Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Screening the Structural Space of Bicyclo-DNA: Synthesis and Properties of Bicyclo-DNA Functionalized at C(6’)

The synthesis of a novel bicyclo-thymidine nucleoside bearing an ester functionality at C(6') (bc(alpha-alk)-nucleosides) is reported. This nucleoside was incorporated into oligodeoxynucleotides via solid phase phosphoramidite chemistry, and the ester moiety was post-synthetically converted to an amide or a carboxy group, or was left unchanged. Thermal melting data (T-m) with complementary DNA and RNA were collected and compared to natural DNA and to bc- and bc(ox)-DNA. It was found that single incorporations of bc(alpha-alk)-nucleosides in DNA duplexes were destabilizing by 0.5 to 2.5 degrees C/mod, whereas two consecutive bc(alpha-alk)-residues were less destabilizing, and in some cases even stabilizing by 0.5 degrees C/mod. In duplexes with complementary RNA, isolated bc(alpha-alk)-residues destabilized the duplex by -1.0 to -4.0 degrees C/mod, depending on the chemical nature of the substituent, whereas two consecutive modifications were only destabilizing by 0.3-1.0 degrees C/mod. The pairing selectivity was similar to that of unmodified or bc-DNA.

Brain injury in experimental neonatal meningitis due to group B streptococci

We have characterized the pattern of brain injury in a rat model of meningitis caused by group B streptococci (GBS). Infant rats (12-14 days old; n = 69) were infected intracisternally with 10 microliters of GBS (log10(2.3) to 4.5 colony-forming units). Twenty hours later, illness was assessed clinically and cerebrospinal fluid was cultured. Animals were either immediately euthanized for brain histopathology or treated with antibiotics and examined later. Early GBS meningitis was characterized clinically by severe obtundation and seizures, and histopathologically by acute inflammation in the subarachnoid space and ventricles, a vasculopathy characterized by vascular engorgement, and neuronal injury that was most prominent in the cortex and often followed a vascular pattern. Incidence of seizures, vasculopathy and neuronal injury correlated with the inoculum size (p < 0.01). Early injury was almost completely prevented by treatment with dexamethasone. Within days after meningitis, injured areas became well demarcated and showed new cellular infiltrates. Thirty days post-infection, brain weights of infected animals treated with antibiotics were decreased compared to uninfected controls (1.39 +/- 0.18 vs 1.64 +/- 0.1 g; p < 0.05). Thus, GBS meningitis in this model caused extensive cortical neuronal injury resembling severe neonatal meningitis in humans.

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Composition Space Analysis in the Development of Copper Molybdate Hybrids Decorated by a Bifunctional Pyrazolyl/1,2,4-Triazole Ligand

A bitopic ligand, 4-(3,5-dimethylpyrazol-4-yl)-1,2,4-triazole (Hpz-tr) (1), containing two different heterocyclic moieties was employed for the design of copper(II)–molybdate solids under hydrothermal conditions. In the multicomponent CuII/Hpz-tr/MoVI system, a diverse set of coordination hybrids, [Cu(Hpz-tr)2SO4]·3H2O (2), [Cu(Hpz-tr)Mo3O10] (3), [Cu4(OH)4(Hpz-tr)4Mo8O26]·6H2O (4), [Cu(Hpz-tr)2Mo4O13] (5), and [Mo2O6(Hpz-tr)]·H2O (6), was prepared and characterized. A systematic investigation of these systems in the form of a ternary crystallization diagram approach was utilized to show the influence of the molar ratios of starting reagents, the metal (CuII and MoVI) sources, the temperature, etc., on the reaction products outcome. Complexes 2–4 dominate throughout a wide crystallization range of the composition triangle, while the other two compounds 5 and 6 crystallize as minor phases in a narrow concentration range. In the crystal structures of 2–6, the organic ligand behaves as a short [N–N]-triazole linker between metal centers Cu···Cu in 2–4, Cu···Mo in 5, and Mo···Mo in 6, while the pyrazolyl function remains uncoordinated. This is the reason for the exceptional formation of low-dimensional coordination motifs: 1D for 2, 4, and 6 and 2D for 3 and 5. In all cases, the pyrazolyl group is involved in H bonding (H-donor/H-acceptor) and is responsible for π–π stacking, thus connecting the chain and layer structures in more complicated H-bonding architectures. These compounds possess moderate thermal stability up to 250–300 °C. The magnetic measurements were performed for 2–4, revealing in all three cases antiferromagnetic exchange interactions between neighboring CuII centers and long-range order with a net moment below Tc of 13 K for compound 4.

