scholarly journals Application of quasiconformal mapping methods to the investigation of the explosive processes impact on the environment

2019 ◽  
pp. 17-18
Author(s):  
Kateryna Mykolaiivna Malash ◽  
Andrii Yaroslavovych Bomba
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Quasiconformal Mapping ◽  
Quasiconformal Mappings ◽  
Practical Application

The mathematical models used to study explosive processes are given. A class of problems investigating the influence of explosive processes on the environment by the quasiconformal mappings numerical methods are outlined and their practical application are described

scholarly journals RESIDUAL DISPLACEMENTS‘ PROGRESIVE ANALYSIS OF THE MULTISUPPORTED BEAM / DAUGIAATRAMĖS SIJOS LIEKAMŲJŲ POSLINKIŲ PROGRESINĖ ANALIZĖ

2014 ◽  
Vol 6 (5) ◽  
pp. 461-467 ◽  
Author(s):  
Liudas Liepa ◽  
Agnė Gervytė ◽  
Ela Jarmolajeva ◽  
Juozas Atkočiūnas
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Analysis Problem ◽  
Residual Displacements ◽  
Repeated Load ◽  
Energy Principles

This paper focuses on a shakedown behaviour of the ideally elasto-plastic beams system under variable repeated load. The mathematical models of the analysis problems are created using numerical methods, extremum energy principles and mathematic programming. It is shown that during the shakedown process the residual displacements vary non-monotonically. By solving analysis problem, where the load locus is being progressively expanded, it is possible to determine the upper and lower bounds of residual displacements. Suggested methods are ilustrated by solving multisupported beam example problem. The results are obtained considering principle of the small displacements. Nagrinėjamas idealiai tampriai plastinės lenkiamos strypinės sistemos prisitaikomumo būvis, veikiant kartotinei kintamajai apkrovai. Analizės uždavinių matematiniai modeliai sudaromi, pasitelkus skaitinius metodus, ekstreminius energinius principus ir matematinį programavimą. Parodoma, kad prisitaikant konstrukcijai jos liekamieji poslinkiai gali kisti nemonotoniškai. Išsprendus analizės uždavinį, kuriame progresyviai plečiama apkrovos veikimo sritis, galima nustatyti viršutines ir apatines liekamųjų poslinkių kitimo ribas. Siūloma metodika iliustruota daugiaatramės sijos liekamųjų poslinkių skaičiavimo pavyzdžiu. Rezultatai gauti, esant mažų poslinkių prielaidai.

Modelling and computation of liquid crystals

Acta Numerica ◽  
2021 ◽  
Vol 30 ◽  
pp. 765-851
Author(s):  
Wei Wang ◽  
Lei Zhang ◽  
Pingwen Zhang
Keyword(s):  
Liquid Crystals ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Soft Matter ◽  
Scientific Research ◽  
Crystalline Solids ◽  
The Past ◽  
Tremendous Progress

Liquid crystals are a type of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the past four decades, which is of great importance for fundamental scientific research and has widespread applications in industry. In this paper we review the mathematical models and their connections to liquid crystals, and survey the developments of numerical methods for finding rich configurations of liquid crystals.

Mathematical models and numerical methods for the forward problem in cardiac electrophysiology

2002 ◽  
Vol 5 (4) ◽  
pp. 215-239 ◽  
Author(s):  
G.T. Lines ◽  
M.L. Buist ◽  
P. Grottum ◽  
A.J. Pullan ◽  
J. Sundnes ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Cardiac Electrophysiology ◽  
Forward Problem

scholarly journals NUMERICAL MODELING OF GAS TURBINE COOLED BLADES

Aviation ◽  
2005 ◽  
Vol 9 (3) ◽  
pp. 9-18
Author(s):  
Arif Pashayev ◽  
Djakhangir Askerov ◽  
Ramiz Ali Cabar oqlu Sadiqov
Keyword(s):  
Numerical Modeling ◽  
Temperature Field ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Gas Turbine ◽  
Point Of View ◽  
Theoretical Substantiation ◽  
Stationary Temperature Field ◽  
Methods Of Calculation ◽  
Effective Combination

In contrast to methods that do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasi‐stationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A. Ziqmound continuity modules have been received.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Computer Program ◽  
Iterative Methods ◽  
Error Propagation ◽  
Random Variables ◽  
Regression Analyses ◽  
Practical Application ◽  
Numeral Systems ◽  
Roots Of Polynomials ◽  
Digital Computers

Textbook of several universities. 2nd edition. The color edition is also available at Glasstree Bookstore. It is recommended for students. The series of books Numerical Methods is written primarily for students at technical universities, but also as a useful handbook for engineers, PhD students and scientists. This volume introduces the reader into numeral systems and representation of numbers in digital computers. Possibly the most important part of this book are descriptions of differences between constant and random variables, related types of errors and error propagation. These topics are supplemented with various types of regression analyses. Finally, direct and iterative methods for finding roots of polynomials are explained. Practical application is supported by 77 examples and 13 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be included in any computer program.

scholarly journals On a Theorem of Schwarz Type for Quasiconformal Mappings in Space

1967 ◽  
Vol 29 ◽  
pp. 19-30
Author(s):  
Kazuo Ikoma
Keyword(s):  
Conformal Mapping ◽  
Quasiconformal Mapping ◽  
Quasiconformal Mappings ◽  
Space Domain ◽  
Moebius Transformation ◽  
Modulus Condition

A space ring R is defined as a domain whose complement in the Moebius space consists of two components. The modulus of R can be defined in variously different but essentially equivalent ways (see e.g. Gehring [3] and Krivov [5]), which is denoted by mod R. Following Gehring [2], we refer to a homeomorphism y(x) of a space domain D as a k-quasiconformal mapping, if the modulus conditionis satisfied for all bounded rings R with their closure , where y(R) denotes the image of R by y = y(x). Then, it is evident that the inverse of a k-quasi-conformal mapping is itself k-quasiconformal and that a k1-quasiconformal mapping followed by a k2-quasiconformal one is k1k2-quasiconformal. It is also well known that the restriction of a Moebius transformation to a space domain is equivalent to a 1-quasiconformal mapping of its domain.

Current and future potential of alternative techniques

1998 ◽  
Vol 22 ◽  
pp. 161-171
Author(s):  
D. I. Givens ◽  
M. Gill
Keyword(s):  
Mathematical Models ◽  
Volatile Fatty Acids ◽  
Physical Structure ◽  
Practical Application ◽  
In Vitro Techniques ◽  
Predicting Factors ◽  
In Vitro Systems ◽  
Future Potential ◽  
Alternative Techniques

AbstractRuminant animal production faces numerous challenges and it seems that both economic and biological benefits will be derived from moving food characterization from simple energy and protein-based approaches to those which assess nutrient supply in some detail. In vitro systems will need to reflect this change and this paper considers in particular, the need for estimations of rumen volatile fatty acids and microbial protein supplies. Emphasis is placed on the possibility that in vitro techniques can be used to provide biochemical data which can themselves be used in mathematical models of wider processes. This paper also examines the need for in vitro techniques to reflect the microbial!animal response to the physical structure of foods and also the requirement for in vitro approaches which ask why a food has a certain value rather than simply what the value is. In vitro techniques also have a substantial role outside the digestive tract in predicting factors such as voluntary food intake and some aspects of tissue metabolism and some of these aspects are considered. Tor practical application in vitro techniques will need to provide value for money and be compatible as parameters in mathematical models to have an impact at farm level. In this regard physical in vitro techniques such as NIRS seem to have enormous potential.

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