Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators

In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered.

The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings

We study theoretically and numerically the occurrence of Fano resonances in a metagrating made of slits with some symmetry breaking resulting in a dual period. At low frequency, a grating composed of long enough slits supports Fabry–Pérot resonances on which Fano resonances superimpose when the grating acquires dual period. The resulting spectrum exhibits flat-banded peaks interrupted by sharp dips with successions of perfect and zero transmissions. To model these scattering properties, homogenization theory is used resulting in an effective problem governing the solutions in the two, non-identical, slits, which are coupled through jump conditions at the grating interfaces. These jumps efficiently encode the effect of the evanescent field able to resonate in the radiative region due to the folding of the spoof plasmon polaritons branches. The model is validated with direct numerics and a local analysis allows us to characterize the resonant mechanisms.

Features of Cu and TiO2 in the flow of engine oil subject to thermal jump conditions

The recent work investigates the heat transfer attributes in the flow of engine oil which comprises of nano-particles such as Cu and TiO2. The performance of Copper and Titanium oxide is over looked in the flow of engine oil. The energy equation is amended by the features of thermal radiation, viscous dissipation, and heat generation. The mathematical model signifies the porosity, entropy generation and moving flat horizontal surface with the non-uniform stretching velocity. Quasi-linearization, which is a persuasive numerical technique to solve the complex coupled differential equations, is used to acquire the numerical solution of the problem. Flow and heat transfer aspects of Cu–TiO2 in the flow are examined against the preeminent parameters. The flow is significantly affected by the thermal jump conditions and porous media. It is observed here that the temperature as well as heat transport rate is reduced with the effect of involved preeminent parameters. However, such fluids must be used with caution in applications where a control on the heat transfer is required. We may conclude that the recent study will provide assistance in thermal cooling systems such as engine and generator cooling, nuclear system cooling, aircraft refrigeration system, and so forth.

A Hybrid Adjoint Network Model for Thermoacoustic Optimization

A method is proposed that allows the computation of the continuous adjoint of a thermoacoustic network model based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. In this way, the need to derive the adjoint equations for every element of the network model is eliminated. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved whilst maintaining the flexibility of the discrete adjoint. It is demonstrated how the obtained adjoint system may be utilized to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor.