Execution of novel explicit RKARMS(4,4) technique in determining initial configurations of extra-solar protoplanets formed by disk instability

Implementation of a novel embedded Runge–Kutta fourth order four stage arithmetic root mean square technique to determine initial configurations of extra-solar protoplanets formed by gravitational instability is the main goal of this present paper. A general mathematical framework for the introduced numerical technique is described in addition to error estimation description. It is noticed that the numerical outputs through the employed novel RKARMS(4,4) method are found to be more effective and efficient in comparison with the results obtained by the classical Runge–Kutta technique

Exploration on initial structures of extrasolar protoplanets via new explicit RKAHeM(4,4) method

In this paper, a newly proposed embedded Runge–Kutta fourth order with four stages arithmetic Heronian mean method is employed and verified in determining the distribution of thermodynamic variables inside the extra-solar protoplanets formed through gravitational instability at their initial stages. In specific, the case of conduction–radiation is considered regarding the transference of heat inside the protoplanets. A general brief theoretical framework for the proposed numerical method is stated in addition to pseudo code followed by error estimation description. The results based on newly proposed explicit RKAHeM(4,4) method are found to be optimal and efficient in comparison with the ones obtained with classical fourth order Runge–Kutta method

Decomposition and kinetics of CH2(OH)C(O•)(CH3)CH2Cl radical in the atmosphere: A quantum mechanical study

957-963The quantum mechanical calculations of the decomposition pathways of 1, 2-hydroxy alkoxy radical i.e., CH2(OH)C(O•)(CH3)CH2Cl radical have been performed. This radical species has been formed from the successive reactions with O2 molecule and NOx or HO2 radicals with the most stable primary oxidation product of 3-chloro-2-methyl-1-propene and OH radical reaction. Geometry optimization and frequency calculations of all the stable species including transition states in the three possible C-C bond scission pathways (i.e., C-CH3, C-CH2Cl and C-CH2OH) of CH2(OH)C(O•)(CH3)CH2Cl radical have been performed at M06-2X/6-31+G(d,p) level of theory. Single point energy calculations of all the optimized species at the higher level of CCSD(T) method along with cc-pVTZ triple-zeta basis set have been performed. The rate constants for the various decomposition reactions have been evaluated using Canonical Transition State Theory (CTST) within the temperature range of 250–400 K. Rate constants for C–C bond scissions of C-CH3, C-CH2Cl and C-CH2OH of the 1, 2-hydroxy alkoxy radical have been found to be 4.17×101, 1.59×103 and 1.38×109 s-1 respectively at 298 K and 1 atm. The energetic and kinetics results suggest that C–CH2OH bond scission of titled radical has been more dominant than other decomposition channels

Implementation of polytropic method to study initial structures of gas giant protoplanets

In this paper we have determined the initial structures of gas giant protoplanets, formed via disk instability, having a mass range of 0.3–10 Jupiter masses by the simple polytropic method. The polytropic protoplanets or polytropes have been assumed to be spheres of solar composition, each of which is in a steady state of quasi-static equilibrium, where the only source of energy is the gravitational contraction of the gas. The results of our calculations for the polytropes with polytropic indices n = 1 and n = 1.5 are found to be closer to reality and are in good agreement with the findings obtained by other investigations with more rigorous treatment of the problem

Development of a cylindrical polar coordinates shallow water storm surge model for the coast of Bangladesh

