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.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Understanding the two-component sensing System of virulent bacteria

Report for the scientific sojourn carried out at the l’ Institute for Computational Molecular Science of the Temple University, United States, from 2010 to 2012. Two-component systems (TCS) are used by pathogenic bacteria to sense the environment within a host and activate mechanisms related to virulence and antimicrobial resistance. A prototypical example is the PhoQ/PhoP system, which is the major regulator of virulence in Salmonella. Hence, PhoQ is an attractive target for the design of new antibiotics against foodborne diseases. Inhibition of the PhoQ-mediated bacterial virulence does not result in growth inhibition, presenting less selective pressure for the generation of antibiotic resistance. Moreover, PhoQ is a histidine kinase (HK) and it is absent in animals. Nevertheless, the design of satisfactory HK inhibitors has been proven to be a challenge. To compete with the intracellular ATP concentrations, the affinity of a HK inhibidor must be in the micromolar-nanomolar range, whereas the current lead compounds have at best millimolar affinities. Moreover, the drug selectivity depends on the conformation of a highly variable loop, referred to as the “ATP-lid, which is difficult to study by X-Ray crystallography due to its flexibility. I have investigated the binding of different HK inhibitors to PhoQ. In particular, all-atom molecular dynamics simulations have been combined with enhanced sampling techniques in order to provide structural and dynamic information of the conformation of the ATP-lid. Transient interactions between these drugs and the ATP-lid have been identified and the free energy of the different binding modes has been estimated. The results obtained pinpoint the importance of protein flexibility in the HK-inhibitor binding, and constitute a first step in developing more potent and selective drugs. The computational resources of the hosting institution as well as the experience of the members of the group in drug binding and free energy methods have been crucial to carry out this work.

New insights on the crystalline forms in binary systems of n-alkanes: Characterization of the solid ordered phases in the phase diagram tricosane + pentacosane

X-ray diffraction analyses of the pure components n-tricosane and n-pentacosane and of their binary mixed samples have enabled us to characterize the crystalline phases observed at low temperature. On the contrary to what was announced in literature on the structural behavior of mixed samples in odd-odd binary systems with D n = 2, the three domains are not all orthorhombic. This work has enabled us to show that two of the domains are, in fact, monoclinic, (Aa, Z = 4) and the other one is orthorhombic (Pca21, Z = 4). The conclusions drawn in this work can be easily transposed to other binary systems of n-alkanes.

Pairing in a two-component ultracold Fermi gas: Phases with broken-space symmetries

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li atoms trapped in two different hyperfine states.

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.

Potts fully frustrated model: Thermodynamics, percolation and dynamics in two dimensions

We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass transition in the high-temperature region. We show that the onset of these phenomena can be related to a thermodynamic transition. Furthermore, this transition can be mapped onto a percolation transition. We numerically study the phase diagram in two dimensions (2D) for this model with frustration and without disorder and we compare it to the phase diagram of (i) the model with frustration and disorder and (ii) the ferromagnetic model. Introducing a parameter that connects the three models, we generalize the exact expression of the ferromagnetic Potts transition temperature in 2D to the other cases. Finally, we estimate the dynamic critical exponents related to the Potts order parameter and to the energy.

Influence of an inert electrolyte on the morphology of quasi-two-dimensional electrodeposits

The influence of an inert electrolyte (sodium sulfate) on quasi-two-dimensional copper electrodeposition from a nondeaerated aqueous copper sulfate solution has been analyzed. The different morphologies for a fixed concentration of CuSO4 have been classified in a diagram in terms of the applied potential and the inert electrolyte concentration. The main conclusion is the extension of the well-known Ohmic model for the homogeneous growth regime for copper sulfate solutions with small amounts of sodium sulfate. Moreover, we have observed the formation of fingerlike deposits at large applied potential and inert electrolyte concentration values, before hydrogen evolution becomes the main electrode reaction.

Traveling waves and nonequilibrium stationary patterns in two-component reactive Langmuir monolayers

A simple kinetic model of a two-component phase-separating Langmuir monolayer with a chemical reaction is proposed. Its analysis and numerical simulations show that nonequilibrium periodic stationary structures and patterns of traveling stripes can spontaneously develop. The nonequilibrium phase diagram of this system is constructed and the properties of the patterns are discussed.

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

Un análisis comparativo del papel del bucle fonológico versus la agenda visoespacial en el cálculo en niños de 7-8 años = A comparative analysis of the phonological loop versus the visuo-spatial sketchpad in mental arithmetic tasks in 7-8 y.o. children

En esta investigación se ha estudiado la relación entre dos subsistemas de la memoria de trabajo (buclefonológico y agenda viso-espacial) y el rendimiento en cálculo con una muestra de 94 niños españolesde 7-8 años. Hemos administrado dos pruebas de cálculo diseñadas para este estudio y seis medidassimples de memoria de trabajo (de contenido verbal, numérico y espacial) de la «Batería de Testsde Memoria de Treball» de Pickering, Baqués y Gathercole (1999), y dos pruebas visuales complementarias.Los resultados muestran una correlación importante entre las medidas de contenido verbaly numérico y el rendimiento en cálculo. En cambio, no hemos encontrado ninguna relación con las medidasespaciales. Se concluye, por lo tanto, que en escolares españoles existe una relación importanteentre el bucle fonológico y el rendimiento en tareas de cálculo. En cambio, el rol de la agenda viso-espaciales nulo

Coexistence of Two Kinds of Fluorinated Hydrogenated Micelles as Building Blocks for the Design of Bimodal Mesoporous Silica with Two Ordered Mesopore Networks

A simple and effective route has been developed for the synthesis of bimodal (3.6 and 9.4 nm) mesoporous silica materials that have two ordered interconnected pore networks. Mesostructures have been prepared through the self assembly mechanism by using a mixture of polyoxyethylene fluoroalkyl ether and triblock copolymer as building block. The investigation of the RF8(EO)9/P123/water phase diagram evidences that in the considered surfactant range of concentrations, the system is micellar (L1). DLS measurements indicate that this micellar phase is composed of two types of micelles, the size of the first one at around 7.6 nm corresponds unambiguously to the pure fluorinated micelles. The second type of micelles at higher diameter consists of fluorinated micelles which have accommodated a weak fraction of P123 molecules. Thus, in this study the bimodal mesoporous silica are really templated by two kinds of micelles.