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numerical reconstruction of one-photon mixed states by means of the degree of linear polarisation

JOURNAL OF MODERN OPTICS 2012年第19期59卷 1700-1704页

作者： Michalik, Lukasz Domanski, Andrzej W. Warsaw Univ Technol Fac Phys PL-00662 Warsaw Poland

In this paper the authors present the idea for reconstructing one-photon states. Reconstructing a quantum state means measuring the probability distribution P that allows one to write the density operator for the analysed state. The most commonly known approach for the quantum reconstruction is the quantum tomography. Our alternative method assumes that the analysed field is coupled with the reference field which is described by the parameters settled during a measurement. In the proposed gedankenexperiment the degree of linear polarisation (DOLP) of this combined beam is measured using a rotating linear polariser. We state that it is possible to obtain the P-function by changing the parameters of reference beams and by preparing the series of DOLP measurements. This series of data leads to the system of equations. The values of the P-function at chosen points are the unknowns of this system. This article focuses on the numerical algorithm for solving these equations.

关键词： photons degree of linear polarisation quantum state reconstruction numerical algorithm

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numerical and experimental study of the viscosity and mechanical parameters effect on tow feeding quality during automated fiber placement

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JOURNAL OF MANUFACTURING PROCESSES 2023年 96卷 31-40页

作者： Li, Yan Zheng, Chenggan Jiang, Junxia Wang, Han Zhu, Weidong Wang, Qing Chen, Chao Zhang, Shuai Ke, Yinglin Zhejiang Univ Sch Mech Engn State Key Lab Fluid Power & Mechatron Syst Hangzhou 310027 Peoples R China Zhejiang Univ Sch Mech Engn Key Lab Adv Mfg Technol Zhejiang Prov Hangzhou 310027 Peoples R China Hiwing Mat Ind Co Ltd Suzhou 215131 Peoples R China

For automated fiber placement (AFP), it is crucial to research the contact characteristics between tow and roller during the tow feeding process. However, it has not been widely explored. In this paper, a theoretical model of contact characteristics for the tow feeding process is established by analyzing the distribution of normal stress, tangential stress, adhesion zone, and slip zone, respectively. The model proposed a numerical algorithm for calculating the contact characteristic. Then the contact characteristic of the tow feeding system can be acquired and validated by the experiment and finite element method. The model that provides theoretical support for AFP optimization. Furthermore, proper pressure (P = 0.6Mpa) and tension (T = 3 N) for towpreg feeding under experimental conditions were obtained.

关键词： Automated fiber placement Tow feeding system Contact characteristic numerical algorithm

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IMPROVED numerical TECHNIQUE FOR OSCILLATOR FREQUENCY STABILITY ANALYSIS

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ELECTRONICS LETTERS 1989年第1期25卷 71-72页

作者： WAN, KW VILAR, E ROBERTS, JH PLESSEY ELECTR SYST RES LTD ROMSEY SO51 0ENHANTSENGLAND

Introduces a statistical quantity, termed the extended Hadamard variance, for the spectral analysis of the frequency fluctuations nu (t) of an oscillator. The samples of the time series nu (t) are the gated averages nu tau or counts of a digital frequency counter spaced by the dead time tau d. The analysis technique and the numerical algorithm combine the flexibility of the extended two-sample variance with a much higher resolution spectral analysis capability, as shown by experimental results. The limitations are also indicated.

