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Mesh-ray model and method for calculating the laser radiation absorption

Mathematical Models and Computer Simulations 2016年第4期8卷 382-390页

作者： Tsygvintsev, I.P. Krukovskiy, A. Yu. Gasilov, V.A. Novikov, V.G. Popov, I.V. Keldysh Institute of Applied Mathematics Russian Academy of Sciences Miusskaya pl. 4 Moscow 125047 Russian Federation

The present paper puts forward a mathematical model of laser radiation absorption in a laser target, which combines approximations of geometrical and wave optics and the corresponding numerical algorithm. This model depends on the principles of geometrical optics in the range of weak variation of the plasma refractive index on the scale of the wave length. This enables one to describe the refraction of the radiation. A transition to wave approximation is carried out near the surface of critical density, where the approximation of the geometrical optics is a fortiori inapplicable. For this aim, the plasma medium is approximately represented as a set of plane layers, on which the one-dimensional Helmholtz equation is solved. This makes it possible to construct a simple and relatively accurate method for calculating the absorption and reflection of laser radiation near the critical density surface in order to effectively take into account the dependence of the interaction of radiation with matter on the polarization direction, etc. The proposed model is adapted for implementation in the radiation gas dynamics (RGD) code. A numerical computation subroutine is presented based on the analytical solution of the differential equations corresponding to the optical ray model of the laser radiation energy flux. This solution is obtained under the assumption that the squared gradient of the refractive index is constant in any cell of the mesh. The convergence rates of the proposed algorithms are estimated using the data obtained in the numerical experiments. © 2016, Pleiades Publishing, Ltd.

关键词： computer simulation geometrical optics laser radiation numerical algorithm radiation gas dynamics

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ADVANCED KINEMATIC SCHEME OF STRUCTURAL CALCULATION OF THIN MULTILAYER LAMINATE WITH ESSENTIALLY DIVERSE LAYER'S STIFFNESS

ADVANCED KINEMATIC SCHEME OF STRUCTURAL CALCULATION OF THIN ...

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ASME International Mechanical Engineering Congress and Exposition (IMECE)

作者： Gaynutdinov, V. G. Kazan State Tech Univ AN Tupolev Dept Aircraft Design Kazan Russia

ISBN: (纸本)9780791854877

Composite structure consists of a system of layers bonded together. The layers can have different mechanical properties and thicknesses. The main task is to predict the behavior of a laminate as a system of layers with given properties. We suggest advanced kinematic scheme for structural calculation and heuristic numerical algorithm of prediction behavior of a multilayer structures with essentially diverse layer's stiffness. Kinematic scheme can be compared in adequacy with three-dimensional approach of structural calculation of thin multilayer laminate, but is more economical in view of required resource for numerical calculation.

关键词： thin multilayer structure advanced kinematic scheme numerical algorithm structural calculation

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Conditional Parameter Identification with Asymmetrical Losses of Estimation Errors

Conditional Parameter Identification with Asymmetrical Losse...

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4th International Conference on Computational Collective Intelligence - Technologies and Applications (ICCCI)

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Polish Acad Sci Syst Res Inst Ctr Informat Technol Data Anal Methods PL-01447 Warsaw Poland

ISBN: (纸本)9783642346309

In many scientific and practical tasks, the classical concepts for parameter identification are satisfactory and generally applied with success, although many specialized problems necessitate the use of methods created with specifically defined assumptions and conditions. This paper investigates the method of parameter identification for the case where losses resulting from estimation errors can be described in polynomial form with additional asymmetry representing different results of under- and overestimation. Most importantly, the method presented here considers the conditionality of this parameter, which in practice means its significant dependence on other quantities whose values can be obtained metrologically. To solve a problem in this form the Bayes approach was used, allowing a minimum expected value of losses to be achieved. The methodology was based on the nonparametric technique of statistical kernel estimators, which freed the worked out procedure from forms of probability distributions characterizing both the parameter under investigation and conditioning quantities. As a result, a ready to direct use algorithm has been presented here.

