On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.

Shape design optimization of road acoustic barriers featuring top-edge devices by using Genetic Algotithms and Boundary Elements

[EN] This paper presents a Boundary Elements (BE) approach for the efficiency improvement of road acoustic barriers, mora specifically, for the shape design optimization of top-edge devices in the search for the best designs in terms of screening performance, usually represented by the insertion loss (IL).

3-D Boundary element-finite element method for the dynamic analysis of piled buildings.

[EN]A boundary element-finite element model is presented for the three-dimensional dynamic analysis of piled buildings in the frequency domain. Piles are modelled as compressible Euler-Bernoulli beams founded on a linear, isotropic, viscoelastic, zoned-homogeneous, unbounded layered soil, while multi-storey buildings are assumed to be comprised of vertical compressible piers and rigid slabs.

Application of evolutionary algorithms and the boundary element method in the optimization of noise barrier profiles

[EN]This Ph.D. thesis presents a general, robust methodology that may cover any type of 2D acoustic optimization problem. A procedure involving the coupling of Boundary Elements (BE) and Evolutionary Algorithms is proposed for systematic geometric modifications of road barriers that lead to designs with ever-increasing screening performance. Numerical simulations involving single- and multi-objective optimizations of noise barriers of varied nature are included in this document. results disclosed justify the implementation of this methodology by leading to optimal solutions of previously defined topologies that, in general, greatly outperform the acoustic efficiency of classical, widely used barrier designs normally erected near roads.

Tetrahedral mesh optimization combining boundary and inner node relocation and adaptive local refinement

[EN]This work introduces a new technique for tetrahedral mesh optimization. The procedure relocates boundary and inner nodes without changing the mesh topology. In order to maintain the boundary approximation while boundary nodes are moved, a local refinement of tetrahedra with faces on the solid boundary is necessary in some cases. New nodes are projected on the boundary by using a surface parameterization. In this work, the proposed method is applied to tetrahedral meshes of genus-zero solids that are generated by the meccano method. In this case, the solid boundary is automatically decomposed into six surface patches which are parameterized into the six faces of a cube with the Floater parameterization...

Modeling the gas and aqueous phase chemistry of the marine boundary layer

Ein eindimensionales numerisches Modell der maritimenGrenzschicht (MBL) wurde erweitert, um chemische Reaktionenin der Gasphase, von Aerosolpartikeln und Wolkentropfen zu beschreiben. Ein Schwerpunkt war dabei die Betrachtung derReaktionszyklen von Halogenen. Soweit Ergebnisse vonMesskampagnen zur Verfuegung standen, wurden diese zurValidierung des Modells benutzt. Die Ergebnisse von frueheren Boxmodellstudien konntenbestaetigt werden. Diese zeigten die saeurekatalysierteAktivierung von Brom aus Seesalzaerosolen, die Bedeutung vonHalogenradikalen fuer die Zerstoerung von O3, diepotentielle Rolle von BrO bei der Oxidation von DMS und dievon HOBr und HOCl in der Oxidation von S(IV). Es wurde gezeigt, dass die Beruecksichtigung derVertikalprofile von meteorologischen und chemischen Groessenvon grosser Bedeutung ist. Dies spiegelt sich darin wider,dass Maxima des Saeuregehaltes von Seesalzaerosolen und vonreaktiven Halogenen am Oberrand der MBL gefunden wurden.Darueber hinaus wurde die Bedeutung von Sulfataerosolen beidem aktiven Recyceln von weniger aktiven zu photolysierbarenBromspezies gezeigt. Wolken haben grosse Auswirkungen auf die Evolution und denTagesgang der Halogene. Dies ist nicht auf Wolkenschichtenbeschraenkt. Der Tagesgang der meisten Halogene ist aufgrundeiner erhoehten Aufnahme der chemischen Substanzen in die Fluessigphase veraendert. Diese Ergebnisse betonen dieWichtigkeit der genauen Dokumentation der meteorologischenBedingungen bei Messkampagnen (besonders Wolkenbedeckungsgrad und Fluessigwassergehalt), um dieErgebnisse richtig interpretieren und mit Modellresultatenvergleichen zu koennen. Dieses eindimensionale Modell wurde zusammen mit einemBoxmodell der MBL verwendet, um die Auswirkungen vonSchiffemissionen auf die MBL abzuschaetzen, wobei dieVerduennung der Abgasfahne parameterisiert wurde. DieAuswirkungen der Emissionen sind am staerksten, wenn sie insauberen Gebieten stattfinden, die Hoehe der MBL gering istund das Einmischen von Hintergrundluft schwach ist.Chemische Reaktionen auf Hintergrundaerosolen spielen nureine geringe Rolle. In Ozeangebieten mit schwachemSchiffsverkehr sind die Auswirkungen auf die Chemie der MBL beschraenkt. In staerker befahrenen Gebieten ueberlappensich die Abgasfahnen mehrerer Schiffe und sorgen fuerdeutliche Auswirkungen. Diese Abschaetzung wurde mitSimulationen verglichen, bei denen die Emissionen alskontinuierliche Quellen behandelt wurden, wie das inglobalen Chemiemodellen der Fall ist. Wenn die Entwicklungder Abgasfahne beruecksichtigt wird, sind die Auswirkungendeutlich geringer da die Lebenszeit der Abgase in der erstenPhase nach Emission deutlich reduziert ist.

