Volume 16, Issue 1 -

This paper points out that the Bratu-like equation for the charged jet in electrospinning process (Yu-Qin Wan, Qian Guo & Ning Pan, International Journal of Nonlinear Sciences and Numerical Simulation, 5(1), pp. 5–8) requires much improvement.

The article presents results of multi-criteria optimization of air nozzle topology. The optimization in the Computational Fluid Dynamics (CFD) has been recently developed since equations of flow in porous media were applied among others governing equations. Optimization is a seeking for extremum of an objective function with respect to the function constraints. With this definition in mind, the optimization by using a continuous adjoint for the current cases is a finding such channel topology which minimizes for example pressure or energy loss when the constraints of objective function are in the form of flow governing equations of momentum and continuity. This methodology of optimization makes a design process faster comparing to the methods related to Design of Experiments (DoE). However, for the sake of flow governing equations nonlinearity, the continuous adjoint method can be successfully applied only in relatively simply and steady-state cases. The method consists in seeking of a global extremum of objective function. This extremum can sometimes be find in only simple and stationary events. The results of optimization of two selected cases are presented in the article and show advantages and limitations of the method applied. The continuous adjoint simulation results indicate the nozzles design directions and can be applied in industry with limited reliability. The object of research reported in the article is the nozzle which is augmented equipment used with a pneumatic pulsator. The pulsators are devices that utilize an air stream to destruct vaults created in loose material structure. The pulsator productivity equipped with a nozzle depends on outlet pressure. Therefore, the optimization problem was stated so that pressure loss is to be as low as possible.

The main objective of this study is to obtain and validate a mathematical model to describe a complex homogeneous Sono-Fenton (HSF) process used for the removal of 4-chlorophenol model pollutant from aqueous effluents. The investigated process parameters (acoustic amplitude, power density depending on the surface of the tip, initial pollutant concentration and time) serve as input parameters for the statistical modeling, while the output parameters considered are the final pollutant concentration and energy delivered to the sample. The accuracy of the models is analyzed by the values of the determination coefficients and by graphical tools available in MATLAB software such as: the Kolmogorov–Smirnov test (KS test), the graphical sensitivity tools, e.g. contribution to the sample mean (CSM) and variance (CSV) plots. The robustness of the model is also analyzed by global sensitivity analysis. Furthermore, the optimum set of operating conditions are determined by using the nlintool function.

The classical non-dimensionalization process of governing equations is a low-cost method commonly applied for a first approximation to the dimensionless numbers that determine the solution patterns in many problems; however, this procedure fails in complex problems, where it is not even possible to define reference quantities – because they are not established in the statement of the problem – to make the dependent or independent variables dimensionless. The application of discrimination corrects this obstacle and allows suitable dimensionless groups to be defined. These, in turn, have two interesting properties: (i) they are of order of magnitude unity, and (ii) they have a clear meaning in terms of balance of physical quantities that counteract each other in a domain or sub-domain of the problem. In this paper, discriminated non-dimensionalization is applied to geothermal scenarios of Bénard-type convective flow, large horizontal boundary sides under a temperature gradient in porous media, to determine the dimensionless groups that control the steady temperature and stream patterns and, from these, the order of magnitude of the main unknowns of the problem. The results were checked numerically for many cases.

In this paper, we investigate the properties of a sequential maximum likelihood estimator of the unknown linear drift parameter for the Rayleigh diffusion process. The estimator is shown to be closed, unbiased, normally distributed and strongly consistent. Finally a simulation study is presented to illustrate the efficiency of the estimator.

Shallow water wave equation has increasing use in many applications for its success in eliminating spurious oscillation, and has been widely studied. In this paper, we investigate (3+1)-dimensional generalized shallow water equation system. Based on the (G′/G)$(G'/G)$-expansion method and the variable separation method, we choose ξ(x,y,z,t)=f(y+cz)+ax+h(t)$\xi (x,y,z,t) = f(y + cz) + ax + h(t)$ and suppose that ai(i=1,2,…,m)${a_i}(i = 1,2, \ldots,m)$ is an undetermined function about x,y,z,t$x,y,z,t$ instead of a constant in eq. (3), which are different from those in previous literatures. With the aid of symbolic computation, we obtain a family of exact solutions of the (3+1)-dimensional generalized shallow water equation system in forms of the hyperbolic functions and the trigonometric functions. When the parameters take special values, in addition to traveling wave solutions, we also get the nontraveling wave solutions by using our method; these obtained solutions possess abundant structures. The figures corresponding to these solutions are illustrated to show the particular localized excitations and the interactions between two solitary waves. The (G′/G)$(G'/G)$-expansion method is a very general and powerful tool that will lead to further insights and improvements of the nonlinear models.

The systems of three and four spherical bodies with the dipole magnetic moment have been investigated using a numerical analysis. It was shown that in the initial state with the zero total magnetic moment under the influence of the alternating magnetic field, various regimes of the induced magnetic moment including quasistatic states are established. Revealed are the significant differences between these regimes related to different systems. The magnitude and direction of the magnetic moment of the system, as well the states of dynamic bistability, have been investigated. The possibilities of the induced magnetic moment control due to the changes in amplitude or frequency of the alternating field have been considered.