scholarly journals Multiple Scattering by Two PEC Spheres Using Translation Addition Theorem

Electronics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 126
Author(s):  
Sidra Batool ◽  
Mehwish Nisar ◽  
Lorenzo Dinia ◽  
Fabio Mangini ◽  
Fabrizio Frezza
Keyword(s):  
Multiple Scattering ◽  
Electric Fields ◽  
Spherical Harmonics ◽  
Addition Theorem ◽  
Simulation Software ◽  
Biological Molecules ◽  
Spherical Particles ◽  
Near Zone ◽  
Comsol Simulation ◽  
Spherical Vector

An analysis of multiple scattering by two Perfect Electric Conducting (PEC) spheres using translation Addition Theorem (AT) for spherical vector wave functions is presented. Specifically, the Cruzan formalism is used to represent the AT for spherical harmonics, which introduces the translation coefficients for transformation of spherical harmonics from one coordinate to another. The adoption of these coefficients with the use of two PEC spheres in a near zone region makes the calculation of multiple scattering electric fields very efficient. As an illustration, the mathematical formation using advanced computational approaches was inspected. Then, the generic truncation criteria in the scattered electric field by two PEC spheres was deeply investigated using translation AT. However, the numerical validation was obtained using Comsol simulation software. This approach will allow to evaluate the scattering from macro-structures composed of spherical particles, i.e., biological molecules, clouds of airborne particles, etc. An original and fully general solution to the problem using vector quantities is introduced, and the convergence of the solution in several numerical examples is also demonstrated. This approach takes into account the effect of multiple scattering by two PEC spheres for spherical vector function.

scholarly journals Derivatives of addition theorems for Legendre functions

1995 ◽  
Vol 37 (2) ◽  
pp. 212-234 ◽  
Author(s):  
D.E. Winch ◽  
P.H. Roberts
Keyword(s):  
Spherical Harmonics ◽  
Chebyshev Polynomials ◽  
Legendre Polynomials ◽  
Addition Theorem ◽  
Legendre Functions ◽  
Addition Theorems ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Derivatives Of

AbstractDifferentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.

scholarly journals Study and Simulation of a Sensor Based on 2D Photonic Crystals for the Detection of Aromatic Compounds: C6H5I, C6H5F and C6H5Cl

2021 ◽  
Vol 45 (4) ◽  
pp. 335-339
Author(s):  
Mehdi Ghoumazi ◽  
Messaoud Hameurlain
Keyword(s):  
Refractive Index ◽  
Energy Density ◽  
Photonic Crystals ◽  
Ring Resonator ◽  
Organic Materials ◽  
Simulation Software ◽  
Dielectric Constants ◽  
Total Energy Density ◽  
Materials Used ◽  
Comsol Simulation

A new study was presented on a new sensor based on two-dimensional photonic crystals (Phc's) to detect the following three organic materials: iodobenzene (C6H5I), fluorobenzene (C6H5F), chlorobenzene (C6H5Cl). These materials have dielectric constants (εr) equal to 2.623; 2.140; 2.318, respectively. The proposed sensor is a structure made of silicon rods submerged in air plus a ring resonator. The ring resonator is stuck between two horizontal waveguides. At the end of the ends of the structure there are four ports where port 1 and 2 belong to the top guide and port (3) and (4) the bottom one. In order to analyze the behavior of the sensor, a plane wave expansion approach (PWE) and the finite element method (FEM) are applied. Thanks to the MATLAB and COMSOL simulation software, we were able to obtain the following numerical results: the norm of the electric field, the total energy density and this last magnitude according to the refractive indices of the different organic materials used. We could observe variations in energy density for each material. So, this change is due to their refractive index which varies from one material to another. In this study, we have fixed the other parameters like the constant of the lattice "a" and the radius "r" and we are interested in the dielectric constants (εr) or more precisely the refractive index (n), the latter proves that it is one of the important parameters for detection.

scholarly journals AC Electrokinetics of Salt-Free Multilayered Polymer-Grafted Particles

