Bifurcation Process Research Articles

Functional diversity of prokaryotic HdrA(BC) modules: Role in flavin-based electron bifurcation processes and beyond

In methanogenic archaea, the archetypical complex of heterodisulfide reductase (HdrABC) and hydrogenase (MvhAGD) couples the endergonic reduction of CO2 by H2 to the exergonic reduction of the CoB-S-S-CoM heterodisulfide by H2 via flavin-based electron bifurcation. Presently known enzymes containing HdrA(BC)-like components play key roles in methanogenesis, acetogenesis, respiratory sulfate reduction, lithotrophic reduced sulfur compound oxidation, aromatic compound degradation, fermentations, and probably many further processes. This functional diversity is achieved by a modular architecture of HdrA(BC) enzymes, where a big variety of electron input/output modules may be connected either directly or via adaptor modules to the HdrA(BC) components. Many, but not all HdrA(BC) complexes are proposed to catalyse a flavin-based electron bifurcation/confurcation. Despite the availability of HdrA(BC) crystal structures, fundamental questions of electron transfer and energy coupling processes remain. Here, we address the common properties and functional diversity of HdrA(BC) core modules integrated into electron-transfer machineries of outstanding complexity.

On bifurcations and chaos of a forced rectangular plate with large deflection loaded by subsonic airflow

This paper aims at the bifurcations and chaotic motions of a harmonically driven rectangular plate subjected to a uniform incompressible subsonic airflow. The plate equation of motion is derived by considering the von Karman’s large deflection and Kelvin’s type damping of material. A Galerkin-type solution is applied for the plate stress function and the aerodynamic force. The governing partial differential equation of the system is transformed into ordinary differential equations using the Galerkin method. The divergence instability and the pitchfork-like bifurcation of the plate are explored by theoretical and numerical analysis. The bifurcations of fixed points and periodic motions are thoroughly analyzed. The periodic motions can experience symmetry breaking/restoring bifurcations, period-doubling bifurcations, and saddle–node-like bifurcations, which are vital to the transition between different types of motions. Two typical bifurcation processes feature the bifurcation structure. The first one describes the change between the small and the large periodic orbits; the second one refers to the change between various large periodic orbits. Two criteria are used to predict the chaotic motions, which play a significant role in the transition between the small-orbit and the large-orbit periodic motions. The first one is the classical Holmes–Melnikov’s criterion, and the second one is an approximated criterion that is newly developed from the resonant-response analysis of a reduced system. Results show that the current criterion brings some noticeable improvements compared with Holmes–Melnikov’s criterion.

CHAOTIC STATES OF A MULTILAYER NEURAL NETWORK

The study of the influence of learning speed η on the learning process of a multilayer neural network was studied. The program for the multilayer neural network was written in Python. We determined the speed of learning at which the best learning is observed. To analyze the impact of learning speed on the learning process, a logistic function was used, which describes the doubling of frequency. It is shown that the learning error function is characterized by bifurcation processes that lead to a chaotic state at η> 0.8. The optimal value of the learning speed is determined, which determines the appearance of the process of doubling the number of local minima. Increasing the number of hidden layers and the number of neurons in each layer does not lead to a radical change in the diagram of the logistics function, and hence the optimal value of the learning speed. It is shown that the increase in the number of hidden layers, as well as the number of neurons in them, with increasing speed of learning is accompanied by the appearance of a chaotic state. The chaotic state is characterized by the lack of a learning process. Using the Fourier transform of the error function, the bifurcation process depending on the learning speed was investigated. On the basis of these researches the program for definition of size of optimum speed of training of a neural network is developed. The text of the article adds program codes for a multilayer neural network with the ability to build a branching diagram and a program to determine the presence or absence of the learning process, taking into account the value of optimal learning speed and error. Key words : multilayer neural network, optimal learning speed, bifurcations, chaotic states.

