Search results for "matrix method"

Determination of the effective permittivity of dielectric mixtures with the transmission line matrix methodDetermination of the effective permittivit…

2007

In this article, the effective permittivity of two-phase dielectric mixtures is calculated by applying the transmission line matrix (TLM) method. Two slightly different TLM algorithms are considered: a hybrid approach, which combines the TLM method with a subgriding technique based on dual capacitor circuits, to allow a refined description of the material, and a standard or pure TLM approach, which uses a mesh size smaller than the typical dimension of insertions in order to appropriately describe details of the geometry. A study of the statistical distribution of permittivity for insertions in random positions is also presented, showing that the effective permittivity of the mixture tends …

FDTD simulation for electromagnetic radiated emissions in 42 V vehicle electrical systems

2005

In this paper a full 3D approach, based on finite difference time domain method, is used to predict the electromagnetic radiated emissions from 42 V vehicle electrical loads. An experimental set-up has been arranged on purpose. A comparative analysis among measured and computed results is performed. The good agreement obtained among simulated and measured data enables to validate the numerical scheme. The proposed methodology contributes to predict electromagnetic emissions in the automotive environment since the design stage. Moreover, the proposed numerical tool can be used to define, for new vehicle electrical architectures, low cost test methods for electromagnetic compatibility and sui…

Acoustics of porous materials with partially opened porosity

2013

International audience; A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont et al. The present article provides a description of partially opened porosity systems and their numerous potential applications in the general context of the study of porous materials, the classical models describing them, and the characterization techniques. It is shown that the dead-end pore effect can be treated independently and that the description of this effect can be associated with any acoustic model of porous media. Different theoretical developments describing the dead-end porosity effect ar…

Multiple low-frequency broad band gaps generated by a phononic crystal of periodic circular cavity sandwich plates

2017

Abstract We propose a new type of phononic crystal (PnC) composed of a periodic alternation of circular cavity sandwich plates. In the low-frequency regime, the crystal can modulate the propagation of flexural waves. Governing equations are deduced basing on the classical theory of coupled extensional and flexural vibrations of plates. The dispersion relation of the infinite PnC is calculated by combining the transfer matrix method with Bloch theory. The dynamic response of the PnC with finite unit cells is further studied with finite element analysis. An experiment is carried out to demonstrate the performance of the PnC in vibration isolation. Numerical results and experimental results bo…

Acoustic characterization of Silica aerogel clamped plates for perfect absorption purpose

2017

International audience; Silica aerogel has been widely studied as bulk material for its extremely low density and thermal conductivity. Plates or membranes made of this extremely soft materials exhibits interesting properties for sound absorption. A novel signal processing method for the characterization of an acoustic metamaterial made of silica aerogel clamped plates is presented. The acoustic impedance of a silica aerogel clamped plate is derived from the elastic theory for the flexural waves, while the transfer matrix method is used to model reflection and transmission coefficients of a single plate. Experimental results are obtained by using an acoustic impedance tube. The difference b…

A numerical study of atmospheric signals in the Earth-ionosphere electromagnetic cavity with the Transmission Line Matrix method

2006

[1] The effect of the Earth-ionosphere electromagnetic cavity on the spectrum of an atmospheric signal generated by a broadband electrical current source is analyzed numerically by means of the Transmission Line Matrix (TLM) method. Two new TLM meshes are developed, one with transmission lines connected in parallel and the other with connections in series. The equations describing propagation through these parallel or series meshes are equivalent to the Maxwell equations for TEr or TMr modes in the spherical Earth-ionosphere cavity, respectively. The numerical algorithm obtains Schumann resonance frequencies very close to the experimental ones, confirming that this methodology is a valid nu…

Effect of amorphous sequences on the longitudinal acoustic modes in partially crystalline polymers. I. Transfer matrix method

1983

A novel theoretical scheme is developed which enables the determination of the LAM-like vibrations of polymer chains made up of crystalline and amorphous parts as they occur in partially crystalline structures. The boundary conditions effective at the junction points are formulated in terms of the compliances of the associated amorphous sequences. These compliances can be derived from their eigenfrequencies and eigenvectors in a disconnected state. The treatment uses a matrix formalism which can be extended to include bending and torsional motions in a general state of vibration of the crystalline stem. A first numerical example demonstrates that the LA mode of a crystalline stem can be str…

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

2021

<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…

Improving the transmittance of an epsilon-near-zero-based wavefront shaper

2016

Although Epsilon-Near-Zero metamaterials (ENZ) offer many unconventional ways to play with light, the optical impedance mismatch with surroundings can limit the efficiency of future devices. We report here on the improvement of the transmittance of an Epsilon-Near-Zero (ENZ) wavefront shaper. We first address in this paper the way to enhance the transmittance of a plane wave through a layer of ENZ material thanks to a numerical optimization approach based on the Transfer Matrix Method. We then transpose the one dimensional approach to a two dimensional case where the emission of a dipole is shaped into a plane wave by an ENZ device with a design that optimizes the transmittance. As a result…

2019

Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…