Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition

We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter region where the uniform solution is stable against a localized perturbation. We also found an oscillatory solution in the linearly unstable region and its period is not commensurate with the periodicity of the car index space. The oscillatory solution has some features in common with the synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp

Secular theory of the orbital evolution of the young stellar disc in the Galactic Centre

We investigate the orbital evolution of a system of N mutually interacting stars on initially circular orbits around the dominating central mass. We include perturbative influence of a distant axisymmetric source and an extended spherical potential. In particular, we focus on the case when the secular evolution of orbital eccentricities is suppressed by the spherical perturbation. By means of standard perturbation methods, we derive semi-analytic formulae for the evolution of normal vectors of the individual orbits. We find its two qualitatively different modes. Either the orbits interact strongly and, under such circumstances, they become dynamically coupled, precessing synchronously in the potential of the axisymmetric perturbation. Or, if their mutual interaction is weaker, the orbits precess independently, interchanging periodically their angular momentum, which leads to oscillations of inclinations. We argue that these processes may have been fundamental for the evolution of the disc of young stars orbiting the supermassive black hole in the centre of the Milky Way.Comment: Accepted for publication in MNRAS; 11 pages, 6 figure

Instability of dilute granular flow on rough slope

We study numerically the stability of granular flow on a rough slope in collisional flow regime in the two-dimension. We examine the density dependence of the flowing behavior in low density region, and demonstrate that the particle collisions stabilize the flow above a certain density in the parameter region where a single particle shows an accelerated behavior. Within this parameter regime, however, the uniform flow is only metastable and is shown to be unstable against clustering when the particle density is not high enough.Comment: 4 pages, 6 figures, submitted to J. Phys. Soc. Jpn.; Fig. 2 replaced; references added; comments added; misprints correcte

Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile

We investigate the formation processes of a sandpile using numerical simulation. We find a new relation between the fluctuation of the motion of the top and the surface state of a sandpile. The top moves frequently as particles are fed one by one every time interval T. The time series of the top location has the power spectrum which obeys a power law, S(f)~f^{\alpha}, and its exponent \alpha depends on T and the system size w. The surface state is characterized by two time scales; the lifetime of an avalanche, T_{a}, and the time required to cause an avalanche, T_{s}. The surface state is fluid-like when T_{a}~T_{s}, and it is solid-like when T_{a}<<T_{s}. Our numerical results show that \alpha is a function of T_{s}/T_{a}.Comment: 15 pages, 13 figure

First operation and performance of a 200 lt double phase LAr LEM-TPC with a 40x76 cm^2 readout

In this paper we describe the design, construction, and operation of a first large area double-phase liquid argon Large Electron Multiplier Time Projection Chamber (LAr LEM-TPC). The detector has a maximum drift length of 60 cm and the readout consists of a $40\times 76$ cm$^2$ LEM and 2D projective anode to multiply and collect drifting charges. Scintillation light is detected by means of cryogenic PMTs positioned below the cathode. To record both charge and light signals, we have developed a compact acquisition system, which is scalable up to ton-scale detectors with thousands of charge readout channels. The acquisition system, as well as the design and the performance of custom-made charge sensitive preamplifiers, are described. The complete experimental setup has been operated for a first time during a period of four weeks at CERN in the cryostat of the ArDM experiment, which was equipped with liquid and gas argon purification systems. The detector, exposed to cosmic rays, recorded events with a single-channel signal-to-noise ratio in excess of 30 for minimum ionising particles. Cosmic muon tracks and their $\delta$-rays were used to assess the performance of the detector, and to estimate the liquid argon purity and the gain at different amplification fields.Comment: 23 pages, 21 figure

Nuclear currents based on the integral form of the continuity equation

We present an approach to obtain new forms of the nuclear electromagnetic current, which is based on an integral form of the continuity equation. The procedure can be used to restore current conservation in model calculations in which the continuity equation is not verified. Besides, it provides, as a particular result, the so-called Siegert's form of the nuclear current, first obtained by Friar and Fallieros by extending Siegert's theorem to arbitrary values of the momentum transfer. The new currents are explicitly conserved and permit a straightforward analysis of their behavior at both low and high momentum transfers. The results are illustrated with a simple nuclear model which includes a harmonic oscillator mean potential.Comment: 19 pages, revtex, plus 2 PS figure

First operation and drift field performance of a large area double phase LAr Electron Multiplier Time Projection Chamber with an immersed Greinacher high-voltage multiplier

We have operated a liquid-argon large-electron-multiplier time-projection chamber (LAr LEM-TPC) with a large active area of 76 $\times$ 40 cm$^2$ and a drift length of 60 cm. This setup represents the largest chamber ever achieved with this novel detector concept. The chamber is equipped with an immersed built-in cryogenic Greinacher multi-stage high-voltage (HV) multiplier, which, when subjected to an external AC HV of $\sim$1 kV$_{\mathrm{pp}}$, statically charges up to a voltage a factor of $\sim$30 higher inside the LAr vessel, creating a uniform drift field of $\sim$0.5 kV/cm over the full drift length. This large LAr LEM-TPC was brought into successful operation in the double-phase (liquid-vapor) operation mode and tested during a period of $\sim$1 month, recording impressive three-dimensional images of very high-quality from cosmic particles traversing or interacting in the sensitive volume. The double phase readout and HV systems achieved stable operation in cryogenic conditions demonstrating their good characteristics, which particularly suit applications for next-generation giant-scale LAr-TPCs.Comment: 26 pages, 19 figure