Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

The loop group and the cobar construction

"Vegeu el resum a l'inici del document del fitxer adjunt."

Estudio y diseño de filtros pasobanda y en banda dual basados en resonadores microstrip open-loop acoplados

El proyecto está dedicado al estudio y diseño de filtros paso-banda y en banda dual con tecnología microstrip mediante estructuras resonantes de tipo open-loop. Se ha llevado a cabo el diseño de un filtro paso-banda con respuesta Chebyshev, un filtro pasobanda con ceros de transmisión y un filtro de banda dual para WCDMA y WiFi, empleado el método de diseño para filtros basados en resonadores inter-acoplados. Se presentan los modelos eléctricos de los filtros de RF simulados junto con sus respectivos layouts y se comparan las respuestas obtenidas de los dispositivos con las respuestas ideales. En el proyecto se realiza un estudio del comportamiento de los diferentes tipos de acoplamiento entre resonadores open-loop en función de la geometría de la estructura. Las tendencias de comportamiento de los acoplamientos permiten el diseño y colocación de los resonadores para satisfacer las especificaciones del filtro.

Matching at one loop for the four-quark operators in NRQCD

The matching coefficients for the four-quark operators in NRQCD (NRQED) are calculated at one loop using dimensional regularization for ultraviolet and infrared divergences. The matching for the electromagnetic current follows easily from our results. Both the unequal and equal mass cases are considered. The role played by the Coulomb infrared singularities is explained in detail.

Loop bifurcation and magnetization rotation in exchange-biased Ni/FeF2

Exchange-biased Ni/FeF2 films have been investigated using vector coil vibrating-sample magnetometry as a function of the cooling field strength HFC . In films with epitaxial FeF2 , a loop bifurcation develops with increasing HFC as it divides into two sub-loops shifted oppositely from zero field by the same amount. The positively biased sub-loop grows in size with HFC until only a single positively shifted loop is found. Throughout this process, the negative and positive (sub)loop shifts maintain the same discrete value. This is in sharp contrast to films with twinned FeF2 where the exchange field gradually changes with increasing HFC . The transverse magnetization shows clear correlations with the longitudinal subloops. Interestingly, over 85% of the Ni reverses its magnetization by rotation, either in one step or through two successive rotations. These results are due to the single-crystal nature of the antiferromagnetic FeF2 , which breaks down into two opposite regions of large domains.

Particle orientation distribution in Y-Fe2O3magnetic tapes by Mössbauer and hysteresis loop measurements

The particle orientation in several Y-Fe2O3magnetic tapes has been quantitatively evaluated by using the data of both Mössbauer and hysteresis loop measurements performed in the three orthogonal directions. A texture function has been obtained as a development of real harmonics. The profile of the texture function gives the quality of the different magnetic tapes. A different degree of particle orientation at the surface of the tape is evidenced by means of conversion electron Mössbauer spectra.

Producció de biopolímers amb cultius bacterians mixtes. Comparació de tres reactors discontinus seqüencials (SBR) amb diferents condicions operacionals

