The charge and current densities are associated with the so-called “free” charges, and for a sourcefree medium, J = 0 and ρ = 0. The Gauss magnetic field law and the continuity equation should be treated as auxiliary or dependent equations in the entire system of equations (1.1)–(1.5). Which expresses the conservation of electric charge. Analogously, taking the divergence of Maxwell–Ampere law and using the Gauss electric field law we obtain the continuity equation: The first three equations in Maxwell’s theory are independent, because the Gauss magnetic field law can be obtained from Faraday’s law by taking the divergence and by setting the integration constant with respect to time equal to zero. Where t is time, E the electric field, H the magnetic field, B the magnetic induction, D the electric displacement and ρ and J the electric charge density and current density, respectively. The behavior of the macroscopic field at interior points in material media is governed by Maxwell’s equations:Ģ 1 Basic Theory of Electromagnetic Scattering , Jackson, van de Hulst, Kerker, Bohren and Hu man, and Born and Wolf. Other excellent textbooks on classical electrodynamics and optics have been given by Stratton, Tsang et al. Our presentation follows the treatment of Kong and Mishchenko et al. We present the fundamental laws of electromagnetism, derive the boundary conditions and describe the properties of isotropic, anisotropic and chiral media by constitutive relations. In this section, we formulate the Maxwell equations that govern the behavior of the electromagnetic fields.
Therefore, the integral and orthogonality relations, the addition theorems and the basic properties of the scalar and vector spherical wave functions are reviewed in Appendices A and B.ġ.1 Maxwell’s Equations and Constitutive Relations We decided to leave out some technical details in the presentation. We then derive new systems of vector functions for internal field approximations by analyzing wave propagation in isotropic, anisotropic and chiral media, and present the T -matrix formulation for electromagnetic scattering. We begin with a brief discussion on the physical background of Maxwell’s equations and establish vector spherical wave expansions for the incident field. This chapter is devoted to present the fundamentals of the electromagnetic scattering theory which are relevant in the analysis of the null-field method. 317īasic Theory of Electromagnetic Scattering ĭ Completeness of Vector Spherical Wave Functions. 276Ĭ Computational Aspects in E ective Medium Theory. 242 3.9 Particle on or Near a Plane Surface. 198ģ.3 Homogeneous, Axisymmetric and Nonaxisymmetric Particles. 185ģ.1.2 Incomplete Uniform Distribution Function. 183ģ.1.1 Complete Uniform Distribution Function. 164 2.10.2 Particle on or near an Arbitrary Surface.
164 2.10.1 Particle on or near a Plane Surface. 162Ģ.10 Particle on or near an Infinite Surface. 159 2.9.3 Generalized Ewald–Oseen Extinction Theorem. 150 2.9.2 Generalized Lorentz–Lorenz Law. 143 2.7.3 Formulation with Discrete Sources. 139 2.7.2 Formulation for a Particle with N Constituents. 136 2.6.5 Recursive Aggregate T -matrix Algorithm. 132 2.6.4 Formulation with Phase Shift Terms. 131 2.6.3 Superposition T -matrix Method. 124 2.6.2 Formulation for a System with N Particles.
120 2.5.4 Concentrically Layered Spheres. 118 2.5.3 Formulation with Discrete Sources. 106 2.4.2 Formulation without Addition Theorem. 105 2.4.1 Formulation with Addition Theorem.
Read a full list of new features in X-Particles 3.2.4 Inhomogeneous Particles. Indsydium has also simplified the pricing of new licences of the software, dispensing with the old £340 node-locked licence, and reducing the price of floating licences from £440 to £390 (around $590).įor studios, there is also a new multi-seat option that doesn’t require an active internet connection.
X-Particles 3.5 is available now for any 64-bit edition of Cinema 4D R13 and above, on Windows and OS X. In addition, Cinema 4D lights can trigger particle emission from surfaces particles can be used as single falloff objects and the group object now has three modes, from display only to control over particle properties.
The update also adds a new Trail Deformer, while the existing xpFollowPath Modifier now has direct access to Cinema 4D’s MoGraph Cloner, enabling users to use closed splines within a Cloner object.
New features in version 3.5 include the new xpSound Modifier (above), which enables audio to drive particles’ speed, colour, size and other parameters for instant music visualisation. New audio modifier and trail deformer, illumination-based emission and better grouping The update adds a new trail deformer and audio-driven modifier, and cuts the price of floating licences. Insydium has released X-Particles 3.5, the latest update to its versatile Cinema 4D particle simulation tool.