scholarly journals The finite-dipole dynamical system

Author(s):  
Andrew A. Tchieu ◽  
Eva Kanso ◽  
Paul K. Newton

The notion of a finite dipole is introduced as a pair of equal and opposite strength point vortices (i.e. a vortex dipole) separated by a finite distance. Equations of motion for N finite dipoles interacting in an unbounded inviscid fluid are derived from the modified interaction of 2 N independent vortices subject to the constraint that the inter-vortex spacing of each constrained dipole, ℓ, remains constant. In the absence of all other dipoles and background flow, a single dipole moves in a straight line along the perpendicular bisector of the line segment joining the two point vortices comprising the dipole, with a self-induced velocity inversely proportional to ℓ. When more than one dipole is present, the velocity of the dipole centre is the sum of the self-induced velocity and the average of the induced velocities on each vortex comprising the pair due to all the other dipoles. Each dipole orients in the direction of shear gradient based on the difference in velocities on each of the two vortices in the pair. Several numerical experiments are shown to illustrate the interactions between two and three dipoles in abreast and tandem configurations. We also show that equilibria (multi-poles) can form as a result of the interactions, and we study the stability of polygonal equilibria, showing that the N =3 case is linearly stable, whereas the N >3 case is linearly unstable.

SIMULATION ◽  
1967 ◽  
Vol 9 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Arthur I. Rubin ◽  
Stanley Driban ◽  
Wayne W. Miessner

The steps necessary to derive the regression differential equations for a set of unknown parameters are presented. A simple straight-line algebraic regression problem is re viewed. A real problem, that of finding the aerodynamic stability derivatives for the lateral equations of motion of an airplane, is presented. Preliminary results, using real airplane transient time histories, are compared with simu lated transients obtained using wind-tunnel values for the stability derivatives.


Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton

The vibration behavior of constrained high speed rotating disks is of interest in industries as diverse as: aerospace, computer disk manufacture and saw design and usage. The purpose of this study is to investigate the stability behavior of guided circular disks with different boundary conditions. The equations of motion are developed for circular rotating disks constrained by space fixed linear, mass, spring, damper systems. The resulting equation of motion is a two dimensional fourth order partial differential equation that requires numerical solution. The Galerkin Method is employed using the eigenfunctions of the stationary non-constrained disk as approximation functions. Of interest is the effect on stability of conditions at the inner boundary. In particular the difference in behavior for centrally clamped, and splined disks (those disks that run on a spline arbor) is investigated. Also discussed is the effect of constraints on the flutter and divergence instability boundaries. Preliminary experimental results are presented for constrained splined disks, and these results are compared with the analytical predictions.


1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.


1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.


