The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Feature-point detection using distance transforms: Application to tracking tropical convective complexes

The identification, tracking, and statistical analysis of tropical convective complexes using satellite imagery is explored in the context of identifying feature points suitable for tracking. The feature points are determined based on the shape of complexes using the distance transform technique. This approach has been applied to the determination feature points for tropical convective complexes identified in a time series of global cloud imagery. The feature points are used to track the complexes, and from the tracks statistical diagnostic fields are computed. This approach allows the nature and distribution of organized deep convection in the Tropics to be explored.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Mineral and geochemical characterization of a leptic aluandic soil and a thapto aluandic-ferralsol developed on trachytes in Mount Bambouto (Cameroon volcanic line)

Mineral and geochemical investigations were carried out on soil samples and fresh rock (trachytes) from two selected soil profiles (TM profile on leptic aluandic soils and TL profile on thapto aluandic-ferralsols) from Mount Bambouto to better understand geochemical processes and mineral paragenesis involved in the development of soils in this environment. In TM profile, the hydrated halloysites and goethite occur in the weathered saprolite boulders of BC horizon while dehydrated halloysite, gibbsite and goethite dominate the soils matrices of BC and A horizons. In TL profile, the dehydrated halloysites and goethite are the most abundant secondary minerals in the weathered saprolites of C and BC horizons while gibbsite, hematite and kaolinite occur in the soil matrices of BC, B and A horizons. The highest gibbsite content is in the platy nodules of B horizon. In both soil profiles, organo-metal complexes (most likely of AI and Fe) are present in the surface A horizon. Geochemically, between the fresh rock and the weathered saprolites in both soils, SiO2, K2O, CaO, Na2O and MgO contents decrease strongly while Fe2O3 and Al2O3 tend to accumulate. The molar ratio of SiO2/Al2O3 (Ki) and the sum of Ca, Mg, K and Na ions (TRB) also decreases abruptly between fresh rocks and the weathered saprolites, but increases significantly at the soil surface. The TM profile shows intense Al enrichment whereas the TL profile highlights enrichment in both AI and Fe as the weathering progresses upwards. Both soil profiles are enriched in Ni, Cu, Ba and Co and depleted in U, Th, Ta, Hf, Y, Sr, Pb, Zr and Zn relative to fresh rock. They also show a relatively low fractionation of the rare earth elements (REE: La, Nd, Sm, Eu, Tb, Yb and Lu), except for Ce which tends to be enriched in soils compared to CI chondrite. All these results give evidence of intense hydrolysis at soil deep in Mount Bambouto resulting in the formation of halloysite which progressively transforms into gibbsite and/or dehydrated halloysite. At the soil surface, the prominent pedogenetic process refers to andosolization with formation of organo-metal complexes. In TL profile, the presence of kaolinite in soil matrices BC and B horizons is consistent with ferralitization at soil deep. In conclusion, soil forming processes in Mount Bambouto are strongly influenced by local climate: (i) in the upper mountain (>2000 m), the fresh, misty and humid climate favors andosolization; whereas (ii) in the middle lands (1700-2000 m) with a relatively dry climate, both andosolization at the soil surface and ferralitization at soil deep act together. (C) 2009 Elsevier B.V. All rights reserved.

Remote estimation of thermal inertia and soil heat flux for bare soil

A method is presented which allows thermal inertia (the soil heat capacity times the square root of the soil thermal diffusivity, C(h)rootD(h)), to be estimated remotely from micrometeorological observations. The method uses the drop in surface temperature, T-s, between sunset and sunrise, and the average night-time net radiation during that period, for clear, still nights. A Fourier series analysis was applied to analyse the time series of T-s . The Fourier series constants, together with the remote estimate of thermal inertia, were used in an analytical expression to calculate diurnal estimates of the soil heat flux, G. These remote estimates of C(h)rootD(h) and G compared well with values derived from in situ sensors. The remote and in situ estimates of C(h)rootD(h) both correlated well with topsoil moisture content. This method potentially allows area-average estimates of thermal inertia and soil heat flux to be derived from remote sensing, e.g. METEOSAT Second Generation, where the area is determined by the sensor's height and viewing angle. (C) 2003 Elsevier B.V. All rights reserved.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

Assessment of the consistency of near-infrared water vapor line intensities using high-spectral-resolution ground-based Fourier transform measurements of solar radiation

