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This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree =. Some of these formulas are expressed in terms of the Cartesian expansion of the spherical harmonics into polynomials in x , y , z , and r .
Inverting the matrix form of the Zoeppritz equations give the coefficients as a function of angle. Although the four equations can be solved for the four unknowns, they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved (density, velocity etc.). [3]
Integrating over a hemisphere then affords the flux perpendicular to a plane (F, [W/m 2]). Schwarzschild's equation is the formula by which you may calculate the intensity of any flux of electromagnetic energy after passage through a non-scattering medium when all variables are fixed, provided we know the temperature, pressure, and composition ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface. Right: The reduction in flux passing through a surface can be visualized by reduction in F or d S equivalently (resolved into components , θ is angle to ...
The general form of wavefunction for a system of particles, each with position r i and z-component of spin s z i. Sums are over the discrete variable s z , integrals over continuous positions r . For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is ...
Conversion and its related terms yield and selectivity are important terms in chemical reaction engineering.They are described as ratios of how much of a reactant has reacted (X — conversion, normally between zero and one), how much of a desired product was formed (Y — yield, normally also between zero and one) and how much desired product was formed in ratio to the undesired product(s) (S ...
The maximum value of f without light concentration (with reflectors for example) is just f ω /2, or 1.09 × 10 −5, according to the authors. Using the above-mentioned values of Q s and Q c, this gives a ratio of open-circuit voltage to thermal voltage of 32.4 (V oc equal to 77% of the band gap). The authors derive the equation
Stochastic integrals can rarely be solved in analytic form, making stochastic numerical integration an important topic in all uses of stochastic integrals. Various numerical approximations converge to the Stratonovich integral, and variations of these are used to solve Stratonovich SDEs (Kloeden & Platen 1992).