Stability Investigation of the Non-linear Periodic Oscillations

The stability of the non-linear periodic oscillations is discussed by solving a variational equation which characterizes. small variations from the periodic states of equilibrium. This variational equation leads to a linear equation in which the coefficient is periodic in the time. If all solutions of this equation are bounded, then the oscillation is said to be stable, otherwise unstable. In order to establish the stability criterion, the characteristic exponents for the unbounded solutions are calculated by Whittaker's method. Then, the generalized stability condition is derived by comparing the said characteristic exponents with the damping of the system considered. Since the solutions of the variational equation have the form: e[μT] [sin(nζ-a)+···], our stability condition is secured not only for the unbounded solutions having the fundamental frequency (n=l), but also for the unbounded solutions with higher harmonic frequencies (n=2, 3, 4, •·····). Hence the generalized stability condition obtained in this way is particularly effective in studying the oscillations in which the higher harmonics are excited. Finally our investigation is compared with one of the stability conditions derived by Mandelstam and Papalexi for the subharmonic oscillations. In the appendix, the characteristic exponents are calculated at some length for the unbounded solutions of a variational equation in which the periodic coefficient involves sine series as well as cosine series

Forced Oscillations with Nonlinear Restoring Force

Forced oscillations with nonlinear restoring force are studied in transient states as well as in steady states. The differential equations which govern the oscillations are under some. restrictions transformed to the form : dy/dx = Y(x, y)/X(x, y), and the integral curves of this equation are studied according to Poincare and Bendixson with the basic idea that the singularities of the above equation are correlated with the periodic steady states of oscillation and the integral curves with transient states. With this method of investigation we have first studied the harmonic oscillations in Part I, then the subharmonic oscillations in Part II. In both cases the theoretical analyses are compared with experimental results, and the satisfactory agreement is found between them

Subharmonic Oscillations in Non-linear Systems

This paper deals with the subharmonic oscillations which occur in systems with non-linear restoring force. It is first investigated that the order of the subharmonics has the close connection to the form of the non-linear characteristics. Then the subharmonic oscillation of order 1/3, i.e., the oscillation whose fundamental frequency is one-third that of the applied force, is particularly investigated for the cases in which the non-linear characteristics are expressed by (1) cubic and (2) quintic functions. In both cases the stability problem of the periodic solutions is discussed in detail following the stability criterion given previously by the present author. The analysis has revealed that in the latter case (2) the second higher-harmonc of the subharmonic, i.e., the oscillation of order 2/3 causes the collapse of the original subharmonic oscillation under certain circumstances

Self-Excited Oscillations in a System with Two Degrees of Freedom

The behavior of a negative-resistance oscillator with two resonant circuits is studied. The amplitude and frequency characteristics of the self-excited oscillation are calculated and shown graphically for some combinations of the system parameters. The stability of the oscillation is discussed. Particular attention is directed toward the internal resonance of the two resonant circuits which occurs when a certain relationship exists between their natural frequencies

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Cosmic Star Formation Activity at z=2.2 Probed by H-alpha Emission Line Galaxies

We present a pilot narrow-band survey of H-alpha emitters at z=2.2 in the Great Observatories Origins Deep Survey North (GOODS-N) field with MOIRCS instrument on the Subaru telescope. The survey reached a 3 sigma limiting magnitude of 23.6 (NB209) which corresponds to a 3 sigma limiting line flux of 2.5 x 10^-17 erg s^-1 cm^-2 over a 56 arcmnin^2 contiguous area (excluding a shallower area). From this survey, we have identified 11 H-alpha emitters and one AGN at z=2.2 on the basis of narrow-band excesses and photometric redshifts. We obtained spectra for seven new objects among them, including one AGN, and an emission line above 3 sigma is detected from all of them. We have estimated star formation rates (SFR) and stellar masses (M_star) for individual galaxies. The average SFR and M_star is 27.8M_solar yr^-1 and 4.0 x 10^10M_solar, respectivly. Their specific star formation rates are inversely correlated with their stellar masses. Fitting to a Schechter function yields the H-alpha luminosity function with log L = 42.82, log phi = -2.78 and alpha = -1.37. The average star formation rate density in the survey volume is estimated to be 0.31M_solar yr^-1Mpc^-3 according to the Kennicutt relation between H-alpha luminosity and star formation rate. We compare our H-alpha emitters at z=2.2 in GOODS-N with narrow-band line emitters in other field and clusters to see their time evolution and environmental dependence. We find that the star formation activity is reduced rapidly from z=2.5 to z=0.8 in the cluster environment, while it is only moderately changed in the field environment. This result suggests that the timescale of galaxy formation is different among different environments, and the star forming activities in high density regions eventually overtake those in lower density regions as a consequence of "galaxy formation bias" at high redshifts.Comment: Accepted for publication in PASJ Subaru Special Issue, 11 pages, 10 figure

High-pressure synthesis of new filled skutterudite compounds SrT4As12 (T = Fe, Ru, Os)

We have succeeded in synthesizing samples of new filled skutterudite compounds SrT 4As12 (T = Fe, Ru, and Os) using a high-pressure synthesis technique. These compounds have lattice constants of 8.351, 8.521, and 8.561 Å, respectively. The physical properties of the compounds are reported for the first time. The temperature dependences of the electrical resistivity for SrT 4As12 (T = Fe, Ru, and Os) exhibit metallic behaviors. The electrical resistivity and magnetic measurements indicates that SrOs4As12 is a new superconductor with a transition temperature of 4.8 K. A broad maximum of magnetic susceptibility at around 50 K and a large electronic specific heat coefficient of 58 mJ mol−1 K−2 suggest that SrFe4As12 is a nearly ferromagnetic metal with spin fluctuations of Fe 3d electrons

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