The aim of this paper is to analyze the effect of magnetic field on a boundary layer flow and heat transfer of a dusty fluid over an exponentially stretching surface with an exponential temperature distribution. The governing boundary layer equations are reduced into system of coupled non-linear ordinary differential equations with the help of similarity transformation. The transformed equations are then solved numerically using RKF-45 method. The effects of various physical parameters such as local fluid-particle interaction parameter, Prandtl Number, Eckert Number and Magnetic parameter on velocity and temperature profiles are discussed in detail.
The aim of this paper is to evaluate and study the Kullback–Leibler divergence of the γ–ordered Normal distribution, a generalization of Normal distribution emerged from the generalized Fisher’s information measure, over the scaled t–distribution. We investigate this evaluation through a series of bounds and approximations while the asymptotic behavior of the divergence is also studied. Moreover, we obtain a generalization of the known Kullback–Leibler information measure between two normal distributions, as well as the K–L divergence between Uniform or Laplace distribution over Normal distribution.
The correspondence between dierent versions of the Gauss-Weingarten equation is investigated. The compatibility condition for one version of the Gauss-Weingarten equation gives the Gauss-Mainardi-Codazzi system. A deformation of the surface is postulated which takes the same form as the original system but contains an evolution parameter. The compatibility condition of this new augmented system gives the deformed Gauss-Mainardi-Codazzi system. A Lax representation in terms of a spectral parameter associated with the deformed system is established. Several important examples of integrable equations based on the deformed system are then obtained. It is shown that the Gauss-Mainardi-Codazzi system can be obtained as a type of reduction of the self-dual Yang-Mills equations.
Coupling heterogeneous mathematical models is today commonly used, and effective solution methods for the resulting hybrid problem have recently become available for several systems. Even if in certain circumstances, asymptotic evaluations of the location of the interfaces are available, no strategy are proposed for locating the interfaces in numerical simulations. In this article, a semilinear elliptic problem is considered. By reformulating the problem in a mixed formulation context and by using an a posteriori error estimate, we propose an indicator of the error due to a wrong position of the junction. Minimizing this indicator allows us to determine accurately the location of the junction. By comparing this indicator with a mesh error indicator, this allows to decide if it is better to refine the mesh or to move the interface. Some numerical results are presented showing the efficiency of the proposed indicator.
In this paper, we introduce a new subclass of k-uniformly p-valent starlike and convex functions in the open unit disk using a fractional differential operator. We obtain coefï¬cient estimates, distortion theorems, extermal properties, closure theorems, and inclusion properties. The radii for k-uniformly starlikeness, convexity and close-to-convexity for functions belonging to this class are also determined.
A mathematical model for coral growth in a well stirred tank is proposed based on nutrient availability. The proposed model is a system of ODEs. Stability analysis of the solutions of the system of ODEs is done for various acceptable parameter regions. Growth forms of corals in different parameter regions are observed based on the solution of the model equations. Numerical calculations and qualitative analysis reveal some interesting global behaviors such as limit cycles, homoclinic connections and heterioclinic connections of the solution trajectories. Unstable growing limit cycles are observed for some parameter values where the corresponding largest limit cycle approaches a homoclinic connection. These behaviors of the solutions of the system closely have biological consequences on coral growth.