Polymers ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2097
Author(s):  
Silvia Ahualli ◽  
Sara Bermúdez ◽  
Félix Carrique ◽  
María L. Jiménez ◽  
Ángel V. Delgado
Keyword(s):  
Electric Fields ◽  
Polystyrene Latex ◽  
Spherical Particles ◽  
Layer By Layer ◽  
Ac Electrokinetics ◽  
Grafted Polymer ◽  
Coated Particle ◽  
Alternating Electric Fields ◽  
Dispersion Media ◽  
Grafted Nanoparticles

Interest in the electrical properties of the interface between soft (or polymer-grafted) nanoparticles and solutions is considerable. Of particular significance is the case of polyelectrolyte-coated particles, mainly taking into account that the layer-by-layer procedure allows the control of the thickness and permeability of the layer, and the overall charge of the coated particle. Like in simpler systems, electrokinetic determinations in AC fields (including dielectric dispersion in the 1 kHz–1 MHz frequency range and dynamic electrophoresis by electroacoustic methods in the 1–18 MHz range) provide a large amount of information about the physics of the interface. Different models have dealt with the electrokinetics of particles coated by a single polymer layer, but studies regarding multi-layered particles are far scarcer. This is even more significant in the case of so-called salt-free systems; ideally, the only charges existing in this case consist of the charge in the layer(s) and the core particle itself, and their corresponding countercharges, with no other ions added. The aims of this paper are as follows: (i) the elaboration of a model for the evaluation of the electrokinetics of multi-grafted polymer particles in the presence of alternating electric fields, in dispersion media where no salts are added; (ii) to carry out an experimental evaluation of the frequency dependence of the dynamic (or AC) electrophoretic mobility and the dielectric permittivity of suspensions of polystyrene latex spherical particles coated with successive layers of cationic, anionic, and neutral polymers; and (iii) finally, to perform a comparison between predictions and experimental results, so that it can be demonstrated that the electrokinetic analysis is a useful tool for the in situ characterization of multilayered particles.

Electroelastic Response of Isotropic Dielectric Elastomer Composites with Deformation-Dependent Apparent-Permittivity Matrix

2020 ◽  
Vol 87 (9) ◽  
Author(s):  
Victor Lefèvre
Keyword(s):  
Free Energy ◽  
Electric Fields ◽  
Dielectric Response ◽  
Dielectric Elastomer ◽  
Spherical Particles ◽  
Full Field ◽  
The Matrix ◽  
Elastomer Composites ◽  
Non Gaussian ◽  
Elastic Dielectric

Abstract This paper puts forth an approximate yet accurate free energy for the elastic dielectric response—under finite deformations and finite electric fields—of non-percolative dielectric elastomer composites made out of a non-Gaussian dielectric elastomer matrix with deformation-dependent apparent permittivity isotropically filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. While the proposed free energy applies in its most general form to arbitrary isotropic non-percolative microstructures, closed-form specializations are recorded for the practically relevant cases of rigid or liquid-like spherical particles. The proposed free energy is exact by construction in the asymptotic context of small deformations and moderate electric fields and is shown to remain accurate for arbitrary large deformations and electric fields via comparisons with full-field finite-element simulations. The proposed constitutive model is deployed to probe the electrostriction response of these dielectric elastomer composites and corresponding results reveal that their elastic dielectric response strongly depends on the deformation-dependent apparent permittivity of the matrix they comprise.

On the expansion of a Coulomb potential in spherical harmonics

1950 ◽  
Vol 46 (4) ◽  
pp. 626-633 ◽  
Author(s):  
B. C. Carlson ◽  
G. S. Rushbrooke
Keyword(s):  
Spherical Harmonics ◽  
Coulomb Potential ◽  
Addition Theorem ◽  
Electrostatic Potentials ◽  
Legendre Functions ◽  
Expansion Formula ◽  
Image Position

The addition theorem for Legendre functions leads, as is well known, to a useful expansion formula of importance in the theory of electrostatic potentials,or, in an alternative notation,

scholarly journals Modeling multiple scattering transient of an ultrashort laser pulse by spherical particles

2022 ◽  
pp. 110696
Author(s):  
Geoffroy Chaussonnet ◽  
Loïc Mees ◽  
Miloš Šormaz ◽  
Patrick Jenny ◽  
Philippe M. Bardet
Keyword(s):  
Laser Pulse ◽  
Multiple Scattering ◽  
Ultrashort Laser Pulse ◽  
Spherical Particles ◽  
Ultrashort Laser

scholarly journals Experimental and theoretical study of a new CDI device for the treatment of desulfurization wastewater

