By Wei Cai
A distinct 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 tools defined comprise: • Statistical fluctuation formulae for the dielectric constant • Particle-Mesh-Ewald, Fast-Multipole-Method and image-based response box approach for long-range interactions • High-order singular/hypersingular (Nyström collocation/Galerkin) boundary and quantity vital 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 components • High-order discontinuous Galerkin (DG) and Yee finite distinction time-domain tools • Finite point and aircraft wave frequency-domain tools for periodic buildings • Generalized DG beam propagation process for optical waveguides • NEGF(Non-equilibrium Green's functionality) and Wigner kinetic equipment for quantum transport • High-order WENO and Godunov and vital schemes for hydrodynamic delivery • Vlasov-Fokker-Planck and PIC and limited MHD shipping in plasmas
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Additional info for Computational Methods for Electromagnetic Phenomena: Electrostatics in Solvation, Scattering, and Electron Transport
124) Assuming a z-directed uniform external ﬁeld E = (0, 0, Ez ), we have ΔMz = λ|V |Ez . , Aαβ = 0, Hzz = 1 kB T Mz Mz − Mz 2 . 129) we have the Clausius–Mossotti type ﬂuctuation formula (Neumann, 1983; Stern & Feller, 2003) for the dielectric constant: 3( − 1) 1 = 3 0 |V |kB T r +2 r M2 − M 2 . 130) can be obtained by molecular dynamics simulation of the system in various ensembles (constant temperature in this case) (Frenkel & Smit, 2001). 130) is for a periodic system and other ﬂuctuation formulae for diﬀerent conﬁgurations are derived for planar layers (Ballenegger & Hansen, 2005) and liquids encapsulated in spherical cavities (Berendsen, 1972; Adams & McDonald, 1976; Powles, Fowler, & Evans, 1984).
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).
X)−φ∞ = (φOHP − φ∞ ) e−1 , giving ldouble-layer = d + κ−1 . 25) The existence and the size of the double layer demonstrate the need to include the ion size in a theory for ionic solvents, especially in the presence of a charged surface associated with biomolecules. It is clear that the packing density of the ions near the charged surface within the Helmholtz layer will generate a saturation limit for the ion density near the charged surface, while, on the contrary, the PB model is known to produce unbounded ion density as the surface charge increases.