Author(s):  
Ю.И. Цой

Задача получения однородного состава ЛКМ сводится к правильному выбору пленкообразователей и соответствующих растворителей и, в случае необходимости, разбавителей и добавок. На основе положений теории растворимости была проведена оценка совместимости компонентов и стабильности таких систем. Критериями оценки были приняты параметры растворимости и термодинамического взаимодействия. Исследовали совместимость алкидных лаков с аминоформальдегидными смолами в бутаноле, и результаты этих исследований представлены в треугольной фазовой диаграмме. Для оценки совместимости смол по результатам расчета параметров термодинамического взаимодействия были построены спинодали для тройных систем. Как показывает анализ результатов проведенных исследований, даже при большой разности ?? = |?12 – ?13| = 0,2 наблюдается небольшая область несовместимости. С уменьшением разности ?? область несовместимости сужается. При ?23 > ?с область несовместимости расширяется как для ? = 0,2, так и для ?? = 0,1 и ?? = 0. Таким образом, для таких систем на совместимость компонентов, в первую очередь, влияет их взаимодействие между собой – чем оно больше, тем лучше они совместимы. Проведенные исследования показали, что парциальные параметры растворимости, учитывающие природу когезионных сил, более объективно характеризуют растворимость пленкообразующих смол в органических растворителях, чем их общий параметр растворимости. Растворимость пленкообразующих алкидных и этерифицированных аминоформальдегидных смол в органических растворителях обусловлена термодинамическим взаимодействием молекулярных сил различной природы. Стабильность смеси алкидной и этерифицированной аминоформальдегидной смолы в бутаноле обусловлена в большей степени термодинамическим взаимодействием молекулярных сил; при этом степень бутанолизации меламиноформальдегидной смолы оказывает наибольшее влияние на стабильность cистемы. Проведенные исследования по стабильности лакокрасочных смесей из различных пленкообразующих смол на основе рассмотренных критериев оценки могут быть использованы для совершенствования технологии защитно-декоративной отделки древесины. The problem of obtaining a homogeneous composition of the coatings is reduced to the proper selection of film-forming agents, and diluent and, if appropriate, diluents and additives. On the basis of the theory of solubility, we have carried out the assessment of the compatibility of the components and stability of such systems. The evaluation criteria were adopted the parameters of the solubility and thermodynamic interaction. Researched the compatibility with alkyd varnishes aminoformaldehyde resin in butanol, and the results of these studies are presented in the triangular phase diagram. To evaluate the compatibility of the resins according to the results of calculation of thermodynamic parameters of interaction were built spinodal for ternary systems. As the analysis of the results of the studies, even when the difference ??|?12 – ?13| = 0,2 there is a small area of incompatibility. With the decrease of the difference ? ? region incompatibility narrows. When ?23> ?с region incompatibility extends to ?? = 0,2, and for ?? = 0.1 and ?? = 0. Thus, for such systems, compatibility of components, primarily, affects their interaction with each other – the further away it is, the better they are compatible. Studies have shown that the partial solubility parameters, which take into account the nature of cohesive forces, more objectively characterize the solubility of film-forming resins in organic solvents than their total solubility parameter. The solubility and film-forming aminoformaldehyde esterified alkyd resins in organic solvents due to thermodynamic interaction of molecular forces of different nature. Тhe stability of the mixture and aminoformaldehyde esterified alkyd resin in butanol is generated largely by thermodynamic forces of molecular interaction; the degree of butanolate melamine-formaldehyde resin has the greatest effect on the stability of the system. Conducted research on the stability of the paint mixtures of various film-forming resins on the basis of the evaluation criteria can be used to improve the technology of protective and decorative wood finish.


Author(s):  
Yong Wang

The purpose of this study is to explore the stability and interaction between parental pressure and social research report, as well as the role of employment status and family income levels in this process. This study used a special study on Korean children (PSKC) 2–4 waves. Use t-test, correlation and autoregressive cross-delay modeling to analyze the data. The main findings of this study are: First, over time, parental pressure and mother’s social research report are consistent. Secondly, the pressure of motherhood and childcare has an obvious lagging effect on upbringing, and vice versa. Third, there is no significant difference between working mothers and non-working mothers in terms of the stability of working parents' pressure, social research report and social research report for children's pressure channels. However, parental pressure can only predict the social research report of working mothers. Fourth, there is no significant difference between the stability and interaction of these two structures in household income levels. In short, the results show that, over time, parental pressure is consistent with mother’s social research report. The results also show that there is a significant cross-lag effect between the mothers’ perceptions of mutual pressure analysis. In the process from parental pressure to social research report, I found the difference between working and non-working mothers. The advantage of this study is that the expected longitudinal design was adopted during infancy and the priority between the two structures can be considered. The results of this study can be used as a source of intervention plans to help parents withstand severe parenting pressure and lack of social research report.


2021 ◽  
Vol 13 (4) ◽  
pp. 793
Author(s):  
Guoqiang Jiao ◽  
Shuli Song ◽  
Qinming Chen ◽  
Chao Huang ◽  
Ke Su ◽  
...  

BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for the BDS-2 and BDS-3 default civil service signals (B1I/B3I) and the increase of new signals (B1C/B2a) for BDS-3, a systemically bias exists in the receiver-end when receiving and processing BDS-2 and BDS-3 signals, which leads to the inter-system bias (ISB) between BDS-2 and BDS-3 on the receiver side. To fully utilize BDS, the BDS-2 and BDS-3 combined precise time and frequency transfer are investigated considering the effect of the ISB. Four kinds of ISB stochastic models are presented, which are ignoring ISB (ISBNO), estimating ISB as random constant (ISBCV), random walk process (ISBRW), and white noise process (ISBWN). The results demonstrate that the datum of receiver clock offsets can be unified and the ISB deduced datum confusion can be avoided by estimating the ISB. The ISBCV and ISBRW models are superior to ISBWN. For the BDS-2 and BDS-3 combined precise time and frequency transfer using ISBNO, ISBCV, ISBRW, and ISBWN, the stability of clock differences of old signals can be enhanced by 20.18%, 23.89%, 23.96%, and 11.46% over BDS-2-only, respectively. For new signals, the enhancements are −50.77%, 20.22%, 17.53%, and −3.69%, respectively. Moreover, ISBCV and ISBRW models have the better frequency transfer stability. Consequently, we recommended the optimal ISBCV or suboptimal ISBRW model for BDS-2 and BDS-3 combined precise time and frequency transfer when processing the old as well as the new signals.


Author(s):  
Harald Fripertinger ◽  
Jens Schwaiger

AbstractIt was proved in Forti and Schwaiger (C R Math Acad Sci Soc R Can 11(6):215–220, 1989), Schwaiger (Aequ Math 35:120–121, 1988) and with different methods in Schwaiger (Developments in functional equations and related topics. Selected papers based on the presentations at the 16th international conference on functional equations and inequalities, ICFEI, Bȩdlewo, Poland, May 17–23, 2015, Springer, Cham, pp 275–295, 2017) that under the assumption that every function defined on suitable abelian semigroups with values in a normed space such that the norm of its Cauchy difference is bounded by a constant (function) is close to some additive function, i.e., the norm of the difference between the given function and that additive function is also bounded by a constant, the normed space must necessarily be complete. By Schwaiger (Ann Math Sil 34:151–163, 2020) this is also true in the non-archimedean case. Here we discuss the situation when the bound is a suitable non-constant function.


2014 ◽  
Vol 887-888 ◽  
pp. 1328-1332
Author(s):  
Wang Biao Qiu ◽  
Wei Xing Chen

The article based on different frequency pulse equiponderance electromagnetic destressing comparison experiment, using vertical optical measurement to survey the changes of bearing ferrules size, study the difference between the effect of different frequency electromagnetic in removing residual stress, find the frequency of magnetic treatment pulse that help to maintain the stability of the thin-wall bearing collars' size, effectively improve the cycle of bearing ferrules process .


2009 ◽  
Vol 76-78 ◽  
pp. 459-464
Author(s):  
Jae Won Baik ◽  
Chang Wook Kang

Chemical mechanical polishing (CMP) is a technique used in semiconductor fabrication for planarizing the top surface of an in-process semiconductor wafer. Especially, Post-CMP thickness variations are known to have a severe impact on the stability of downstream processes and ultimately on device yield. Hence understanding how to quantify and characterize this non-uniformity is significant step towards statistical process control to achieve higher quality and enhanced productivity. The main reason is that the non-uniformed interface between the wafer and the machine-pad adversely affects the polishing performance and ultimate surface uniformity. The purpose of this paper is to suggest a new measure that estimates the uniformity of wafer surface considering the difference of the amount of abrasion between the center and the edge. This new measure which is called the Coefficient of Uniformity is defined as the following ratio: Geometric Mean (GM) / Arithmetic Mean (AM). This metric can be evaluated regionally to quantify the non-uniformity on the wafer surface from the center to the edge. Further simulations show that this new measure is insensitive to shift of the wafer center and sensitive to shift of the wafer edge. This trend indicates that this new measure is a very useful to test the non-uniformity of wafer after CMP polishing.


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