Синергетичний підхід до дослідження феномену дизайн-мислення

The article focuses on describing the phenomenon of design thinking on the basis of synergetic approach methodology. The author studies the category of design thinking as a methodology of generating innovations, as well as determines its characteristic features, namely, accumulating ideas with the help of creative thinking; making risky decisions at the primary stages of a project; empathy with the user of the service; no fear of failure; testing ideas on a number of customers in advance; ergonomic value of a service or product. The realisation of the synergetic approach in accord with the category of design thinking is described by means of the main principles of synergy, including its homeostatic, hierarchic and open character, linearity / non-linearity, observation. The author comes to the conclusion that design thinking as a methodology of solving non-linear tasks is an open system with non-linear relations between the components and sub-systems which is capable of self-development and self-organisation. Moreover, the development of such a system includes the processes of bifurcation which re-direct the self-development of a system towards innovation.

A MIXED TIME-FREQUENCY DOMAIN APPROACH FOR THE QUALITATIVE ANALYSIS OF AN HYSTERETIC OSCILLATOR

Frequency domain techniques, like harmonic balance and describing function, are classical methods for studying and designing electronic oscillators and nonlinear microwave circuits. In most applications spectral techniques have been used for determining the steady-state behavior of nonlinear circuits that exhibit a single periodic attractor. On the other hand, the global dynamics of nonlinear networks and systems is usually investigated through time-domain techniques, that require to introduce rather complex and sophisticated concepts. Recently some HB based techniques have been proposed for investigating bifurcation processes in nonlinear circuits that present several attractors (the authors have considered systems that admits of a Lur’e representation). Their approach presents the advantages of providing a simple and qualitative description of the system dynamics, that can be effectively exploited for design purposes. In this manuscript we will examine a third order hysteretic oscillator, that cannot be decribed in the classical Lur’e form and we will show that its dynamics can be investigated through the joint application of the describing function technique and of a suitable time-domain method for estimating Floquet’s multipliers.

Chaos and Bifurcation of Control Feedback System Using Variational Iteration Method

Chaos theory discusses the behavior of some complex systems which are sensitive to initial condition. It entails some interesting properties such as space-filling, sensitivity to initial conditions, control synchronization and dynamics which can be accessed using different control methods. This paper considers a non-linear feedback control system of underlying symmetries of chaos and bifurcation with periodic equations. Bifurcation theory plays a very vital role in the analysis of Chaos dynamics. Therefore, bifurcation process of chaotic systems involving Lyapunov exponents are studied. The work describes nonlinear systems where small changes produce notable change in the space phase with all the possible states corresponding to a unique point. A Variational Iteration Method (VIM) is adopted to determine the solution stability and bifurcation paths of the dynamic system. Thus. in the paper, state problems of the system are decomposed using Lagrange multiplier to obtain the Adomian polynomials. The polynomials generated in turn minimize the problem by providing an approximate solution that is very close to the analytic solution. A numerical illustration has been presented of a nonlinear coupled equation using VIM. Illustrations showing the graph of the phase space structure, the paths displayed in motion and the region of stability of the numerical scheme was obtained. The result shows that the chaotic nonlinear system is stable.

Radio frequency field-induced electron mobility in an ultracold plasma state of arrested relaxation

Penning ionization releases electrons in a state-selected Rydberg gas of nitric oxide entrained in a supersonic molecular beam. Subsequent processes of electron impact avalanche, bifurcation, and quench form a strongly coupled, spatially correlated ultracold plasma of NO$^+$ ions and electrons that exhibits characteristics of self-organized criticality. This plasma contains a residue of nitric oxide Rydberg molecules. A conventional fluid dynamics of ion-electron-Rydberg quasi-equilibrium predicts rapid decay to neutral atoms. Instead, the NO plasma endures for a millisecond or more, suggesting that quenched disorder creates a state of suppressed electron mobility. Supporting this proposition, a 60 MHz radiofrequency field with a peak-to-peak amplitude less than 1 V cm$^{-1}$ acts dramatically to mobilize electrons, causing the plasma to dissipate by dissociative recombination and Rydberg predissociation. An evident density dependence shows that this effect relies on collisions, giving weight to the idea of arrested relaxation as a cooperative property of the ensemble.