Geological and Structural evolution of the Eurasia Africa plate boundary in the Gulf of Cadiz Central Eastern Atlantic Sea.

Iberia Africa plate boundary, cross, roughly W-E, connecting the eastern Atlantic Ocean from Azores triple junction to the Continental margin of Morocco. Relative movement between the two plate change along the boundary, from transtensive near the Azores archipelago, through trascurrent movement in the middle at the Gloria Fracture Zone, to transpressive in the Gulf of Cadiz area. This study presents the results of geophysical and geological analysis on the plate boundary area offshore Gibraltar. The main topic is to clarify the geodynamic evolution of this area from Oligocene to Quaternary. Recent studies have shown that the new plate boundary is represented by a 600 km long set of aligned, dextral trascurrent faults (the SWIM lineaments) connecting the Gloria fault to the Riff orogene. The western termination of these lineaments crosscuts the Gibraltar accretionary prism and seems to reach the Moroccan continental shelf. In the past two years newly acquired bathymetric data collected in the Moroccan offshore permit to enlighten the present position of the eastern portion of the plate boundary, previously thought to be a diffuse plate boundary. The plate boundary evolution, from the onset of compression in the Oligocene to the Late Pliocene activation of trascurrent structures, is not yet well constrained. The review of available seismics lines, gravity and bathymetric data, together with the analysis of new acquired bathymetric and high resolution seismic data offshore Morocco, allows to understand how the deformation acted at lithospheric scale under the compressive regime. Lithospheric folding in the area is suggested, and a new conceptual model is proposed for the propagation of the deformation acting in the brittle crust during this process. Our results show that lithospheric folding, both in oceanic and thinned continental crust, produced large wavelength synclines bounded by short wavelength, top thrust, anticlines. Two of these anticlines are located in the Gulf of Cadiz, and are represented by the Gorringe Ridge and Coral Patch seamounts. Lithospheric folding probably interacted with the Monchique – Madeira hotspot during the 72 Ma to Recent, NNE – SSW transit. Plume related volcanism is for the first time described on top of the Coral Patch seamount, where nine volcanoes are found by means of bathymetric data. 40Ar-39Ar age of 31.4±1.98 Ma are measured from one rock sample of one of these volcanoes. Analysis on biogenic samples show how the Coral Patch act as a starved offshore seamount since the Chattian. We proposed that compression stress formed lithospheric scale structures playing as a reserved lane for the upwelling of mantle material during the hotspot transit. The interaction between lithospheric folding and the hotspot emplacement can be also responsible for the irregularly spacing, and anomalous alignments, of individual islands and seamounts belonging to the Monchique - Madeira hotspot.

