Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory

A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent with the energy density is found to be well described by a quadratic power law.Comment: REVTeX, 9 pages, 4 PostScript figures include

Programmed buckling by controlled lateral swelling in a thin elastic sheet

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure

A Comprehensive Mechanism Reproducing the Mass and Mixing Parameters of Quarks and Leptons

It is shown that if, from the starting point of a universal rank-one mass matrix long favoured by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only 6 real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles $\theta_{12}, \theta_{13}, \theta_{23}$ in $\nu$-oscillation, and the masses $m_c, m_\mu, m_e$) agree well with experiment, mostly to within experimental errors; 4 others ($m_s, m_u, m_d, m_{\nu_2}$), the experimental values for which can only be inferred, agree reasonably well; while 2 others ($m_{\nu_1}, \delta_{CP}$ for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass $m_{\nu_R}$ and (ii) the strong CP angle $\theta$ inherent in QCD. One notes in particular that the output value for $\sin^2 2 \theta_{13}$ from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit 2 new testable constraints: (i) that $\theta_{23}$ must depart from its "maximal" value: $\sin^2 2 \theta_{23} \sim 0.935 \pm 0.021$, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only $|\sin \delta_{CP}| \leq 0.31$ if not vanishing altogether.Comment: 37 pages, 1 figur

Interface mediated interactions between particles -- a geometrical approach

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any "smallness" assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy based approach.Comment: 18 pages, 7 figures, REVTeX4 style; final version, as appeared in Phys. Rev. E. Compared to v2 several minor mistakes, as well as one important minus sign in Eqn. (18a) have been cured. Compared to v1, this version is significantly extended: Lipid tilt degrees of freedom for membranes are included in the stress framework, more technical details are given, estimates for the magnitude of forces are mad

Geometry of the energy landscape of the self-gravitating ring

We study the global geometry of the energy landscape of a simple model of a self-gravitating system, the self-gravitating ring (SGR). This is done by endowing the configuration space with a metric such that the dynamical trajectories are identified with geodesics. The average curvature and curvature fluctuations of the energy landscape are computed by means of Monte Carlo simulations and, when possible, of a mean-field method, showing that these global geometric quantities provide a clear geometric characterization of the collapse phase transition occurring in the SGR as the transition from a flat landscape at high energies to a landscape with mainly positive but fluctuating curvature in the collapsed phase. Moreover, curvature fluctuations show a maximum in correspondence with the energy of a possible further transition, occurring at lower energies than the collapse one, whose existence had been previously conjectured on the basis of a local analysis of the energy landscape and whose effect on the usual thermodynamic quantities, if any, is extremely weak. We also estimate the largest Lyapunov exponent $\lambda$ of the SGR using the geometric observables. The geometric estimate always gives the correct order of magnitude of $\lambda$ and is also quantitatively correct at small energy densities and, in the limit $N\to\infty$, in the whole homogeneous phase.Comment: 20 pages, 12 figure

Transformação genética de mamoeiros: 15 anos de sucesso.

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Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations

Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along any contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the membrane. Symmetric two-particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime; in particular, the problem may be solved exactly in the case of two membrane-bound parallel cylinders. This apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane-mediated interactions.Comment: 16 pages, 10 figures, REVTeX4 style. The Gaussian curvature term was included in the membrane Hamiltonian; section II.B was rephrased to smoothen the flow of presentatio

Evidence for a nuclear compartment of transcription and splicing located at chromosome domain boundaries

The nuclear topography of splicing snRNPs, mRNA transcripts and chromosome domains in various mammalian cell types are described. The visualization of splicing snRNPs, defined by the Sm antigen, and coiled bodies, revealed distinctly different distribution patterns in these cell types. Heat shock experiments confirmed that the distribution patterns also depend on physiological parameters. Using a combination of fluorescencein situ hybridization and immunodetection protocols, individual chromosome domains were visualized simultaneously with the Sm antigen or the transcript of an integrated human papilloma virus genome. Three-dimensional analysis of fluorescence-stained target regions was performed by confocal laser scanning microscopy. RNA transcripts and components of the splicing machinery were found to be generally excluded from the interior of the territories occupied by the individual chromosomes. Based on these findings we present a model for the functional compartmentalization of the cell nucleus. According to this model the space between chromosome domains, including the surface areas of these domains, defines a three-dimensional network-like compartment, termed the interchromosome domain (ICD) compartment, in which transcription and splicing of mRNA occurs

