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This article presents an improved analytical spatial harmonics subdomain (SHSD) model for analyzing the influence of individual spatial harmonics, in stator magneto-motive forces (MMFs), on the performance of multiphase cage rotor induction motors (CRIMs). The proposed SHSD model is an extension of conventional techniques that consider each MMF spatial harmonic, caused by stator slots with tooth-tips, to be individual excitations when quantitatively analyzing the resulting physical effects. The solution domain was divided into four subdomains (SDs) in 2-D polar coordinates, including 1) rotor bars described by the Helmholtz equation; 2) air gaps; 3) slot openings described by Laplace’s equation; 4) stator slots represented by pure forced vibration equations. Current density in the stator structure was decomposed in a Fourier series of position angles to obtain MMF spatial harmonics. This produced a set of pure forced vibration equations in the stator slots, which were first solved in 2-D polar coordinates rather than the typical Poisson’s equation. This approach establishes a relationship between electromagnetic performance and stator parameters, for further optimization of IMs and analysis of electromagnetic vibrations. The proposed analytical model was validated using a series of finite element simulations, which exhibited high accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

Objective: To investigate the importance of membrane charge oscillations and redistribution in multi-compartmental ultrasonic neuromodulation (UNMOD) intramembrane cavitation models. Methods: The Neuronal Intramembrane Cavitation Excitation (NICE) model and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC) of UNMOD are compared for a nanoscale multi-compartmental and point neuron approximation of the bilayer sonophore and surrounding proteins. The temporal dynamics of charge oscillations and their effect on the resulting voltage oscillations are investigated by fourier series analysis. Results: Comparison of excitation thresholds and neuronal response between nanoscale multi-compartmental and point models, implemented in the SONIC and NICE framework, demonstrates that the explicit modeling of fast spatial charge redistribution is critical for an accurate multi-compartmental UNMOD-model. Furthermore, the importance of modeling partial protein coverage is quantified by the excitability thresholds. Subsequently, we establish by fourier analysis that these charge oscillations are slowly changing in time. Conclusion: Fast charge redistribution significantly alters neuronal excitability in a multi-compartmental nanoscale UNMOD-model. Also the mutual exclusivity between protein and sonophore coverage should be taken into account, when simulating the dependency of neuronal excitability on coverage fractions. Charge oscillations are periodic and their fourier components change on a slow timescale. Furthermore, the resulting voltage oscillations decrease in energy with overtone number, implying that an extension of the existing multiscale model (SONIC) to multi-compartmental neurons is possible by taking into account a limited number of fourier components. Significance: First steps are taken towards a morphologically realistic and computationally efficient UNMOD-model, improving our understanding of the underlying ultrasonic neuromodulation mechanisms. [ABSTRACT FROM AUTHOR]