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This paper aims to investigate the singular Hopf bifurcation and mixed mode oscillations (MMOs) in the perturbed Bonhoeffer-van der Pol (BVP) circuit. There is a singular periodic orbit constructed by the switching between the stable focus and large amplitude relaxation cycles. Using a generalized fast/slow analysis, the authors show the generation mechanism of two distinct kinds of MMOs.

The parametric modulation can be used to generate complicated dynamics. The BVP circuit is constructed as an example for second-order differential equation with periodic perturbation. Then the authors draw the bifurcation parameter diagram in terms of a containing two attractive regions, i.e. the stable relaxation cycle and the stable focus. The transition mechanism and characteristic features are investigated intensively by one-fast/two-slow analysis combined with bifurcation theory.

Periodic perturbation can suppress nonlinear circuit dynamic to a singular periodic orbit. The combination of these small oscillations with the large amplitude oscillations that occur due to canard cycles yields such MMOs. The results connect the theory of the singular Hopf bifurcation enabling easier calculations of where the oscillations occur.

By treating the perturbation as the second slow variable, the authors obtain that the MMOs are due to the canards in a supercritical case or in a subcritical case. This study can reveal the transition mechanism for multi-time scale characteristics in perturbed circuit. The information gained from such results can be extended to periodically perturbed circuits.

Kathy Charmaz, a developer of constructivist grounded theory (CGT), advocated the use of grounded theory as a tool to attain social justice through research. We developed the grounded text mining approach (GTxA) method by integrating Charmaz's CGT with text mining. This technique is aimed at facilitating the systematic and comprehensive understanding of textual data. GTxA helps researchers engage in abductive reasoning by encouraging them to transition between CGT and text mining analyses. This chapter illustrates an example of how GTxA was utilized when a group of researchers analyzed depositions and semi-structured interview data of a defendant in an actual criminal case in Japan and, thus, detected the possibility of a coerced false confession. The chapter concludes by encouraging researchers to utilize GTxA for attaining social justice.

The flexible manufacturing system now in operation at Fujitsu Fanuc has attracted much attention, particularly in the aspect use of an industrial robot combined with a CNC machine to form an unmanned machining operation.

The aim of this work is to study numerically and analytically flow and heat transfer characteristics and multiplicity of steady states for natural convection in a horizontal rectangular cavity, filled with non‐Newtonian power‐law fluids and heated from all sides.

The governing equations are discretised by using the well known second‐order central finite difference method and integrated by combining the ADI and PSOR techniques. The analytical approach is based on the parallel flow assumption.

Natural and anti‐natural flows existence is proved when the Rayleigh number exceeds a critical value and the side lateral heating intensity values is chosen inside a specific range. The analytical results are found to agree well with those obtained numerically. The fluid flow and the heat transfer are found to be rather sensitive to the non‐Newtonian power‐law behaviour.

The obtained results are limited to non‐Newtonian power‐law fluids and cannot be extended to fluids having other behaviours.

The problem is implied in some industrial thermal processes.

Existence of multiple steady state‐solutions in the range of the side lateral heating intensity values ensuring, that is reduced by the shear‐thickening behaviour and extended by the shear‐thinning one for a given value of Rayleigh number.

Rapid satellite capture by a free-floating space robot is a challenge problem because of no-fixed base and time-delay issues. This paper aims to present a modified target capturing control scheme for improving the control performance.

For handling such control problem including time delay, the modified scheme is achieved by adding a delay calibration algorithm into the visual servoing loop. To identify end-effector motions in real time, a motion predictor is developed by partly linearizing the space robot kinematics equation. By this approach, only ground-fixed robot kinematics are involved in the predicting computation excluding the complex space robot kinematics calculations. With the newly developed predictor, a delay compensator is designed to take error control into account. For determining the compensation parameters, the asymptotic stability condition of the proposed compensation algorithm is also presented.

The proposed method is conducted by a credible three-dimensional ground experimental system, and the experimental results illustrate the effectiveness of the proposed method.

Because the delayed camera signals are compensated with only ground-fixed robot kinematics, this proposed satellite capturing scheme is particularly suitable for commercial on-orbit services with cheaper on-board computers.

This paper is original as an attempt trying to compensate the time delay by taking both space robot motion predictions and compensation error control into consideration and is valuable for rapid and accurate satellite capture tasks.

To study quantitatively the effects of combined temperature dependent thermodynamics and transport fluid properties on the heat transfer rate, heat function fields and profiles in a fluid filled square enclosure.