The coast of Bangladesh is funnel shaped. The narrowing of the Meghna estuary along with its peculiar topography creates a funneling effect that has a large impact on surge response. In order to have an accurate estimation of surge levels, the impacts of the estuary should be treated with due importance. To represent in detail the real complexities of the estuary, a very high resolution is required, which in turn necessitates more computational cost. Considering the facts into account, a location specific vertically integrated shallow water model in cylindrical polar coordinates is developed in this study to foresee water levels associated with a storm. A one-way nested grid technique is used to incorporate coastal complicities with minimum cost. In specific, a fine mesh scheme (FMS) capable of incorporating coastal complexities with acceptable accuracy is nested into a coarse mesh scheme (CMS) covering up to 15°N latitude in the Bay of Bengal. The coastal and island boundaries are approximated through appropriate stair step representation and the model equations are solved by a conditionally stable semi-implicit finite difference technique using a structured C-grid. Numerical experiments are performed using the model to estimate water levels due to surge associated with the April 1991 and AILA, 2009 cyclones, which struck the coast of Bangladesh. Time series of tidal level is generated from an available tide table through a cubic spline interpolation method. The computed surge response is superimposed linearly with the generated time series of tidal oscillation to obtain the time series of total water levels. The model results exhibit a good agreement with observation and reported data

Revisiting the spatiotemporal dynamics of a diffusive predator-prey system: An analytical approach

This study investigates some analytic solutions and phase portraits to the diffusive predator-prey system in studying the spatiotemporal dynamics of a predator-prey community in ecology through an analytical approach and a qualitative theory of planar dynamical systems, respectively. To accomplish such aims, a simple wave transformation is applied to the diffusive predator-prey system for converting it into a system of ordinary differential equations with a planar dynamical system for analyzing the behavior of bifurcation properties and analytic solutions. Then, the analytical unified method is employed to the attained system. The applied wave transformation is put back to the obtained solutions of the system of ordinary differential equations. Finally, the analytic solutions namely, kink, anti-kink, singular, periodic-singular, and sinusoidal wave solutions are attained to the considered system. All the constructed wave solutions are found to be new from the viewpoint of the application of the unified method. In order to verify the biological wave phenomena of predator and prey populations, some graphs are presented for illustrating the analytic solutions, which have interesting implications in ecology. The effects of free parameters and wave celerity on the attained solutions are demonstrated graphically along with their physical descriptions. The graphical outputs reveal that the predator and prey population densities are changed with the change in the free parameters. Wave solutions to the fractional diffusive predator-prey system are also reported with Atangana conformable derivative sense. As the value of the fractional parameter increases, the smoothness of the anti-kink wave profile is found to increase gradually, but the steepness decreases. For the sinusoidal wave profile, the periodicity and smoothness increase as the value of the fractional parameter increases. Thus, the present study may enrich the interpretation of the spatiotemporal dynamics of predator-prey interaction in a real environment. It is also found that the applied method and the relevant transformation are effective and easy to use for acquiring new analytic solutions to the diffusive predator-prey system over the other analytic methods. The method of interest is novel and efficient because it overcomes the weaknesses and deficiencies of the other analytic methods. Therefore, the method can be applied to further studies to explain various physical phenomena arising in ecology

Estimating water levels caused by a tropical storm along the Bangladesh coast: A numerical approach

In this study, water levels resulting from the dynamic interaction of tide and surge are estimated by solving a 2-D vertically integrated shallow water equations numerically. To solve the equations on the specific 2-D grid, the explicit Leapfrog scheme is implemented, adopting a staggered Arakawa C-grid. The domain's complex land-sea interface is approximated through the stair-step method in order to employ the finite difference technique. To incorporate the complexity of the domain with a considerably high accuracy and to reduce computational cost, one-way nested grid models are embraced. The Meghna River freshwater discharge is incorporated into the innermost child model. A stable tidal regime over the region of interest is generated by applying the four vital tidal constituents, namely M2 (principal lunar semidiurnal), S2 (principal solar semidiurnal), O1 (principal lunar diurnal) and K1 (luni-solar diurnal) in the southern open boundary of the outermost model. This previously effectuated tidal regime is used as the initial state of the sea in getting total water levels due to the dynamic interaction of tide and surge. Numerical experiments are performed with the storm AILA that hit the coast of Bangladesh on May 25, 2009. The simulated results are found to closely match observed and reported data