GRB Afterglows from Anisotropic Jets

Some progenitor models of gamma-ray bursts (GRBs) (e.g., collapsars) may produce anisotropic jets in which the energy per unit solid angle is a power-law function of the angle ($\propto\theta^{-k}$). We calculate light curves and spectra for GRB afterglows when such jets expand either in the interstellar medium or in the wind medium. In particular, we take into account two kinds of wind: one ($n\propto r^{-3/2}$) possibly from a typical red supergiant star and another ($n\propto r^{-2}$) possibly from a Wolf-Rayet star. We find that in each type of medium, one break appears in the late-time afterglow light curve for small $k$ but becomes weaker and smoother as $k$ increases. When $k\ge 2$, the break seems to disappear but the afterglow decays rapidly. Thus, one expects that the emission from expanding, highly anisotropic jets provides a plausible explanation for some rapidly fading afteglows whose light curves have no break. We also present good fits to the optical afterglow light curve of GRB 991208. Finally, we argue that this burst might arise from a highly anisotropic jet expanding in the wind ($n\propto r^{-3/2}$) from a red supergiant to interpret the observed radio-to-optical-band afterglow data (spectrum and light curve).Comment: 12 pages + 10 figures, accepted by Ap

Reduced dynamics of Ward solitons

The moduli space of static finite energy solutions to Ward's integrable chiral model is the space $M_N$ of based rational maps from \CP^1 to itself with degree $N$. The Lagrangian of Ward's model gives rise to a K\"ahler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes, and the approximate non--relativistic solutions to Ward's model correspond to a geodesic motion on $M_N$. These solutions can be compared with exact solutions which describe non--scattering or scattering solitons.Comment: Final version, to appear in Nonlinearit

The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries

The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core (excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin $j$, and compare it with the results obtained by other methods. By this approach the equation of state for a two-dimensional hard-sphere gas can be calculated directly.Comment: 9 pages, 1 figur

Dietary Nutrient Intake and Obesity Prevalence Among Native American Adolescents

The prevalence of obesity among adolescent minority populations has been long recognized, but little research has been done on Native Americans adolescents. Using anthropometric measurements and dietary assessments, the findings within each study have shown to obtain baseline measures to determine the prevalence of obesity within the Sherman Indian High School's Native American adolescent population. Data of each assessment appear to be of use for predicting obesity and creating effective future interventions. Compiling data using the Harvard School of Public Health Youth/Adolescent Questionnaire (HSPH YAQ), a semi-quantitative food frequency questionnaire allowed significant data to be found between normal and obese weight students. Utilizing each finding allows more effective ways of targeting and reversing the inclining rate of obesity among Native American adolescents. Results show that antioxidants being examined on such as vitamin E and lycopene are beneficial in lowering the obesity rate among Native American adolescents. Levels of fiber, thiamin and folate consumption was significantly lower among the obese population in Sherman Indian High School's Native American adolescents. Moreover, dietary mineral intake was shown to be lower among obese Native American adolescents comparing with the normal weight group. The results suggested that dietary consumption of these nutrients might correlate and predict obesity and lead to the development of effective interventions for Native Americans. This study also found the effects of total fiber and vitamin B in diets with lifestyle intervention in prediabetic adults, showing that total fiber intake among the normal weight students is significantly higher than obese students, indicating that fiber and vitamin profile could be important determinants of the effect of dietary intervention

The Afterglow of GRB 990123 and a Dense Medium

Recent observations show that the temporal decay of the R-band afterglow from GRB 990123 steepened about 2.5 days after the burst. We here propose a possible explanation for such a steepening: a shock expanding in a dense medium has undergone the transition from a relativistic phase to a nonrelativistic phase. We find that this model is consistent with the observations if the medium density is about $3\times 10^6 {\rm cm}^{-3}$. By fitting our model to the observed optical and X-ray afterglow quantitatively, we further infer the electron and magnetic energy fractions of the shocked medium and find these two parameters are about 0.1 and $2\times 10^{-8}$ respectively. The former parameter is near the equipartition value while the latter is about six orders of magnitude smaller than inferred from the GRB 970508 afterglow. We also discuss possibilities that the dense medium can be produced.Comment: 12 pages, LaTeX, published in ApJ Letter

