A Mean-field statistical theory for the nonlinear Schrodinger equation

A statistical model of self-organization in a generic class of one-dimensional nonlinear Schrodinger (NLS) equations on a bounded interval is developed. The main prediction of this model is that the statistically preferred state for such equations consists of a deterministic coherent structure coupled with fine-scale, random fluctuations, or radiation. The model is derived from equilibrium statistical mechanics by using a mean-field approximation of the conserved Hamiltonian and particle number for finite-dimensional spectral truncations of the NLS dynamics. The continuum limits of these approximated statistical equilibrium ensembles on finite-dimensional phase spaces are analyzed, holding the energy and particle number at fixed, finite values. The analysis shows that the coherent structure minimizes total energy for a given value of particle number and hence is a solution to the NLS ground state equation, and that the remaining energy resides in Gaussian fluctuations equipartitioned over wavenumbers. Some results of direct numerical integration of the NLS equation are included to validate empirically these properties of the most probable states for the statistical model. Moreover, a theoretical justification of the mean-field approximation is given, in which the approximate ensembles are shown to concentrate on the associated microcanonical ensemble in the continuum limit.Comment: 24 pages, 2 figure

Understanding the nature of FRII optical nuclei: a new diagnostic plane for radio galaxies

We extend our study of the nuclei of 3CR FR II radio galaxies through HST optical images up to z=0.3. In the majority of them an unresolved nucleus (central compact core, CCC) is found. We analyze their position in the plane formed by the radio and optical nuclear luminosities in relation to their optical spectral properties. The broad-lined objects (BLO) have the brightest nuclei: they are present only at optical luminosities nu L_nu > 4 X 10^42 erg s^-1 which we suggest might represent a threshold in the radiative efficiency combined to a small range of black hole masses. About 40 % of the high and low excitation galaxies (HEG and LEG) show CCC which resemble those previously detected in FR I galaxies, in apparent contrast to the unification model. The equivalent width of the [OIII] emission line (with respect to the nuclear luminosity) reveals the nature of these nuclei, indicating that the nuclei of HEG are obscured to our line of sight and only scattered radiation is observed. This implies that the population of FR II is composed by objects with different nuclear properties, and only a fraction of them can be unified with quasars.Comment: 11 pages, 6 figures, in press on Astronomy & Astrophysics, minor changes have been mad

Discrete Velocity Fields with Explicitly Computable Lagrangian Law

We introduce a class of random velocity fields on the periodic lattice and in discrete time having a certain hidden Markov structure. The generalized Lagrangian velocity (the velocity field as viewed from the location of a single moving particle) has similar hidden Markov structure, and its law is found explicitly. Its rate of convergence to equilibrium is studied in small numerical examples and in rigorous results giving absolute and relative bounds on the size of the second–largest eigenvalue modulus. The effect of molecular diffusion on the rate of convergence is also investigated; in some cases it slows convergence to equilibrium. After repeating the velocity field periodically throughout the integer lattice, it is shown that, with the usual diffusive rescaling, the single–particle motion converges to Brownian motion in both compressible and incompressible cases. An exact formula for the effective diffusivity is given and numerical examples are shown

Frequency and Isostericity of RNA Base Pairs

Most of the hairpin, internal and junction loops that appear single-stranded in standard RNA secondary structures form recurrent 3D motifs, where non-WatsonCrick base pairs play a central role. Non-WatsonCrick base pairs also play crucial roles in tertiary contacts in structured RNA molecules. We previously classified RNA base pairs geometrically so as to group together those base pairs that are structurally similar (isosteric) and therefore able to substitute for each other by mutation without disrupting the 3D structure. Here, we introduce a quantitative measure of base pair isostericity, the IsoDiscrepancy Index (IDI), to more accurately determine which base pair substitutions can potentially occur in conserved motifs. We extract and classify base pairs from a reduced-redundancy set of RNA 3D structures from the Protein Data Bank (PDB) and calculate centroids (exemplars) for each base combination and geometric base pair type (family). We use the exemplars and IDI values to update our online Basepair Catalog and the Isostericity Matrices (IM) for each base pair family. From the database of base pairs observed in 3D structures we derive base pair occurrence frequencies for each of the 12 geometric base pair families. In order to improve the statistics from the 3D structures, we also derive base pair occurrence frequencies from rRNA sequence alignments

The first bent double lobe radio source in a known cluster filament: Constraints on the intra-filament medium

