Dynamical behavior of a dissipative particle in a periodic potential subject to chaotic noise: Retrieval of chaotic determinism with broken parity

Dynamical behaviors of a dissipative particle in a periodic potential subject to chaotic noise are reported. We discovered a macroscopic symmetry breaking effect of chaotic noise on a dissipative particle in a multi-stable systems emerging, even when the noise has a uniform invariant density with parity symmetry and white Fourier spectrum. The broken parity symmetry of the multi-stable potential is not necessary for the dynamics with broken symmetry. We explain the mechanism of the symmetry breaking and estimate the average velocity of a particle under chaotic noise in terms of unstable fixed points.Comment: 4 pages, 7 Postscript figures (Revtex, tar+compress+uuencode); to appear in Phys.Rev.Let

流体における時空カオス

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Mathematics and Mathematics Education

With the 17-th century an essentially new period in the development of mathematics began. The circle of quantitative relations and spatial forms of mathematics studied now was no longer exhausted by numbers, quantities and geometric figures. On this basis there resulted the explicit introduction into mathematics of the ideas of motions and change. Being inseparably connected with the needs of natural science, the accumulation of quantitaive relations and spacial forms studied in mathematics was continuously expanding. However, in addition to this quantitative grouth, at the end of the 18-th and the beginning of the 19-th centuries a number of essentially new features were observed in the development of mathematics. The enormous amount of factual material which had been accumulated in the 17-th and 18-th centuries led to the demand for a deep logical analysis and unification of it from a new point of view. In essence, the relationship between mathematics and natural science was no loss close but was now increased in complexity. The majority of new theories arose from internal requirements of mathematics itself. However, the circle of applications to problems of science and technology was greately expanding at this time. In this way, as a result of both the internal requirements of mathematics and the new needs of science and technology, the circle of quantitative relations and spatial forms studied in mathematics was greately expanded: relations between elements of arbitrary groups, operations in function spaces, etc. are now parts of mathematics. In this paper, we are concerned with mathematical thought. Several ideas of great scientists are introduced, and we know the essence of mathematical thought. The power of mathematical thought can be brought up by means of a deep thought. The relationship between mathematical thought and creativity is also studied

Diffusion of Slufur in Liquid Iron. I : Diffusion in Pure Iron

The diffusion coefficient of sulfur in liquid iron has been measured at the temperature range from 1, 560°to 1, 670℃. Since the concentration of sulfur was low in the present investigation, the diffusion coefficient was calculated by assuming as constants independent of the concentration. The result was expressed as follows : D=4.9×10^exp(-4350/T). The diffusion coefficient and the activation energy are nearly the same as those of carbon, cobalt and phosphorus in liquid iron. The activation energy is about one-tenth of the heat of vaporization and this shows that the holes in liquid iron are small. The theoretical values derived from the absolute reaction rate theory and the diffusion coefficient calculated by the Stokes-Einstein equation are compared with the experimental results