Finite-time stability results for fractional damped dynamical systems with time delays

This paper is explored with the stability procedure for linear nonautonomous multiterm fractional damped systems involving time delay. Finite-time stability (FTS) criteria have been developed based on the extended form of Gronwall inequality. Also, the result is deduced to a linear autonomous case. Two examples of applications of stability analysis in numerical formulation are described showing the expertise of theoretical prediction.

Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite difference approximation. The energy method is used to investigate the rate of convergence and unconditional stability of the temporal discretization. The interpolation of moving Kriging technique is then used to approximate the space derivative, yielding a meshless numerical formulation. We conclude with some numerical experiments that validate the theoretical findings.

Electro-Magnetic and Structural Analysis of Six-Pole Hybrid-Excited Permanent Magnet Motors

Potentials and limits of the Hybrid-Excitation Permanent-Magnet (HEPM) synchronous machine are dealt with in this paper. A six-pole machine is taken into consideration, and both parallel and series configurations are analysed and compared. Taking advantage of the rotor excitation coils, the permanent magnet (PM) rotor flux can be adjusted according to the operating speed to improve its performance parameters. The electro-magnetic force is analysed in its first harmonic and in the complete shape. Moreover, a comparison between analytical and numerical formulation has been done for the rotor current control. In particular, the speed range is extended, and electro-mechanical torque and power are increased, as well as the efficiency. It will be shown that the rotor flux reduction by using the excitation winding yields an improvement of the motor performance. The main advantage will be obtained during the flux-weakening operations. In this paper, different rotor topologies will be analysed to highlight the advantages and drawbacks of each of them, and how it is possible to achieve higher speed with higher torque and without high saliency ratio. A magnetic network will be introduced to explain the different contribution of the excitation winding to the rotor flux. Furthermore, a comparison of the amount of the volume of PM, copper and iron in internal permanent magnet (IPM) motor and HEPM motor will be analysed. Actually, an analysis of the harmonic content in the electro-motive force even varying the excitation current and a mechanical stress analysis of each machine will be shown. Finally, it will be verified that the excitation losses represent a minimum component of the total losses.

SU2-NEMO: An Open-Source Framework for High-Mach Nonequilibrium Multi-Species Flows

SU2-NEMO, a recent extension of the open-source SU2 multiphysics suite’s set of physical models and code architecture, is presented with the aim of introducing its enhanced capabilities in addressing high-enthalpy and high-Mach number flows. This paper discusses the thermal nonequilibrium and finite-rate chemistry models adopted, including a link to the Mutation++ physio-chemical library. Further, the paper discusses how the software architecture has been designed to ensure modularity, incorporating the ability to introduce additional models in an efficient manner. A review of the numerical formulation and the discretization schemes utilized for the convective fluxes is also presented. Several test cases in two- and three-dimensions are examined for validation purposes and to illustrate the performance of the solver in addressing complex nonequilibrium flows.

Platonism and Mathematical Explanations

Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a non numerical formulation of some explanans may be obtained so that the platonistic force of the best numerical-based account of the explanandum is also undermined (Rizza), the parsimony principle has been respected. Since derivations resorting to conservative mathematics and proofs involved in non numerical best explanations also require abstract objects, concepts, and principles under the usual reading of “abstract,” one might complain that such accounts turn out to be as metaphysically loaded as their platonistic counterparts. One might then urge that ontological parsimony is also required of these nominalistic accounts. It might, however, prove more fruitful to leave this particular worry to the side, to free oneself, as it were, from parsimony thus construed and to look at other important aspects of the defeating or undermining strategies that have been lavished on the disposal of platonism. Two aspects are worthy of our attention: epistemic cost and debunking claims. Our knowledge that applied mathematics is conservative is established at a cost, and so is our knowledge that nominalistic proofs play a genuine theoretical role in best explanations. I will suggest that the knowledge one must acquire to show that nominalistic deductions and explanations do indeed play their respective theoretical role involves some question-begging assumptions regarding the nature and validity of proofs. As for debunking, even if the face value content of either non numerical claims, or conservative mathematical claims, or platonistic mathematical claims didn’t figure in our causal explanation of why we hold the mathematical beliefs that we do, construed or understood as beliefs about such contents, or as beliefs held in either of these three ways, we could still be justified in holding them, so that the distinction between nominalistic deductions or non numerical explanations on the one hand and platonistic ones on the other turns out to be spurious with respect to the relevant propositional attitude, i.e., with respect to belief.