One of the key open problems in the field of theoretical fluid mechanics concerns the possibility of the singularity formation in solutions of the 3D Navier-Stokes system in finite time. This phenomenon is associated with the behaviour of the enstrophy, which is an L2 norm of the vorticity and must become unbounded if such a singularity occurs. Although there is no blow-up in the 2D Navier-Stokes equation, we would like to investigate how much enstrophy can a planar incompressible flow in a bounded domain produce given certain initial enstrophy. We address this issue by formulating an optimization problem in which the time derivative of the enstrophy serves as the objective functional and solve it using tools of the optimization theory and calculus of variations. We propose an efficient computational approach which is based on the iterative steepest-ascent procedure. In addition, we introduce an easy-to-implement method of computing the gradient of the objective functional. Finally, we present computational results addressing the key question of this project and provide numerical evidence that the maximum enstrophy growth exhibits the scaling dE/dt ~ C*E*E for C>0 and very small E. All computations are performed using the Chebyshev spectral method. / Thesis / Master of Science (MSc) / For many decades, scientists have been investigating fundamental aspects of the Navier-Stokes equation, a central mathematical model arising in fluid mechanics. Although the equation is widely used by engineers to describe numerous flow phenomena, it is still an open question whether the Navier-Stokes system always admits physically meaningful solutions. To address this issue, we want to explore its mathematical aspects deeper by analyzing the behaviour of the enstrophy, which is a quantity associated with the vorticity of the flow and a convenient measure of the regularity of the solution. In this study, we consider a planar and incompressible flow bounded by solid walls. Using basic tools of mathematical analysis and optimization theory, we propose a computational method enabling us to find out how much enstrophy can such a flow produce instantaneously. We present numerical evidence that this instantaneous growth of enstrophy has a well-defined asymptotic behavior, which is consistent with physical assumptions.

Yes / In this paper, a set of singular integral formulations are derived to calculate the surface impedance matrix on the antenna array elements. The proposed mathematical model enables electrodynamic analysis of antenna arrays designed using metamaterial-inspired structures. The formulations allow the determination of the array’s impedance, spatial and polarization characteristics at significantly low computational cost compared to conventional electromagnetic solvers based on method-of-moments (MoM) numerical technique. The accuracy of the surface impedance results obtained from the theoretical formulations are verified using the full wave EM software. It is shown that there is excellent agreement between the proposed formulations and EM software. The accuracy of the theoretical model presented is valid for single layer structures. / RTI2018-095499-B-C31, Funded by Ministerio de Ciencia, Innovación y Universidades, Gobierno de España (MCIU/AEI/FEDER,UE), and innovation programme under grant agreement H2020-MSCA-ITN-2016 SECRET-722424 and the financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/E022936/1

no / The African Youth Charter requires African countries to formulate and adopt an integrated national youth policy to address youth concerns. The United Nations Convention on the Rights of the Child and the African Children’s Charter also confer on children and young people the right to participate in matters that concern them. Therefore in the formulation and adoption of national youth policies the perspectives of young people need to be incorporated. This research examined how young people participated as strategic stakeholders in the formulation of Ghana’s youth policy. The paper presents a step-by-step analysis of the strategies used to involve young people in the formulation of the national youth policy of Ghana. Findings show that although young people had limited opportunities to participate in the formulation of the youth policy, they have been excluded from the implementation process. The paper concludes that the limited opportunities given to young people to participate in the formulation of the youth policy signifies a gradual drift towards youth engagement in the formulation of public policies in Ghana.

Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. Experiments on a convection-diffusion problem give promising results. / Master of Science

No / In the pharmaceutical field, current practice in gaining process understanding by data analysis or knowledge discovery has generally focused on dealing with single experimental databases. This limits the level of knowledge extracted in the situation where data from a number of sources, so called fractured data, contain interrelated information. This situation is particularly relevant for complex processes involving a number of operating variables, such as a fluid-bed granulation. This study investigated three data mining strategies to discover and integrate knowledge "hidden" in a number of small experimental databases for a fluid-bed granulation process using neurofuzzy logic technology. Results showed that more comprehensive domain knowledge was discovered from multiple databases via an appropriate data mining strategy. This study also demonstrated that the textual information excluded in individual databases was a critical parameter and often acted as the precondition for integrating knowledge extracted from different databases. Consequently generic knowledge of the domain was discovered, leading to an improved understanding of the granulation process.

Yes / There is a need to understand the nature of aggregation of cyclodextrins (CDs) with guest molecules in increasingly complex formulation systems. To this end an innovative application of Taylor dispersion analysis (TDA) and comparison with dynamic light scattering (DLS) have been carried out to probe the nature of ICT01-2588 (ICT-2588), a novel tumor-targeted vascular disrupting agent, in solvents including a potential buffered formulation containing 10% hydroxypropyl-β-cyclodextrin. The two hydrodynamic sizing techniques give measurement responses are that fundamentally different for aggregated solutions containing the target molecule, and the benefits of using TDA in conjunction with DLS are that systems are characterised through measurement of both mass- and z-average hydrodynamic radii. Whereas DLS measurements primarily resolve the large aggregates of ICT01-2588 in its formulation medium, methodology for TDA is described to determine the size and notably to quantify the proportion of monomers in the presence of large aggregates, and at the same time measure the formulation viscosity. Interestingly TDA and DLS have also distinguished between aggregate profiles formed using HP-β-CD samples from different suppliers. The approach is expected to be widely applicable to this important class of drug formulations where drug solubility is enhanced by cyclodextrin and other excipients.

Yes / Extensive research has demonstrated the potential effectiveness of curcumin against various diseases, including asthma and cancers. However, few studies have used liquid-based vehicles in the preparation of curcumin formulations. Therefore, the current study proposed the use of nanoemulsion and microsuspension formulations to prepare nebulised curcuminoid for lung delivery. Furthermore, this work expressed a new approach to understanding the aerosol performance of nanoparticles compared to microsuspension formulations. The genotoxicity of the formulations was also assessed. Curcuminoid nanoemulsion formulations were prepared in three concentrations (100, 250 and 500 µg/ml) using limonene and oleic acid as oil phases, while microsuspension solutions were prepared by suspending curcuminoid particles in isotonic solution (saline solution) of 0.02% Tween 80. The average fine particle fraction (FPF) and mass median aerodynamic diameter (MMAD) of the nebulised microsuspension formulations ranged from 26% and 7.1 µm to 40% and 5.7 µm, for 1000 µg/ml and 100 µg/ml respectively. In a comparison of the low and high drug concentrations of the nebulised nanoemulsion, the average FPF and MMAD of the nebulised nanoemulsion formulations prepared with limonene oil ranged from 50% and 4.6 µm to 45% and 5.6 µm, respectively; whereas the FPF and MMAD of the nebulised nanoemulsion prepared with oleic acid oil ranged from 46% and 4.9 µm to 44% and 5.6 µm, respectively. The aerosol performance of the microsuspension formulations were concentration dependent, while the nanoemulsion formulations did not appear to be dependent on the curcuminoids concentration. The performance and genotoxicity results of the formulations suggest the suitability of these preparations for further inhalation studies in animals.

Yes / Purpose: Dexibuprofen is an enantiomer of ibuprofen with low bioavailability which results from its hydrophobic nature. Nanosuspensions have developed a podium to solve the in vitro dissolution problem that frequently occurs in current research. Materials and methods: The drug and polymer solutions were mixed in a microchannel fluid reactor and the successive embryonic nanosuspension was decanted into a vial having the polymer solution. The impact of different process and formulation parameters including inlet angle, antisolvent and solvent flow rate(s), mixing time, drug concentration, polymer type and concentration was evaluated. Results and discussion: Stable dexibuprofen nanocrystals with a particle size of 45±3.0 nm and polydispersity index of 0.19±0.06 were obtained. Differential scanning calorimetry and powder X-ray diffraction confirmed the crystallinity. The key parameters observed were inlet angle 10°, antisolvent to solvent volume of 2.0/0.5 mL/min, 60 minutes mixing with 5 minutes sonication, Poloxamer-407 with a concentration of 0.5% w/v and drug concentration (5 mg/mm). The 60-day stability studies revealed that the nanocrystals were stable at 4°C and 25°C. The scanning electron microscopy and transmission electron microscopy images showed crystalline morphology with a homogeneous distribution. Conclusion: Stable dexibuprofen nanocrystals with retentive distinctive characteristics and having marked dissolution rate compared to raw and marketed formulations were efficiently fabricated. In future perspectives, these nanocrystals could be converted to solid dosage form and the process can be industrialized by chemical engineering approach

Ce travail apporte une contribution à la modélisation numérique du forgeage à chaud à grande vitesse. Dans ce cadre, une formulation dynamique partiellement explicite en accélération/pression est proposée. Tout d'abord, plusieurs formulations implicites vitesse/pression (quasi-statique et dynamique) sont présentées et discutées. Leur solution est considérée comme référence par la suite. La formulation dynamique partiellement explicite est ensuite présentée dans le contexte viscoplastique. La vitesse courante étant supposée connue, le traitement du comportement non-linéaire du matériau est évité. Ainsi, le système associé au problème est linéaire. La discrétisation éléments finis est basée sur le mini-élément P1 + /P1. Son application à une approche dynamique mixte accélération/pression est examinée et quelques approximations sont effectuées afin de simplifier la formulation. Cette nouvelle approche a été implémentée avec succès dans une version du code FORGE2. Des comparaisons avec les approches implicites de référence ont été réalisées pour des tests de traction et de compression et prouvent la pertinence de notre approche. Une amélioration concernant la perte de volume est constatée. De plus, une réduction du CPU d'au moins 20% est obtenue lorsque le même pas de temps est utilisé dans les cas implicite et partiellement explicite. La procédure est généralisée au cas élasto-viscoplastique. Afin de simplifier la résolution du problème, une nouvelle stratégie est explorée. Elle consiste à résoudre un système linéaire uniquement en pression. L'accélération est calculée ensuite explicitement en fonction de la pression. Les estimations réalisées nous font envisager des gains significatifs de temps de calcul en 2D et en 3D. La formulation partiellement explicite proposée représente donc une alternative pour la simulation du forgeage à chaud.

Le développement de vaccins à ARNm est en plein essor dans le domaine de la vaccinologie. Un des défis majeurs de ces approches est de parvenir à transporter et délivrer les ARNm dans le cytoplasme des cellules dendritiques (DC) pour permettre la production d’antigène et l’activation des réponses immunitaires.L’objectif de ce travail a porté sur la conception et l’évaluation de nouvelles stratégies de vectorisation des ARNm par des nanoparticules de poly(acide lactique) (NP-PLA). Une stratégie basée sur l’adsorption des ARNm à la surface des NP-PLA par l’intermédiaire du LAH4-L1, un peptide cationique amphipathique, a été développée. Des polyplexes formés suite à la condensation de l’ARNm par le LAH4-L1 ont été adsorbés sur les NP-PLA pour former des nanocomplexes. L’intérêt des polyplexes et nanocomplexes pour le ciblage des DC et l’activation des réponses immunitaires in vitro a été évalué. Dans des tests de transfection, ces formulations ont induit une expression efficace d’ARNm modèles dans des DC. La présence des NP-PLA dans les formulations semble favoriser l’expression des ARNm. Le traitement avec des inhibiteurs a révélé que les polyplexes et nanocomplexes semblent internalisés par phagocytose et endocytose clathrine-dépendante, et s’échappent des endosomes par un mécanisme dépendant de la pompe à protons v-ATPase. Suite à la transfection de DC dérivées de monocytes (moDC), nous avons montré que nos formulations stimulent les récepteurs de l’immunité innée et induisent une réponse pro-inflammatoire. Cette activation est associée à la maturation des moDC, à la présentation de peptides antigéniques sur le CMH-I et -II et à la sécrétion de cytokines et chémokines impliquées dans l’immunité adaptative. Ces données soulignent l’intérêt des NP-PLA associées au LAH4-L1 pour vectoriser des ARNm, cibler des DC et activer les réponses immunitaires. Dans le contexte du VIH-1, ce type de réponse pourrait aider le système immunitaire à contrôler la charge virale / MRNA-based vaccines currently raise a growing interest in vaccinology. However, the transport and delivery of mRNAs to DC cytoplasm in order to induce antigen production and immune responses remains challenging. The objective of this thesis concerns the design and evaluation of novel strategies to vectorize vaccine mRNAs by poly(lactic acid) nanoparticles (PLA-NPs). We developed a strategy based on mRNA adsorption onto PLA-NPs using, as intermediate, LAH4-L1, an amphipathic cationic peptide. To do this, mRNAs were condensed by LAH4-L1 to form polyplexes which was then adsorbed onto PLA-NPs in a second step to form nanocomplexes. The LAH4-L1/mRNA polyplexes and PLA-NP/LAH4-L1/mRNA nanocomplexes ability to target DCs and induce immune responses in vitro was evaluated. We showed that formulations induce an efficient transfection of mRNA in DCs in vitro. The addition of PLA-NPs in formulations seems to increase sustained expression of mRNAs. DC treatment by inhibitors revealed that polyplexes and nanocomplexes are taken up by phagocytosis and clathrin-dependent endocytosis, and escape endosomes by a v-ATPase-dependent mechanism. Transfection of monocyte-derived DCs (moDCs) showed that LAH4-L1/mRNA polyplexes and PLA-NP/LAH4-L1/mRNA nanocomplexes trigger innate-sensing activation with pro-inflammatory responses. This activation is associated with moDCs maturation, MHC-I and MHC-II presentation, and the secretion cytokines and chemokines involved in adaptive immunity.These data highlight the interest of these new platform formulations to vectorize mRNAs, target DCs and induce immune responses, which in the context of HIV-1, could help the immune system to control the viral load