Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions

We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of solution of the harmonic oscillator problem.Comment: 9 pages, 3 figure

The Cluster Abundance in Flat and Open Cosmologies

We use the galaxy cluster X-ray temperature distribution function to constrain the amplitude of the power spectrum of density inhomogeneities on the scale corresponding to clusters. We carry out the analysis for critical density universes, for low density universes with a cosmological constant included to restore spatial flatness and for genuinely open universes. That clusters with the same present temperature but different formation times have different virial masses is included. We model cluster mergers using two completely different approaches, and show that the final results from each are extremely similar. We give careful consideration to the uncertainties involved, carrying out a Monte Carlo analysis to determine the cumulative errors. For critical density our result agrees with previous papers, but we believe the result carries a larger uncertainty. For low density universes, either flat or open, the required amplitude of the power spectrum increases as the density is decreased. If all the dark matter is taken to be cold, then the cluster abundance constraint remains compatible with both galaxy correlation data and the {\it COBE} measurement of microwave background anisotropies for any reasonable density.Comment: Uuencoded package containing LaTeX file (uses mn.sty) plus 7 postscript figures incorporated using epsf. Total length 10 pages. Final version, to appear MNRAS. COBE comparison changed to 4yr data. No change to results or conclusion

On time-varying collaboration networks

The patterns of scientific collaboration have been frequently investigated in terms of complex networks without reference to time evolution. In the present work, we derive collaborative networks (from the arXiv repository) parameterized along time. By defining the concept of affine group, we identify several interesting trends in scientific collaboration, including the fact that the average size of the affine groups grows exponentially, while the number of authors increases as a power law. We were therefore able to identify, through extrapolation, the possible date when a single affine group is expected to emerge. Characteristic collaboration patterns were identified for each researcher, and their analysis revealed that larger affine groups tend to be less stable

INFLUÊNCIA DO CONSUMO DE FARINHA DE YACON NA GLICEMIA, PERFIL LIPÍDICO, COMPOSIÇÃO CORPORAL E CONSUMO ALIMENTAR COM MULHERES COM DIABETES TIPO 2 E COM EXCESSO DE PESO

O yacon é uma raiz tuberosa ainda pouco consumida no Brasil, sendo ultimamente muito estudada na saúde humana devido à presença dos fruto-oligossacarídeos (FOS). No presente estudo foi produzida a farinha de yacon e avaliou-se a influência de sua ingestão por mulheres portadoras de diabetes tipo 2 durante 60 dias (T0: início; T30: após 30 dias; T60: após 60 dias). As participantes foram divididas em grupo controle (GC: n = 29) e grupo yacon (GY: n = 23), que consumiu 11 g de FOS presentes na farinha de yacon. Foram avaliados os parâmetros de glicose em jejum, perfil lipídico, composição corporal e consumo alimentar, adotando um nível de 5% de significância nos testes estatísticos. A farinha de yacon apresentou 6,50% de rendimento, 1,15% de umidade, 4,52% de proteína total, 0,33% de gordura, 2,94% de cinzas, 10,23% de fibra bruta, 91,0% de carboidratos totais e 35,06% de FOS. No GY foi encontrado aumento significativo do HDL entre os três tempos do estudo (p < 0,0001) e também de colesterol total de T0 para T60 (p = 0,03) e redução significativa do percentual de gordura corporal de T0 para T60 (p = 0,03). No GC, um aumento significativo foi encontrado no HDL de T0 e T30 para T60 (p < 0,0001) e de triacilgliceróis de T0 para T30 (p = 0,01). Em relação ao consumo alimentar, houve diferença significativa entre os grupos em relação às fibras em T30 e T60 (p = 0,01/p = 0,009). O GY apresentou uma redução significativa de calorias (p = 0,02) e ácidos graxos saturados (p = 0,02) de T0 para T60, enquanto o GC apresentou redução significativa da ingestão de carboidratos de T0 para T30 (p = 0,03). A diminuição do percentual de gordura corporal e da ingestão energética do GY sugere um possível efeito benéfico dos FOS

Cold dark matter models with high baryon content

Recent results have suggested that the density of baryons in the Universe, OmegaB, is much more uncertain than previously thought, and may be significantly higher. We demonstrate that a higher OmegaB increases the viability of critical-density cold dark matter (CDM) models. High baryon fraction offers the twin benefits of boosting the first peak in the microwave anisotropy power spectrum and of suppressing short-scale power in the matter power spectrum. These enable viable CDM models to have a larger Hubble constant than otherwise possible. We carry out a general exploration of high OmegaB CDM models, varying the Hubble constant h and the spectral index n. We confront a variety of observational constraints and discuss specific predictions. Although some observational evidence may favour baryon fractions as high as 20 per cent, we find that values around 10 to 15 per cent provide a reasonable fit to a wide range of data. We suggest that models with OmegaB in this range, with h about 0.5 and n about 0.8, are currently the best critical-density CDM models.Comment: 14 pages, LaTeX, with 9 included figures, to appear in MNRAS. Revised version includes updated references, some changes to section 4. Conclusions unchange

Effective transport barriers in nontwist systems

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.FAPESPCNPqCAPESMCT/CNEN (Rede Nacional de Fusao)Fundacao AraucariaUS Department of Energy DE-FG05-80ET-53088Physic

Pursuing Parameters for Critical Density Dark Matter Models

We present an extensive comparison of models of structure formation with observations, based on linear and quasi-linear theory. We assume a critical matter density, and study both cold dark matter models and cold plus hot dark matter models. We explore a wide range of parameters, by varying the fraction of hot dark matter $\Omega_{\nu}$, the Hubble parameter $h$ and the spectral index of density perturbations $n$, and allowing for the possibility of gravitational waves from inflation influencing large-angle microwave background anisotropies. New calculations are made of the transfer functions describing the linear power spectrum, with special emphasis on improving the accuracy on short scales where there are strong constraints. For assessing early object formation, the transfer functions are explicitly evaluated at the appropriate redshift. The observations considered are the four-year {\it COBE} observations of microwave background anisotropies, peculiar velocity flows, the galaxy correlation function, and the abundances of galaxy clusters, quasars and damped Lyman alpha systems. Each observation is interpreted in terms of the power spectrum filtered by a top-hat window function. We find that there remains a viable region of parameter space for critical-density models when all the dark matter is cold, though $h$ must be less than 0.5 before any fit is found and $n$ significantly below unity is preferred. Once a hot dark matter component is invoked, a wide parameter space is acceptable, including $n\simeq 1$. The allowed region is characterized by \Omega_\nu \la 0.35 and 0.60 \la n \la 1.25, at 95 per cent confidence on at least one piece of data. There is no useful lower bound on $h$, and for curious combinations of the other parameters it is possible to fit the data with $h$ as high as 0.65.Comment: 19 pages LaTeX file (uses mn.sty). Figures *not* included due to length. We strongly recommend obtaining the full paper, either by WWW at http://star-www.maps.susx.ac.uk/papers/lsstru_papers.html (UK) or http://www.bartol.udel.edu/~bob/papers (US), or by e-mailing ARL. Final version, to appear MNRAS. Main revision is update to four-year COBE data. Miscellaneous other changes and reference updates. No significant changes to principal conclusion