scholarly journals Spatial-phase focusing of matrix simulator radiators at two receiving points

2020 ◽  
pp. 60-67
Author(s):  
Timur Sabitov ◽  
Keyword(s):  
Simulation Modeling ◽  
Numerical Experiments ◽  
Angular Size ◽  
Position System ◽  
One Dimensional ◽  
Direction Finder ◽  
Straight Line ◽  
Spaced Antennas ◽  
The Given ◽  
Theoretical Results

This paper discusses the issues of constructing the configuration of a coherent matrix simulator for modeling echo signals of a two-position system. The condition is formulated in the form of a system of equations that the emitted signals are in-phase at both points of reception. A matrix satisfying this condition provides a simulation of a target in the same position for two spaced antennas. To ensure in-phase operation, it is proposed to use the possibilities of placing the radiators and controlling the initial phases of the signals. Relations are obtained for calculating the coordinates of the 2-point configuration and for calculating the phase addition value. Based on these relations, an algorithm for the synthesis of an extended one-dimensional matrix with the required angular size is developed. It is shown that the points of such a matrix can be located on one straight line. The obtained algorithm was used to synthesize a configuration of seven emitters for the given parameters of the two-position system. Using numerical experiments, the adequacy of the model was verified. Different positions of the point target were set, and a monopulse direction finder model was used to find its direction. The results of numerical experiments confirm the reliability of the theoretical results. They can be used in mathematical and simulation modeling of reflections from real radar targets for two-position systems.

Learning Control of Time-Delay Chaotic Systems and its Applications

1998 ◽  
Vol 08 (12) ◽  
pp. 2457-2465 ◽  
Author(s):  
Keiji Konishi ◽  
Hideki Kokame
Keyword(s):  
Control System ◽  
Time Delay ◽  
Chaotic System ◽  
Numerical Experiments ◽  
Chaotic Systems ◽  
Learning Control ◽  
Uncertain Information ◽  
Stable Orbit ◽  
One Dimensional ◽  
Theoretical Results

The present paper proposes a learning control system that automatically stabilizes one-dimensional time-delayed chaotic systems. We give a systematic procedure to design the control system using a few pieces of uncertain information on the chaotic system. Furthermore, this control system can be applied to a technique that moves a stable orbit of nonchaotic systems to coexistent unstable points and stabilizes the moving orbit onto these unstable points. To check the theoretical results, we demonstrate some numerical experiments.

Analysis of Geometrically Consistent Schemes with Finite Range Interaction

2017 ◽  
Vol 22 (5) ◽  
pp. 1333-1361
Author(s):  
Hongliang Li ◽  
Pingbing Ming
Keyword(s):  
Error Estimate ◽  
Numerical Experiments ◽  
Optimal Error Estimate ◽  
Finite Range ◽  
Dimensional Problem ◽  
Optimal Error ◽  
Range Interaction ◽  
One Dimensional ◽  
Sharp Stability ◽  
Theoretical Results

AbstractWe analyze the geometrically consistent schemes proposed by E. Lu and Yang [6] for one-dimensional problem with finite range interaction. The existence of the reconstruction coefficients is proved, and optimal error estimate is derived under sharp stability condition. Numerical experiments are performed to confirm the theoretical results.

scholarly journals Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type

2013 ◽  
Vol 23 (2) ◽  
pp. 341-355 ◽  
Author(s):  
Babak Shiri ◽  
Sedaghat Shahmorad ◽  
Gholamreza Hojjati
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Collocation Methods ◽  
Algebraic Equations ◽  
Convergence Properties ◽  
Piecewise Continuous ◽  
The Given ◽  
Uniqueness Of A Solution ◽  
Theoretical Results

In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.

