Microscopic heat from the energetics of stochastic phenomena

The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can be removed by adding to these quantities the reversible heat associated with the mesoscopic free energy.Comment: 4 pages, 0 figur

Simulation, modelling and development of the metris RCA

In partnership with Metris UK we discuss the utilisation of modelling and simulation methods in the development of a revolutionary 7-axis Robot CMM Arm (RCA). An offline virtual model is described, facilitating pre-emptive collision avoidance and assessment of optimal placement of the RCA relative to scan specimens. Workspace accessibility of the RCA is examined under a range of geometrical assumptions and we discuss the effects of arbitrary offsets resulting from manufacturing tolerances. Degeneracy is identified in the number of ways a given pose may be attained and it is demonstrated how a simplified model may be exploited to solve the inverse kinematics problem of finding the “correct” set of joint angles. We demonstrate how the seventh axis may be utilised to avoid obstacles or otherwise awkward poses, giving the unit greater dexterity than traditional CMMs. The results of finite element analysis and static force modelling on the RCA are presented which provide an estimate of the forces exerted on the internal measurement arm in a range of poses

The distribution of H13CN in the circumstellar envelope around IRC+10216

H13CN J=8-7 sub-millimetre line emission produced in the circumstellar envelope around the extreme carbon star IRC+10216 has been imaged at sub-arcsecond angular resolution using the SMA. Supplemented by a detailed excitation analysis the average fractional abundance of H13CN in the inner wind (< 5E15 cm) is estimated to be about 4E-7, translating into a total HCN fractional abundance of 2E-5 using the isotopic ratio 12C/13C=50. Multi-transitional single-dish observations further requires the H13CN fractional abundance to remain more or less constant in the envelope out to a radius of about 4E16 cm, where the HCN molecules are effectively destroyed, most probably, by photodissociation. The large amount of HCN present in the inner wind provides effective line cooling that can dominate over that generated from CO line emission. It is also shown that great care needs to be taken in the radiative transfer modelling where non-local, and non-LTE, effects are important and where the radiation field from thermal dust grains plays a major role in exciting the HCN molecules. The amount of HCN present in the circumstellar envelope around IRC+10216 is consistent with predicted photospheric values based on equilibrium chemical models and indicates that any non-equilibrium chemistry occurring in the extended pulsating atmosphere has no drastic net effect on the fractional abundance of HCN molecules that enters the outer envelope. It further suggests that few HCN molecules are incorporated into dust grains.Comment: Accepted for publication in ApJ. 20 pages, 7 figure

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Gravitational Radiation from Cylindrical Naked Singularity

We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singularity. We find a boundary condition that all the metric and matter variables are everywhere finite at least up to the first order approximation. This implies that the spacetime singularity formed by this high-speed dust collapse is very similar to that formed by the null dust and thus the gravitational emission from a naked singularity formed by the cylindrical dust collapse can be gentle.Comment: 20 pages, 1 figur

Supersymmetric Wilson Loops in IIB Matrix Model

We show that the supersymmetric Wilson loops in IIB matrix model give a transition operator from reduced supersymmetric Yang-Mills theory to supersymmetric space-time theory. In comparison with Green-Schwarz superstring we identify the supersymmetric Wilson loops with the asymptotic states of IIB superstring. It is pointed out that the supersymmetry transformation law of the Wilson loops is the inverse of that for the vertex operators of massless modes in the U(N) open superstring with Dirichlet boundary condition.Comment: 10 pages, Latex, minor typos correcte

Large stellar disks in small elliptical galaxies

We present the rotation velocities V and velocity dispersions sigma along the principal axes of seven elliptical galaxies less luminous than M_B= -19.5. These kinematics extend beyond the half-light radii for all systems in this photometrically selected sample. At large radii the kinematics not only confirm that rotation and "diskiness" are important in faint ellipticals, as was previously known, but also demonstrate that in most sample galaxies the stars at large galactocentric distances have (V/sigma)_max of about 2, similar to the disks in bona-fide S0 galaxies. Comparing this high degree of ordered stellar motion in all sample galaxies with numerical simulations of dissipationless mergers argues against mergers with mass ratios <=3:1 as an important mechanism in the final shaping of low-luminosity ellipticals, and favors instead the dissipative formation of a disk.Comment: 11 pages LaTex with 4 Postscript figure