METHOD OF FINDING LOSSES IN THE THROTTLE WINDING AS A RESULT OF THE SKIN EFFECT AND THE PROXIMITY EFFECT

2022 ◽  
pp. 87-94
Author(s):  
А.А. Моисеенко ◽  
С.М. Фёдоров
Keyword(s):  
Electromagnetic Fields ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Variable Number ◽  
Distributed Software ◽  
Good Convergence ◽  
Analytical Formulas ◽  
Round Section ◽  
Winding Wire ◽  
Comparison Of The Results

Представлен метод использования расчетных методик и моделирования магнитных полей в двухмерном пространстве для нахождения высокочастотных потерь в обмотке моточных изделий, таких как дроссель или трансформатор. Была проведена работа по анализу литературы по данной теме, а также поднят вопрос оптимизации и адаптации аналитических формул для случая использования проводников круглого сечения и намотки, имеющей неоднородное распределение слоев в окне сердечника. Был также поднят вопрос об аналитическом нахождении длины обмоточного провода намотки с различным количеством слоев и переменного количества используемых при этом витков. Для проведения автоматизации расчета с помощью формул был написан скрипт, строящий зависимость сопротивления переменному току относительно частоты, используя аналитические формулы. Была написана программа для автоматической постановки начальных условий и граничных значений параметров моделирования, процесса самого моделирования электромагнитных полей, анализа полученных данных, а также формирования массива для построения графика полученной при этом зависимости сопротивления от частоты. В данном методе используется свободно распространяемое программное обеспечение как для математических расчетов, так и моделирования электромагнитных полей. Итогом данной работы стало сравнение полученных результатов, которые показали хорошую сходимость и преемственность этапов данного метода Here we present a method for using computational methods and modeling magnetic fields in two-dimensional space to find high-frequency losses in the winding of winding products, such as a choke or transformer. We analyzed the literature on this topic, as well as the issue of optimization and adaptation of analytical formulas for the case of using round-section conductors and winding having a non-uniform distribution of layers in the core window. We discussed the analytical finding of the length of the winding wire of the winding with a different number of layers and a variable number of turns used in this case. To automate the calculation using formulas, we wrote a script that builds the dependence of the resistance to alternating current relative to the frequency using analytical formulas. In addition, we wrote a program for automatically setting the initial conditions and boundary values of the modeling parameters, the process of modeling electromagnetic fields itself, analyzing the data obtained, as well as forming an array for plotting the resulting dependence of resistance on frequency. This method uses freely distributed software for both mathematical calculations and modeling of electromagnetic fields. The result of this work was a comparison of the results obtained, which showed good convergence and continuity of the stages of this method

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

Robust and Dynamically Consistent Reduced Order Models

2013 ◽  
Author(s):  
David B. Segala ◽  
David Chelidze
Keyword(s):  
Initial Conditions ◽  
Dimensional Space ◽  
Full Scale ◽  
Three Dimensions ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Random Forcing ◽  
Technological Advances ◽  
Model Complex ◽  
Dynamical Consistency

The need for reduced order models (ROMs) has become considerable higher with the increasing technological advances that allows one to model complex dynamical systems. When using ROMs, the following two questions always arise: 1) “What is the lowest dimensional ROM?” and 2) “How well does the ROM capture the dynamics of the full scale system model?” This paper considers the newly developed concepts the authors refer to as subspace robustness — the ROM is valid over a range of initial conditions, forcing functions, and system parameters — and dynamical consistency — the ROM embeds the nonlinear manifold — which quanitatively answers each question. An eighteen degree-of-freedom pinned-pinned beam which is supported by two nonlinear springs is forced periodically and stochastically for building ROMs. Smooth and proper orthogonal decompositions (SOD and POD, respectively) based ROMs are dynamically consistent in four or greater dimensions. In the strictest sense POD-based ROMs are not considered coherent whereas, SOD-based ROMs are coherent in roughly five dimesions and greater. Is is shown that in the periodically forced case, the full scale dynamics are captured in a five-dimensional POD and SOD-based ROM. For the randomly forced case, POD and SOD-based ROMs need three dimensions but SOD captures the dynamics better in a lower-dimensional space. When the ROM is developed from a different set of initial conditions and forcing values, SOD outperforms POD in periodic forcing case and are equal in the random forcing case.

Risk of gully erosion: methods and examples of estimates

2020 ◽  
Author(s):  
Aleksey Sidorchuk ◽  
Andrei Entin
Keyword(s):  
Initial Conditions ◽  
Measurement Data ◽  
Field Measurements ◽  
Gully Erosion ◽  
The Arctic ◽  
Yamal Peninsula ◽  
Rfbr Grant ◽  
Runoff Depth ◽  
Express Methods ◽  
Comparison Of The Results

