Numerical solutions for equations of weak turbulence theory that describe the beam-plasma interaction are obtained in two dimensions (2D). The self-consistent theory governs quasilinear processes as well as nonlinear decay and scattering processes. It is found that the Langmuir turbulence scatters into a quasi-circular ring spectrum in 2D wave number space, accompanied by quasi-isotropic heating of the electrons. When projected onto the one-dimensional (1D) space, 2D Langmuir turbulence spectrum appears as an inverse cascade, when in reality, the wavelength of the turbulence does not change but only the wave propagation angle changes. These findings are similar to those obtained in a previous analysis in which scattering processes were not taken into account, but it is found that the scattering term leads to a quantifiably higher scattering rate.

OBJECTIVES: To assess the prevalence, extent, and risk indicators of tooth loss in a representative young urban population from south Brazil. METHODS: A representative sample was drawn using a multi-stage probability cluster sampling strategy, and consisted of 612 subjects 14-29 years of age in the metropolitan area of Porto Alegre, Brazil. A clinical examination was carried out by 4 calibrated examiners in a mobile examination center. RESULTS: The prevalence of tooth loss was 44.8%, 26%, and 60%, and the mean tooth loss was 1.4, 0.6, and 2.4 teeth in the age groups 14-29, 14-19 and 25-29 years, respectively. First molars were the most frequently missing teeth, and the mandibular incisors and canines were the least missing teeth. Tooth loss increased sharply with age, and was similar in males and females. Having > or =4 missing teeth was significantly associated with low socioeconomic status and heavy smoking, and was significantly more likely in persons who had > or =2 teeth with caries/fillings and/or > or =5 mm attachment loss. CONCLUSION: Tooth loss is a dental health concern in this young Brazilian population. Community-based oral diseases prevention programs targeting groups having these risk factors should be implemented to reduce tooth loss.