7,925 research outputs found

### 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

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