2021 ◽  
Author(s):  
Chang Liu ◽  
Lan Ma ◽  
Yongyi Xu ◽  
Feng Wang ◽  
Yu Tan ◽  
...  
Keyword(s):  
Simulation Software ◽  
Capacitive Deionization ◽  
Adsorption Model ◽  
Isothermal Adsorption ◽  
Freundlich Model ◽  
Theoretical Support ◽  
Alkaline Conditions ◽  
Comsol Simulation ◽  
Desulfurization Wastewater ◽  
Excellent Stability

Abstract According to the characteristics of desulfurization wastewater, A new capacitive deionization (CDI) device was designed to study the desalination characteristics of desulfurization wastewater in this paper. The experiments investigated the desalination efficiency under different conditions which find that the best desalination efficiency is achieved at a voltage of 1.2V, pH = 11 and 50℃. Besides, the ion adsorption is more favorable under acidic and alkaline conditions. The anion and cation removal performance experiments showed that the order of cation removal is Mg2+༞Na+༞Ca2+༞K+ and the order of anion removal is Cl−༞CO32−༞NO3−༞SO42−༞HCO3−. The mechanism of CDI was studied and analyzed by isothermal adsorption model and COMSOL simulation software. It was found that the Freundlich model and Redlich-Peterson model have a good fit with the experimental results. The experiments show that the CDI device has excellent stability. CDI device was used to treat actual desulfurization wastewater. Furthermore, the study provides theoretical support for the industrial application of CDI for desulfurization wastewater treatment in the future.

Simulation and Experimental Research for Microparticles in Microchannels With Dielectrophoretic Field-Flow Fractionation

2010 ◽  
Author(s):  
Minghao Song ◽  
Hongwei Sun
Keyword(s):  
Microfluidic Channel ◽  
Biological Molecules ◽  
Spherical Particles ◽  
Uniform Electric Field ◽  
Field Flow Fractionation ◽  
Particle Movement ◽  
Moment Theory ◽  
Particle Hydrodynamics ◽  
Flow Fractionation ◽  
Good Agreement

The Dielectrophoretic Field-flow Fractionation (DEP-FFF) is a very promising separation technique for particles and biological molecules. To further explore this technology, we conducted a computational and experimental investigation of a single particle movement in a PDMS microfluidic channel under DEP force, where both electrokinetic effects and particle hydrodynamics are considered. The model was first validated with dipole moment theory, and a polystyrene particle (∼10 μm) behavior in a non-uniform electric field created by a pair of non-symmetrical electrodes was then studied numerically. The simulation results were compared with experimental results and a good agreement was obtained. Further research is underway to study the behavior of non-spherical particles (such as nanowire, nanorod, and nanofiber) in other microfluidic systems.

scholarly journals Fingerprints of the Cosmological Constant: Folds in the Profiles of the Axionic Dark Matter Distribution in a Dyon Exterior

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 455 ◽  
Author(s):  
Alexander Balakin ◽  
Dmitry Groshev
Keyword(s):  
Dark Matter ◽  
Cosmological Constant ◽  
Electric Fields ◽  
Double Electric Layer ◽  
De Sitter ◽  
Electric Structure ◽  
Near Zone ◽  
Sitter Model ◽  
Dark Matter Distribution ◽  
The Right

We consider the magnetic monopole in the axionic dark matter environment (axionic dyon) in the framework of the Reissner-Nordström-de Sitter model. Our aim is to study the distribution of the pseudoscalar (axion) and electric fields near the so-called folds, which are characterized by the profiles with the central minimum, the barrier on the left, and the maximum on the right of this minimum. The electric field in the fold-like zones is shown to change the sign twice, i.e., the electric structure of the near zone of the axionic dyon contains the domain similar to a double electric layer. We have shown that the described fold-like structures in the profile of the gravitational potential, and in the profiles of the electric and axion fields can exist, when the value of the dyon mass belongs to the interval enclosed between two critical masses, which depend on the cosmological constant.

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