Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation

We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting mathematical feature of the model, which is a coupled pair of partial differential equations, is that the bacterial density satisfies a degenerate nonlinear diffusion equation. It was shown numerically that this model can exhibit quasi-one-dimensional constant speed travelling wave solutions. We present an analytic study of the existence and uniqueness problem for constant speed travelling wave solutions. We find that such solutions exist only for speeds greater than some threshold speed giving minimum speed waves which have a sharp profile. For speeds greater than this minimum speed the waves are smooth. We also characterise the dependence of the wave profile on the decay of the front of the initial perturbation in bacterial density. An investigation of the partial differential equation problem establishes,via a global existence and uniqueness argument, that these waves are the only long time solutions supported by the problem. Numerical solutions of the partial differential equation problem are presented and they confirm the results of the analysis

Quantum Entanglement in (d−1)(d-1)-Spherium

There are very few systems of interacting particles (with continuous variables) for which the entanglement of the concomitant eigenfunctions can be computed in an exact, analytical way. Here we present analytical calculations of the amount of entanglement exhibited by $s$-states of \emph{spherium}. This is a system of two particles (electrons) interacting via a Coulomb potential and confined to a $(d-1)$-sphere (that is, to the surface of a $d$-dimensional ball). We investigate the dependence of entanglement on the radius $R$ of the system, on the spatial dimensionality $d$, and on energy. We find that entanglement increases monotonically with $R$, decreases with $d$, and also tends to increase with the energy of the eigenstates. These trends are discussed and compared with those observed in other two-electron atomic-like models where entanglement has been investigated.Comment: 14 pages, 6 figures. J. Phys. A (2015). Accepte

Information theory of quantum systems with some hydrogenic applications

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.Comment: 9 pages, 3 figure

Evidence of ongoing radial migration in NGC 6754: Azimuthal variations of the gas properties

Understanding the nature of spiral structure in disk galaxies is one of the main, and still unsolved questions in galactic astronomy. However, theoretical works are proposing new testable predictions whose detection is becoming feasible with recent development in instrumentation. In particular, streaming motions along spiral arms are expected to induce azimuthal variations in the chemical composition of a galaxy at a given galactic radius. In this letter we analyse the gas content in NGC 6754 with VLT/MUSE data to characterise its 2D chemical composition and H$\alpha$ line-of-sight velocity distribution. We find that the trailing (leading) edge of the NGC 6754 spiral arms show signatures of tangentially-slower, radially-outward (tangentially-faster, radially-inward) streaming motions of metal-rich (poor) gas over a large range of radii. These results show direct evidence of gas radial migration for the first time. We compare our results with the gas behaviour in a $N$-body disk simulation showing spiral morphological features rotating with a similar speed as the gas at every radius, in good agreement with the observed trend. This indicates that the spiral arm features in NGC 6754 may be transient and rotate similarly as the gas does at a large range of radii.Comment: 8 pages, 4 figures, accepted for publication in ApJL 2016 September 2

The cosmic evolution of the spatially-resolved star formation rate and stellar mass of the CALIFA survey

We investigate the cosmic evolution of the absolute and specific star formation rate (SFR, sSFR) of galaxies as derived from a spatially-resolved study of the stellar populations in a set of 366 nearby galaxies from the CALIFA survey. The analysis combines GALEX and SDSS images with the 4000 break, H_beta, and [MgFe] indices measured from the datacubes, to constrain parametric models for the SFH, which are then used to study the cosmic evolution of the star formation rate density (SFRD), the sSFR, the main sequence of star formation (MSSF), and the stellar mass density (SMD). A delayed-tau model, provides the best results, in good agreement with those obtained from cosmological surveys. Our main results from this model are: a) The time since the onset of the star formation is larger in the inner regions than in the outer ones, while tau is similar or smaller in the inner than in the outer regions. b) The sSFR declines rapidly as the Universe evolves, and faster for early than for late type galaxies, and for the inner than for the outer regions of galaxies. c) SFRD and SMD agree well with results from cosmological surveys. At z< 0.5, most star formation takes place in the outer regions of late spiral galaxies, while at z>2 the inner regions of the progenitors of the current E and S0 are the major contributors to SFRD. d) The inner regions of galaxies are the major contributor to SMD at z> 0.5, growing their mass faster than the outer regions, with a lookback time at 50% SMD of 9 and 6 Gyr for the inner and outer regions. e) The MSSF follows a power-law at high redshift, with the slope evolving with time, but always being sub-linear. f) In agreement with galaxy surveys at different redshifts, the average SFH of CALIFA galaxies indicates that galaxies grow their mass mainly in a mode that is well represented by a delayed-tau model, with the peak at z~2 and an e-folding time of 3.9 Gyr.Comment: 23 pages, 16 figures, 6 tables, accepted for publication in Astronomy & Astrophysics. *Abridged abstract

Anderson Localization in Disordered Vibrating Rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.Comment: 10 pages, 6 figure