Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses

We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the: Rabi frequency Omega (c) of the cavity field to that of the Rabi frequency Omega of the driving field. For Omega (c)

Galaxy threshing and the origin of ultra-compact dwarf galaxies in the Fornax cluster

A recent all-object spectroscopic survey centred on the Fornax cluster of galaxies has discovered a population of subluminous and extremely compact members, called 'ultra-compact dwarf' (UCD) galaxies. In order to clarify the origin of these objects, we have used self-consistent numerical simulations to study the dynamical evolution a nucleated dwarf galaxy would undergo if orbiting the centre of the Fornax cluster and suffering from its strong tidal gravitational field. We find that the outer stellar components of a nucleated dwarf are removed by the strong tidal field of the cluster, whereas the nucleus manages to survive as a result of its initially compact nature. The developed naked nucleus is found to have physical properties (e. g. size and mass) similar to those observed for UCDs. We also find that although this formation process does not have a strong dependence on the initial total luminosity of the nucleated dwarf, it does depend on the radial density profile of the dark halo in the sense that UCDs are less likely to be formed from dwarfs embedded in dark matter haloes with central 'cuspy' density profiles. Our simulations also suggest that very massive and compact stellar systems can be rapidly and efficiently formed in the central regions of dwarfs through the merging of smaller star clusters. We provide some theoretical predictions on the total number and radial number density profile of UCDs in a cluster and their dependencies on cluster masses.

The evolution and star formation of dwarf galaxies in the Fornax Cluster

We present the results of a spectroscopic survey of 675 bright (16.5 < b(J) < 18) galaxies in a 6 degrees field centred on the Fornax cluster with the FLAIR-II spectrograph on the UK Schmidt Telescope. Three galaxy samples were observed: compact galaxies to search for new blue compact dwarfs, candidate M 32-like compact dwarf ellipticals, and a subset of the brightest known cluster members in order to study the cluster dynamics. We measured redshifts for 516 galaxies, of which 108 were members of the Fornax Cluster. Defining dwarf galaxies to be those with b(J) greater than or equal to 15 (M-B greater than or equal to - 16.5), there are a total of 62 dwarf cluster galaxies in our sample. Nine of these are new cluster members previously misidentified as background galaxies. The cluster dynamics show that the dwarf galaxies are still falling into the cluster whereas the giants are virialized. We classified the observed galaxies as late-type if we detected H alpha emission at an equivalent width greater than 1 Angstrom. The spectra were obtained through fixed apertures, so they reflect activity in the galaxy cores, but this does not significantly bias the classifications of the compact dwarfs in our sample. The new classifications reveal a higher rate of star formation among the dwarf galaxies than suggested by morphological classification: 35 per cent have significant H alpha emission indicative of star formations but only 19 per cent were morphologically classified as late-types. The star-forming dwarf galaxies span the full range of physical sizes and we find no evidence in our data for a distinct class of star-forming blue compact dwarf (BCD) galaxy. The distribution of scale sizes is consistent with evolutionary processes which transform late-type dwarfs to early-type dwarfs. The fraction of dwarfs with active star formation drops rapidly towards the cluster centre: this is the usual density-morphology relation confirmed here for dwarf galaxies. The star-forming dwarfs are concentrated in the outer regions of the cluster, the most extreme in an infalling subcluster. We estimate gas depletion time-scales for five dwarfs with detected Hi emission: these are long (of order 10(10) yr), indicating that an active gas removal process must be involved if they are transformed into gas-poor dwarfs as they fall further into the cluster. Finally, in agreement with our previous results, we find no compact dwarf elliptical (M 32-like) galaxies in the Fornax Cluster.