The Chemical Space Project

One of the simplest questions that can be asked about molecular diversity is how many organic molecules are possible in total? To answer this question, my research group has computationally enumerated all possible organic molecules up to a certain size to gain an unbiased insight into the entire chemical space. Our latest database, GDB-17, contains 166.4 billion molecules of up to 17 atoms of C, N, O, S, and halogens, by far the largest small molecule database reported to date. Molecules allowed by valency rules but unstable or nonsynthesizable due to strained topologies or reactive functional groups were not considered, which reduced the enumeration by at least 10 orders of magnitude and was essential to arrive at a manageable database size. Despite these restrictions, GDB-17 is highly relevant with respect to known molecules. Beyond enumeration, understanding and exploiting GDBs (generated databases) led us to develop methods for virtual screening and visualization of very large databases in the form of a “periodic system of molecules” comprising six different fingerprint spaces, with web-browsers for nearest neighbor searches, and the MQN- and SMIfp-Mapplet application for exploring color-coded principal component maps of GDB and other large databases. Proof-of-concept applications of GDB for drug discovery were realized by combining virtual screening with chemical synthesis and activity testing for neurotransmitter receptor and transporter ligands. One surprising lesson from using GDB for drug analog searches is the incredible depth of chemical space, that is, the fact that millions of very close analogs of any molecule can be readily identified by nearest-neighbor searches in the MQN-space of the various GDBs. The chemical space project has opened an unprecedented door on chemical diversity. Ongoing and yet unmet challenges concern enumerating molecules beyond 17 atoms and synthesizing GDB molecules with innovative scaffolds and pharmacophores.

Nitrogen dioxide exposures among a selected group of residents of substandard housing in Houston, Texas

Nitrogen dioxide (NO$\sb2)$ levels in sixteen substandard houses located in Houston, Texas were examined. The classification of the houses as substandard was based on an assessment of structural integrity which would affect air exchange rates. In these homes, unvented gas space heaters were operated as the primary source of heat.^ The Ogawa passive sampling device was used to measure NO$\sb2$ concentrations over 24 to 48-hour periods during generally cold weather. A sampler was placed in the kitchen and bedroom of each house. The female head of household was asked to wear a monitor during area monitoring to assess her personal exposure. Outdoor levels of NO$\sb2$ were also measured.^ Mean (standard deviation) levels of kitchen, bedroom and personal exposures were 280 (125) ppb, 256 (155) ppb and 164 (102) ppb, respectively. Additional short-term ($<$24 hours) samples were measured in three houses. The mean level of NO$\sb2$ measured outdoors was 51 ppb over the course of the study.^ The measurements obtained with the Ogawa sampler were compared to those levels obtained using a reference method (chemiluminescence). Outdoor levels measured with the diffusion samplers were 48% higher.^ These results suggest that wintertime NO$\sb2$ levels within substandard houses using gas appliances for heating and cooking are extremely elevated. Further work is needed to investigate the prevalence of possible health effects associated with these exposures. ^

Steps Ahead in the Few-Group CRoss-Section Library Generation at the Pin Level

There exists an interest in performing pin-by-pin calculations coupled with thermal hydraulics so as to improve the accuracy of nuclear reactor analysis. In the framework of the EU NURISP project, INRNE and UPM have generated an experimental version of a few group diffusion cross sections library with discontinuity factors intended for VVER analysis at the pin level with the COBAYA3 code. The transport code APOLLO2 was used to perform the branching calculations. As a first proof of principle the library was created for fresh fuel and covers almost the full parameter space of steady state and transient conditions. The main objective is to test the calculation schemes and post-processing procedures, including multi-pin branching calculations. Two library options are being studied: one based on linear table interpolation and another one using a functional fitting of the cross sections. The libraries generated with APOLLO2 have been tested with the pin-by-pin diffusion model in COBAYA3 including discontinuity factors; first comparing 2D results against the APOLLO2 reference solutions and afterwards using the libraries to compute a 3D assembly problem coupled with a simplified thermal-hydraulic model.

