The calculation of the distance to a nearby defective matrix

In this paper a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linear Algebra Appl., 396 (2005), pp.~273--301) and reduces to finding when a parameter-dependent matrix is singular subject to a constraint. The solution is achieved by an extension of the Implicit Determinant Method introduced by Spence & Poulton (J. Comput. Phys., 204 (2005), pp.~65--81). Numerical results for several examples illustrate the performance of the algorithm.Comment: 12 page

Introduction to Library Trends 23 (3) Winter 1975: Music and Fine Arts in the General Library

published or submitted for publicatio

Role of Single Defects in Electronic Transport through Carbon Nanotube Field-Effect Transistors

The influence of defects on electron transport in single-wall carbon nanotube field effect transistors (CNFETs) is probed by combined scanning gate microscopy (SGM) and scanning impedance microscopy (SIM). SGM reveals a localized field effect at discrete defects along the CNFET length. The depletion surface potential of individual defects is quantified from the SGM-imaged radius of the defect as a function of tip bias voltage. This provides a measure of the Fermi level at the defect with zero tip voltage, which is as small as 20 meV for the strongest defects. The effect of defects on transport is probed by SIM as a function of backgate and tip-gate voltage. When the backgate voltage is set so the CNFET is "on" (conducting), SIM reveals a uniform potential drop along its length, consistent with diffusive transport. In contrast, when the CNFET is "off", potential steps develop at the position of depleted defects. Finally, high-resolution imaging of a second set of weak defects is achieved in a new "tip-gated" SIM mode.Comment: to appear in Physical Review Letter

Runaway collisions in young star clusters. II. Numerical results

We present a new study of the collisional runaway scenario to form an intermediate-mass black hole (IMBH, MBH > 100 Msun) at the centre of a young, compact stellar cluster. The first phase is the formation of a very dense central core of massive stars (Mstar =~ 30-120 Msun) through mass segregation and gravothermal collapse. Previous work established the conditions for this to happen before the massive stars evolve off the main sequence (MS). In this and a companion paper, we investigate the next stage by implementing direct collisions between stars. Using a Monte Carlo stellar dynamics code, we follow the core collapse and subsequent collisional phase in more than 100 models with varying cluster mass, size, and initial concentration. Collisions are treated either as ideal, ``sticky-sphere'' mergers or using realistic prescriptions derived from 3-D hydrodynamics computations. In all cases for which the core collapse happens in less than the MS lifetime of massive stars (~3 Myr), we obtain the growth of a single very massive star (VMS, Mstar =~ 400-4000 Msun) through a runaway sequence of mergers. Mass loss from collisions, even for velocity dispersions as high as sigma1D ~ 1000 km/s, does not prevent the runaway. The region of cluster parameter space leading to runaway is even more extended than predicted in previous work because, in clusters with sigma1D > 300 km/s, collisions accelerate (and, in extreme cases, drive) core collapse. Although the VMS grows rapidly to > 1000 Msun in models exhibiting runaway, we cannot predict accurately its final mass. This is because the termination of the runaway process must eventually be determined by a complex interplay between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS. [abridged]Comment: 23 pages, 24 figures. For publication in MNRAS. Paper revised to follow requests and suggestions of referee. Companion paper to Freitag, Rasio & Baumgardt 200

The influence of initial mass segregation on the runaway merging of stars

We have investigated the effect of initial mass segregation on the runaway merging of stars. The evolution of multi-mass, dense star clusters was followed by means of direct N-body simulations of up to 131.072 stars. All clusters started from King models with dimensionless central potentials of 3.0 <= W_0 <= 9.0. Initial mass segregation was realized by varying the minimum mass of a certain fraction of stars whose either (1) distances were closest to the cluster center or (2) total energies were lowest. The second case is more favorable to promote the runaway merging of stars by creating a high-mass core of massive, low-energy stars. Initial mass segregation could decrease the central relaxation time and thus help the formation of a high-mass core. However, we found that initial mass segregation does not help the runaway stellar merger to happen if the overall mass density profile is kept constant. This is due to the fact that the collision rate of stars is not increased due to initial mass segregation. Our simulations show that initial mass segregation is not sufficient to allow runaway merging of stars to occur in clusters with central densities typical for star clusters in the Milky Way.Comment: 25 pages, 9 figures, 3 tables, accepted for publication in Ap

Tip-gating Effect in Scanning Impedance Microscopy of Nanoelectronic Devices

Electronic transport in semiconducting single-wall carbon nanotubes is studied by combined scanning gate microscopy and scanning impedance microscopy (SIM). Depending on the probe potential, SIM can be performed in both invasive and non-invasive mode. High-resolution imaging of the defects is achieved when the probe acts as a local gate and simultaneously an electrostatic probe of local potential. A class of weak defects becomes observable even if they are located in the vicinity of strong defects. The imaging mechanism of tip-gating scanning impedance microscopy is discussed.Comment: 11 pages, 3 figures, to be published in Appl. Phys. Let