关键词： parameter identification Bayes approach asymmetrical losses of estimation errors conditional factors nonparametric estimation statistical kernel estimators numerical algorithm

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Solving schemes for computational magneto-aerodynamics

Solving schemes for computational magneto-aerodynamics

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Workshop on Advances and Challenges in Time-Integration of PDEs

作者： Shang, JS Wright State Univ Dayton OH 45435 USA

The electromagnetic force introduces a new physics dimension for enhancing aerodynamic performance of aerospace vehicles. In order to simulate interdisciplinary phenomena, the Navier-Stokes and Maxwell equations in the time domain must be integrated on a common frame of reference. For a wide range of applications from subsonic unmanned vehicles to hypersonic flight control, the resultant nonlinear partial differential equations offer a formidable challenge for numerical analysis. The experience and physical insight using the approximate Riemann and compact-differencing formulation as well as several temporal discritizations will be shared. The most recent development and advancement in numerical procedures for solving this system of governing equations are delineated.

关键词： numerical algorithm computational magneto-aerodynamics

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Gaussian Two-way Relay Channel with Arbitrary Inputs

Gaussian Two-way Relay Channel with Arbitrary Inputs

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21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

作者： Guenduez, Deniz Payaro, Miquel CTTC Barcelona 08860 Spain

ISBN: (纸本)9781424480166

A two-way relay channel with independent parallel Gaussian channels between the relay and the two terminals is considered. Focusing on the decode-and-forward protocol, the second phase of the communication, in which the relay broadcasts the two messages to their respective receivers, is studied. Precisely, the problem of computing the power allocation among the parallel channels that maximizes the weighted sum rate assuming arbitrarily distributed channel inputs (such as m-QAM) is stated and shown to be convex. A numerical algorithm is provided to solve the problem for the general case and, for the particular cases of high and low power regimes, expressions for the optimal power allocation are derived in closed form.

关键词： Gaussian channels Gaussian two-way relay channel arbitrarily distributed channel inputs broadcast channels decode and forward communication decode-and-forward protocol numerical algorithm optimal power allocation parallel Gaussian channel protocols radio receivers relay broadcast relays weighted sum rate

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Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation

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Computational Mathematics and Mathematical Physics 2006年第4期46卷 680-690页

作者： Mikhailov, G.A. Rogazinsky, S.V. Ureva, N.M. Institute of Computational Mathematics and Mathematical Geophysics Siberian Division Russian Academy of Sciences Novosibirsk 630090 pr. Akademika Lavrent'eva 6 Russian Federation

New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number N ₀ of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is O(N ₀ ^-1 ). Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient. © MAIK "Nauka/Interperiodica" (Russia), 2006.

关键词： Monte Carlo method numerical algorithm Smoluchowski equation

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A Proposed Machine Learning Model for Forecasting Impact of Traffic-Induced Vibrations on Buildings 20th

A Proposed Machine Learning Model for Forecasting Impact of ...

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20th Annual International Conference on Computational Science (ICCS)

作者： Jakubczyk-Galczynska, Anna Jankowski, Robert Gdansk Univ Technol Fac Civil & Environm Engn PL-80233 Gdansk Poland

ISBN: (纸本)9783030504205;9783030504199

Traffic-induced vibrations may cause various damages to buildings located near the road, including cracking of plaster, cracks in load-bearing elements or even collapse of the whole structure. Measurements of vibrations of real buildings are costly and laborious. Therefore the aim of the research is to propose the original numerical algorithm which allows us to predict, with high probability, the negative dynamic impact of traffic-induced vibrations on the examined building. The model has been based on machine learning. Firstly, the experimental tests have been conducted on different buildings using specialized equipment taking into account six factors: distance from the building to the edge of the road, type of surface, condition of road surface, condition of the building, the absorption of soil and the type of vehicle. Then, the numerical algorithm based on machine learning (using support vector machine) has been created. The results of the conducted analysis clearly show that the method can be considered as a good tool for predicting the impact of traffic-induced vibrations on buildings, being characterized by high reliability.

关键词： Buildings Vibrations Machine learning numerical algorithm

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About one gradient procedure of determination of the branching points of nonlinear integral equation arising in the theory of antenna synthesis 4

About one gradient procedure of determination of the branchi...