关键词： digital frequency counter experimental results extended Hadamard variance extended two-sample variance frequency fluctuations frequency stability gated averages higher resolution spectral analysis capability limitations numerical algorithm oscillator frequency stability analysis oscillators signal processing spectral analysis spectral analysis statistical quantity time series

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Reconstruction of the 1783 Scilla landslide, Italy: numerical investigations on the flow-like behaviour of landslides

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LANDSLIDES 2019年第6期16卷 1065-1076页

作者： Wang, Liang Zaniboni, Filippo Tinti, Stefano Zhang, Xue Univ Bologna Dipartimento Fis & Astron DIFA Viale Berti Pichat 8 I-40127 Bologna Italy Univ Liverpool Dept Civil Engn & Ind Design Liverpool Merseyside England

This paper presents a mass flow model that includes gravity force, material stresses, drag force and topography effects solving a set of hyperbolic partial differential equations by using a so-called depth-averaged technique. The model is non-linear and general enough to tackle various problems of interest for geophysics and environmental engineering, such as the dynamic evolution of flow-like avalanches, the dam break problem (involving only water flow) and the generation of tsunami waves by landslides. The model is based on a Eulerian fluid solver, using a second-order central scheme with a minmod-like limiter;is tested against a number of typical benchmark cases, including analytical solutions and experimental laboratory data;and also compared with other numerical codes. Through this model, we study a historical tsunamigenic event occurred in 1783 in Scilla, Italy, that resulted to be catastrophic with a toll exceeding 1500 fatalities. The landslide is reconstructed by a mixture debris flow, and results are compared with the observational data and other numerical simulations.

关键词： Geophysical flow models numerical algorithm Cartesian coordinate system Flow-like landslides

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Control of tumor growth modeled by system of PDE, numerical analysis of optimality conditions

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2022年第16期45卷 9371-9385页

作者： Nowakowski, Andrzej Krawczyk, Anita Univ Lodz Fac Math & Comp Sci Banacha 22 PL-90238 Lodz Poland

We analyze a mathematical model of a tumor that includes the interactions among tumor cells (live or dead), macrophages, endothelial cells, and the cytokines based on a system of partial differential equations which describes inhibition of tumor growth by granulocyte-macrophage colony-stimulating factor (GM-CSF) treatment. The aim of the model is to predict the growth of the tumor volume under partial blocking of hypoxia-inducible factor (HIF)-1 or stabilization of HIF-2, with injection of GM-CSF It was assumed that tumor is a spherical and the treatment by GM-CSF is not optimized. In this paper, we do not assume that tumor is a spherical model and we develop a dual dynamic programming approach to formulate a verification condition of an approximate treatment for an injection of GM-CSF. Next, we analyze numerically an epsilon-optimal treatment.

关键词： dual dynamic programming inhibition of tumor growth mathematical model of tumor growth numerical algorithm sufficient epsilon-optimality

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Analysis and numerical simulations of a dynamic contact problem with adhesion

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MATHEMATICAL AND COMPUTER MODELLING 2003年第12-13期37卷 1317-1333页

作者： Fernández, JR Shillor, M Sofonea, M Univ Santiago de Compostela Fac Matemat Dept Matemat Aplicada Santiago De Compostela 15706 Spain Oakland Univ Dept Math & Stat Rochester MI 48309 USA Univ Perpignan Lab Theorie Syst F-66860 Perpignan France

The dynamic process of frictionless contact between a viscoelastic body and a reactive foundation is modelled, analyzed, and simulated. The contact is adhesive and it is described by introducing an internal variable, the bonding field beta, which measures the fractional density of active bonds. The evolution of beta is described by an ordinary differential equation that depends on the process history, taking into account possible adhesive degradation during cycles of debonding and rebonding. The existence of the unique weak solution of the model is proved by using arguments of nonlinear evolutionary equations with monotone operators and a fixed-point theorem. A fully discrete numerical scheme is proposed for the model and implemented in a computer code. numerical simulations of one- and two-dimensional examples are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： adhesive contact normal compliance bonding field history dependence adhesion weak solution numerical algorithm numerical simulations

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Matrix-less methods for the spectral approximation of large non-Hermitian Toeplitz matrices: A concise theoretical analysis and a numerical study

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numerical LINEAR ALGEBRA WITH APPLICATIONS 2024年第4期31卷 e2545-e2545页