The mechanism of vortex bifurcation vis-à-vis axial switching in rectangular synthetic jets

The present study investigates the vortex dynamics of the rectangular shaped synthetic jet and reports the occurrence of vortex ring bifurcation along with other reported modes such as axial switching and the vortex suction. The novel finding of vortex ring bifurcation of rectangular synthetic jets has been observed without any other mode of excitation except the periodic axial actuation. The experiments on synthetic jets have been conducted at different actuation frequencies and both qualitative and quantitative characterization of the flow structures has been carried out using Laser Induced Fluorescence (LIF) and Laser Doppler Velocimetry, respectively. LIF flow visualization provides insights into the size of the vortex and the vortex evolution with respect to time, enabling us to propose the flow physics behind the axial switching and the vortex bifurcation processes for rectangular synthetic jets. The proposed flow physics is then quantitatively evidenced by the time-averaged velocity measurements. Vortex splitting or bifurcation is found to occur in the minor axis plane of orifice and the divergence angle depends on the actuation frequency and average velocity of fluid expelled through the orifice in the forward stroke of diaphragm. In the case of occurrence of axial switching, a maximum of three axial switching events are observed before vortex breakup. Finally, by systematically carrying out experiments across a wide range of operational parameters, a narrow region corresponding to the vortex bifurcation has been identified on a Reynolds Number–Strouhal Number map, along with other modes such as axial switching regime and the vortex suction regime. Based on our measurements, a mechanism of vortex bifurcation vis-à-vis axial switching has also been suggested.

Simulation of Copper Electrodeposition in Millimeter Size Through-Silicon Vias

Computational predictions of copper deposition in millimeter size through-silicon vias (mm-TSV) are presented based on localized breakdown of a co-adsorbed polyether-chloride suppressor layer. The model builds upon previous work on localized Cu deposition in microscale TSV and through-holes by incorporating 3D fluid flow calculations to more effectively evaluate chemical transport of cupric ion and additives, both of which are critical to adlayer formation and disruption within the via. Simulations using potentiostatic and potentiodynamic waveforms are compared to previously reported filling experiments. Alternatively, the utility of galvanostatic control and variations in fluid flow are explored computationally. For appropriate applied potential(s) or current, deposition is localized to the via bottom, with subsequent growth proceeding in a bottom-up fashion. Selection of inappropriate current or potential waveforms, or forced convection conditions that supply insufficient cupric ion to the bottom of the via, results in prediction of voids. Simulations of deposition in via arrays (4 × 1) predict non-uniform growth across the arrays, with the passivation of individual vias associated with minor variations in convective flow and/or numerical perturbations in the simulation, that reflects the critical nature of the bifurcation process.

(Electrodeposition Division Early Career Investigator Award Address) Metal Patterning by Electrodeposition: Local Bipolar Electrochemistry and Additive-Derived Electrode Bifurcation

One of electrodeposition’s highest value applications is in manufacturing of electronic devices, ranging in scale from nanometer connections in integrated circuits up to millimeter scale features in printed circuit boards. The wide-range of feature geometries and substrate complexity (conducting, semiconducting, insulating, etc.) in this constantly evolving industry has driven extensive efforts to tailor both lateral and vertical material growth characteristics, diverging from more traditional electroplating applications focused on uniform films as applied to coatings. Like the electronics industry, techniques for 3D control of electrodeposition are consistently evolving. These methods include deposition through patterned masks (through-mask plating), use of sacrificial materials to form patterns (EFAB), localized electrodeposition using confined electrodes, and surface adsorbates that drive spatially-dependent active/passive regions through the coupling of local chemical and electrical gradients.In this presentation, I will highlight recent advances in two of these areas: electrodeposition through confined electrodes and by influencing deposition kinetics with surface adsorbates. In the former, bipolar electrochemistry is combined with microjet electrodes to permit localized electrodeposition of a ‘pixel’ on a conductive surface without requiring electrical contact; patterns are produced by rastering the microjet similar to commercial 3D-printing methods. In the latter, electrolyte additives that inhibit deposition can induce spontaneous formation of spatially bifurcated active and passive regions; characteristics of the electrode topography, surface heterogeneity, and electro(chemical) transport through the cell determine the shape of 2D pattern formation. Electroanalytical measurements of these active/passive systems inform electrode shape-change models describing the interplay between transport and electrochemical kinetics. This fundamental insight permits control of an otherwise random bifurcation process that can be tailored for a variety of applications.

