Noise Limited Computational Speed

In modern transistor based logic gates, the impact of noise on computation has become increasingly relevant since the voltage scaling strategy, aimed at decreasing the dissipated power, has increased the probability of error due to the reduced switching threshold voltages. In this paper we discuss the role of noise in a two state model that mimic the dynamics of standard logic gates and show that the presence of the noise sets a fundamental limit to the computing speed. An optimal idle time interval that minimizes the error probability, is derived

The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: II. Saturation Level and Critical Magnetic Reynolds Number

The nonlinear evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks, including the effect of the Hall term and ohmic dissipation, is investigated using local three-dimensional MHD simulations and various initial magnetic field geometries. When the magnetic Reynolds number, Re_M \equiv v_A^2 / \eta \Omega (where v_A is the Alfven speed, \eta the magnetic diffusivity, and \Omega the angular frequency), is initially larger than a critical value Re_{M, crit}, the MRI evolves into MHD turbulence in which angular momentum is transported efficiently by the Maxwell stress. If Re_M < Re_{M, crit}, however, ohmic dissipation suppresses the MRI, and the stress is reduced by several orders of magnitude. The critical value is in the range of 1 - 30 depending on the initial field configuration. The Hall effect does not modify the critical magnetic Reynolds number by much, but enhances the saturation level of the Maxwell stress by a factor of a few. We show that the saturation level of the MRI is characterized by v_{Az}^2 / \eta \Omega, where v_{Az} is the Alfven speed in the nonlinear regime along the vertical component of the field. The condition for turbulence and significant transport is given by v_{Az}^2 / \eta \Omega \gtrsim 1, and this critical value is independent of the strength and geometry of the magnetic field or the size of the Hall term. If the magnetic field strength in an accretion disk can be estimated observationally, and the magnetic Reynolds number v_A^2 / \eta \Omega is larger than about 30, this would imply the MRI is operating in the disk.Comment: 43 pages, 8 tables, 20 figures, accepted for publication in ApJ, postscript version also available from http://www.astro.umd.edu/~sano/publications

Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional UU-VV Model at Quarter filling

The one-dimensional extended Hubbard model with both the on-site $U$ and the nearest neighbor $V$ interactions at quarter filling is studied by using a novel finite size scaling. We diagonalize finite size systems numerically and calculate the Luttinger-liquid parameter $K_{\rho}$ which is substituted into the renormalization group equation as an initial condition. It leads $K_\rho$ in the infinite size system and the result agrees very well with the available exact result with $U=\infty$. This approach also yields the charge gap in the insulating state near the metal-insulator transition where the characteristic energy becomes exponentially small and the usual finite size scaling is not applicable.Comment: 7 pages, 8 figures,submitted to PR

Dynamics of a deformable self-propelled domain

We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the center of gravity and two tensor variables characterizing deformations. The other is an active cell model which has an internal mechanism of motility and is represented by the partial differential equation for deformations. Numerical simulations show a rich variety of dynamics, some of which are common to the two model systems. The origin of the similarity and the difference is discussed.Comment: 6 pages, 6 figure

Ferromagnetism and Superconductivity in the multi-orbital Hubbard Model: Hund's Rule Coupling versus Crystal-Field Splitting

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $\Delta$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $\Delta$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter $K_{\rho}>1$ is observed for the singlet ground state in this region.Comment: 4 pages,5 figures,submitted to J.Phys.Soc.Jp