A new second order method for blind signal separation from convolutive mixtures

This paper presents a new approach to separate colored signals mixed by FIR (finite impulse response) and MIMO (multiple-input multiple-output) channels. A cost function is proposed by employing linear constrainit to the de mixing vectors. The linear constraint is shown to be sufficient for avoiding trivial solution. The minimization of the cost function is performed using the Lagrangian method. Simulation results demonstrate the performance of the algorithm.<br /

New gravity-capillary waves at low speeds. Part 1: Linear geometries

When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear nature of the obstruction, asymptotic expansions in the low-Froude or low-Bond number limits can be derived, but here, the solutions invariably predict a waveless surface at every order. This is because the waves are in fact, exponentially small, and thus beyond-all-orders of regular asymptotics; their formation is a consequence of the divergence of the asymptotic series and the associated Stokes Phenomenon. By applying techniques in exponential asymptotics to this problem, we have discovered the existence of new classes of gravity-capillary waves, from which the usual linear solutions form but a special case. In this paper, we present the initial theory for deriving these waves through a study of gravity-capillary flow over a linearised step; this will be done using two approaches: in the first, we derive the surface waves using the the standard method of Fourier transforms; in the second, we derive the same result using exponential asymptotics. Ultimately, these two methods give the same result, but conceptually, they offer different insights into the study of the low-Froude, low-Bond number problem

Design of scalar functional observers of order less than (v-1)

This paper presents a new method of designing scalar functional observers of order less than the well-known upper bound (&nu; - 1). A condition for the existence of observers of order p where 1 &le; p &le; (&nu; - 1) is given. A simple and effective algorithm for solving the constrained generalized Sylvester equation is proposed. Several numerical examples are given to illustrate the attractiveness of the design algorithm. <br /

Nonlinear Modes of Liquid Drops as Solitary Waves

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such ``rotons'' were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to drop-like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.Comment: 11 pages RevTex, 1 figure p

Groups of two galaxies in SDSS: implications of colours on star formation quenching time-scales

We have devised a method to select galaxies that are isolated in their dark matter halo (N=1 systems) and galaxies that reside in a group of exactly two (N=2 systems). Our N=2 systems are widely-separated (up to $\sim$\,200\,$h^{-1}$\,kpc), where close galaxy-galaxy interactions are not dominant. We apply our selection criteria to two volume-limited samples of galaxies from SDSS DR6 with $M_{r}-5 \log_{10} h \leq$ -19 and -20 to study the effects of the environment of very sparse groups on galaxy colour. For satellite galaxies in a group of two, we find a red excess attributed to star formation quenching of 0.15\,$\pm$\,0.01 and 0.14\,$\pm$\,0.01 for the -19 and -20 samples, respectively, relative to isolated galaxies of the same stellar mass. Assuming N=1 systems are the progenitors of N=2 systems, an immediate-rapid star formation quenching scenario is inconsistent with these observations. A delayed-then-rapid star formation quenching scenario with a delay time of 3.3 and 3.7\,Gyr for the -19 and -20 samples, respectively, yields a red excess prediction in agreement with the observations. The observations also reveal that central galaxies in a group of two have a slight blue excess of 0.06\,$\pm$\,0.02 and 0.02\,$\pm$\,0.01 for the -19 and -20 samples, respectively, relative to N=1 populations of the same stellar mass. Our results demonstrate that even the environment of very sparse groups of luminous galaxies influence galaxy evolution and in-depth studies of these simple systems are an essential step towards understanding galaxy evolution in general.Comment: 17 pages, 11 figures, accepted to MNRA

Curvature suppresses the Rayleigh-Taylor instability

The dynamics of a thin liquid film on the underside of a curved cylindrical substrate is studied. The evolution of the liquid layer is investigated as the film thickness and the radius of curvature of the substrate are varied. A dimensionless parameter (a modified Bond number) that incorporates both geometric parameters, gravity, and surface tension is identified, and allows the observations to be classified according to three different flow regimes: stable films, films with transient growth of perturbations followed by decay, and unstable films. Experiments and theory confirm that, below a critical value of the Bond number, curvature of the substrate suppresses the Rayleigh-Taylor instability