Bostonia. Volume 6

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity

For a family of logistic-like maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflexion of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig

Nonextensivity and multifractality in low-dimensional dissipative systems

Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently introduced by one of us (C.T.) and characterized by the entropic index $q$. We show that general scaling arguments imply that $1/(1-q) = 1/\alpha_{min}-1/\alpha_{max}$, where $\alpha_{min}$ and $\alpha_{max}$ are the extremes of the multifractal singularity spectrum $f(\alpha)$ of the attractor. This relation is numerically checked to hold in standard one-dimensional dissipative maps. The above result sheds light on a long-standing puzzle concerning the relation between the entropic index $q$ and the underlying microscopic dynamics.Comment: 12 pages, TeX, 4 ps figure

An extended-phase-space dynamics for the generalized nonextensive thermostatistics

We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a deterministic connection between the generalized nonextensive entropy and power law behavior. For the case of a simple one-dimensional harmonic oscillator, we confirm by numerical simulation of the dynamics that the distribution of energy H follows precisely the canonical q-statistics for different values of the parameter q. The approach is further tested for classical many-particle systems by means of molecular dynamics simulations. The results indicate that the intrinsic nonlinear features of the nonextensive formalism are capable to generate energy fluctuations that obey anomalous probability laws. For q<1 a broad distribution of energy is observed, while for q>1 the resulting distribution is confined to a compact support.Comment: 4 pages, 5 figure

A Dynamic Approach to the Thermodynamics of Superdiffusion

We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Levy index alpha, and using dynamical rather than probabilistic arguments.Comment: 4 pages, new revised version resubmitted to Phys. Rev. Let

Gene-based mapping of trehalose biosynthetic pathway genes reveals association with source- and sink-related yield traits in a spring wheat panel

Trehalose 6-phosphate (T6P) signalling regulates carbon use and allocation and is a target to improve crop yields. However, the specific contributions of trehalose phosphate synthase (TPS) and trehalose phosphate phosphatase (TPP) genes to source- and sink-related traits remain largely unknown. We used enrichment-capture sequencing on TPS and TPP genes to estimate and partition the genetic variation of yield-related traits in a spring wheat (Triticum aestivum) breeding panel specifically built to capture the diversity across the 75,000 CIMMYT wheat cultivar collection. Twelve phenotypes were correlated to variation in TPS and TPP genes including plant height and biomass (source), spikelets per spike, spike growth, and grain filling traits (sink) which showed indications of both positive and negative gene selection. Individual genes explained proportions of heritability for biomass and grain-related traits. Three TPS1 homeologues were particularly significant for trait variation. Epistatic interactions were found within and between the TPS and TPP gene families for both plant height and grain-related traits. Gene-based prediction improved predictive ability for grain weight when gene effects were combined with the whole-genome markers. Our study has generated a wealth of information on natural variation of TPS and TPP genes related to yield potential which confirms the role for T6P in resource allocation and in affecting traits such as grain number and size confirming other studies which now opens up the possibility of harnessing natural genetic variation more widely to better understand the contribution of native genes to yield traits for incorporation into breeding programmes

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^{\alpha}$. We found that for $\alpha < 1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha = 1$ a faster divergence of $\xi$ is obtained. For any $\alpha > 1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.

Characteristics of nodule bacteria from Mimosa spp grown in soils of the Brazilian semiarid region.

The Brazilian Northeastern dry forest (Caatinga) is one of the diversification centers of Mimosa species. We determined the characteristics of native rhizobia isolates from nodules of Mimosa tenuiflora and Mimosa paraibana grown in pots with soils collected under Caatinga vegetation and compared the restriction ribosomal DNA profiles of the isolates with those of 16 reference strains. All plants formed abundant indeterminate nodules and all nodule isolates formed fast growing colonies. No colony altered the medium to an alkaline reaction and most of them produced low or medium amounts of extracellular polysaccharides. White and creamy colonies predominated among the isolates but orange and green colonies were present. Differences among the isolates from the Mimosa species tested are indicated by the greater phenotypic diversity of those obtained from M. tenuiflora. The analysis of the 16S rDNA gene suggests that the isolates from M. tenuiflora and M. paraibana are closely related and closer to B-rhizobia than to &#945;-rhizobia. However, the similarity with all the tested B-rhizobia reference strains was relatively low suggesting that the isolates may belong to different bacteria species

Thin Domain Walls in Lyra Geometry

This paper studies thin domain walls within the frame work of Lyra Geometry. We have considered two models. First one is the thin domain wall with negligible pressures perpendicular and transverse direction to the wall and secondly, we take a particular type of thin domain wall where the pressure in the perpendicular direction is negligible but transverse pressures are existed. It is shown that the thin domain walls have no particle horizon and the gravitational force due to them is attractive.Comment: 8 pages, typos are corrected, published Astrophysics and Space Sciences 305, 337 (2006