scholarly journals NONSTATIONARY STAGE OF QUASI‐CHERENKOV BEAM INSTABILITY IN PERIODICAL STRUCTURES

2005 ◽  
Vol 12 (1) ◽  
pp. 1-8
Author(s):  
K. Batrakov ◽  
S. Sytova
Keyword(s):  
Electron Beam ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Numerical Experiments ◽  
Distributed Feedback ◽  
Beam Instability ◽  
Nonstationary Solution ◽  
Nonstationary Stage ◽  
Cherenkov Instability

Analysis of nonstationary stage of quasi‐Cherenkov instability of electron beam in the case of two‐wave distributed feedback is carried out. Mathematical models and numerical methods of nonstationary quasi‐Cherenkov electron beam instability are proposed. Results of numerical experiments are proposed. Bifurcations of nonstationary solution are discussed. Straipsnyje analizuojama nestacionariosios fazes kvazi‐Cherenkovo elektronu spinduliuotes nestabilumas esant dvieju bangu saveikai su grižtamo ryšio pernešimu. Pasiūlyti šios elektronu spinduliuotes nestacionariosios fazes atveju matematiniai ir skaitiniai sprendimo metodai. Pateikti skaitinio eksperimento rezultatai. Aptartos nestacionariojo sprendinio bifurkacijos.

MODELLING OF QUASI‐CHERENKOV ELECTRON BEAM INSTABILITY IN PERIODICAL STRUCTURES

2005 ◽  
Vol 9 (1) ◽  
pp. 1-8
Author(s):  
K. Batrakov ◽  
S. Sytova
Keyword(s):  
Mathematical Model ◽  
Electron Beam ◽  
Numerical Method ◽  
Differential System ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Distributed Feedback ◽  
Beam Instability ◽  
Nonlinear Stage ◽  
Cherenkov Instability

Nonlinear stage of quasi‐Cherenkov instability of electron beam under conditions of two‐ and three‐dimensional distributed feedback is simulated. The scheme of distributed feedback with two strong coupled waves is considered. Mathematical model of quasi‐Cherenkov electron beam instability is proposed. Numerical method to solve the nonlinear integro‐differential system, describing such instability, is worked out. Results of numerical experiments are discussed. Modeliuojama elektronu spindulio kvazi‐Cherenkovo nestabilumo netiesine faze su dvimačio ir trimačio paskirstytojo grižtamojo ryšio salyga. Nagrinejama schema su grižtamuoju ryšiu su dviem susietomis stipriomis bangomis. Pateiktas kvazi‐Cherenkovo elektroninio spindulio nestabilumo matematinis modelis. Pasiūlytas veiksmingas skaitinis algoritmas, skirtas netiesinems integro‐diferencialinems lygčiu sistemoms su tokio tipo nestabilumu, spresti. Apžvelgti skaitinio eksperimento rezultai.

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 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 Spatio temporal evolution of electron beam instability in collisionless plasmas

2005 ◽  
Vol 54 (5) ◽  
pp. 2138
Author(s):  
Zheng Chun-Yang ◽  
Liu Zhan-Jun ◽  
Li Ji-Wei ◽  
Zhang Ai-Qing ◽  
Pei Wen-Bing
Keyword(s):  
Electron Beam ◽  
Temporal Evolution ◽  
Beam Instability ◽  
Collisionless Plasmas ◽  
Spatio Temporal

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.

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