The Dynamics of a Ligament-Suspended North-Seeking Gyroscope

1979 ◽  
Vol 21 (2) ◽  
pp. 123-131 ◽  
Author(s):  
C. H. J. Fox ◽  
L. Maunder
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Free Vibration ◽  
Higher Order ◽  
Experimental Confirmation ◽  
Order Effects ◽  
Linear Vibration ◽  
First Order ◽  
Dynamical Characteristics ◽  
Theoretical Predictions

The dynamical characteristics of a North-seeking gyroscope are ivestigated. Five modes of free vibration are predicted. The response to harmonic horizontal disturbances of the point of suspension contains resonances associated with the natural fequencies that are predictable from first-order linear vibration theory. A higher order approximate solution shows that significant second-order effects occur in the form of ultra-harmonic resonances and a steady-state error in indicated North. Experimental confirmation of the theoretical predictions is reported.

scholarly journals Reputations for Resolve and Higher-Order Beliefs in Crisis Bargaining

2021 ◽  
pp. 002200272199554
Author(s):  
Allan Dafoe ◽  
Remco Zwetsloot ◽  
Matthew Cebul
Keyword(s):  
Belief Change ◽  
Higher Order ◽  
Future Research ◽  
Order Effects ◽  
Survey Experiment ◽  
Experimental Setting ◽  
Crisis Bargaining ◽  
First Order ◽  
Qualitative Evidence ◽  
Higher Order Effects

Reputations for resolve are said to be one of the few things worth fighting for, yet they remain inadequately understood. Discussions of reputation focus almost exclusively on first-order belief change— A stands firm, B updates its beliefs about A’s resolve. Such first-order reputational effects are important, but they are not the whole story. Higher-order beliefs—what A believes about B’s beliefs, and so on—matter a great deal as well. When A comes to believe that B is more resolved, this may decrease A’s resolve, and this in turn may increase B’s resolve, and so on. In other words, resolve is interdependent. We offer a framework for estimating higher-order effects, and find evidence of such reasoning in a survey experiment on quasi-elites. Our findings indicate both that states and leaders can develop potent reputations for resolve, and that higher-order beliefs are often responsible for a large proportion of these effects (40 percent to 70 percent in our experimental setting). We conclude by complementing the survey with qualitative evidence and laying the groundwork for future research.

Laminar natural convection boundary layers on near-horizontal plates

1976 ◽  
Vol 352 (1669) ◽  
pp. 249-274 ◽  
Keyword(s):  
Natural Convection ◽  
Higher Order ◽  
Convection Flow ◽  
Order Effects ◽  
Heated Plate ◽  
Matching Problems ◽  
Transfer Rates ◽  
Theoretical Predictions ◽  
Laminar Natural Convection ◽  
Higher Order Corrections

The first order boundary-layer analysis for the laminar natural convection flow over a semi-infinite horizontal or near-horizontal heated plate has been extended to include variable properties effects. Detailed calculations are presented for air and water flows. It is shown further how these calculations can be extended to predict heat transfer rates on plates of rectangular planforms. Because of the lack of sufficiently detailed experimental data, a thorough comparison between the latter and the present calculations has not been possible. However, such comparisons as have been possible are encouraging and a significant improvement on previous theoretical predictions has been achieved. Although higher order corrections have not been discussed in detail, possible matching problems have been investigated briefly. Furthermore, it has been shown that stress work effects in the energy equation and the influence of pressure on density and temperature in the state relation are not only solely higher order effects but are of little significance at such orders.

Numerical Investigation of the Physics of Higher Order Effects Generated by Wave Paddles

2020 ◽  
Author(s):  
Yun Zhi Law ◽  
Hui Liang ◽  
Harrif Santo ◽  
Kian Yew Lim ◽  
Eng Soon Chan
Keyword(s):  
Free Surface ◽  
Higher Order ◽  
The Other ◽  
Order Effects ◽  
Harmonic Waves ◽  
Regular Wave ◽  
Wave Tank ◽  
First Order ◽  
Higher Harmonic ◽  
Higher Order Effects

Abstract When free-surface waves are generated using wave paddles to produce the desired waves, higher order effects might be inevitable for some cases. These can be due to the mismatch in the wave paddle displacement and non-linear free-surface wave kinematics, as well as the moving boundary of wave paddles. Such higher order effects are often manifested as higher harmonic waves, which can propagate independently (or free waves). The presence of such waves will contaminate the quality of the tank test, and together with effects due to scaling and finite size of tank, it is important to reduce or mitigate such effects as much as possible in a wave tank in order to simulate a more realistic scenario. This study investigates the above problem in a systematic manner by using a fully-nonlinear numerical wave tank based on the three-dimensional time-domain Harmonic Polynomial Cell (HPC) method. Wave is generated by flap-type wave paddles on one end of the tank, and is damped on the other end. The paddle boundary conditions are satisfied on the instantaneous paddles surfaces, and the free surface is tracked by the generalized semi-Lagrangian scheme. In this study, first order paddle signal is used to generate regular waves, and the focus is on characterising the behaviour of the generated free higher harmonic waves. We first look into a rectangular wave tank where the paddles are distributed at one side of the tank. Upon the generation of an oblique regular wave (primary wave), it is observed that the generated free waves propagate at a different angle/direction. An explicit analytical expression is derived for the direction of the free waves, which agrees with the numerical observation. Besides propagating at a different direction, the free waves also interact with the primary waves resulting in additional bound waves of the first and third harmonics. Next, we consider a circular wave tank, where paddles along half of the circumference are used to generate planar regular wave, while paddles at the other half are assumed to be able to fully absorb the wave. The generated free waves are observed to focus at a particular region in the tank due to constructive interference. To eliminate or at least mitigate such undesired waves, correction to first order paddle signal is required. Second order correction scheme based on Schaffer (1996) is implemented for such purpose. Preliminary results seem to suggest that second order correction to the paddle signal can only mitigate but cannot completely eliminate the existence of free higher harmonic waves.