Detection and Modeling of Boundary Layer Height

This thesis tackles the problem of the automated detection of the atmospheric boundary layer (BL) height, h, from aerosol lidar/ceilometer observations. A new method, the Bayesian Selective Method (BSM), is presented. It implements a Bayesian statistical inference procedure which combines in an statistically optimal way different sources of information. Firstly atmospheric stratification boundaries are located from discontinuities in the ceilometer back-scattered signal. The BSM then identifies the discontinuity edge that has the highest probability to effectively mark the BL height. Information from the contemporaneus physical boundary layer model simulations and a climatological dataset of BL height evolution are combined in the assimilation framework to assist this choice. The BSM algorithm has been tested for four months of continuous ceilometer measurements collected during the BASE:ALFA project and is shown to realistically diagnose the BL depth evolution in many different weather conditions. Then the BASE:ALFA dataset is used to investigate the boundary layer structure in stable conditions. Functions from the Obukhov similarity theory are used as regression curves to fit observed velocity and temperature profiles in the lower half of the stable boundary layer. Surface fluxes of heat and momentum are best-fitting parameters in this exercise and are compared with what measured by a sonic anemometer. The comparison shows remarkable discrepancies, more evident in cases for which the bulk Richardson number turns out to be quite large. This analysis supports earlier results, that surface turbulent fluxes are not the appropriate scaling parameters for profiles of mean quantities in very stable conditions. One of the practical consequences is that boundary layer height diagnostic formulations which mainly rely on surface fluxes are in disagreement to what obtained by inspecting co-located radiosounding profiles.

Modelling the stable, nocturnal boundary layer: different approaches to turbulence closure problem

Il lavoro è dedicato all'analisi fisica e alla modellizzazione dello strato limite atmosferico in condizioni stabili. L'obiettivo principale è quello di migliorare i modelli di parametrizzazione della turbulenza attualmente utilizzati dai modelli meteorologici a grande scala. Questi modelli di parametrizzazione della turbolenza consistono nell' esprimere gli stress di Reynolds come funzioni dei campi medi (componenti orizzontali della velocità e temperatura potenziale) usando delle chiusure. La maggior parte delle chiusure sono state sviluppate per i casi quasi-neutrali, e la difficoltà è trattare l'effetto della stabilità in modo rigoroso. Studieremo in dettaglio due differenti modelli di chiusura della turbolenza per lo strato limite stabile basati su assunzioni diverse: uno schema TKE-l (Mellor-Yamada,1982), che è usato nel modello di previsione BOLAM (Bologna Limited Area Model), e uno schema sviluppato recentemente da Mauritsen et al. (2007). Le assunzioni delle chiusure dei due schemi sono analizzate con dati sperimentali provenienti dalla torre di Cabauw in Olanda e dal sito CIBA in Spagna. Questi schemi di parametrizzazione della turbolenza sono quindi inseriti all'interno di un modello colonnare dello strato limite atmosferico, per testare le loro predizioni senza influenze esterne. Il confronto tra i differenti schemi è effettuato su un caso ben documentato in letteratura, il "GABLS1". Per confermare la validità delle predizioni, un dataset tridimensionale è creato simulando lo stesso caso GABLS1 con una Large Eddy Simulation. ARPS (Advanced Regional Prediction System) è stato usato per questo scopo. La stratificazione stabile vincola il passo di griglia, poichè la LES deve essere ad una risoluzione abbastanza elevata affinchè le tipiche scale verticali di moto siano correttamente risolte. Il confronto di questo dataset tridimensionale con le predizioni degli schemi turbolenti permettono di proporre un insieme di nuove chiusure atte a migliorare il modello di turbolenza di BOLAM. Il lavoro è stato compiuto all' ISAC-CNR di Bologna e al LEGI di Grenoble.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Iodine speciation in atmospheric aerosols in the marine boundary layer

