Collective motion occurs inevitably in a class of populations of globally coupled chaotic elements

We discovered numerically a scaling law obeyed by the amplitude of collective mo tion in large populations of chaotic elements. Our analysis strongly suggests that such populations generically exhibit collective motion in the presence of interaction, however weak it may be. A phase diagram for the collective motion, which is characterized by peculiar structures similar to Arnold tongues, is obtained.Comment: 6 pages, 9 Postscript figures, uses revtex.st

Analytical Approach for the Determination of the Luminosity Distance in a Flat Universe with Dark Energy

Recent cosmological observations indicate that the present universe is flat and dark energy dominated. In such a universe, the calculation of the luminosity distance, d_L, involve repeated numerical calculations. In this paper, it is shown that a quite efficient approximate analytical expression, having very small uncertainties, can be obtained for d_L. The analytical calculation is shown to be exceedingly efficient, as compared to the traditional numerical methods and is potentially useful for Monte-Carlo simulations involving luminosity distances.Comment: 3 pages, 4 figures, Accepted for publication in MNRA

Thermodynamic Irreversibility from high-dimensional Hamiltonian Chaos

This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to characterize the thermodynamic irreversibility. It is proved that this new quantity satisfies an inequality associated with the second law of thermodynamics. Based on the assumption that these systems possess the mixing property and certain large deviation properties in the thermodynamic limit, it is argued reasonably that the most probable value of the irreversible information loss is equal to the change of the Boltzmann entropy in statistical mechanics, and that it is always a non-negative value. The consistency of our argument is confirmed by numerical experiments with the aid of the definition of a quantity we refer to as the excess information loss.Comment: LaTeX 43 pages (using ptptex macros) with 11 figure

Kink Solution in a Fluid Model of Traffic Flows

Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.Comment: RevTeX v3.1, 6 pages, and 2 figure

A heat pump at a molecular scale controlled by a mechanical force

We show that a mesoscopic system such as Feynman's ratchet may operate as a heat pump, and clarify a underlying physical picture. We consider a system of a particle moving along an asymmetric periodic structure . When put into a contact with two distinct heat baths of equal temperature, the system transfers heat between two baths as the particle is dragged. We examine Onsager relation for the heat flow and the particle flow, and show that the reciprocity coefficient is a product of the characteristic heat and the diffusion constant of the particle. The characteristic heat is the heat transfer between the baths associated with a barrier-overcoming process. Because of the correlation between the heat flow and the particle flow, the system can work as a heat pump when the particle is dragged. This pump is particularly effective at molecular scales where the energy barrier is of the order of the thermal energy.Comment: 7 pages, 5 figures; revise

Continued fractions and Newton\u27s approximations

We generalise the relationship between continued fractions and Newton\u27s approximations

On the number of solutions of the Diophantine equation of Frobenius - General case

We determine the number of solutions of the equation $a_1 x_1+a_2 x_2+cdots+a_m x_m=b$ in non-negative integers $x_1$, $x_2$, $dots$, $x_n$. If $m=2$, then the largest $b$ for which no solution exists is $a_1 a_2-a_1-a_2$, and an explicit formula for the number of solutions is known. In this paper we give the method for computing the desired number. The method is illustrated with several examples