La producció de biopolímers (polihidroxialcanoats (PHA) i substàncies polimèriques extracel·lulars (EPS)) a nivell industrial, resulta una nova àrea d’investigació que recull diverses disciplines, entre elles les Ciències Ambientals. Aquest projecte final de carrera amb el títol: “Producció de biopolímers amb cultius bacterians mixtes”, s’ha desenvolupat sota la supervisió de la directora de projecte Dra. María Eugenia Suárez Ojeda del Departament d’Enginyeria Química de la Universitat Autònoma de Barcelona (UAB) i s’ha dut a terme per l’estudiant Jordi Pérez i Forner de la Llicenciatura de Ciències Ambientals, Facultat de Ciències de la UAB, en el Departament d’Enginyeria Química de la mateixa universitat. L’objectiu d’aquest projecte ha estat produir biopolímers simultàniament amb l’eliminació de fòsfor i matèria orgànica en aigües residuals per obtenir un residu final amb un alt valor afegit. Aquests biopolímers reuneixen les característiques necessàries per a poder competir amb els plàstics convencionals i així, reduir l’elevat consum del petroli i la generació de residus no biodegradables. En aquest projecte s’ha dut a terme la posta en marxa d’un reactor discontinu seqüencial (SBR) per a l’acumulació de biopolímers amb cultius bacterians mixtes. Diferents investigadors han estudiat que aquests tipus de cultius bacterians arriben a nivells de fins el 53-97% [Pijuan et al., 2009] de contingut de biopolímers a la biomassa, sometent als microorganismes a diferents situacions d’estrés ja sigui per dèficit de nutrients o per variacions en les fases de feast-famine (festí-fam). Durant el projecte, s’ha realitzat el monitoratge del reactor alimentat amb una aigua sintètica, elaborada en el laboratori, amb les característiques d’un aigua residual provinent de la industria làctica. S’ha sotmès als microorganismes a diferents condicions operacionals, una d’elles amb limitació de fòsfor com a nutrient i una tercera condició amb una variació a les fases feast-famine. D’altra banda, com a segon objectiu, s’ha analitzat el contingut de biopolímers a la biomassa de dos SBRs més, del grup de recerca Bio-GLS del Departament d’Enginyeria Química de la UAB, alimentats amb diferents fonts de carboni, glicerol i àcids grassos de cadena llarga (AGCLL), per observar les influències que té el tipus de substrat en l’acumulació de biopolímers. Els resultats obtinguts en la primera part d’aquest projecte han estat similars als resultats d’altres investigadors [Pijuan et al., 2009; Guerrero et al., 2012]. S’ha determinat que sotmetre als microorganismes a situacions d’estrés té un efecte directe pel que fa a l’acumulació de biopolímers. També s’ha observat com al mateix temps que acumulaven aquests compostos, els microorganismes desenvolupaven la seva tasca de depurar l’aigua residual, obtenint al final del cicle una aigua amb un baix contingut en matèria orgànica i altres contaminants com amoni i fòsfor, en aquest cas. En la segona part del projecte, s’ha observat com el tipus de substrat té un efecte directe pel que fa a l’acumulació de biopolímers i també a l’activitat metabòlica dels microorganismes. Per tant, s’ha conclòs que la producció de biopolímers mitjançant la depuració d’aigües residuals es una via d’investigació molt prometedora pel que fa als resultats obtinguts. Alhora que es tracta un residu, s’obté una producte residual amb un alt valor afegit que pot ser utilitzat per la producció de bioplàstics 100% biodegradables.

Smith Predictor Sliding Mode Closed-loop Glucose Controller in Type 1 Diabetes

Type 1 diabetic patients depend on external insulin delivery to keep their blood glucose within near-normal ranges. In this work, two robust closed-loop controllers for blood glucose regulation are developed to prevent the life-threatening hypoglycemia, as well as to avoid extended hyperglycemia. The proposed controllers are designed by using the sliding mode control technique in a Smith predictor structure. To improve meal disturbance rejection, a simple feedforward controller is added to inject meal-time insulin bolus. Simulations scenarios were used to test the controllers, and showed the controllers ability to maintain the glucose levels within the safe limits in the presence of errors in measurements, modeling and meal estimation

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Sequentially aerated membrane biofilm reactors for autotrophic nitrogen removal: microbial community composition and dynamics

Membrane-aerated biofilm reactors performing autotrophic nitrogen removal can be successfully applied to treat concentrated nitrogen streams. However, their process performance is seriously hampered by the growth of nitrite oxidizing bacteria (NOB). In this work we document how sequential aeration can bring the rapid and long-term suppression of NOB and the onset of the activity of anaerobic ammonium oxidizing bacteria (AnAOB). Real-time quantitative polymerase chain reaction analyses confirmed that such shift in performance was mirrored by a change in population densities, with a very drastic reduction of the NOB Nitrospira and Nitrobacter and a 10-fold increase in AnAOB numbers. The study of biofilm sections with relevant 16S rRNA fluorescent probes revealed strongly stratified biofilm structures fostering aerobic ammonium oxidizing bacteria (AOB) in biofilm areas close to the membrane surface (rich in oxygen) and AnAOB in regions neighbouring the liquid phase. Both communities were separated by a transition region potentially populated by denitrifying heterotrophic bacteria. AOB and AnAOB bacterial groups were more abundant and diverse than NOB, and dominated by the r-strategists Nitrosomonas europaea and Ca. Brocadia anammoxidans, respectively. Taken together, the present work presents tools to better engineer, monitor and control the microbial communities that support robust, sustainable and efficient nitrogen removal

Protein loop compaction and the origin of the effect of arginine and glutamic acid mixtures on solubility, stability and transient oligomerization of proteins

Addition of a 50 mM mixture of l-arginine and l-glutamic acid (RE) is extensively used to improve protein solubility and stability, although the origin of the effect is not well understood. We present Small Angle X-ray Scattering (SAXS) and Nuclear Magnetic Resonance (NMR) results showing that RE induces protein compaction by collapsing flexible loops on the protein core. This is suggested to be a general mechanism preventing aggregation and improving resistance to proteases and to originate from the polyelectrolyte nature of RE. Molecular polyelectrolyte mixtures are expected to display long range correlation effects according to dressed interaction site theory. We hypothesize that perturbation of the RE solution by dissolved proteins is proportional to the volume occupied by the protein. As a consequence, loop collapse, minimizing the effective protein volume, is favored in the presence of RE.