Bioprospecção de bactérias com potencial antagônico a fusarium spp. associado à morte de brachiaria brizantha

Há uma crescente busca nos últimos tempos por sistemas agropecuários que sejam produtivos, econômicos e sustentáveis. A síndrome da morte do capim Marandu (Brachiaria brizantha cv. Marandu) é um problema que vem crescendo nos últimos anos, um dos principais sinais de baixa sustentabilidade da pecuária brasileira. A morte das plantas forrageiras ocorre na época chuvosa, geralmente em solos mal drenados, devido a falta de adaptação da planta à baixa oxigenação das raízes, deixando-a suscetível ao ataque de fitopatógenos oportunistas. Diante da problemática, objetivou-se isolar e selecionar bactérias com potencial antagônico a Fusarium spp., um dos agentes fitopatogênicos que participam desse processo. Foram avaliados 10 sistemas, no período de chuva e seca: 1-F: floresta; 2-L: lavoura; 3-P: pecuária; 4-iPL: integração pecuária-lavoura; 5-iLP: integração lavoura-pecuária; 6-iLF: integração lavoura-floresta; 7-iPF: integração pecuária-floresta; 8-iLPF: lavoura e floresta por 2 anos e após pecuária e floresta por 2 anos; 9iLPF: pecuária e floresta por 2 anos e lavoura e floresta por 2 anos; 10-iLPF: integração lavoura-pecuária-floresta; além da mata nativa e área de pousio, distribuídos em blocos casualizados com 4 repetições. Os isolados bacterianos foram obtidos de amostras de solo diluídas, aplicadas em meio de cultura TSA 10% (Triptona soja ágar) e incubadas a 28ºC. Após a purificação os isolados foram armazenados em solução de glicerol 20% a -80°C. Foram testadas 20 bactérias em cada sistema. O método para avaliação de antagonismo foi o de cultura pareada em placa de Petri, por confronto direto, e em meio sólido BDA (Batata dextrose ágar). Na avaliação, foi considerado como positivo as bactérias que formaram halo de inibição ou quando o crescimento do corpo fúngico não encostou na bactéria. Dois isolados foram testados, Fusarium spp. isolado de planta de soja acometida (1) e Fusarium spp. isolado de solo onde ocorreu a morte da forrageira (2). Primeiramente, todos os isolados bacterianos foram testados contra o patógeno 1 e então, somente as bactérias antagônicas foram testadas contra o patógeno 2. Para o patógeno 1, na época da chuva, 7,5% dos isolados testados apresentaram antagonismo enquanto na seca esse valor foi maior (15%). Para o patógeno 2, nem todos os isolados positivos para o patógeno 1 foram eficientes no controle, demonstrando a ocorrência de interações entre isolados bacterianos e Fusarium spp. Quando considerados os sistemas, na chuva, para o patógeno 1, a mata apresentou maior número de isolados positivos (20%). Na seca, mata, 1-F e 8-iLPF para o patógeno 1, foram os que apresentaram maior número de positivos (25%). Dentre as épocas avaliadas, a seca teve mais bactérias antagonistas, e o tratamento 8-iLPF apresentou melhores resultados. O que demonstra possibilidade de encontrar um controlador biológico à Fusarium spp. neste sistema. Os sistemas mais biodiversos parecem favorecer o equilíbrio entre os microrganismos (antagonismo), o que pode reduzir ação do Fusarium spp. no capim Marandu. Isso deve ser evidenciado em análises posteriores com testes in vivo, a fim de comprovar e desenvolver novas biotecnologias. Palavras-chave: controle biológico, forragem, microbiologia