Influence of Controller’s Parameters on Static Bifurcation of Magnetic-Liquid Double Suspension Bearing

Magnetic-Liquid Double Suspension Bearing (MLDSB) is composed of an electromagnetic supporting and a hydrostatic supporting system. Due to greater supporting capacity and static stiffness, it is appropriate for occasions of middle speed, overloading, and frequent starting. Because of the complicated structure of the supporting system, the probability and degree of static bifurcation of MLDSB can be increased by the coupling of hydrostatic force and electromagnetism force, and then the supporting capacity and operation stability are reduced. As the key part of MLDSB, the controller makes an important impact on its supporting capacity, operation stability, and reliability. Firstly, the mathematical model of MLDSB is established in the paper. Secondly, the static bifurcation point of MLDSB is determined, and the influence of parameters of the controller on singular point characteristics is analyzed. Finally, the influence of parameters of the controller on phase trajectories and basin of attraction is analyzed. The result showed that the pitchfork bifurcation will occur as proportional feedback coefficient Kp increases, and the static bifurcation point is Kp = −60.55. When Kp < −60.55, the supporting system only has one stable node (0, 0). When Kp > −60.55, the supporting system has one unstable saddle (0, 0) and two stable non-null focuses or nodes. The shape of the basin of attraction changed greatly as Kp increases from −60.55 to 30, while the outline of the basin of attraction is basically fixed as Kp increases from 30 to 80. Differential feedback coefficient Kd has no effect on the static bifurcation of MLDSB. The rotor phase trajectory obtained from theoretical simulation and experimental tests are basically consistent, and the error is due to the leakage and damping effect of the hydrostatic system within the allowable range of the engineering. The research in the paper can provide theoretical reference for static bifurcation analysis of MLDSB.

Macro-semantic rhythmic structures in popular author songs

Certain author song of the 1950s &ndash; 1980s are characterized with such structural peculiarity as semantic rhythms. This pattern manifests itself in two forms: dialectical juxtaposition of the particular and the general (PG-rhythm); as well as the conflict of non-entropic and entropic processes, order and chaos (OC-rhythm). For broader understanding of this phenomenon, it is necessary to determine its place within the framework of the author song as a large-scale cultural phenomenon. The author mass processing of popular compositions using the method of almost full enumeration. The research material includes all 5 thematic national collections that feature 487 songs. The analysis of the lyrics reveals the total number of works with the initial semantic rhythmics: 43% with the PG-structure and 23% with the OC-structure. The application of various strategies of analysis indicates that the sampling of no less than 70-80 compositions should be used for achieving accurate results in partial studies (for example, by authors) . In the course of research, the author determines new versions of manifestation of the semantic structures: PG-structure of fable-type, as well as variability of Brodsky's saw in songs with entropic rhythmics. There are also songs with intersection of both types of semantic rhythms. Correlation is established between the social processes of cultural environment associated with the author song and the dynamics of semantic rhythms in popular compositions. In the early 1970s, a bifurcation point is noticed in the moods of the corresponding social community.

So be Hudprom! 1963 Reform of Kharkiv State Institute of Arts: Myths and Facts About the Role of Rector M. Shaposhnikov in the Preservation and Reorganization of Kharkiv Art Institute

The article is dedicated to the famous reform of Kharkiv Institute of Arts in 1963. The article provides an overview of the causes and consequences of reform of an ordinary art institute (KSIA) into essentially new Art and Industrial Institute (KAII). The historical and cultural basis of that reform is also examined. For the first time in 60 years of existence of Art and Industrial Institute and its successor, the modern Academy (KSADA), photocopies of documents from KSADA archives are provided reflecting the logic and tools of implementation of that complex and controversial reform. The article features the orders of the rector of KSIA and KAII. Thanks to the analysis of these documents, it is proved that in fact training of art designers in Kharkiv began in October 1962, that is almost a year before the legal registration of KAII. We publish a fragment of Rector M. Shaposhnikov’s report, read at the 21st session of Presidium of Academy of Arts of the USSR (December, 1963), which discussed the initial state of industrial art education in Kharkiv. Particular attention is paid to the problem of qualitative renewal of the KAII teaching staff, which began in 1967, when the first art designers graduated. The central place in the publication is given to the person of Mykhailo Shaposhnikov (1909–1987), rector of Kharkiv Art Institute of that time. Portrait of personality of the then Rector of KSADA is given: as a person, as a head of an institute, as an experienced manager. There are some recollections of eyewitnesses of that reform and of the rector himself. The final part of the article says that the 1963 reform was the bifurcation point from which the development of modern Kharkiv art school began, in which all the “muses of art” and modern directions of creativity are represented. The article ends with a rather rhetorical question: “Could the modern Kharkiv State Academy of Design and Arts exist if not for creative determination and some managerial adventurism of Rector M. Shaposhnikov?...”.