A class of compact dwarf galaxies from disruptive processes in galaxy clusters

Dwarf galaxies have attracted increased attention in recent years, because of their susceptibility to galaxy transformation processes within rich galaxy clusters. Direct evidence for these processes, however, has been difficult to obtain, with a small number of diffuse light trails and intra-cluster stars, being the only signs of galaxy disruption. Furthermore, our current knowledge of dwarf galaxy populations may be very incomplete, because traditional galaxy surveys are insensitive to extremely diffuse or compact galaxies. Aware of these concerns, we recently undertook an all-object survey of the Fornax galaxy cluster. This revealed a new population of compact members, overlooked in previous conventional surveys. Here we demonstrate that these 'ultra-compact' dwarf galaxies are structurally and dynamically distinct from both globular star clusters and known types of dwarf galaxy, and thus represent a new class of dwarf galaxy. Our data are consistent with the interpretation that these are the remnant nuclei of disrupted dwarf galaxies, making them an easily observed tracer of galaxy disruption.

Galaxy threshing and the origin of intracluster stellar objects

We numerically investigate the dynamical evolution of non-nucleated dwarf elliptical/spiral galaxies (dE) and nucleated ones (dE,Ns) in clusters of galaxies in order to understand the origin of intracluster stellar objects, such as intracluster stars (ICSs), GCs (ICGCs), and ultracompact dwarfs (UCDs) recently discovered by all-object spectroscopic survey centred on the Fornax cluster of galaxies. We find that the outer stellar components of a nucleated dwarf are removed by the strong tidal field of the cluster, whereas the nucleus manages to survive as a result of its initially compact nature. The developed naked nucleus is found to have physical properties (e.g., size and mass) similar to those observed for UCDs. We also find that the UCD formation process, does depend on the radial density profile of the dark halo in the sense that UCDs are less likely to be formed from dwarfs embedded in dark matter halos with central 'cuspy' density profiles. Our simulations also suggest that very massive and compact stellar systems can be rapidly and efficiently formed in the central regions of dwarfs through the merging of smaller GCs. GCs initially in the outer part of dE and dE,Ns are found to be stripped to form ICGCs.

HI observations of interacting galaxy pair NGC 4038/9

We present the results of new radio interferometer Hi line observations for the merging galaxy pair NGC 4038/9 ('The Antennae'), obtained using the Australia Telescope Compact Array. The results improve substantially with respect to those of van der Hulst and show in detail the two merging galactic discs and the two tidal tails produced by their interaction. The small edge-on spiral dwarf galaxy ESO 572-G045 is also seen near the tip of the southern tail, but distinct from it. It shows no signs of tidal interaction. The northern tidal tail of the Antennae shows no HI connection to the discs and has an extension towards the west. The southern tidal tail is continuous, with a prominent HI concentration at its tip, roughly at the location of the tidal dwarf galaxy observed optically by Mirabel, Dottori & Lutz. Clear velocity structure is seen along the tidal tails and in the galactic discs. Radio continuum images at 20 and 13 cm are also presented, showing the discs in detail.

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Using patients' and rheumatologists' opinions to specify a short form of the WOMAC function subscale

Background: The WOMAC ( Western Ontario and McMaster Universities) function subscale is widely used in clinical trials of hip and knee osteoarthritis. Reducing the number of items of the subscale would enhance efficiency and compliance, particularly for use in clinical practice applications. Objective: To develop a short form of the WOMAC function subscale based on patients' and experts' opinions ( WOMAC function short form). Methods: WOMAC function subscale data ( Likert version) were obtained from 1218 outpatients with painful hip or knee osteoarthritis. These patients and their rheumatologists selected the five items that they considered most in need of improvement. The rheumatologists were asked to select the five items for which patients in general are the most impaired. Items that were least important to patients and experts, those with a high proportion of missing data, and those with a response distribution showing a floor or ceiling response were excluded, along with one of a pair of items with a correlation coefficient >0.75. Results: The WOMAC function short form included items 1, 2, 3, 6, 7, 8, 9, and 15 of the long form. The short form did not differ substantially from the long form in responsiveness ( standardised response mean of 0.84 v 0.80). Conclusions: A short form of the WOMAC function subscale was developed according to the views of patients and rheumatologists, based on the responses of 1218 patients and 399 rheumatologists. The clinical relevance and applicability of this WOMAC function subscale short form require further evaluation.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.