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The nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations including both Kadomtsev-Petviashvili (KP) and modified KP (mKP) equations are derved using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis while the qualitative behavior is studied by dint of the dynamical system approach. The solutions to the mKP equation hold at a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs) whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of kappa spectral index is studied and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with gegative charge are observed by various satellite missions.

Theoretical investigation of electrostatic ion acoustic periodic (cnoidal) waves and solitons with warm ions is presented with electrons that are assumed to follow the double spectral index distribution function. The double spectral index distribution imitates effectively the distributions that have often been seen in space plasmas. Using the standard reductive perturbation technique, the Korteweg–de Vries (KdV) equation is derived which describes the nonlinear periodic waves with appropriate boundary conditions. By using planar dynamical system to this KdV equation, the existence of solitary wave solutions and periodic wave solutions are found. It is shown that changing the electron population in regions of low and high phase space density regions alter the propagation characteristics of nonlinear ion acoustic periodic and solitary structures. Comparison of non-Maxwellian distribution functions with Maxwellian distribution is also made. The importance of the present work with regard to space plasmas is also pointed out.

The properties of ion acoustic solitary and periodic structures are studied in magnetized two-ion component (O+ − H+ − e) plasmas with (r, q) distributed electrons. It is found that two modes of ion acoustic waves, namely, fast and slow modes, can propagate in such a plasma. The nonlinear Zakharov–Kuznetsov equation is derived using the well-known reductive perturbation method. Employing the theory of planar dynamical systems, the system under consideration is found to admit compressive (hump) and rarefactive (dip) solitary structures and periodic wave solutions. It is found that behavior of propagation of nonlinear ion acoustic solitary structures is different for fast and slow modes owing to the difference in physics of the two modes. The effect of the double spectral indices r and q is thoroughly explored. It is shown that altering the shape of the distribution function through these indices radically alter the propagation characteristics of nonlinear ion acoustic waves. The ratio of concentration of heavy (O+) to light ions (H+) is found to change the fast mode, whereas the temperature ratio is observed to alter the slow mode. We have applied our study to the upper ionosphere where bi-ion plasmas and the presence of non-Maxwellian electrons have been observed by various satellite missions.

Objective: The aim of the study was to find out the relationship between ‘chronological age and skeletal maturation’ and ‘gender and skeletal maturation. Materials and Methods: The lateral cephalometric radiographs of 103 patients of age ranging from 8-18 years, both genders were taken. Cervical vertebrae maturation (CVM) method was used to determine development stages and its co-relation with the chronological age and gender of the patient. For corelation between the chronological age and developmental age, Spearman rank order correlation coefficient was used. And Fishers exact test was used to determine the correlation between gender and developmental stage. Results: Spearman rank order correlation coefficient was 0.835, between chronological age and cervical vertebral maturation stages. Fishers exact test was found to be significant i.e. p=0.02 between gender and CVM stage. In males the stage 2 of cervical vertebrae stages were the most frequent followed by stage 1. Stage 4 followed by stage 1 in females were the most frequent stages. Conclusion: A statistically significant correlation between chronological age and cervical vertebral maturation stages along with the gender and cervical vertebral maturation stages was concluded. The pubertal growth spurt (i.e. CVM 2 and CVM 3) occupies the age group of 10-14 years.