Iodine chemistry plays an important role in the tropospheric ozone depletion and the new particle formation in the Marine Boundary Layer (MBL). The sources, reaction pathways, and the sinks of iodine are investigated using lab experiments and field observations. The aims of this work are, firstly, to develop analytical methods for iodine measurements of marine aerosol samples especially for iodine speciation in the soluble iodine; secondly, to apply the analytical methods in field collected aerosol samples, and to estimate the characteristics of aerosol iodine in the MBL. Inductively Coupled Plasma – Mass Spectrometry (ICP-MS) was the technique used for iodine measurements. Offline methods using water extraction and Tetra-methyl-ammonium-hydroxide (TMAH) extraction were applied to measure total soluble iodine (TSI) and total insoluble iodine (TII) in the marine aerosol samples. External standard calibration and isotope dilution analysis (IDA) were both conducted for iodine quantification and the limits of detection (LODs) were both 0.1 μg L-1 for TSI and TII measurements. Online couplings of Ion Chromatography (IC)-ICP-MS and Gel electrophoresis (GE)-ICP-MS were both developed for soluble iodine speciation. Anion exchange columns were adopted for IC-ICP-MS systems. Iodide, iodate, and unknown signal(s) were observed in these methods. Iodide and iodate were separated successfully and the LODs were 0.1 and 0.5 μg L-1, respectively. Unknown signals were soluble organic iodine species (SOI) and quantified by the calibration curve of iodide, but not clearly identified and quantified yet. These analytical methods were all applied to the iodine measurements of marine aerosol samples from the worldwide filed campaigns. The TSI and TII concentrations (medians) in PM2.5 were found to be 240.87 pmol m-3 and 105.37 pmol m-3 at Mace Head, west coast of Ireland, as well as 119.10 pmol m-3 and 97.88 pmol m-3 in the cruise campaign over the North Atlantic Ocean, during June – July 2006. Inorganic iodine, namely iodide and iodate, was the minor iodine fraction in both campaigns, accounting for 7.3% (median) and 5.8% (median) in PM2.5 iodine at Mace Head and over the North Atlantic Ocean, respectively. Iodide concentrations were higher than iodate in most of the samples. In the contrast, more than 90% of TSI was SOI and the SOI concentration was correlated significantly with the iodide concentration. The correlation coefficients (R2) were both higher than 0.5 at Mace Head and in the first leg of the cruise. Size fractionated aerosol samples collected by 5 stage Berner impactor cascade sampler showed similar proportions of inorganic and organic iodine. Significant correlations were obtained in the particle size ranges of 0.25 – 0.71 μm and 0.71 – 2.0 μm between SOI and iodide, and better correlations were found in sunny days. TSI and iodide existed mainly in fine particle size range (< 2.0 μm) and iodate resided in coarse range (2.0 – 10 μm). Aerosol iodine was suggested to be related to the primary iodine release in the tidal zone. Natural meteorological conditions such as solar radiation, raining etc were observed to have influence on the aerosol iodine. During the ship campaign over the North Atlantic Ocean (January – February 2007), the TSI concentrations (medians) ranged 35.14 – 60.63 pmol m-3 among the 5 stages. Likewise, SOI was found to be the most abundant iodine fraction in TSI with a median of 98.6%. Significant correlation also presented between SOI and iodide in the size range of 2.0 – 5.9 μm. Higher iodate concentration was again found in the higher particle size range, similar to that at Mace Head. Airmass transport from the biogenic bloom region and the Antarctic ice front sector was observed to play an important role in aerosol iodine enhancement. The TSI concentrations observed along the 30,000 km long cruise round trip from East Asia to Antarctica during November 2005 – March 2006 were much lower than in the other campaigns, with a median of 6.51 pmol m-3. Approximately 70% of the TSI was SOI on average. The abundances of inorganic iodine including iodine and iodide were less than 30% of TSI. The median value of iodide was 1.49 pmol m-3, which was more than four fold higher than that of iodate (median, 0.28 pmol m-3). Spatial variation indicated highest aerosol iodine appearing in the tropical area. Iodine level was considerably lower in coastal Antarctica with the TSI median of 3.22 pmol m-3. However, airmass transport from the ice front sector was correlated with the enhance TSI level, suggesting the unrevealed source of iodine in the polar region. In addition, significant correlation between SOI and iodide was also shown in this campaign. A global distribution in aerosol was shown in the field campaigns in this work. SOI was verified globally ubiquitous due to the presence in the different sampling locations and its high proportion in TSI in the marine aerosols. The correlations between SOI and iodide were obtained not only in different locations but also in different seasons, implying the possible mechanism of iodide production through SOI decomposition. Nevertheless, future studies are needed for improving the current understanding of iodine chemistry in the MBL (e.g. SOI identification and quantification as well as the update modeling involving organic matters).

Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.