scholarly journals Interaction between the forced and parametric excitations with different degrees of smallness

1998 ◽  
Vol 20 (2) ◽  
pp. 11-17
Author(s):  
Nguyen Van Dao

The nonlinear system under consideration in this paper has a specification which can be stated as an interaction between the first order of smallness no resonance parametric excitation and the second order of smallness resonance forced excitation. In the first approximation these excitations have no effect. However, they do interact one with another in the second approximation.The equations for the amplitude and phase of oscillation are found by means of the asymptotic method. The stationary oscillations and their stability are of special interest.

Author(s):  
Uriah Kriegel

Brentano’s theory of judgment serves as a springboard for his conception of reality, indeed for his ontology. It does so, indirectly, by inspiring a very specific metaontology. To a first approximation, ontology is concerned with what exists, metaontology with what it means to say that something exists. So understood, metaontology has been dominated by three views: (i) existence as a substantive first-order property that some things have and some do not, (ii) existence as a formal first-order property that everything has, and (iii) existence as a second-order property of existents’ distinctive properties. Brentano offers a fourth and completely different approach to existence talk, however, one which falls naturally out of his theory of judgment. The purpose of this chapter is to present and motivate Brentano’s approach.


1998 ◽  
Vol 20 (1) ◽  
pp. 9-20
Author(s):  
Nguyen Van Dao

In nonlinear systems, the first order of smallness terms of nonresonance forced and parametric excitations have no effect on the oscillation in the first an approximation. However, they do interact one with another in the second approximation.Using the asymptotic method of nonlinear mechanics [1] we obtain the equations for the amplitudes and phases of oscillation. The amplitude curves are drawn digital computer. The stationary oscillations and their stability are of special interest.


1975 ◽  
Vol 42 (1) ◽  
pp. 176-182 ◽  
Author(s):  
C. S. Hsu

A second-order nonlinear system subjected to parametric excitation is investigated. The nonlinear factors included are nonlinear damping and a cubic term in displacement. The primary purpose of the paper is to study the limiting effects of these nonlinear factors on the growth of motion for those systems which are otherwise unstable and have an exponential growth. Through an asymptotic analysis formulas are found for evaluating the limit cycle response amplitude in the first and second instability regions of the Ince-Strutt chart. Some results calculated from these formulas for the important case of velocity square damping are compared against those obtained by direct numerical integration in order to assess their accuracy.


Author(s):  
Yukio Ishida ◽  
Kimihiko Yasuda ◽  
Shin Murakami

Abstract Nonstationary vibrations at the major critical speed of a rotating shaft with nonlinear spring characteristics are discussced. Firstly, the first order approximate solutions of steady-state and nonstationary oscillations are obtained by the asymptotic method. The relations between these approximate solutions and the nonlinear components in the polar coordinate expression are investigated. It is clarified that, similar to the case of the stationary oscillations, only the isotropic nonlinear component has influence on nonstationary oscillations in the first order approximation. Secondly, the complex-FFT method where non-stationary time histories obtained by numerical integrations of the equations of motion are treated as complex numbers in the complex plane which coincides with the whirling plane are proposed. By this method, the amplitude variation curves of each vibration component are obtained. From the comparison of the amplitude variation curves of the first approximation of the asymptotic method, the solution of the complex-FFT method, and direct numerical integration, it is clarified that, although all these solutions coincide well in the case of stationary solutions, the first approximation of the asymptotic method has comparatively large quantitative error in the case of nonstationary solutions. In addition, the influences of the anisotropic nonlinear components which do not appear in the first approximation of the asymptotic method are investigated.


2016 ◽  
Vol 30 (35) ◽  
pp. 1650412 ◽  
Author(s):  
Xi-Yang Xie ◽  
Bo Tian ◽  
Lei Liu ◽  
Xiao-Yu Wu ◽  
Yan Jiang

In this paper, we investigate a nonlinear system, which describes the marginally unstable baroclinic wave packets in the geophysical fluid. Based on the symbolic computation and Hirota method, bright one- and two-soliton solutions for such a system are derived. Propagation and collisions of the solitons are graphically shown and discussed with [Formula: see text], which reflects the collision between the wave packet and mean flow, [Formula: see text], which measures the state of the basic flow, and group velocity [Formula: see text]. [Formula: see text] is observed to affect the amplitudes of the solitons, and [Formula: see text] can influence the solitons’ traveling directions. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions are derived. Properties of the first- and second-order rogue waves are graphically presented and analyzed: The first-order rogue waves are shown in the figures. [Formula: see text] has no effects on A, which is the amplitude of the wave packet, but with the increase of [Formula: see text], amplitude of B, which is a quantity measuring the correction of the basic flow, decreases. When [Formula: see text] is chosen differently, A and B do not keep their shapes invariant. With the value of [Formula: see text] increasing, amplitudes of A and B become larger. The second-order rogue wave is presented, from which we observe that with [Formula: see text] increasing, amplitude of B decreases, but [Formula: see text] has no effects on A. Collision features of A and B alter with the value of [Formula: see text] changing. When we make the value of [Formula: see text] larger, amplitudes of A and B increase.


1990 ◽  
Vol 12 (3) ◽  
pp. 1-7
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Tien Khiem

The influence of the periodic force on the nonlinear first order systems with delay is investigated by the asymptotic method Crulov-Bogoliubov-Mitropolski. A detailed research of the response of Duffing and Van der Pol systems to external periodic force is given. The obtained results are compared with well-known ones in such second order systems without delay.


1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.


2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 


2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.


Author(s):  
Tim Button ◽  
Sean Walsh

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.


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