IEEE Log Number 8610179. 'We include only three segments of the five-segment piecewise-linear u-i curve because the two outermost segments do not play any role in the formation of the double scroll.

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Single-crystal Fe16N2 films have been grown epitaxially on Fe(001)/InGaAs(001) and InGaAs(001) substrates by molecular beam epitaxy (MBE). Saturation flux density Bs of Fe16N2 films has been demonstrated to be 2.8–3.0 T at room temperature, which is very close to the value obtained by Kim and Takahashi using polycrystalline evaporated Fe–N films. Temperature dependence of Bs has been measured. Bs changed with temperature reversibly up to 400 °C, while beyond 400 °C, Bs decreased irreversibly. X-ray diffraction showed that Fe16N2 crystal is stable up to 400 °C, while beyond 400 °C, Fe16N2 dissolves into Fe and Fe4N, and also some chemical reactions between Fe16N2 and the substrate occurs. This caused the temperature dependence of Bs mentioned above. From the temperature dependence of Bs up to 400 °C, the Curie temperature of Fe16N2 is estimated to be around 540 °C by using the Langevin function. The above mentioned Bs of 2.9 T at room temperature and 3.2 T at −268 °C corresponded to an average magnetic moment of 3.2μB per Fe atom and 3.5μB, respectively. These values of the magnetic moment of Fe atoms are literally giant, far beyond the Slater–Pauling curves. The origin of the giant magnetic moment has been discussed based on the calculation carried out by Sakuma. However, there was a significant disagreement between experimental values and calculated ones, so the origin remained to be clarified. Also, magneto-crystalline anisotropy of Fe16N2 films has been investigated.

Single-phase, single-crystal Fe16N2(001) films and Fe-11 at. %N martensite films of 200–900 Å thickness have been epitaxially grown on In0.2Ga0.8As(001) substrates by evaporating Fe in an atmosphere of mixed gas of N2 and NH3, followed by annealing. The saturation magnetizations 4πMs’s for Fe16N2 and Fe-N martensite films have been measured to be around 29 and 24 kG at room temperature, respectively, and almost constant in the above thickness range by using a vibrating sample magnetometer. 4πMs for Fe-N martensite films has been increased with ordering of N atoms caused by annealing and finally reached around 29 kG for Fe16N2. Mössbauer spectra have been measured for those films. The spectrum for Fe-N martensite films was a superposed one with hyperfine fields of 360, 310, and 250 kOe, similar to those previously reported for martensite. While the spectrum became simpler with ordering, finally reaching a single hyperfine field of 330 kOe for Fe16N2. 4πMs of 29 kG for Fe16N2 (3.2 μB/Fe atom) and 4πMs of 24 kG for martensite (2.6 μB/Fe atom) has not been explained based on the conventional band theory of 3d metal magnetism. Behaviors of Mössbauer spectra could not be understood based on the conventional concept either. Thus a new physical concept is likely to be needed for clarification of giant magnetic moments and Mössbauer spectra for Fe16N2 and Fe-N martensites.

Fe-N films with thicknesses of 70–1000 Å were deposited by MBE onto Fe films which were epitaxially grown onto GaAs(100) substrates. Without the Fe layer, epitaxially grown Fe-N films could not be obtained due to a reaction between Fe-N and GaAs. TEM observations and x-ray diffraction patterns showed that the epitaxially grown Fe-N films consist of Fe16N2 and Fe, and that crystal orientation is Fe16N2 (001)//Fe(110). It was found that the saturation magnetic flux density (Bs) increases as the thickness of the Fe-N films decreases. This is because the volume ratio of Fe16N2 in the Fe-N films increases with decreasing Fe-N film thickness. The maximum value for Bs is 2.66 T, and the volume ratio is 85%. These results indicate that Fe16N2 has a high saturation magnetic flux density of 2.8–3.0 T.

Nonlinear finite element (FE) analyses are performed to simulate the behavior of top-and seat-angle connections. Contact model with small sliding option is applied between contact pair surfaces of all connecting elements. Bolt pretension force is introduced in the initial steps of analysis. Numerical analysis results together with the prediction by Kishi-Chen power model are compared with experimental ones to examine the applicability of proposed analysis method and power model. The study is farther extended by analyzing the models varying connection parameters, material properties of connection assemblages, and magnitude of bolt pretension. The following results are obtained: 1) bolt sustains additional tensile force due to prying action; 2) prying force develops more quickly due to increment of bolt diameter, gage distance from angle heel to the centerline of bolt hole, and reduction of angle thickness; and 3) bolt pretension increases the initial connection stiffness.

The average magnetic moment per Fe atom for a single-phase, single-crystal Fe16N2(001) film epitaxially grown on a GaAs(001) substrate by molecular beam epitaxy has been confirmed to be 3.5μB at room temperature by using a vibrating sample magnetometer (VSM) and Rutherford backscattering. The value was in good agreement with that obtained by using a VSM and by measuring the film thickness (3.3μB per Fe atom). The saturation magnetization 4πMs has been found to increase with decreasing temperature, obeying T3/2 law at lower temperatures. The slope was steeper than that of a pure Fe film, suggesting a lower exchange constant for Fe16N2. The g factor for Fe16N2 has been accurately measured to be 2.17 by using ferromagnetic resonance with changing frequencies of 35.5–115 GHz, which is not unusual compared with the g factor of 2.16 for pure Fe. The resistivity for Fe16N2 has been measured to be around 30 μΩ cm at room temperature compared with 10 μΩ cm for pure Fe and decreases linearly with decreasing temperature. The behavior was that for normal metal and nothing unusual was seen. The anomalous Hall resistivity for Fe16N2 was 4×10−7 V cm/A, which is about three times as large as that for pure Fe. The relationship between the giant magnetic moment and the anomalous Hall resistivity has not been clarified yet.

An in-depth analysis is made of the global 2-parameter bifurcation structures of the double scroll circuit in terms of their homoclinic, heteroclinic, and periodic orbits. Many fine details are uncovered via a 3-dimensional "unfolding" of the 2-parameter bifurcation structures. Major findings are: (i) The parameter sets which give rise to the homoclinic and heteroclinic orbits (homoclinic and heteroclinic bifurcation sets) studied in this paper are found to be all connected to each other via only one family of periodic orbits. (ii) Moreover, the structure of the windows of this family essentially determines the global structure of the periodic windows of the double scroll circuit. These bifurcation analyses are accomplished by deriving first the relevant bifurcation equations in exact analytic form and then solving these nonlinear equations by iterations. No numerical integration formula for differential equations are used.