scholarly journals Calculation of the optimal parameters of corrective elements in induction acceleration systems

2021 ◽  
pp. 107-114
Author(s):  
L. Pantalienko ◽  
Keyword(s):  
Mathematical Formulation ◽  
Linear Constraints ◽  
Practical Stability ◽  
Initial Moment ◽  
Inhomogeneous System ◽  
Numerical Estimation ◽  
Closed Set ◽  
Linear Induction ◽  
Phase Coordinates ◽  
Induction System

The formulations of a number of optimization problems for a linear induction acceleration system with respect to the adjustment parameters are considered. The dynamics of the transverse motion of electrons in the horizontal plane is investigated in the presence of given energy values for each resonator period: the particles at the initial moment of time are somewhat displaced relative to the accelerator axis (we neglect the displacements of the ends of the solenoids and the centers of the accelerating gaps relative to the accelerator axis). A connection is established between the initial and final coordinates and the components of the momentum. The presence of parasitic electric and magnetic fields arising as a result of the displacement of particles relative to the axis of the accelerator, which change the transverse components of the pulses, is taken into account. For the mathematical formulation of problems, in order to apply algorithms of practical stability, the original difference model of the induction system was converted to a linear form. By introducing into consideration the vector of parameters, the scatter of phase coordinates, and tolerances on the parameters, the problem of calculating the tolerances for given linear constraints on the scatter of phase coordinates for the corresponding inhomogeneous system is formulated. For the case of nonlinear dynamic constraints on the spread of the vector of phase coordinates, it is proposed to approximate a convex closed set by tangent hyperplanes. Numerical estimation of the range of tolerances for the parameters of correcting elements is reduced to the problems of practical stability of discrete parametric systems. In this case, the region of the initial conditions on the state vector, the tolerances on the parameters, are given structurally in the form of an ellipsoid, which makes it possible to numerically solve the original problem as an extremal one. From the standpoint of practical stability in the corresponding space of functions, the problem of assessing the range of tolerances for the parameters of correcting elements in the presence of specified restrictions on the spread of the quality criterion is considered. Attention is focused on an important class of problems of numerical modelling of a linear induction acceleration system − problems of practical stability. Numerical estimation of the region of initial displacements of the transverse coordinates of the linear induction acceleration system in the given structures in the presence of linear constraints on the vector of phase coordinates in dynamics is carried out. Key words: modeling, induction system of acceleration, solenoid, parameters, elements of correction, optimization, stability

An Overview on a Nonideal System With Three and a Half Degrees of Freedom

2005 ◽  
Author(s):  
Karen de Lolo Guilherme ◽  
Jose´ Manoel Balthazar ◽  
Paulo Roberto Gardel Kurka ◽  
Masayoshi Tsuchida
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Dynamical Behavior ◽  
Mathematical Formulation ◽  
Rotation Frequency ◽  
Steady State Solution ◽  
Dc Motor ◽  
Physical Parameters ◽  
Phase Coordinates ◽  
Limited Power

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor.

scholarly journals Solving the two-dimensional packing problem with m-M calculus

2011 ◽  
Vol 21 (1) ◽  
pp. 93-102 ◽  
Author(s):  
Aleksandar Savic ◽  
Tijana Sukilovic ◽  
Vladimir Filipovic
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Mathematical Formulation ◽  
Packing Problem ◽  
Linear Constraints ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Computational Performance ◽  
Non Linear ◽  
Rectangular Packing

This paper considers the two dimensional rectangular packing problem. The mathematical formulation is based on the optimization of a non-linear function with piecewise linear constraints with a small number of real variables. The presented method of m-M calculus finds all optimal solutions on small instances. Computational performance is good on smaller instances.

Discussion of the Oblique Rotator Model Cases Of 108 Aqr and x Serp.

1976 ◽  
Vol 32 ◽  
pp. 577-588
Author(s):  
C. Mégessier ◽  
V. Khokhlova ◽  
T. Ryabchikova
Keyword(s):  
Mathematical Formulation ◽  
The Other ◽  
Rotator Model ◽  
Oblique Rotator ◽  
First Results

My talk will be on the oblique rotator model which was first proposed by Stibbs (1950), and since received success and further developments. I shall present two different attempts at describing a star according to this model and the first results obtained in the framework of a Russian-French collaboration in order to test the precision of the two methods. The aim is to give the best possible representation of the element distributions on the Ap stellar surfaces. The first method is the mathematical formulation proposed by Deutsch (1958-1970) and applied by Deutsch (1958) to HD 125248, by Pyper (1969) to α2CVn and by Mégessier (1975) to 108 Aqr. The other one was proposed by Khokhlova (1974) and used by her group.

Under- and Over-Estimation

2011 ◽  
Vol 58 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Virginie Crollen ◽  
Julie Castronovo ◽  
Xavier Seron
Keyword(s):  
Empirical Data ◽  
Accurate Estimation ◽  
Numerical Estimation ◽  
Production Task ◽  
Estimation Task ◽  
Reproduction Task ◽  
Perception Task ◽  
Adult Participants ◽  
Mapping Hypothesis ◽  
Task Perception

Over the last 30 years, numerical estimation has been largely studied. Recently, Castronovo and Seron (2007) proposed the bi-directional mapping hypothesis in order to account for the finding that dependent on the type of estimation task (perception vs. production of numerosities), reverse patterns of performance are found (i.e., under- and over-estimation, respectively). Here, we further investigated this hypothesis by submitting adult participants to three types of numerical estimation task: (1) a perception task, in which participants had to estimate the numerosity of a non-symbolic collection; (2) a production task, in which participants had to approximately produce the numerosity of a symbolic numerical input; and (3) a reproduction task, in which participants had to reproduce the numerosity of a non-symbolic numerical input. Our results gave further support to the finding that different patterns of performance are found according to the type of estimation task: (1) under-estimation in the perception task; (2) over-estimation in the production task; and (3) accurate estimation in the reproduction task. Moreover, correlation analyses revealed that the more a participant under-estimated in the perception task, the more he/she over-estimated in the production task. We discussed these empirical data by showing how they can be accounted by the bi-directional mapping hypothesis ( Castronovo & Seron, 2007 ).

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

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