Navier‐Stokes equations in two‐dimensions, which are the flow governing equations, were transformed into stream function and vorticity transport equations. These equations together with the energy and heat function equations were cast into their non‐dimensional forms. Numerical solutions of the resulting equations were done by the use of finite‐difference method.

The numerical investigations conducted covered the Rayleigh and Prandtl numbers in the range 10³≤Ra≤10⁶ and 0.01≤Pr≤450, respectively, and expansion parameter ε=(T_h−T_c)/T_R in the range 0.05≤ε≤1. Results show that Boussinesq‐approximation is not sufficient to simulate natural convective flow when the difference between T_h and T_c is high and close to the reference state temperature. The effects of the other fluids properties other than density can be disregarded in computation without significant loss of accuracy. Combined fluid properties have very strong effects on the heat transfer, heat function fields and profiles.

The results of this study will serve as baseline information to designers of heat transfer or process equipment in which fluid at very high temperature occurs.

The stability of two‐dimensional natural convection of water near its density maximum (cold water) inside a vertical rectangular enclosure with an aspect ratio of eight is investigated via a series of direct numerical simulations. The simulations aim to clarify, under the influence of density inversion, the physical nature of the instability mechanism responsible for the laminar buoyancy‐driven flow transition from a steady state to an oscillatory state in the enclosure filled with cold water. Two values of the density inversion parameter, _m= 0.4 and 0.5, where the density inversion of cold water may exert strong influence on the flow, are considered in the present study. The results show that the transition from steady state to periodically oscillatory convection arises in the cold‐water‐filled enclosure through a Hopf bifurcation. The oscillatory convection in the water‐filled enclosure for both values of _m is found to feature an oscillatory multicellular structure within the contra‐rotating bicellular flow regions. A traveling wave motion accordingly results along the maximum density contour, which demarcates the contra‐rotating bicellular flows in the enclosure. For both cases the nature of transition into unsteadiness is found to be buoyancy‐driven. The critical Rayleigh number for the bifurcation at _m = 0.4 is found to be markedly higher than that at _m = 0.5.

The outbreak of the COVID-19 pandemic forced many educational institutions to move face-to-face education to entirely online education. This digital transformation has, in turn, reinforced the digital divide between learners who have easy access to digital devices and the Internet and other learners who do not have those. In addition to the digital divide, the differences in their genders and educational levels potentially impact leveling up learning. Therefore, the study in the present chapter has aimed to examine university-level sophomore and junior students’ differences in learning online during the COVID-19 pandemic in terms of gender, educational level, and the digital divide. Data from a survey indicate that both females and males, and sophomores and juniors had different attitudes toward using digital devices, attending virtual classes and accessing online courses through the mobile phone or the home Internet. Based on the findings on their differences, the chapter makes some implications and recommendations for policymakers, course designers and teachers in the course design, especially in the emergence.

A numerical study of the flow in and heat transfer across a vertical cavity containing pure water when the aspect ratio of the cavity is low, i.e. 1 or less, has been undertaken. One vertical wall of the cavity is kept at a temperature that is below the freezing point of water while the opposite wall is kept at a temperature that is above this freezing temperature. Ice therefore forms in part of the cavity, the conditions being such that there can be significant natural convection in the water. The upper surface of the cavity is open i.e. the water has a free surface, heat transfer from this surface being assumed negligible. The lower surface of the cavity is assumed to be adiabatic. Only the steady state has been considered here. It has been assumed that the flow is laminar and two‐dimensional and that liquid and solid properties are constant except for the water density change with temperature which gives rise to the buoyancy forces. The governing equations have been written in dimensionless form and these equations have been solved using a finite element‐based procedure in which the position of the solid‐liquid interface is obtained using an iterative approach. Solutions have been obtained for modified Rayleigh numbers of between 10³ and 10⁸ for various degrees of under‐cooling and for cavity aspect ratios of between 0.25 and 1. The density inversion that occurs with water has been shown to have a large effect on the steady state freezing of water in a cavity. The aspect ratio of the cavity has also been shown to have a significant influence on the results when the aspect ratio is less than 0.5.

The problems of transient natural convection from a corrugated plate embedded in an enclosed porous medium is studied numerically. The non‐Darcian effects as well as the acceleration terms are taken into consideration in the momentum equation. The governing equations in terms of vorticity, stream function and temperature are expressed in a body‐fitted coordinates system, which were solved numerically by the finite difference method. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers, with Darcy‐Rayleigh number ranging from 0 to 1000, and Darcy number from 10^–4 to 10^–1, for several aspect ratios of the cavity and plate positions. The flow and heat transfer characteristics for a corrugated plate and a flat plate and the numerical results solved with four different mathematical models are also compared.