作者： Bogoya, Manuel Ekstrom, Sven-Erik Serra-Capizzano, Stefano Vassalos, Paris Univ Valle Dept Matemat Cali Colombia Uppsala Univ Dept Informat Technol Div Sci Comp Box 337 SE-75105 Uppsala Sweden Univ Insubria Dipartimento Sci & Alta Tecnol Como Italy Athens Univ Econ & Business Sch Informat Sci & Technol Athens Greece

It is known that the generating function of a sequence of Toeplitz matrices may not describe the asymptotic distribution of the eigenvalues of the considered matrix sequence in the non-Hermitian setting. In a recent work, under the assumption that the eigenvalues are real, admitting an asymptotic expansion whose first term is the distribution function, fast algorithms computing all the spectra were proposed in different settings. In the current work, we extend this idea to non-Hermitian Toeplitz matrices with complex eigenvalues, in the case where the range of the generating function does not disconnect the complex field or the limiting set of the spectra, as the matrix-size tends to infinity, has one nonclosed analytic arc. For a generating function having a power singularity, we prove the existence of an asymptotic expansion, that can be used as a theoretical base for the respective numerical algorithm. Different generating functions are explored, highlighting different numerical and theoretical aspects;for example, non-Hermitian and complex symmetric matrix sequences, the reconstruction of the generating function, a consistent eigenvalue ordering, the requirements of high-precision data types. Several numerical experiments are reported and critically discussed, and avenues of possible future research are presented.

关键词： asymptotic expansion eigenvalues GLT sequences numerical algorithm spectral symbols Toeplitz matrices

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numerical Construction of Nash and Stackelberg Solutions in a Two-Player Linear Non-Zero-Sum Positional Differential Game

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PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS 2010年第1期269卷 S147-S161页

作者： Kleimenov, A. F. Kuvshinov, D. R. Osipov, S. I. Russian Acad Sci Inst Math & Mech Ural Div Ul S Kovalevskoi 16 Ekaterinburg 620990 Russia Ural State Univ Ekaterinburg 620083 Russia

numerical methods are proposed for constructing Nash and Stackelberg solutions in a two-player linear non-zero-sum positional differential game with terminal cost functionals and geometric constraints on the players' controls. The formalization of the players' strategies and of the motions generated by them is based on the formalization and results from the theory of positional zero-sum differential games developed by N.N. Krasovskii and his school. It is assumed that the game is reduced to a planar game and the constraints on the players' controls are given in the form of convex polygons. The problem of finding solutions of the game may be reduced to solving nonstandard optimal control problems. Several computational geometry algorithms are used to construct approximate trajectories in these problems, in particular, algorithms for constructing the convex hull as well as the union, intersection, and algebraic sum of polygons.

关键词： non-zero-sum positional differential game Nash solution Stackelberg solution numerical algorithm

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High order algorithms for numerical solution of fractional differential equations

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ADVANCES IN DIFFERENCE EQUATIONS 2021年第1期2021卷 1-23页

作者： Asl, Mohammad Shahbazi Javidi, Mohammad Yan, Yubin Univ Tabriz Dept Math Tabriz Iran Univ Chester Dept Math Chester CH1 4BJ Cheshire England

In this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.

关键词： numerical algorithm Fractional differential equation Caputo fractional derivative Stability analysis Error estimates 26A33 65D05 65D30

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On numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations

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BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 2024年第4期50卷 1-20页

作者： Huang, Canwei Wang, Youjun South China Univ Technol Dept Math Guangzhou 510640 Peoples R China

We study the numerical solutions for a class of quasilinear Schr & ouml;dinger equations arising from the self-channeling of high-power ultra short lasers in matter, which are associated with energy functionals with nonlinear principle parts so that the classical algorithm cannot directly be used. By the method of variable replacement to transform the quasilinear Schr & ouml;dinger equation into an semilinear elliptic equation, the numerical mountain pass algorithm is then applied. Some numerical experiments are also performed, including zero potential, nonzero constant potential and singular problem.

关键词： Mountain pass solutions Quasilinear equations numerical algorithm

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