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4th International Conference on Antenna Theory and Techniques

作者： Podlevskyi, BM NASU Pidstryhach Inst Appl Problems Mech & Math UA-79000 Lvov Ukraine

ISBN: (纸本)0780378814

The problem of building a numerical algorithm for determination of branching points of one nonlinear integral operator, which arises in the theory of antennas synthesis according to the given amplitude radiation pattern, is considered. The basic difficulty, consists in that the kernel of an integral operator nonlinearly depends oil two parameters, which play role of the spectral ones. For such problems, except a special case. the existing numerical algorithms are not applicable. For building an algorithm for solving such problems, the equivalent variational statement is used. The problem is reduced to a sequence of linear two-parameter eigenvalue problems with application of one gradient procedure for simultaneous evaluation of two spectral parameters being the branching points of an initial nonlinear integral operator.

关键词： antennas synthesis branching points nonlinear integral operator two-parameter eigenvalue problem numerical algorithm eigenvalue gradient procedure

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Collatz Conjecture for 2¹⁰⁰⁰⁰⁰-1 is True - algorithms for Verifying Extremely Large Numbers 4

Collatz Conjecture for 2<SUP>100000</SUP>-1 is True - Algori...

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IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI)

作者： Ren, Wei Li, Simin Xiao, Ruiyang Bi, Wei China Univ Geosci Hubei Key Lab Intelligent Geoinformat Proc Sch Comp Sci Wuhan 430074 Peoples R China Guizhou Univ Guizhou Prov Key Lab Publ Big Data Guizhou Peoples R China China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China China Univ Geosci Sch Comp Sci Sch Math & Phys Wuhan 430074 Peoples R China SeeleTech Corp San Francisco CA 94107 USA

ISBN: (纸本)9781538693803

Collatz conjecture (or 3x+1 problem) has been explored for about 80 years. By now the largest number that has been verified for Collatz conjecture is about 60 bits. In this paper, we propose new algorithms that can verify much greater numbers than known algorithms, i.e., about 100000 bits (30000 digits) on whether they can return 1 after 3*x+1 and x/2 computations. The proposed algorithms change numerical computation to bit computation (or logical computation), and change inner memory data representation to hard disk file manipulation. We make it possible to verify extremely large numbers without concerning computer memory upper-bound. The largest number verified for Collatz conjecture until now in the world is 2(100000) - 1, and this magnitude of extremely large numbers has never been verified. We discovered that this number can return to 1 after 481603 times of 3*x+1 computation, and 863323 times of x/2 computation. At last, we stress that some open problems may be used for the green mining in blockchain-based cryptocurrencies, e.g., BTC. We discuss the applicability of Collatz conjecture for the Proof of Work in Blockchain.

关键词： Collatz Conjecture 3x+1 Problem Computational Algebra algorithmic Number Theory numerical algorithm

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Air Quality Dispersion Modeling in Spherical Coordinates 2nd

Air Quality Dispersion Modeling in Spherical Coordinates

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2nd International Conference on Advanced Technologies for Societal Applications (Techno-Societal)

作者： Rayshanov, Normakhmad Akhmedov, Dilshot Tashkent Univ Informat Technol Tashkent Uzbekistan

ISBN: (纸本)9783030169626;9783030169619

The paper deals with the development of a mathematical model of aerosol fine particles transport and diffusion in the atmosphere in spherical coordinates. This approach allows us to shorten the calculation time and increase the order of approximation with respect to spatial variables. For the numerical solution of the problem, a computational algorithm based on the “straight-line method” was proposed. This algorithm allows us to reduce the multidimensional problem in the form of a partial differential equation to an ordinary differential equation with the corresponding initial and boundary conditions. Based on the developed mathematical support, the main parameters that significantly influenced the process of transporting aerosol fine particles, as well as the rate of their deposition, were investigated. The obtained results can be successfully used as software in the optimal allocation of newly designed facilities in industrial regions, as well as to assess the scale and geography of emissions spread to the environment, to estimate the concentration of harmful substances in the atmosphere and on the underlying surface with subsequent decision making to minimize ecological risks.

关键词： Mathematical model numerical algorithm Transport and diffusion Harmful substances Atmosphere Hydromechanics

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