Bone marrow mesenchymal cells: polymorphism associated with transformation of rough endoplasmic reticulum.

To understand the behavior and function of bone-marrow mesenchymal cells (BMMCs), we overviewed the morphological presentation of BMMCs in bone-marrow granules (b-BMMCs), isolated BMMCs (i-BMMCs), and BMMCs (c-BMMCs) cultured in H4434 methylcellulose semisolid and MEM media. All samples were derived from bone-marrow aspirates of 30 patients with hematocytopenia. Light microscopy exhibited b-BMMCs and i-BMMCs characterized by abundant cytoplasm and irregular shape in bone-marrow smears, as well as c-BMMCs in culture conditions. Scanning electron microscopy demonstrated cultured c-BMMCs with a sheet-like feature enveloping hematopoietic cells. Transmission electron microscopy revealed b-BMMCs constructing a honeycomb-like structure by thin bifurcate processes among hematopoietic cells. Furthermore, i-BMMCs had bifurcate parapodiums on the surface and prominent rough endoplasmic reticulum (rER) connected with the plasmalemma of the parapodiums. The detailed images suggested that rER may serve as a membrane resource for plasmalemmal expansion in BMMCs in bone marrow.

Categorical Bifurcation: The Rite of Spring at the Threshold of Modernism

Pursuing a new theoretical link between sociology of culture and ‘categorization’ research, the article articulates the process whereby new categories emerge through bifurcation of pre-existing categories. The contribution is in conceptualizing and documenting the underlying interaction of endogenous and exogeneous factors. The assumption is that bifurcation is likely to occur where and when individual practices of contrast maximization interact with the internal tendency toward dichotomization. This form of interaction is instrumental in identifying and explaining ‘thresholds’ in cultural change. The framework is illustrated with the archetype of ‘modern ballet’ – The Rite of Spring, choreographed by Vaslav Nijinsky, staged in 1913. By reversing the codes of ‘classical’ ballet, centered on elegance, lightness and flow, the Rite redefined movement, codifying a language of tension, interruption and constraint. It marked the key moment when a critical part of the audience interpreted ‘bad’ ballet as ‘new’ ballet. The analysis draws parallels with bifurcation processes in physics and system dynamics.

Vortex ring bifurcation and secondary structures in a finite-span synthetic jet

Abstract

Geomorphologic Analysis of Small River Basin within the Framework of Fractal Tree

This paper presents the modified framework of geomorphologic analysis based on the concept of fractal tree. Especially, it is intended to provide hydrologic practitioners with the information on the fractal property of small river basins. To this end, the complete drainage path network is applied to a growth process of a fractal tree for the basin of interest by connecting a channel network to overland drainage pathways. The growth process of a fractal tree would occur only within the limited region possessing channel flow properties in a natural river basin. The exponent of the intra basin type of Hack’s law could show a variable trend in small river basins mainly due to anisotropic property of the catchment planform. The bifurcation process of a drainage path network might be more sensitive to the growth step of the fractal tree than the meandering process of drainage path segment. The fractal dimension from the sinuosity of a channel segment is relatively stable compared to the one from the bifurcation process of the network, so that the geomorphologic features of a small river basin can be characterized by the anisotropic property of catchment planform as well as the bifurcation property of drainage path network with the growth of the fractal tree.

Relative equilibria, stability and bifurcations in Hamiltonian galactic tidal models

ABSTRACT We study special solutions of Galactic Tidal models and the existence, stability and bifurcations of relative equilibria. Precisely, we found four equilibria and rectilinear, as well as circular solutions, previous to any manipulation of the original system. Moreover, by averaging of the Keplerian energy and making use of Reeb's theorem, we find four periodic orbits. The stability of these relative equilibria is analysed and determined in several cases that involve a relation between the Keplerian energy and the gravitational parameter. Further averaging on the angle giving the orbital plane node provides the Matese–Whitman model. This Hamiltonian is expressed as a function of the invariants of the twice-reduced space, which is given by three connected components. For the three connected components become attached to each other by two singular points. Although only the bounded component is endowed with physical meaning, we provide a full analysis of the stability and bifurcations for all the equilibria. By doing this, we get an insight into the bifurcation process. Precisely, we observe that for the singular leaf of the reduced space, some of the equilibria in the bounded and unbounded components switch their locations.

