The power quality in electrical energy systems is very important and harmonic is the vital criterion. Traditionally Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) have been used for the harmonic distortion analysis and in the literature harmonic estimations have been made using different methods. As an alternative method, this paper suggested using Support Vector Machine (SVM...

In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L2 harmonic 2-forms on the space. Gibbons found a non-topological L2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manif...

This is in the sequel of our previous work [LW] on the study of the approximated harmonic maps in high dimensions. The main purpose of the present article is to understand the bubbling phenomena as well as the energy quantization beyond the natural conformal dimension two for the Dirichelet integral. This will be important toward our understandings of the defect measures and the energy concentr...

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-ha...

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that...

This is an expository paper which includes several topics related to the Dirichlet form analysis on the Sierpiński gasket. We discuss the analog of the classical Laplacian; approximation by harmonic functions that gives a notion of a gradient; directional energies and an equipartition of energy; analysis with respect to the energy measure; harmonic coordinates; and non self-similar Dirichlet fo...

Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding genera...

In this paper, we propose a new dynamic model to describe the hysteresis phenomenon in harmonic drives. The experimental observation of the dynamic torque-displacement relationship for a harmonic drive shows a hysteresis characteristic indicating the simultaneous presence of energy storage and energy dissipation mechanisms. To completely characterize these mechanisms and yet have a simple repre...