First- and higher-order effects of curvature and torsion on the flow in a helical rectangular duct

1996 ◽  
Vol 314 ◽  
pp. 113-138 ◽  
Author(s):  
C. Jonas Bolinder
Keyword(s):  
Secondary Flow ◽  
Stable Solution ◽  
Higher Order ◽  
Convective Transport ◽  
Order Effects ◽  
First Order ◽  
Order Solution ◽  
Aspect Ratios ◽  
Curvature And Torsion ◽  
Square Ducts

A series expansion method is employed to determine the first-order terms in curvature ε and torsion η of fully developed laminar flow in helical square ducts and in helical rectangular ducts of aspect ratio two. The first-order solutions are compared to solutions of the full governing equations. For toroidal square ducts with zero pitch, the first-order solution is fairly accurate for Dean numbers, De = Re ε1/2, up to about 20, and for straight twisted square ducts the first-order solution is accurate for Germano numbers, Gn = η Re, up to at least 50 where Re is the Reynolds number. Important conclusions are that the flow in a helical duct with a finite pitch or torsion to the first order (i.e. with higher-order terms in ε and η neglected) is obtained as a superposition of the flow in a toroidal duct with zero pitch and a straight twisted duct; that the secondary flow in helical non-circular ducts for sufficiently small Re is dominated by torsion effects; and that for increasing Re, the secondary flow eventually is dominated by effects due to curvature. Torsion has a stronger impact on the flow for aspect ratios greater than one. A characteristic combined higher-order effect of curvature and torsion is an enlargement of the lower vortex of the secondary flow at the expense of the upper vortex, and also a shift of the maximum axial flow towards the upper wall. For higher Reynolds numbers, bifurcation phenomena appear. The extent of a few solution branches for helical ducts with finite pitch or torsion is determined. For ducts with small torsion it is found that the extent of the stable solution branches is affected little by torsion. Physical velocity components are employed to describe the flow. The contravariant components are found useful when describing the convective transport in the duct.

Macroscopic and kinetic modelling of rarefied polyatomic gases

2016 ◽  
Vol 806 ◽  
pp. 437-505 ◽  
Author(s):  
Behnam Rahimi ◽  
Henning Struchtrup
Keyword(s):  
Kinetic Model ◽  
Degrees Of Freedom ◽  
Kinetic Modelling ◽  
Higher Order ◽  
Macroscopic Model ◽  
Order Effects ◽  
Moment Equations ◽  
Polyatomic Gases ◽  
First Order ◽  
Order Set

A kinetic model and corresponding high-order macroscopic model for the accurate description of rarefied polyatomic gas flows are introduced. The different energy exchange processes are accounted for with a two term collision model. The proposed kinetic model, which is an extension of the S-model, predicts correct relaxation of higher moments and delivers the accurate Prandtl ($Pr$) number. Also, the model has a proven linear H-theorem. The order of magnitude method is applied to the primary moment equations to acquire the optimized moment definitions and the final scaled set of Grad’s 36 moment equations for polyatomic gases. At the first order, a modification of the Navier–Stokes–Fourier (NSF) equations is obtained. At third order of accuracy, a set of 19 regularized partial differential equations (R19) is obtained. Furthermore, the terms associated with the internal degrees of freedom yield various intermediate orders of accuracy, a total of 13 different orders. Thereafter, boundary conditions for the proposed macroscopic model are introduced. The unsteady heat conduction of a gas at rest is studied numerically and analytically as an example of a boundary value problem. The results for different gases are given and effects of Knudsen numbers, degrees of freedom, accommodation coefficients and temperature-dependent properties are investigated. For some cases, the higher-order effects are very dominant and the widely used first-order set of the NSF equations fails to accurately capture the gas behaviour and should be replaced by the proposed higher-order set of equations.

scholarly journals Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

2021 ◽  
Vol 5 (11) ◽  
pp. 305
Author(s):  
Slimane Merdaci ◽  
Hadj Mostefa Adda ◽  
Belghoul Hakima ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Vibration Response ◽  
Governing Equations ◽  
First Order ◽  
Fg Plates ◽  
Free Vibration Response

The present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered materials and composite applications.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

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