The Local Spectral Expansion Method for Scattering From One-Dimensional Dielectric-Dielectric Rough Interfaces

1997 ◽  
Vol 11 (6) ◽  
pp. 775-805 ◽  
Author(s):  
A. García-Valenzuela
Keyword(s):  
Expansion Method ◽  
Spectral Expansion ◽  
One Dimensional ◽  
Rough Interfaces

scholarly journals A simple moment model to study the effect of diffusion on the coagulation of nanoparticles due to Brownian motion in the free molecule regime

2012 ◽  
Vol 16 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Wenxi Wang ◽  
Qing He ◽  
Nian Chen ◽  
Mingliang Xie
Keyword(s):  
Method Of Moments ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Particle Coagulation ◽  
Average Volume ◽  
One Dimensional ◽  
The One ◽  
And Diffusion ◽  
Dimensional Domain ◽  
Series Expansion Method

In the study a simple model of coagulation for nanoparticles is developed to study the effect of diffusion on the particle coagulation in the one-dimensional domain using the Taylor-series expansion method of moments. The distributions of number concentration, mass concentration, and particle average volume induced by coagulation and diffusion are obtained.

Linear inversion of gravity data using the spectral expansion method

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 820-824 ◽  
Author(s):  
Rene E. Chavez ◽  
George D. Garland
Keyword(s):  
Inverse Problem ◽  
Gravity Data ◽  
Linear Equations ◽  
Thin Sheet ◽  
Gravity Anomalies ◽  
Expansion Method ◽  
Spectral Expansion ◽  
Uniform Density ◽  
Linear Inversion ◽  
Prismatic Structure

Inversion of gravity anomalies in terms of an anomalous mass distribution with irregular outline but uniform density leads to a nonlinear inverse problem. An alternative approach based on the thin‐sheet approximation can, however, be formulated as a linear inverse problem provided the structures are two‐dimensional. The anomalous mass is represented by a thin sheet, which is located at a depth [Formula: see text] and is divided into M strips with N < M data points. Thus, an underdetermined system of linear equations is obtained which is solved by the spectral expansion method for the surface density distribution of each segment. This set of parameters is then transformed into a prismatic structure with variable depth but uniform density. The modeling procedure involves a noniterative method. A gravity problem is investigated, and the solution obtained compares well with previous interpretations.

Dirac equation and energy levels of electrons in one-dimensional wells: Plane wave expansion method

2020 ◽  
Vol 124 ◽  
pp. 114298
Author(s):  
J.D. Valenzuela-Sau ◽  
Rafael A. Méndez-Sánchez ◽  
R. Aceves ◽  
Raúl García-Llamas
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Energy Levels ◽  
Expansion Method ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
One Dimensional ◽  
Wave Expansion

scholarly journals Second order homogenization of quasi-periodic structures

2018 ◽  
Vol 40 (4) ◽  
pp. 325-348
Author(s):  
Duc Trung Le ◽  
Jean-Jacques Marigo
Keyword(s):  
General Framework ◽  
Volume Fraction ◽  
Effective Properties ◽  
Periodic Structures ◽  
Expansion Method ◽  
Second Order ◽  
Unit Cell ◽  
One Dimensional ◽  
Minimization Problems ◽  
Asymptotic Expansion Method

The paper develops a general framework to derive the effective properties of quasi-periodic elastic medium. By using the asymptotic expansion method, the solution is expanded to the second order by solving a sequence of minimization problems. The effective stiffness tensors fields entering in the expression of the macroscopic energy are obtained by solving several families of microscopic problems posed on the unit cell and which bring into play only the microstructure. As an illustrative example, we consider an anti-plane elastic case of a heterogeneous cylinder made of a bi-layer laminate and submitted to the gravity. The unit cell being one-dimensional, all the associated elementary problems can be solved in a closed form and one shows that the effective energy of the medium expanded up to the second order depends not only on the strain gradient, but also on the gradient of the volume fraction \(\theta\) characterizing the repartition of the two materials in the laminate.

scholarly journals Realization of Twenty Monochromatic Beams using Photonic Structure via Principle of Filtering

2021 ◽  
Author(s):  
K.P. Swain ◽  
Subhankar Das ◽  
Soumya Ranjan Samal ◽  
Sanjay Kumar Sahu ◽  
Gopinath Palai
Keyword(s):  
Wave Equations ◽  
Silicon Monoxide ◽  
Expansion Method ◽  
Critical Parameters ◽  
Infrared Range ◽  
Photonic Structure ◽  
Plane Wave Expansion Method ◽  
One Dimensional ◽  
Different Types ◽  
Silicon Based

Abstract The current work employs silicon-based one dimensional photonic structure which delivers ‘20’ different types of monochromatic beams (wavelengths) via filtering action. The I/P signals are essentially varies from visible to short infrared range to justify the work. Though similar type of works related to filtering application are found in the literature, the present research deals with an output signal which could be deployed in different purposes vis-à-vis dentistry, dermatology, spectroscopy, printing, holography, barcode scanning etc. The physicality of this work incorporates 68 layers of silicon monoxide and silicon based one-dimensional optical waveguide along with their configuration where the plane wave expansion method does fulfill the nitty-gritty of required mathematics to solve out electromagnetic wave equations. Reflectance and transmittance characteristics along with the absorbance are the critical parameters that substantiate the said application.

scholarly journals Spectral expansion method for analysis of a system with shifted Erlang and hyper-Erlang distributions

2021 ◽  
Vol 24 (2) ◽  
pp. 55-61
Author(s):  
Veniamin N. Tarasov ◽  
Nadezhda F. Bakhareva
Keyword(s):  
Waiting Time ◽  
Queuing Theory ◽  
Expansion Method ◽  
Spectral Expansion ◽  
Queuing System ◽  
Erlang Distribution ◽  
Modern Theory ◽  
Calculation Formula ◽  
Average Waiting Time ◽  
Erlang Distributions

In this paper, we obtained a spectral expansion of the solution to the Lindley integral equation for a queuing system with a shifted Erlang input flow of customers and a hyper-Erlang distribution of the service time. On its basis, a calculation formula is derived for the average waiting time in the queue for this system in a closed form. As you know, all other characteristics of the queuing system are derivatives of the average waiting time. The resulting calculation formula complements and expands the well-known unfinished formula for the average waiting time in queue in queuing theory for G/G/1 systems. In the theory of queuing, studies of private systems of the G/G/1 type are relevant due to the fact that they are actively used in the modern theory of teletraffic, as well as in the design and modeling of various data transmission systems.

Sign in / Sign up

Export Citation Format

Share Document