Metabolic profiling reveals coordinated switches in primary carbohydrate metabolism in grape berry (Vitis vinifera L.), a non-climacteric fleshy fruit

Changes in carbohydrate metabolism during grape berry development play a central role in shaping the final composition of the fruit. The present work aimed to identify metabolic switches during grape development and to provide insights into the timing of developmental regulation of carbohydrate metabolism. Metabolites from central carbon metabolism were measured using high-pressure anion-exchange chromatography coupled to tandem mass spectrometry and enzymatic assays during the development of grape berries from either field-grown vines or fruiting cuttings grown in the greenhouse. Principal component analysis readily discriminated the various stages of berry development, with similar trajectories for field-grown and greenhouse samples. This showed that each stage of fruit development had a characteristic metabolic profile and provided compelling evidence that the fruit-bearing cuttings are a useful model system to investigate regulation of central carbon metabolism in grape berry. The metabolites measured showed tight coordination within their respective pathways, clustering into sugars and sugar-phosphate metabolism, glycolysis, and the tricarboxylic acid cycle. In addition, there was a pronounced shift in metabolism around veraison, characterized by rapidly increasing sugar levels and decreasing organic acids. In contrast, glycolytic intermediates and sugar phosphates declined before veraison but remained fairly stable post-veraison. In summary, these detailed and comprehensive metabolite analyses revealed the timing of important switches in primary carbohydrate metabolism, which could be related to transcriptional and developmental changes within the berry to achieve an integrated understanding of grape berry development. The results are discussed in a meta-analysis comparing metabolic changes in climacteric versus non-climacteric fleshy fruits

Identification of the white dwarf companion to millisecond pulsar J2317+1439

We report identification of the optical counterpart to the companion of the millisecond pulsar J2317+1439. At the timing position of the pulsar, we find an object with $g=22.96\pm0.05$, $r=22.86\pm0.04$ and $i=22.82\pm0.05$. The magnitudes and colors of the object are consistent with it being a white dwarf. By comparing with white dwarf cooling models, we estimate that it has a mass of $0.39^{+0.13}_{-0.10}$ M$_{\odot}$, an effective temperature of $8077^{+550}_{-470}$ K and a cooling age of $10.9\pm0.3$ Gyr. Combining our results with published constraints on the orbital parameters obtained through pulsar timing, we estimate the pulsar mass to be $3.4^{+1.4}_{-1.1}$ M$_{\odot}$. Although the constraint on the pulsar mass is still weak, there is a significant possibility that the pulsar could be more massive than two solar mass.Comment: 7 pages, 6 figures, accepted for publication in Ap

Environment and Energy Injection Effects in GRB Afterglows

In a recent paper (Dai & Lu 1999), we have proposed a simple model in which the steepening in the light curve of the R-band afterglow of the gamma-ray burst (GRB) 990123 is caused by the adiabatic shock which has evolved from an ultrarelativistic phase to a nonrelativistic phase in a dense medium. We find that such a model is quite consistent with observations if the medium density is about $3\times 10^6 {\rm cm}^{-3}$. Here we discuss this model in more details. In particular, we investigate the effects of synchrotron self absorption and energy injection. A shock in a dense medium becomes nonrelativistic rapidly after a short relativistic phase. The afterglow from the shock at the nonrelativistic stage decays more rapidly than at the relativistic stage. Since some models for GRB energy sources predict that a strongly magnetic millisecond pulsar may be born during the formation of GRB, we discuss the effect of such a pulsar on the evolution of the nonrelativistic shock through magnetic dipole radiation. We find that after the energy which the shock obtains from the pulsar is much more than the initial energy of the shock, the afterglow decay will flatten significantly. When the pulsar energy input effect disappears, the decay will steepen again. These features are in excellent agreement with the afterglows of GRB 980519, GRB 990510 and GRB 980326. Furthermore, our model fits very well all the observational data of GRB 980519 including the last two detections.Comment: 21 pages, LaTeX, accepted for publication in ApJ, one paragraph adde