<p>Risk of damage of buildings and infrastructure by gully erosion can be estimated on the net of flowlines or by evaluation of depths of gullies with erosion model, or by calculation of some simplified measures of erosion rate, which are correlated with such calculated gullies depths and/or with the measurements of gully erosion. The most exact approach is based on calculation of the transformation of longitudinal profiles of linear erosion features along all flowlines on DEM with GULTEM model. The model includes calculation of gully erosion and thermoerosion, gully bank widening and collapsing. This requires detailed meteorological, hydrological, morphological and lithological information and includes model calibration on the measurement data. The simplified methods are based on the calculation of critical runoff depth at which linear erosion of the soil begins for each point on the catchment. The total sediment yield at each point by all flows above critical or difference between the maximum runoff depth and its critical value is calculated within such approach. This requires much less hydrological, morphological and lithological information, but takes into account only initial conditions on the catchment. Calculations of the risk of gully erosion were performed on the net of flowlines for the gas fields on the Yamal Peninsula with existing and designed structures and buildings. Comparison of the results of evaluating the gully erosion potential by the simplified methods with the data of calculations of gully erosion using the detailed dynamic model and field measurements showed their satisfactory agreement. This confirms the possibility of using express-methods for a quick assessment of the scope of using territories for development with the following detailed calculations with the use of GULTEM on certain areas of construction for evaluation of the risks of landscape and infrastructure disturbance.</p><p><strong>Funding: </strong>This research was funded by RFBR grant 18-05-60147 "Extreme hydrometeorological phenomena in the Kara Sea and the Arctic coast".</p><p> </p>

scholarly journals GEOMETRICAL APPROACH TO LIGHT IN INHOMOGENEOUS MEDIA

2002 ◽  
Vol 17 (11) ◽  
pp. 1543-1558 ◽  
Author(s):  
P. PIWNICKI
Keyword(s):  
Electromagnetic Fields ◽  
Light Propagation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flat Space ◽  
Dielectric Medium ◽  
Index Of Refraction ◽  
Geometrical Approach ◽  
Complex Formulation ◽  
Relativistic Approach

Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only. The introduction of an appropriately chosen three-dimensional metric leads to a significant simplification of the description of light propagation in an inhomogeneous medium: light rays become geodesics of the metric and the field vectors are parallel transported along the rays. The new metric is connected to the usual flat space metric diag[1,1,1] via a conformal transformation leading to new, effective values of the medium parameters [Formula: see text] and [Formula: see text] with [Formula: see text]. The corresponding index of refraction is thus constant and so is the effective velocity of light. Space becomes effectively empty but curved. All deviations from straight-line propagation are now due to curvature. The approach is finally used for a discussion of the Riemann–Silberstein vector, an alternative, complex formulation of the electromagnetic fields.

scholarly journals THE THEOREM OF AVERAGING IN THE CONDITION OF UNLIMETED SPEED FOR ALMOST-PERIODIC FUNCTIONS

2017 ◽  
Vol 19 (3) ◽  
pp. 53-57
Author(s):  
O.P. Filatov
Keyword(s):  
Differential Inclusion ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Almost Periodic ◽  
Independent Variables ◽  
Finite Dimensional ◽  
All Solutions ◽  
Independent Variable ◽  
The Right

It is proved that the limit of maximal mean is an independent variable of initial conditions if an axis exists from the convex hull of a set of permitted speeds out of a finite-dimensional space and the components of direction vector of the axis are the independent variables with respect to a spectrum of almost-periodic function. The set of permitted speeds is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.

scholarly journals Projection Path Explorer: Exploring Visual Patterns in Projected Decision-making Paths

2021 ◽  
Vol 11 (3-4) ◽  
pp. 1-29
Author(s):  
Andreas Hinterreiter ◽  
Christian Steinparz ◽  
Moritz SchÖfl ◽  
Holger Stitz ◽  
Marc Streit
Keyword(s):  
Problem Solving ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Dimensional Representation ◽  
Self Similarity ◽  
Solution Strategies ◽  
Network Training ◽  
Strategy Games ◽  
Lower Dimensional Space

In problem-solving, a path towards a solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of dimensionality reduction, these trajectories can be visualized in lower-dimensional space. Such embedded trajectories have previously been applied to a wide variety of data, but analysis has focused almost exclusively on the self-similarity of single trajectories. In contrast, we describe patterns emerging from drawing many trajectories—for different initial conditions, end states, and solution strategies—in the same embedding space. We argue that general statements about the problem-solving tasks and solving strategies can be made by interpreting these patterns. We explore and characterize such patterns in trajectories resulting from human and machine-made decisions in a variety of application domains: logic puzzles (Rubik’s cube), strategy games (chess), and optimization problems (neural network training). We also discuss the importance of suitably chosen representation spaces and similarity metrics for the embedding.

scholarly journals A New Method to Construct the KD Tree Based on Presorted Results

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yu Cao ◽  
Huizan Wang ◽  
Wenjing Zhao ◽  
Boheng Duan ◽  
Xiaojiang Zhang
Keyword(s):  
Data Structure ◽  
Complex Systems ◽  
Initial Conditions ◽  
Dimensional Space ◽  
New Method ◽  
High Dimensional ◽  
Search Process ◽  
Construction Process ◽  
Tree Construction ◽  
Application Scope

Searching is one of the most fundamental operations in many complex systems. However, the complexity of the search process would increase dramatically in high-dimensional space. K-dimensional (KD) tree, as a classical data structure, has been widely used in high-dimensional vital data search. However, at present, common methods proposed for KD tree construction are either unstable or time-consuming. This paper proposed a new algorithm to construct a balanced KD tree based on presorted results. Compared with previous similar method, the new algorithm could reduce the complexity of the construction process (excluding the presorting process) from O (KNlog2N) level to O (Nlog2N) level, where K is the number of dimensions and N is the number of data. In addition, with the help of presorted results, the performance of the new method is no longer subject to the initial conditions, which expands the application scope of KD tree.

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