The flow of an electroconductive incompressible ternary hybrid nanofluid with heat conduction in a boundary layer including metallic nanoparticles (NPs) over an extended cylindrical with magnetic induction effects is reported in this research. The ternary hybrid nanofluid has been synthesized with the dispersion of titanium dioxide, cobalt ferrite, and magnesium oxide NPs in the base fluid water. For a range of economical and biological applications, a computational model is designed to augment the mass and energy conveyance rate and promote the performance and efficiency of thermal energy propagation. The model has been written as a system of partial differential equations. Which are simplified to the system of ordinary differential equations through similarity replacements. The computing approach parametric continuation method is used to further process the resultant first order differential equations. The results are validated with the bvp4c package for accuracy and validity. The outcomes are displayed and analyzed through Figures and Tables. It has been observed that the inverse Prandtl magnetic number and a larger magnetic constant reduce the fluid flow and elevate the energy profile. The variation of ternary hybrid NPs significantly boosts the thermophysical features of the base fluid.

The present computational model is built to analyze the energy and mass transition rate through a copper and cobalt ferrite water-based hybrid nanofluid (hnf) flow caused by the fluctuating wavy spinning disk. Cobalt ferrite (CoFe₂O₄) and copper (Cu) nanoparticles (nps) are incredibly renowned in engineering and technological research due to their vast potential applications in nano/microscale structures, devices, materials, and systems related to micro- and nanotechnology. The flow mechanism has been formulated in the form of a nonlinear set of PDEs. That set of PDEs has been further reduced to the system of ODEs through resemblance replacements and computationally solved through the parametric continuation method. The outcomes are verified with the Matlab program bvp4c, for accuracy purposes. The statistical outputs and graphical evaluation of physical factors versus velocity, energy, and mass outlines are given through tables and figures. The configuration of a circulating disk affects the energy transformation and velocity distribution desirably. In comparison to a uniform interface, the uneven spinning surface augments energy communication by up to 15%. The addition of nanostructured materials (cobalt ferrite and copper) dramatically improves the solvent physiochemical characteristics. Furthermore, the upward and downward oscillation of the rotating disc also enhances the velocity and energy distribution.

In this study, we consider a regional controllability problem for a class of distributed bilinear systems evolving in a spatial domain Ω. A feedback control is used to steer the system state close to a desired profile at a final time T, only on ω a subregion of the system domain which may be interior or on the boundary of Ω. Our purpose is to prove that an optimal control exists, and characterised as a solution to an optimality system. Numerical algorithm is given and successfully illustrated by simulations.

Time synchronization is critical in distributed environments. A variety of network protocols, middleware and business applications rely on proper time synchronization across the computational infrastructure and depend on the clock accuracy. The Network Time Protocol (NTP) is the current widely accepted standard for synchronizing clocks over the Internet. NTP uses a hierarchical scheme in order to synchronize the clocks in the network. In this paper we present a novel non-hierarchical peer-to-peer approach for time synchronization termed CTP-Classless Time Protocol. This approach exploits convex optimization theory in order to evaluate the impact of each clock offset on the overall objective function. We define the clock offset problem as an optimization problem and derive its optimal solution. Based on the solution we develop a distributed protocol that can be implemented over a communication network, prove its convergence to the optimal clock offsets and show its properties. For compatibility, CTP may use the packet format and number of measurements used by NTP. We also present methodology and numerical results for evaluating and comparing the accuracy of time synchronization schemes. We show that the CTP outperforms hierarchical schemes such as NTP in the sense of clock accuracy with respect to a universal clock

In this study, the authors consider the problem of optimal regional controllability of a distributed bilinear system evolving in a spatial domain Ω. The question is to obtain a bounded feedback control with minimum energy that drives such a system from an initial state to a desired one in finite time, only on a subregion ω of Ω. The purpose of this study is to prove that a regional optimal control exists, and characterised as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.