scholarly journals On the Sampling of the Fresnel Field Intensity over a Full Angular Sector

Electronics ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 832
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Discrete Model ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Continuous Model ◽  
Sampling Theorem ◽  
Theory Approach ◽  
Discretization Scheme ◽  
Lifting Technique ◽  
The Fourier Transform

In this article, the question of how to sample the square amplitude of the radiated field in the framework of phaseless antenna diagnostics is addressed. In particular, the goal of the article is to find a discretization scheme that exploits a non-redundant number of samples and returns a discrete model whose mathematical properties are similar to those of the continuous one. To this end, at first, the lifting technique is used to obtain a linear representation of the square amplitude of the radiated field. Later, a discretization scheme based on the Shannon sampling theorem is exploited to discretize the continuous model. More in detail, the kernel of the related eigenvalue problem is first recast as the Fourier transform of a window function, and after, it is evaluated. Finally, the sampling theory approach is applied to obtain a discrete model whose singular values approximate all the relevant singular values of the continuous linear model. The study refers to a strip source whose square magnitude of the radiated field is observed in the Fresnel zone over a 2D observation domain.

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An SVD Approach for Estimating the Dimension of Phaseless Data on Multiple Arcs in Fresnel Zone

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 606
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Electric Current ◽  
Phase Retrieval ◽  
Fresnel Zone ◽  
Singular Values ◽  
Quadratic Model ◽  
Analytical Prediction ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem ◽  
Lifting Operator

In this article, we tackle the question of evaluating the dimension of the data space in the phase retrieval problem. With the aim to achieve this task, we first exploit the lifting technique to recast the quadratic model as a linear one. After that, we evaluate analytically the singular values of the lifting operator, and we quantify the dimension of the data space by counting the number of “significant” singular values. In the last part of the article, we show some numerical results in order to corroborate our analytical prediction on the singular values’ behavior of the lifting operator and on the dimension of the data space. The analysis is performed for a 2D scalar geometry consisting of an electric current strip whose square magnitude of the radiated field is observed on multiple arcs of circumference in Fresnel zone.

scholarly journals Asymptotic Study of the Radiation Operator for the Strip Current in Near Zone

Electronics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 911
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Eigenvalue Problem ◽  
Near Field ◽  
Measurement Techniques ◽  
Sampling Strategy ◽  
Singular Values ◽  
Continuous Model ◽  
Sampling Theory ◽  
Theory Approach ◽  
Near Zone ◽  
Band Limited

In this paper, we address the problem of how to efficiently sample the radiated field in the framework of near-field measurement techniques. In particular, the aim of the article is to find a sampling strategy for which the discretized model exhibits the same singular values of the continuous problem. The study is done with reference to a strip current whose radiated electric field is observed in the near zone over a bounded line parallel to the source. Differently from far zone configurations, the kernel of the related eigenvalue problem is not of convolution type, and not band-limited. Hence, the sampling-theory approach cannot be directly applied to establish how to efficiently collect the data. In order to surmount this drawback, we first use an asymptotic approach to explicit the kernel of the eigenvalue problem. After, by exploiting a warping technique, we recast the original eigenvalue problem in a new one. The latter, if the observation domain is not too large, involves a convolution operator with a band-limited kernel. Hence, in this case the sampling-theory approach can be applied, and the optimal locations of the sampling points can be found. Differently, if the observation domain is very extended, the kernel of the new eigenvalue problem is still not convolution. In this last case, in order to establish how to discretize the continuous model, we perform a numerical analysis.

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

scholarly journals Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zhaofeng An ◽  
Suxia Zhang ◽  
Jinhu Xu
Keyword(s):  
Public Health ◽  
Health Education ◽  
Differential Equations ◽  
Discrete Model ◽  
Public Health Education ◽  
Continuous Model ◽  
Basic Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme

In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.

scholarly journals A Discrete Model for HIV Infection with Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Brahim EL Boukari ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Time Delays ◽  
Discrete Model ◽  
Distributed Delay ◽  
Continuous Model ◽  
Distributed Time Delays ◽  
A Cell ◽  
The Times ◽  
Theoretical Results

We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.

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