By Wei Cai
A different and finished graduate textual content and reference on numerical equipment for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state of the art numerical equipment defined comprise: • Statistical fluctuation formulae for the dielectric constant • Particle-Mesh-Ewald, Fast-Multipole-Method and image-based response box technique for long-range interactions • High-order singular/hypersingular (Nyström collocation/Galerkin) boundary and quantity fundamental tools in layered media for Poisson-Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots • soaking up and UPML boundary stipulations • High-order hierarchical Nédélec part parts • High-order discontinuous Galerkin (DG) and Yee finite distinction time-domain tools • Finite aspect and aircraft wave frequency-domain tools for periodic buildings • Generalized DG beam propagation strategy for optical waveguides • NEGF(Non-equilibrium Green's functionality) and Wigner kinetic equipment for quantum transport • High-order WENO and Godunov and imperative schemes for hydrodynamic delivery • Vlasov-Fokker-Planck and PIC and limited MHD delivery in plasmas
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Extra info for Computational Methods for Electromagnetic Phenomena: Electrostatics in Solvation, Scattering, and Electron Transport
20) Here κi = 0 as the solute interior is modeled by the Poisson equation. 3) and a decaying condition at inﬁnity, namely lim Φ(r) = 0. 4). It has been found (Borukhov, Andelman, & Orland, 1997) that the PB model overestimates the ion density near charged surfaces such as DNA and amino acids. Near a charged surface, ions of opposite signs will be attracted to the surface, whereas ions of the same sign will be repelled to form a so-called Helmholtz double layer, ﬁrst studied by Helmholtz (1853).
60) where the smoother Wan (r) produces an nth-order continuity of G(r) at r = a. 63) Wa3 (r) = − 10 r 6 + 8 r4 − 6 r 2 + 4 . 2 Generalized Born approximations 39 calculating the Born radius with the FFT possible. 59) can be calculated analytically as 1 4π R3 G(r − ri )dr = 1 4π R3 \S i 1 1 dr + |r − ri |4 4π G(r − ri )dr. 64), the ﬁrst integral on the right-hand side equals to 1/a while the second 1 Wan (r)dr term is the integral of the smoother Wan (r) inside Si and equals 4π Si = 3/(5a), 29/(35a), and 65/(63a) when n = 1, 2, and 3, respectively.
57) where kB is the Boltzmann constant, T is the temperature, and π eμEd cos θ/kB T Z= 0 sin θ dθ. 59) where a = μEd /(kB T ), coth is the hyperbolic cotangent function, and L(a) is the so-called Langevin function. For a 1, we have L(a) = 2a5 a a3 − + + ··· . 61) and the average energy W can be identiﬁed with an averaged dipole moment μ Ed (by a symmetric argument) with a magnitude μ = μ cos θ = μ2 Ed . 54) we have P= 0 χE Ni αi Elocal + = i μ2i Ed . 67) r=R where 1 = r 0 and 2 = 0 . Using the boundary conditions, we can show that all coeﬃcients are zero except B1 = 2 r μ 3 , + 1 4π 0 C1 = − 1 2( 4π 0 2 r r − 1) μ .