Training project management complexity in postgraduate and continuing education programs: a learning strategy in the eshe (European Space of Higher Education) framework

The objective of this paper is to address the methodological process of a teaching strategy for training project management complexity in postgraduate programs. The proposal is made up of different methods —intuitive, comparative, deductive, case study, problem-solving Project-Based Learning— and different activities inside and outside the classroom. This integration of methods motivated the current use of the concept of “learning strategy”. The strategy has two phases: firstly, the integration of the competences —technical, behavioral and contextual—in real projects; and secondly, the learning activity was oriented in upper level of knowledge, the evaluating the complexity for projects management in real situations. Both the competences in the learning strategy and the Project Complexity Evaluation are based on the ICB of IPMA. The learning strategy is applied in an international Postgraduate Program —Erasmus Mundus Master of Science— with the participation of five Universities of the European Union. This master program is fruit of a cooperative experience from one Educative Innovation Group of the UPM -GIE-Project-, two Research Groups of the UPM and the collaboration with other external agents to the university. Some reflections on the experience and the main success factors in the learning strategy were presented in the paper

Training project management complexity in postgraduate and continuing education programs: a learning strategy in the eshe (European Space of Higher Education) framework

The objective of this paper is to address the methodological process of a teaching strategy for training project management complexity in postgraduate programs. The proposal is made up of different methods —intuitive, comparative, deductive, case study, problem-solving Project-Based Learning— and different activities inside and outside the classroom. This integration of methods motivated the current use of the concept of ―learning strategy‖. The strategy has two phases: firstly, the integration of the competences —technical, behavioral and contextual—in real projects; and secondly, the learning activity was oriented in upper level of knowledge, the evaluating the complexity for projects management in real situations. Both the competences in the learning strategy and the Project Complexity Evaluation are based on the ICB of IPMA. The learning strategy is applied in an international Postgraduate Program —Erasmus Mundus Master of Science— with the participation of five Universities of the European Union. This master program is fruit of a cooperative experience from one Educative Innovation Group of the UPM -GIE-Project-, two Research Groups of the UPM and the collaboration with other external agents to the university. Some reflections on the experience and the main success factors in the learning strategy were presented in the paper.

A non-perturbative renormalization group study of the stochastic NavierStokes equation

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4−2 ɛ of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ɛ=2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ɛ dependence of the scaling dimension of the eddy diffusivity at ɛ=3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

Three decades of Space Activities at the Instituto Universitario de Microgravedad "Ignacio Da Riva" / Universidad Politécnica de Madrid (IDR/UPM) en History of Rocketry and Astronautics

Strictly speaking, space related activities at the Escuela Técnica Superior de Ingenieros Aeronáuticos (ETSIA) begun in 1973, when Prof. Ignacio Da Riva got a contract from the European Space Agency (ESA) to compile a handbook on spacecraft thermal control. By the same time, ESA issued an announcement of opportunities offering to the European scientific community the possibility of perform microgravity relevant experiments on board space platform like the European orbital laboratory Spacelab. Prof. Da Riva proposed one of the few selected experiments dealing with fluid physics under microgravity conditions, later flown on Spacelab-1 mission in 1983. These two events were the starting point where Prof. Da Riva, full professor of Aerodynamics at ETSIA, nucleated a small group of young professors and students located at the Laboratorio de Aerodinámica y Mecánica de Fluidos (LAMF) of ETSIA. Such group was leaded by Prof. Da Riva since its creation till 1991, when Prof. Da Riva died, and it was the seed of the more recently created research institute for aerospace science and technology named "Ignacio Da Riva" (IDR) in his honour. In this communication space related activities performed either at LAMF or IDR during the last three decades are briefly described.