carried out in order to obtain uncertainties. The eigen values and the respective eigen vectors of the velocity tensor are computed to analyze the actual deformation pattem for different zones. The results obtained have been discussed in the light of regional tectonics, and their implications in terms of geodynamics have been enumerated.ln the light of recent major earthquakes (26th December 2004 and 28th March 2005 events) and the ongoing seismic activity, we have recalculated the variation in the crustal deformation rates prior and after these earthquakes in Andaman—Sumatra region including the data up to 2005 and the significant results has been presented.ln this chapter, the down going lithosphere along the subduction zone is modeled using the free air gravity data by taking into consideration the thickness of the crustal layer, the thickness of the subducting slab, sediment thickness, presence of volcanism, the proximity of the continental crust etc. Here a systematic and detailed gravity interpretation constrained by seismicity and seismic data in the Andaman arc and the Andaman Sea region in order to delineate the crustal structure and density heterogeneities a Io nagnd across the arc and its correlation with the seismogenic behaviour is presented.