Significance of Activation Energy and Effective Prandtl Number in Accelerated Flow of Jeffrey Nanoparticles With Gyrotactic Microorganisms

Abstract This research addresses the interesting rheological features of Jeffrey nanofluid containing gyrotactic microorganism over an accelerated configuration. The additional consequences of activation energy and thermal radiation are also encountered in the current flow problem. The characteristics of nanofluid is utilized by using Buongiorno’s nanofluid model, while the phenomenon of bioconvection is evaluated by Kuznestov and Nield model. Unlike traditional attempts, the analysis for thermal radiation is performed by using “one parametric approach” by expressing the Prandtl number and thermal radiation parameter in combined form, namely, effective Prandtl number. The governing equations reflecting the flow problem are analytically treated with the help of homotopic algorithm. The impact of flow parameters is graphically elaborated with relevant physical significance. Further, the numerical expressions for effective local Nusselt number, local Sherwood number, and motile density number with variation of flow parameters in articulated tabular form. It is observed that magnitude of skin friction coefficient oscillates periodically with time and magnitude of oscillation increases with increment of Deborah number and mixed convection constant. It is further emphasized that the temperature distribution is enhanced with buoyancy ratio constant and bioconvection Rayleigh number. The microorganism distribution increases with buoyancy ratio constant but reverse trend has been examined for Peclet number. The observations from the reported problem can be more effective for the development of bifurcation processes, biofuels, enzymes, etc.

Behavioral stereotypy and some ecological consequences of entrance-shaft placement of the domichnium Sanctum laurentiensis in Ordovician trepostomate Bryozoa

The ichnofossil Sanctum laurentiensis from the Late Ordovician (Cincinnatian) of Laurentia is a domichnium tunneled into live colonies of ramose and frondose trepostome Bryozoa. A preferred entrance location was chosen by the trace-making endoskeletozoan. The organism chose to tunnel in positions near growing tips of branches where one of two conditions prevailed. At stereotypical sites, here considered “determinate”, domicile entrances were made where a trepostome branch was in the growth process of bifurcation; sites considered “indeterminate” were chosen where one blade or branch was impinging on another, or on some other nearby substrate, thus interfering with normal colony growth in a random, or non-ontogenetic, manner. This stereotypy is a rare example of demonstrable entrance-siting behavior by an unknown invertebrate organism. A skeleto-structural condition was present at both determinate and indeterminate locations on ramose trepostome colonies. Stereotypical entrance-site choices included a location where bryozoan freewall membrane was compromised or thinned and exozone was incompletely developed. Sanctum producers preferred incomplete exozone in order to access the endozone for excavation to form a domichnium. Middle and Late Ordovician diversification of ramose bryozoan forms stimulated escalation of bioeroder and symbiont taxa in living zoaria thus encouraging further trepostome evolution.

THE CONCEPT OF INSTITUTIONAL RESTRUCTURING OF INDUSTRIAL COMPLEXES IN CONDITIONS OF DIGITAL ECONOMY

The article studies acute problems and conceptual issues of transforming industrial enterprises and complexes in conditions of dynamic development of digital technologies and innovation. The author worked out the definition of the concept of institutional restructuring the industrial complex as a system of academic and theoretical views and provisions, which formulate the integral and non-conflicting notion of genesis, content, factors and strategic lines of conducting complex changes at the enterprise in order to ensure its competitiveness, development and higher innovation activity in the digital environment. Basic provisions of the concept were worked out, which characterize preconditions, essence, goals, aspects, tools, process structure and strategy of institutional transformation of the industrial enterprise. The author demonstrates the idea of the integration paradigm and genesis of restructuring, which depicts the logical mechanism of the origin and development of institutional changes in the industrial complex. Classification of fundamental and functional factors of restructuring was carried out and assessment of their appearance in traditional market conditions and conditions of digital economy. To ensure leading positions of the enterprise on market its transformation should be conducted in the pro-active format preventing the period of bifurcation processes and structural shifts in economy. The author proposes a conceptual approach to early restructuring of the industrial complex in respect to market changes. The conceptual scheme of integrating strategic lines in restructuring and developing the industrial complex in conditions of the digital environment was elaborated.