We announce the first discovery of a bent double lobe radio source (DLRS) in a known cluster filament. The bent DLRS is found at a distance of 3.4 Mpc from the center of the rich galaxy cluster, Abell~1763. We derive a bend angle alpha=25deg, and infer that the source is most likely seen at a viewing angle of Phi=10deg. From measuring the flux in the jet between the core and further lobe and assuming a spectral index of 1, we calculate the minimum pressure in the jet, (8.0+-3.2)x10^-13 dyn/cm^2, and derive constraints on the intra-filament medium (IFM) assuming the bend of the jet is due to ram pressure. We constrain the IFM to be between (1-20)x10^-29 gm/cm^3. This is consistent with recent direct probes of the IFM and theoretical models. These observations justify future searches for bent double lobe radio sources located several Mpc from cluster cores, as they may be good markers of super cluster filaments.Comment: 13 pages, 4 figures, accepted in ApJ Letter

Teorias políticas, justiça, exploração e cuidado

Este artigo aborda a omissão das teorias políticas tradicionais sobre os acordos e práticas sociais que delimitam as agentes e as atividades de cuidado ao âmbito do doméstico. Para tanto, o contrato de casamento é evocado, estabelecendo uma relação entre o mesmo e o baixo poder político atribuído às mulheres assim como a exploração de suas atividades para a produção de privilégios concedidos a certos grupos e, em especial, para os homens. O paradigma distributivo das teorias da justiça contemporâneas também é questionado e defende-se a necessidade de incluir discussões sobre gênero, poder e dominação no escopo destas teorias. Por fim, elementos oriundos das teorias do cuidado são apresentados para evidenciar o elevado grau de injustiça resultante da organização desigual das atividades de cuidado bem como de seus benefícios, tanto no doméstico quanto no espaço público. O intuito geral do artigo é o de prover elementos que apontem para a importância da da temática do cuidado para questões políticas e de justiça social

Biopoder e técnicas reprodutivas

A história das técnicas reprodutivas evidencia o que Foucault chamou de fazer viver e deixar morrer como uma estratégia das práticas políticas modernas. A biotecnologia em funcionamento no campo da reprodução humana disponibilizou técnicas centradas na fabricação, controle e manutenção da vida. Este artigo defenderá que as tecnologias reprodutivas não foram desenvolvidas para resolver questões de infertilidade, como anunciavam, mas para controlar os processos reprodutivos do corpo da mulher e, com isso, chegar a controlar aspectos populacionais variados. O artigo divide-se em seis partes. A primeira apresentará a noção foucaultiano de biopolítica, apontando para a centralidade da reprodução humana nesse tipo de política. A segunda parte apresentará o caminho histórico percorrido pelas pesquisas no campo da reprodução humana e a ênfase dada ao corpo de mulheres como campo de experimentação. A manipulação das vidas das mulheres com fins biopolíticos (reprodutivos) será abordada em seguida, ilustrada pelas políticas nacionais de natalidade de períodos pós-guerra. Na quarta parte do artigo, o tema da inseminação artificial será apresentado como um projeto que teve dificuldades de implementação por conta do potencial imaginativo (e prático) para mulheres interessadas em constituir família sem a presença de um homem. A fertilização in vitro será apresentada, em seguida, como elucidativa da visão objetificante dos cientistas em relação às mulheres e de um projeto de controle da reprodução feminina. Por fim, questionar-se-á as intenções das pesquisas reprodutivas feitas em nome do tratamento da infertilidade, relacionando-as com as variadas causas de infertilidade e os interesses do mercado

Collisional stability of fermionic Feshbach molecules

Using a Feshbach resonance, we create ultracold fermionic molecules starting from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly bound molecules provides a rich system for studying few-body collisions because of the variety of atomic collision partners for molecules; either bosonic, fermionic, or distinguishable atoms. Inelastic loss of the molecules near the Feshbach resonance is dramatically affected by the quantum statistics of the colliding particles and the scattering length. In particular, we observe a molecule lifetime as long as 100 ms near the Feshbach resonance.Comment: 4 pages, 4 figures, 1 tabl

The RNA Ontology (RNAO): An ontology for integrating RNA sequence and structure data

Biomedical Ontologies are intended to integrate diverse biomedical data to enable intelligent data-mining and facilitate translation of basic research into useful clinical knowledge. We present the first version of RNAO, an ontology for integrating RNA 3D structural, biochemical and sequence data. While each 3D data file depicts the structure of a specific molecule, such data have broader significance as representatives of classes of homologous molecules, which, while differing in sequence, generally share core structural features of functional importance. Thus, 3D structure data gain value by being linked to homologous sequences in genomic data and databases of sequence alignments. Likewise genomic data can increase in value by annotation of shared structural features, especially when these can be linked to specific functions. The RNAO is being developed in line with the developing standards of the Open Biomedical Ontologies (OBO) Consortium