Calculations of the absorption of solar radiation by atmospheric gases, and water vapor in particular, are dependent on the quality of databases of spectral line parameters. There has been increasing scrutiny of databases such as HITRAN in recent years, but this has mostly been performed on a band-by-band basis. We report nine high-spectral-resolution (0.03 cm(-1)) measurements of the solar radiation reaching the surface in southern England over the wave number range 2000 to 12,500 cm(-1) (0.8 to 5 mm) that allow a unique assessment of the consistency of the spectral line databases over this entire spectral region. The data are assessed in terms of the modeled water vapor column that is required to bring calculations and observations into agreement; for an entirely consistent database, this water vapor column should be constant with frequency. For the HITRAN01 database, the spread in water vapor column is about 11%, with distinct shifts between different spectral regions. The HITRAN04 database is in significantly better agreement (about 5% spread) in the completely updated 3000 to 8000 cm(-1) spectral region, but inconsistencies between individual spectral regions remain: for example, in the 8000 to 9500 cm(-1) spectral region, the results indicate an 18% (+/- 1%) underestimate in line intensities with respect to the 3000 to 8000 cm(-1) region. These measurements also indicate the impact of isotopic fractionation of water vapor in the 2500 to 2900 cm(-1) range, where HDO lines dominate over the lines of the most abundant isotope of H2O.

Key features of the IPSL ocean atmosphere model and its sensitivity to atmospheric resolution

This paper presents the major characteristics of the Institut Pierre Simon Laplace (IPSL) coupled ocean–atmosphere general circulation model. The model components and the coupling methodology are described, as well as the main characteristics of the climatology and interannual variability. The model results of the standard version used for IPCC climate projections, and for intercomparison projects like the Paleoclimate Modeling Intercomparison Project (PMIP 2) are compared to those with a higher resolution in the atmosphere. A focus on the North Atlantic and on the tropics is used to address the impact of the atmosphere resolution on processes and feedbacks. In the North Atlantic, the resolution change leads to an improved representation of the storm-tracks and the North Atlantic oscillation. The better representation of the wind structure increases the northward salt transports, the deep-water formation and the Atlantic meridional overturning circulation. In the tropics, the ocean–atmosphere dynamical coupling, or Bjerknes feedback, improves with the resolution. The amplitude of ENSO (El Niño-Southern oscillation) consequently increases, as the damping processes are left unchanged.

The infrared vibration-rotation spectrum of trans and cis nitrous acid

Infrared spectra of the trans and the cis isomers of nitrous acid, both HONO and DONO, have been observed in the gas phase using a Fourier transform interferometer with a resolution of about 0.05 cm−1 from 4000 to 500 cm−1. Rotational analyses are reported on eleven of the fundamentals and some overtones.

The infrared spectrum, equilibrium structure and harmonic and anharmonic force field of thioborine, HBS

Infrared spectra of the two stretching fundamentals of both HBS and DBS have been observed, using a continuous flow system through a multiple reflection long path cell at a pressure around 1 Torr and a Nicolet Fourier Transform spectrometer with a resolution of about 0•1 cm-1. The v3 BS stretching fundamental of DBS, near 1140 cm-1, is observed in strong Fermi resonance with the overtone of the bend 2v2. The bending fundamental v2 has not been observed and must be a very weak band. The analysis of the results in conjunction with earlier work gives the equilibrium structure (re(BH) = 1•1698(12) , re(BS) = 1•5978(3) ) and the harmonic and anharmonic force field.

Intensities in the v7, v8 and v9 bands of CH2NH, and the harmonic force field of methyleneimine

A high resolution Fourier transform infrared spectrum of methyleneimine, HN=CH2, has been obtained in the gas phase in the region 700 to 1300 cm−1. The rovibrational line intensities of the three lowest fundamentals ν7 (A′), ν8 (A″), and ν9 (A″) have been simulated including all Coriolis interactions between the three bands, and by fitting the observed spectrum the relative signs and magnitudes of the vibrational transition moments have been determined. All of the available spectroscopic data have been used to determine the harmonic force field of methyleneimine.

Simultaneous analysis of v1, v4, 2v2, v2+v5, and 2v5 bands of 12CH3F

The Fourier-transform spectrum of CH3F from 2800 to 3100 cm−1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm−1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν1(A1), ν4(E), 2ν2(A1), ν2 + ν5(E), 2ν50(A1), and 2ν5±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm−1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.