Minimum-uncertaity states and pseudoclassical dynamics. II

The set of initial conditions for which the pseudoclassical evolution algorithm (and minimality conservation) is verified for Hamiltonians of degrees N (N>2) is explicitly determined through a class of restrictions for the corresponding classical trajectories, and it is proved to be at most denumerable. Thus these algorithms are verified if and only if the system is quadratic except for a set of measure zero. The possibility of time-dependent a-equivalence classes is studied and its physical interpretation is presented. The implied equivalence of the pseudoclassical and Ehrenfest algorithms and their relationship with minimality conservation is discussed in detail. Also, the explicit derivation of the general unitary operator which linearly transforms minimum-uncertainty states leads to the derivation, among others, of operators with a general geometrical interpretation in phase space, such as rotations (parity, Fourier).

Numerics of Spacecraft Dynamics

Whenever a spacecraft is launched it is essential that the algorithms in the on-board software systems and at ground control are efficient and reliable over extended periods of time. Geometric numerical integrators, and in particular variational integrators, have both these characteristics. In "Numerics of Spacecraft Dynamics" new numerical integrators are presented and analysed in depth. These algorithms have been designed specifically for the dynamics of spacecraft and artificial satellites in Earth orbits. Full analytical solutions to a class of integrable deformations of the two-body problem in classical mechanics are derived, and a systematic method to compute variational integrators to arbitrary order with a computer algebra system is introduced.

Study of nuclear receptor dynamics by BRET

Les récepteurs nucléaires (RN) sont des facteurs de transcription ligand dépendants qui contrôlent une grande variété de processus biologiques de la physiologie humaine, ce qui a fait d'eux des cibles pharmacologiques privilégiées pour de nombreuses maladies. L'un de ces récepteurs, le récepteur de l’œstrogène alpha (ERα), peut activer la prolifération cellulaire dans certaines sections de l'épithélium mammaire tandis qu’un autre, le récepteur de l'acide rétinoïque alpha (RARα), peut provoquer un arrêt de la croissance et la différenciation cellulaire. La signalisation de ces deux récepteurs peut être altérée dans le cancer du sein, contribuant à la tumorigénèse mammaire. L’activité d’ERα peut être bloquée par les anti-oestrogènes (AE) pour inhiber la prolifération des cellules tumorales mammaires. Par contre, l’activation des voies de RARα avec des rétinoïdes dans un contexte clinique a rencontré peu de succès. Ceci pourrait résulter du manque de spécificité des ligands testés pour RARα et/ou de leur activité seulement dans certains sous-types de tumeurs mammaires. Puisque les récepteurs nucléaires forment des homo- et hétéro-dimères, nous avons cherché à développer de nouveaux essais pharmacologiques pour étudier l'activité de complexes dimériques spécifiques, leur dynamique d’association et la structure quaternaire des récepteurs des œstrogènes. Nous décrivons ici une nouvelle technique FRET, surnommée BRET avec renforcement de fluorescence par transferts combinés (BRETFect), qui permet de détecter la formation de complexes de récepteurs nucléaires ternaires. Le BRETFect peut suivre l'activation des hétérodimères ERα-ERβ et met en évidence un mécanisme allostérique d'activation que chaque récepteur exerce sur son partenaire de dimérisation. L'utilisation de BRETFect en combinaison avec le PCA nous a permis d'observer la formation de multimères d’ERα fonctionnels dans des cellules vivantes pour la première fois. La formation de multimères est favorisée par les AE induisant la dégradation du récepteur des oestrogènes, ce qui pourrait contribuer à leurs propriétés spécifiques. Ces essais de BRET apportent une nette amélioration par rapport aux tests de vecteurs rapporteur luciférase classique, en fournissant des informations spécifiques aux récepteurs en temps réel sans aucune interférence par d'autres processus tels que la transcription et de la traduction. L'utilisation de ces tests nous a permis de caractériser les propriétés de modulation de l’activité des récepteurs nucléaires d’une nouvelle classe de molécules hybrides qui peuvent à la fois lier ERa ou RAR et inhiber les HDACs, conduisant au développement de nouvelles molécules prometteuses bifonctionnelles telles que la molécule hybride RAR-agoniste/HDACi TTNN-HA.

