Search results for "matrix method"
showing 10 items of 32 documents
A finite difference time domain model for the Titan ionosphere Schumann resonances
2007
[1] This paper presents a numerical approach to model the electrical properties of Titan's atmosphere. The finite difference time domain technique is applied to model the atmosphere of Saturn's satellite in order to determine Schumann resonant frequencies and electromagnetic field distributions at the extremely low frequency range. Spherical coordinates are employed, and periodic boundary conditions are implemented in order to exploit the symmetry in rotation of the celestial body. Results are compared with a previous model using the transmission line matrix method up to 180 km altitude. For the first time a numerical FDTD model up to 800 km altitude is carried out, and we report lower freq…
Teaching stable two-mirror resonators through the fractional Fourier transform
2009
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation–lens–propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincid…
A transfer matrix method for the analysis of fractal quantum potentials
2005
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential.
Bloch surface waves engineering in one-dimensional photonic crystals with a chiral cap layer
2019
We investigate the localization properties of surface waves created at the interface between a truncated 1D photonic crystal and homogeneous medium in the presence of a chiral cap layer using the transfer matrix method. The numerical results show that the interface can support surface waves with both transverse electric and transverse magnetic polarizations. We demonstrate that the surface waves can be engineered by varying the chirality parameter of the cap layer, which plays an important role in controlling and localization of surface states. It is shown that the effect of a chirality parameter on surface waves with transverse electric polarization is more remarkable compared with surface…
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…
Rapid parameter determination of discrete damped sinusoidal oscillations
2020
We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time- and frequency-domain-based computational approaches in terms of their accuracy and precision and computational time required in estimating the frequencies of such signals, and observe a general trade-off between precision and speed. Our motivation is precise and rapid analysis of damped sinusoidal signals as these become relevant in view of the recent experimental developments in cavity-enhanced polarimetry and ellipsometry, where the relevant time scales and frequencies are typically within the ∼1 − 10 µs and ∼1 − 100 MHz ranges, …
A New Approach to the Modeling of Anisotropic Media with the Transmission Line Matrix Method
2021
A reformulation of the Transmission Line Matrix (TLM) method is presented to model non-dispersive anisotropic media. Two TLM-based solutions to solve this problem can already be found in the literature, each one with an interesting feature. One can be considered a more conceptual approach, close to the TLM fundamentals, which identifies each TLM in Maxwell’s equations with a specific line. But this simplicity is achieved at the expense of an increase in the memory storage requirements of a general situation. The second existing solution is a more powerful and general formulation that avoids this increase in memory storage. However, it is based on signal processing techniques and considerabl…
Factors selection in landslide susceptibility modelling on large scale following the gis matrix method: application to the river Beiro basin (Spain)
2012
A procedure to select the controlling factors connected to the slope instability has been defined. It allowed us to assess the landslide susceptibility in the Rio Beiro basin (about 10 km2) over the northeastern area of the city of Granada (Spain). Field and remote (Google EarthTM) recognition techniques allowed us to generate a landslide inventory consisting in 127 phenomena. To discriminate between stable and unstable conditions, a diagnostic area had been chosen as the one limited to the crown and the toe of the scarp of the landslide. 15 controlling or determining factors have been defined considering topographic, geologic, geomorphologic and pedologic available data. Univariate tests, …
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…
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…