Subharmonic Resonance of Two Thirds Order of Electrostatically Actuated Bio-MEMS Circular Plates: Amplitude-Frequency Response

This paper deals with subharmonic resonance of two thirds order or electrostatically activated BioMEMS circular plates. Specifically, this paper investigates the frequency amplitude response of this resonance. The system consists of a clamped flexible circular plate above a parallel electrode situated at a distance, and under an AC voltage of frequency near three fourths of the natural frequency of the plate. The method of multiple scales is used to model the hard excitations in the system, hard excitations that are necessary to produce this secondary resonance. This work predicts the response, as well as the effects of parameters such as voltage and damping on the response. This paper predicts that the subharmonic resonance of two thirds order consists of a near zero steady state amplitude, and higher values steady state amplitudes consisting of a stable branch and an unstable branch, and a saddle-node bifurcation point. The predictions regarding the effects of voltage and damping on the response of the BioMEMS plate shows that as the voltage increases, the bifurcation point is shifted to lower frequencies and lower amplitudes, while as the damping increases the bifurcation point is shifted to lower frequencies and high amplitudes. Therefore, the increase of damping leads to a case in which it is harder to reach higher amplitude steady-state solutions since it requires large initial amplitudes of the plate.

Ad hoc solutions to wicked problems: Pandemics and other challenges in context

Wicked problems are considered to be any social, cultural, or other challenges that are difficult to address and hard to devise an effective and sustainable solution for. The utopic wishful thinking humanity relied on for so many decades, that technology and science alone, like a new Deus ex machina, would ultimately save us from any problematic situation we would ever face, and from any possible catastrophe we would ever confront, proved to be unrealistic. Catastrophe is a compound Greek word, literally meaning “approaching a turn”. If you are heading at full speed toward a turn, you either have to slow down and turn toward the road again to save life, or you are going to crash. Unless, of course, you prefer to rest upon an external magical aid, a Deus ex machina, to rescue you at the edge of the cliff. A Catastrophe can be realized as a bifurcation point in terms of complexity theory, a point of chaos and unpredictability, or a tipping point. Behind fueling wicked problems and deadlocks lies a Newtonian conception of reality, where the universe is realized as a mechanical automaton, a timeless space where an infinite knowledgeable entity can predict and leverage everything.

Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect

Galerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material (FGM) close to reality. Mathematical formulations concern the Timoshenko shear deformation theory. Small scale and atomic interactions are shaped as maintained by the nonlocal strain gradient elasticity approach. Since there is no bifurcation point for FGMs, whenever both boundary conditions are rotational and the neutral surface does not match the mid-plane, the clamp configuration is examined only. The fourth-order ordinary differential stability equations will be converted into the sets of algebraic ones utilizing the GWRM whose accuracy was proved before. After that, by simply solving the achieved polynomial constitutive relation, the parametric study can be started due to various predominant and overriding factors. It was found that the flexomagneticity is further visible if the ferric nanobeam is constructed by FGM technology. In addition to this, shear deformations are also efficacious to make the FM detectable.

Stochastic dynamic behavior of FitzHugh–Nagumo neurons stimulated by white noise

Stochastic noise exists widely in the nervous system, and noise plays an extremely important role in the information processing of the nervous system. Noise can enhance the ability of neurons to process information as well as decrease it. For the dynamic behavior of stochastic resonance and coherent resonance shown by neurons under the action of stochastic noise, this paper uses Fourier coefficient and coherence resonance coefficient to measure the behavior of stochastic resonance and coherence resonance, respectively, and some conclusions are drawn by analyzing the effects of additive noise and multiplicative noise. Appropriate noise can make the nonlinear system exhibit stochastic resonance behavior and enhance the detection ability of external signals. It can also make the coherent resonance behavior of the nonlinear system reach its optimal state, and the system becomes more orderly. By comparing the effects of additive and multiplicative noise on the stochastic resonance behavior and coherent resonance behavior of the system, it is found that additive and multiplicative noise can both make the system appear the phenomenon of stochastic resonance and have almost identical discharge state at the same noise intensity. However, with the increase of noise intensity, the coherent resonance of the system occurs, the multiplicative noise intensity is smaller than that of additive noise, but the coherent resonance coefficient of additive noise is smaller and the coherent resonance effect is better. The system whose system parameters are located near the bifurcation point is more prone to coherent resonance, and the closer the bifurcation point is, the more obvious the coherent resonance phenomenon is, and the more regular the system becomes. When the parameters of the system are far away from the bifurcation point, the coherent resonance will hardly appear. Besides, when additive and multiplicative noise interact together, the stochastic resonance and coherent resonance phenomena are more likely to appear at small noise, and the behavior of stochastic resonance and coherent resonance that the system shown is better in the local range.

Unidirectional migration of populations with Allee effect

In this note we consider two populations living on identical patches, connected by unidirectional migration, and subject to strong Allee effect. We show that by increasing the migration rate, there are more bifurcation sequences than previous works showed. In particular, the number of steady states can change from 9 (small migration) to 3 (large migration) at a single bifurcation point, or via a sequences of bifurcations with the system having 9,7,5,3 or 9,7,9,3 steady states, depending on the Allee threshold. This is in contrast with the case of bidirectional migration, where the number of steady states always goes through the same bifurcation sequence of 9,5,3 steady states as we increase the migration rate, regardless of the value of the Allee threshold.