International Journal of Emerging Multidisciplinaries: Mathematics

Current Developments on Extreme Value Copulas: Extended Pickands Dependence Functions

Christophe Chesneau — 2023-09-10

Copulas are mathematical tools used to model the dependence structure between random variables. Extreme value copulas specifically focus on
capturing the tail dependence, which refers to the dependence structure between random variables when they exhibit extreme or rare events. The
Pickands dependence functions are special convex functions that play a crucial role in characterizing extreme value copulas; they quantify the
strength of their tail dependence. The creation of new Pickands dependence functions enhances our understanding of complex interdependencies,
enabling more accurate modeling and risk assessment in diverse systems. In this article, a theoretical contribution to the topic is provided; an
original strategy for generating new Pickands dependence functions based on existing ones is developed. The resulting Pickands dependence
functions have the features of using the functionalities of standard functions (exponential, trigonometric, hyperbolic, etc.) and/or depend on
several tuning parameters of various natures, which are quite uncommon in the literature. Two new extreme value copulas are derived from
our findings. Their asymmetric and tail-dependent flexibility are emphasized. Numerical and graphical illustrations are given to support some
theoretical facts.

Effect of Cattaneo-Christov Model over a Vertical Stretching Cylinder Using SiO2 Nanofluid

Zaffer Elahi — 2023-05-30

This paper represents the heat transfer of SiO2 nano uid over a vertical stretching cylinder. By using, suitable transformations, the governing partial differential equations are changed into non-linear ordinary differential equations, which are then solved by the numerical solver namely BVP4C. The scrutinized results both in the form of graphical and numerically have been developed from the scheme BVP4C. By using pictorial graphs, the physical parameter that appear in temperature profile are discussed. Further, the rate of shear-stress and heat transfer at the surface have been computed and tabulated in Tables 3-4.

Radiation Effects on Boundary Layer Flow and Heat Transfer of the Power Law Fluid Over a Stretching Cylinder with Convective Boundary Conditions

Azeem Shahzad — 2023-05-30

In this work, a power law fluid model is used to examine the boundary layer flow and heat transfer characteristics over an unsteady horizontal stretching cylinder under the influence of convective boundary conditions. It is presumed that partial slip conditions exist and that the thermal conductivity of the nanofluid is a function of temperature at the boundary. Through similarity transformation, the coupled partial differential equations are converted into ordinary differential equations (ODEs), which are then resolved in MATLAB with BVP4C. By contrasting the computed findings with the published results, the validity of the results is proven. The effects of different parameters on the temperature and velocity profiles are carefully looked at and analysed. As the Eckert number increases, the thermal boundary layer thickens. All of the physical factors that affect the local Nusselt number and skin friction coefficient have been studied carefully and are shown in the tables.