The quasi-harmonic approximation is a phonon-based model of solid-state physics used to describe volume-dependent thermal effects, such as the thermal...

thermal expansion of solids, which is usually studied within the quasi-harmonic approximation. Studying vibrating anharmonic systems using quantum mechanics...

_{i}}}{\frac {\partial \omega _{i}}{\partial V}}.} Using the quasi-harmonic approximation for atomic vibrations, the macroscopic Grüneisen parameter (γ)...

Second-harmonic generation (SHG), also known as frequency doubling, is the lowest-order wave-wave nonlinear interaction that occurs in various systems...

In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rates such as speeds...

symmetric positive-definite matrix. The pair of matrix quasi-arithmetic means yields the matrix harmonic mean: M ∇ F ( θ 1 , θ 2 ) = 2 ( θ 1 − 1 + θ 2 − 1...

oscillation Quasi-biennial oscillation Neutron stars Cyclic Model Neutral particle oscillation, e.g. neutrino oscillations Quantum harmonic oscillator...

Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and...

P}{\partial T}}\right)_{V}} . Usually, Mie-Grüneisen-Debye and other Quasi harmonic approximation (QHA) based state functions are being used to estimate volumes...

arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least...

exchange interactions time scales, namely a "normal" atmospheric heat wave is quasi-static, and a pressure wave is not). Adiabatic in the context of mechanics...

Quasi-phase-matching is a technique in nonlinear optics which allows a positive net flow of energy from the pump frequency to the signal and idler frequencies...

becomes very small. Often, this is approached through "quasi-classical" techniques (cf. WKB approximation). More rigorously, the mathematical operation involved...

Here the amplitude of oscillation decays in time, so we call its modes quasi-normal. To a high degree of accuracy, quasinormal ringing can be approximated...

refined iteratively, that is, the values are obtained by successive approximation: β j k + 1 = β j k + Δ β j , {\displaystyle {\beta _{j}}^{k+1}={\beta...

states of light modes, which are harmonic oscillators. Examples of Wigner-function time evolutions in a quantum harmonic oscillator Wigner quasiprobability...

lattice. In general, the analytic solutions are not available, and the approximations required for manageable numerical calculations do not provide accurate...

model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low-temperature dependence...

inverters produce square waves or quasi-square waves. One measure of the purity of a sine wave is the total harmonic distortion (THD). Technical standards...

converted to quasi-sinusoidal AC voltage output using the inverter's active switching elements. VSI drives provide higher power factor and lower harmonic distortion...

A quasi-experiment is a research design used to estimate the causal impact of an intervention. Quasi-experiments share similarities with experiments and...

Weiss, G.; Ipatova, I. (1971). Theory of lattice dynamics in the harmonic approximation. Solid State Physics. Vol. Supplement 3 (Second ed.). New York:...

final result, the approximation of π. There are two important considerations: If the points are not uniformly distributed, the approximation will be poor....

the development of fundamental techniques for the entire field" of approximation algorithms. In the weighted set cover problem, each set is assigned...

observation of two-photon absorption at Bell Labs and the discovery of second-harmonic generation by Peter Franken et al. at University of Michigan, both shortly...

means Arithmetic mean Geometric mean Harmonic mean Geometric–harmonic mean Arithmetic–geometric mean Weighted mean Quasi-arithmetic mean Classical orthogonal...

total harmonic distortion assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation for...

different modes, or harmonics, and when a piano hammer strikes a string it excites multiple harmonics at the same time. The first harmonic (or fundamental...

Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive...

matrices can help overcome these challenges. This approach may be based on harmonic analysis and filtering of signals in the frequency domain using the Fourier...