Self-organized sociopolitical interactions as the best way to achieve organized patterns in human social systems: going beyond the top-down control of classical political regimes

La monografía presenta la auto-organización sociopolítica como la mejor manera de lograr patrones organizados en los sistemas sociales humanos, dada su naturaleza compleja y la imposibilidad de las tareas computacionales de los regímenes políticos clásico, debido a que operan con control jerárquico, el cual ha demostrado no ser óptimo en la producción de orden en los sistemas sociales humanos. En la monografía se extrapola la teoría de la auto-organización en los sistemas biológicos a las dinámicas sociopolíticas humanas, buscando maneras óptimas de organizarlas, y se afirma que redes complejas anárquicas son la estructura emergente de la auto-organización sociopolítica.

Dynamics of convectively driven banded jets in the laboratory

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L(4) and L(5), we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (delta lambda, delta pi) = (+/- 60 degrees, -/+ 120 degrees), where delta lambda is the difference in mean longitudes and delta pi is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as similar to 0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.

Sequence diversity and evolutionary dynamics of the dimorphic antigen merozoite surface protein-6 and other Msp genes of Plasmodium falciparum

Immune evasion by Plasmodium falciparum is favored by extensive allelic diversity of surface antigens. Some of them, most notably the vaccine-candidate merozoite surface protein (MSP)-1, exhibit a poorly understood pattern of allelic dimorphism, in which all observed alleles group into two highly diverged allelic families with few or no inter-family recombinants. Here we describe contrasting levels and patterns of sequence diversity in genes encoding three MSP-1-associated surface antigens of P. falciparum, ranging from an ancient allelic dimorphism in the Msp-6 gene to a near lack of allelic divergence in Msp-9 to a more classical multi-allele polymorphism in Msp-7 Other members of the Msp-7 gene family exhibit very little polymorphism in non-repetitive regions. A comparison of P. falciparum Msp-6 sequences to an orthologous sequence from P. reichenowi provided evidence for distinct evolutionary histories of the 5` and 3` segments of the dimorphic region in PfMsp-6, consistent with one dimorphic lineage having arisen from recombination between now-extinct ancestral alleles. In addition. we uncovered two surprising patterns of evolution in repetitive sequence. Firsts in Msp-6, large deletions are associated with (nearly) identical sequence motifs at their borders. Second, a comparison of PfMsp-9 with the P. reichenowi ortholog indicated retention of a significant inter-unit diversity within an 18-base pair repeat within the coding region of P. falciparum, but homogenization in P. reichenowi. (C) 2009 Elsevier B.V. All rights reserved.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

Classical simulation of deposition of thiophene oligomers on TiO(2)-anatase: Relevance of long-range electrostatic interactions

We performed classical molecular dynamics simulations of the vapor-deposition of alpha-T4 oligomers on the TiO(2)-anatase (101) surface, comparing different sets of charges associated with the atoms of the model. The potential energy surfaces for alpha-T4 and TiO(2) were described by re-parametrizations of the Universal force field with charges given by the charge equilibration (QEq) scheme, or with fixed charges obtained by an ab initio method using the Hirshfeld partition. The two sets of charges lead to completely different results for the interface formation, and for the characteristics of the organic film, with a clearly defined alpha-T4 contact layer in the QEq case, and a more homogeneous molecular distribution when using Hirshfeld charges. The main reason for the discrepancy was found to be the incorrect charge assignment given by QEq to the sulfur and alpha-carbon atoms in thiophenes, and highlight the relevance of long-range interactions in the organization of molecular films. (C) 2009 Elsevier B.V. All rights reserved.

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

DYNAMICS AT INFINITY of A CUBIC CHUA'S SYSTEM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evolutionary dynamics of heterochromatin in the genome of Dichotomius beetles based on chromosomal analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Growth and reproductive dynamics of the South American red shrimp, Pleoticus muelleri (Crustacea: Solenoceridae), from the southeastern coast of Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)