China
Africa
Explore chapters and articles related to this topic
Mesoscopic Systems
Published in James J Y Hsu, Nanocomputing, 2017
There are two solutions, depending on their contours of integration. They may be expressed as the Confluent Hypergeometric Functions. One solution is M(a,c,ρ)=Γ(c)Γ(c-a)Γ(a)∫01esρsa-1(1-s)c-a-1ds, $$ M(a,c,\rho ) = \frac{\Gamma(c)}{{\Gamma(c-a)\Gamma (a)}}\mathop \int \limits_{0}^{1} e^{{ s\rho }} s^{{a - 1}} (1-s)^{{c - a - 1}} ds, $$
Existence Theorems and Special Functions
Published in L.M.B.C. Campos, Singular Differential Equations and Special Functions, 2019
valid in the finite complex plane (9.167b) for 2m not an integer (9.1167a). Since the confluent hypergeometric functions are related to both the Whittaker (note 9.40) and generalized Bessel (subsection 9.9.9) functions, the latter two are also related (note 9.41).
Regimes of optical propagation through turbulence: theory and direct numerical simulations
Published in Waves in Random and Complex Media, 2023
Another simplifying assumption made in classical analyses is that the outer scale () or the largest scales of refractive index fluctuations are infinitely large, that is, . The effect of finite outer scale can be incorporated in the limits of the integral in Equation (9) as At very short distances (formally ), substituting Equation (12) in Equation (15) yields where is a Kummer confluent hypergeometric function and is a generalized hypergeometric function [33, 34]. Equation (16) reduces to Equation (14) when implying that the effects of outer-scale are weak at such short distances and relevant only at low Reynolds number. Similar expressions can also be derived for the and regimes. This is done next.
On the evolution of fuel droplet evaporation zone and its interaction with flame front in ignition of spray flames
Published in Combustion Theory and Modelling, 2022
Qiang Li, Chang Shu, Huangwei Zhang
For heterogeneous flame, the solutions of gas temperature , oxidiser mass fraction , and droplet loading in zones 1–4 are (the number subscripts indicate different zones as shown in Figure 1) here , and are here . and are the Kummer confluent hypergeometric function and the Tricomi confluent hypergeometric function, respectively [46]. They can be expressed as where
Polarization characteristics of radially polarized partially coherent vortex beam in anisotropic plasma turbulence
Published in Waves in Random and Complex Media, 2021
Jiangting Li, Jiachao Li, Lixin Guo, Mingjian Cheng, Luo Xi
This paper mainly studies the propagation characteristics of partially polarized vortex beams with radially polarization in anisotropic plasma turbulence. Therefore, we use a plasma turbulent refractive index fluctuation power spectrum based on fractal theory to improve the von Karman spectrum, as shown in the equation [30] under the condition of Markov approximation, the integral in Equation (7) can be rewritten as Where ; and are the anisotropic factor in two transverse directions, , is the internal scale of anisotropic plasma turbulence, is the external scale, is the refractive-index fluctuation variance, and where, . where, d is the fractal dimension of the anisotropic plasma turbulence. is the confluent hypergeometric function of the second kind.