Microelectrode Studies of S-NDR Copper Electrodeposition: Potentiodynamic and Galvanodynamic Measurements and Simulations

Copper electrodeposition from a CuSO4—H2SO4 electrolyte containing a polyether suppressor and (0 to 100) μmol∙L−1 Cl− is examined using a 25 μm diameter microdisk electrode. Optical imaging during cyclic voltammetry and galvanodynamic measurements reveal hysteresis, overpotential inversions, and the morphological evolution accompanying breakdown of the polyether-chloride inhibition layer. Simulations involving co-adsorption of the suppressor-halide adlayer and its subsequent breakdown capture the positive feedback and negative differential resistance (S-NDR) evident in electroanalytical measurements as well as important aspects of electrode shape evolution. The impact of electrode shape change on simulations of electroanalytical experiments is quantified in comparison to a stationary interface approximation. For potentiodynamic conditions, adlayer breakdown propagates rapidly from the center of the microelectrode surface although the final deposit profile is non-uniform due to enhanced transport to the disk perimeter. In contrast, galvanodynamic experiments in more concentrated Cl− solutions reveal spatially selective suppressor breakdown with deposition initially localized to the microelectrode center followed by outward expansion as applied current is increased. The difference between potentiodynamic and galvanodynamic responses reflects the convolution of S-NDR critical behavior with the respective control-loop load lines. Microelectrodes constrain or frustrate the otherwise random bifurcation process giving rise to predictable morphologies unattainable on macroscale electrodes.

Еволюція підготовки майбутніх учителів музики в Польщі у контексті розвитку педагогічної освіти

Integration of Ukraine into the European educational space necessitates solution of a number of complex problems, including modification of music-pedagogical education, taking into account historical experience of training music teachers in other countries. Taking into account the fact that educational traditions of Ukraine and Poland are very similar, a constructive study of the evolution of music teacher training in the system of pedagogical education of the Second Commonwealth of Poland seem to be timely. The article is aimed at revealing peculiarities of the evolution of music teachers’ training in Poland in the process of development of pedagogical education. In order to achieve this goal, a number of research methods have been used, in particular: analytical (comparative-terminological, historical-pedagogical (historical-genetic, retrospective), comparative-diachronic), structural-typological and empirical (conversations, discussions and e-mailing). The characteristics of the evolution of music teacher training in Poland as a historical reality is carried out in the form of historical-genetic analysis of a set of facts substantiating the theoretical ideas on such development, logical reconstruction of historical-scientific processes, identification of national specificity and All-European development tendencies, which allows us to predict the ways of modernization of music-pedagogical education in Ukraine. It has been proved that, throughout its historical development, despite constant socio-political influences of other states (Austrian, Prussian and Russian empires, later – USSR), Poland has tried to preserve national traditions of teachers’ training, which was primarily reflected in the developed structure, the variety of types of centres of pedagogical education, the search for its optimal models. It has been found out that under modern conditions, bifurcation processes in the systems of higher pedagogical and secondary school education lead to the weakening of the bonds between them. The impact of secondary school reforms on modification of pedagogical education, which is being brutally macadamized, is being greatly decreasing. At the beginning of the XXI century, an external (supranational) attractor – the Bologna Process – started influencing dramatically the development of the higher education system in Poland, in particular pedagogical which aims at ensuring the conformity of the structure and quality of Polish education with the European standards and European dimension of higher education. The results of the study include, in particular, identification of terminological differences in the works of certain Polish and Ukrainian scholars regarding the training of Music teachers; concretization of the heuristic potential of the laws of dialectics and synergetic approach concerning contradictory development of music training of teaches and pedagogical training of Music teachers in the context of historically conditioned changes within the structure of pedagogical education and cultural-musical needs of society. Keywords: Music teacher training, historical-pedagogical discourse, development of pedagogical education, musical training, school reforms, European dimension of higher education, Poland, Ukraine, national traditions.