The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

2016 ◽  
Vol 19 (2) ◽  
pp. 411-441 ◽  
Author(s):  
Zhongguo Zhou ◽  
Dong Liang
Keyword(s):  
Domain Decomposition ◽  
Parabolic Equations ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
One Dimensional ◽  
Splitting Technique ◽  
Theoretical Results

AbstractIn the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in L2-norm. Numerical experiments confirm theoretical results.

scholarly journals Numerical Solution of a Nonlocal Problem Modelling Ohmic Heating of Foods

2009 ◽  
Vol 9 (4) ◽  
pp. 391-411
Author(s):  
C. V. Nikolopoulos
Keyword(s):  
High Resolution ◽  
Numerical Solution ◽  
Numerical Experiments ◽  
Ohmic Heating ◽  
Nonlocal Problem ◽  
Local Problem ◽  
One Dimensional ◽  
Resolution Scheme ◽  
Non Local ◽  
Theoretical Results

Abstract An upwind and a Lax-Wendroff scheme are introduced for the solution of a one-dimensional non-local problem modelling ohmic heating of foods. The schemes are studied regarding their consistency, stability, and the rate of convergence for the cases that the problem attains a global solution in time. A high resolution scheme is also introduced and it is shown that it is total-variation-stable. Finally some numerical experiments are presented in support of the theoretical results.

scholarly journals STUDY OF SYNCHRONIZED MOTIONS IN A ONE-DIMENSIONAL ARRAY OF COUPLED CHAOTIC CIRCUITS

1999 ◽  
Vol 09 (11) ◽  
pp. 2219-2224 ◽  
Author(s):  
ZBIGNIEW GALIAS ◽  
MACIEJ J. OGORZAŁEK
Keyword(s):  
Lyapunov Exponents ◽  
Coupling Strength ◽  
Numerical Experiments ◽  
Variational Equation ◽  
Electronic Circuits ◽  
One Dimensional ◽  
Synchronous Motion ◽  
Chaotic Circuits ◽  
The Stability ◽  
Theoretical Results

We investigate the stability of synchronous motion in an array of bidirectionally coupled electronic circuits. We compute Lyapunov exponents of the generic variational equation associated with directions transversal to the synchronization subspace. Using Lyapunov exponents we derive conditions for the coupling strength for which the stable synchronous solution exists. We also find the limit on the size of the network, which can sustain stable synchronous motion. Theoretical results are compared with the results of numerical experiments.

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

scholarly journals Optimising the AR Engraved Structure on Light-Guide Facets for a Wide Range of Wavelengths

Optics ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 25-42
Author(s):  
Ioseph Gurwich ◽  
Yakov Greenberg ◽  
Kobi Harush ◽  
Yarden Tzabari
Keyword(s):  
Theoretical Analysis ◽  
Light Guide ◽  
Spectral Band ◽  
Angular Range ◽  
The Past ◽  
Input And Output ◽  
Wide Range ◽  
The Given ◽  
Theoretical Results ◽  
Shape And Size

The present study is aimed at designing anti-reflective (AR) engraving on the input–output surfaces of a rectangular light-guide. We estimate AR efficiency, by the transmittance level in the angular range, determined by the light-guide. Using nano-engraving, we achieve a uniform high transmission over a wide range of wavelengths. In the past, we used smoothed conical pins or indentations on the faces of light-guide crystal as the engraved structure. Here, we widen the class of pins under consideration, following the physical model developed in the previous paper. We analyze the smoothed pyramidal pins with different base shapes. The possible effect of randomization of the pins parameters is also examined. The results obtained demonstrate optimized engraved structure with parameters depending on the required spectral range and facet format. The predicted level of transmittance is close to 99%, and its flatness (estimated by the standard deviation) in the required wavelengths range is 0.2%. The theoretical analysis and numerical calculations indicate that the obtained results demonstrate the best transmission (reflection) we can expect for a facet with the given shape and size for the required spectral band. The approach is equally useful for any other form and of the facet. We also discuss a simple way of comparing experimental and theoretical results for a light-guide with the designed input and output features. In this study, as well as in our previous work, we restrict ourselves to rectangular facets. We also consider the limitations on maximal transmission produced by the size and shape of the light-guide facets. The theoretical analysis is performed for an infinite structure and serves as an upper bound on the transmittance for smaller-size apertures.

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