Multimode oscillator analysis via integral manifolds part I: Non-resonant case

This article represents Part I of a two-part paper which provides a rigorous mathematical foundation of the modeanalysis method for analysing the periodic and quasi-periodic oscillations observed in various types of coupled oscillators. Although the results predicted by this method had been confirmed by experiments to some extent, the crucial assumptions used to derive the averaged equations are based on engineering intuition. Moreover, while it is intuitively reasonable to associate an equilibrium solution of the averaged equations whose eigenvalues have negative real parts with that of a stable periodic or quasi-periodic solution of the original equation, the relationship between the solution of the averaged equations and that of the original equations as t tends to infinity, is not clear in a mathematical sense. This paper resolves the theoretical ambiguities of the mode analysis method by using the theory of integral manifolds. In particular, we recalculate the averaged equations in a rigorous way, and show that they coincide with those obtained before. Therefore, the theory of integral manifolds guarantees the existence of an integral manifold in the original system which corresponds to a steady-state periodic or quasi-periodic solution, provided the equilibrium point of the averaged equation has no eigenvalues with a zero real part (i.e. hyberbolic). This rigorous analysis proved that all our previous results obtained from the mode analysis method, i.e. averaged equations and stability analysis were correct.     

Numerical simulation of growth pattern of a fluid-filled subsurface crack under moving hertzian loading

Cracking of a fluid-filled subsurface crack is studied by means of the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The Griffith crack was initially opened by the application of hydrostatic pressure of an incompressible fluid within the crack. A moving Hertz line contact load distribution is applied at the surface of the half-plane in the presence of friction. The stress intensity factors at the tips of the fluid-filled crack are analyzed with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume. When the crack starts to propagate/kink, numerical results show that the internal fluid pressure will be relieved, and as the ratio of the branched crack length to main crack length increases, the elastic strain energy release rate decreases. The crack growth is assumed to be arrested when the energy release rate is below a certain value. Based on the energy criterion, predictions are attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed to simulate the growth pattern of the fluid-filled crack under moving Hertzian loading.     

Compound conditioned emotional response conditioning with differentially salient elements in rats.

R. Rescorla and A. R. Wagner's model of conditioning (1972) implies that, if 2 conditioned-stimulus (CS) elements are independently conditioned to asymptote and then compounded, reinforcement of the compound should reduce the conditioned strength of each element. Further, the more salient element should lose more strength and should ultimately show less conditioned strength than the less salient element. 4 groups of 8 male Holtzman albino rats each, in a conditioned emotional response procedure, provided 2 independent tests of this deduction at different levels of CS salience. Data in each case appear consistent with the model's prediction, significantly so in 1 case. Data in other aspects confirm deductions drawn from the model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Semiconductor Gamma-Cameras in Nuclear Medicine

The availability of semiconductor detectors, principally High Purity Germanium, permits consideration of new generations of nuclear medicine imaging devices. These are characterized by excellent spatial resolution and by simultaneous multiple radioisotope imaging capabilities. The technology and some of its resultant benefits are presented here.     

The determination of the degree of hydrolysis in poly(acrylamides): simple methods using C13 n.m.r., and elementary analysis

C¹³ n.m.r. spectroscopy and C, N elementary analysis have been applied to determine the degree of hydrolysis of commercial polyacrilamide samples. The methods proposed do not involve the weighing of the samples, and thus avoid the problems posed by retained water and the presence of inorganic salts. The C¹³ n.m.r. spectrum is sufficiently resolved to allow peak area determinations of the methine carbon in the hydrolysed and non-hydrolysed moieties. Elementary analysis of the solid samples has been applied to obtain the C/N ratio of the polymers, rather than percentage values based on sample weight. A very good correlation is observed between the data obtained via both methods.     

Crowd size as a factor in the persuasion process: A study of religious crusade meetings.

Tested the proposition that in larger audiences, a greater proportion of audience members will be persuaded by the speaker with data from 4 separate religious crusades led by Billy Graham and Leighton Ford in Australia (N?=?57 meetings). A reliable positive relationship was found between crowd size and the proportion of "inquirers" (attenders who made a decision for Christ) at weekday meetings. (Distinctive patterns of attendance and inquiring made it necessary to distinguish weekend from weekday meetings, but there were too few weekend meetings for separate analysis). Females and young people constituted greater proportions of inquirers in larger crowds, and the proportion of first-time inquirers increased with crowd size. Possible explanations include enhancement of social influence in large crowds and factors related to changes in crowd composition associated with crowd size. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"Relation between mastery behavior in infancy and competence in early childhood": Correction to Messer et al.

Reports an error in "Relation between mastery behavior in infancy and competence in early childhood" by David J. Messer, Mary E. McCarthy, Susan McQuiston, Robert H. MacTurk, Leon J. Yarrow and Peter M. Vietze (Developmental Psychology, 1986[May], Vol 22[3], 366-372). In the article, an incorrect copyright note has been given. The copyright note has been corrected and is included in the erratum. (The following abstract of the original article appeared in record 1986-24138-001.) 53 infants were observed at 6 and 12 mo of age during 2 24-min play sessions. The Bayley Scales of Infant Development (BSID) were given at 6 and 12 mo and the McCarthy Scales of Children's Abilities (MSCA) at 30 mo of age. Results reveal that measures of competence in infancy (successful task completion during play and the BSID scores) were not strongly correlated with the 30-mo MSCA scores. In contrast, infant mastery behavior during play strongly predicted MSCA scores: The time spent investigating toys at 6 mo and persistence in solving tasks at 12 mo of age were behaviors significantly positively correlated with the MSCA scales. It is suggested that infant behaviors that predict later competence do not remain static but change with age and that infants' mastery behavior is a more effective predictor of later development than their competence with either toys or developmental tests. (23 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Responses of virgin mice, and of maternal females, to normal and caesarian-section delivered pups.

Conducted 2 experiments in which Porton strain mouse pups were presented to a total of 100 male and female adult Porton mice. Significantly more mothers and virgin females retrieved pups to the nest than did virgin males. More virgin females than males licked pups, built nests, and assumed lactation posture. Differences were significant even if males that attacked pups were excluded from consideration. Latencies to 1st appearance of maternal activities were higher than reported by most other workers. Possible genetic strain differences in the response of virgin mice to pups are discussed. In Exp II pups delivered by caesarian section with placentas attached were used. More mothers than either virgin males or females cleaned and accepted pups, indicating that pup cleaning may be controlled by factors different from those influencing other maternal activities. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)