Travelling waves in hyperbolic chemotaxis equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically

The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields

The non-commutative theory of charge transport in mesoscopic aperiodic systems under magnetic fields, developed by Bellissard, Shulz-Baldes and collaborators in the 90's, is complemented with a practical numerical implementation. The scheme, which is developed within a $C^*$-algebraic framework, enable efficient evaluations of the non-commutative Kubo formula, with errors that vanish exponentially fast in the thermodynamic limit. Applications to a model of a 2-dimensional Quantum spin-Hall insulator are given. The conductivity tensor is mapped as function of Fermi level, disorder strength and temperature and the phase diagram in the plane of Fermi level and disorder strength is quantitatively derived from the transport simulations. Simulations at finite magnetic field strength are also presented.Comment: 10 figure

Triaxially deformed relativistic point-coupling model for Λ\Lambda hypernuclei: a quantitative analysis of hyperon impurity effect on nuclear collective properties

The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_\Lambda$Li. Many more data on low-lying states of $\Lambda$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $\Lambda$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $\Lambda$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the $\Lambda$ hyperon is injected into the lowest positive-parity ($\Lambda_s$) and negative-parity ($\Lambda_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $\Lambda$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(\beta, \gamma)$ deformation plane. We also calculate the PESs for the $\Lambda$ hypernuclei with good quantum numbers using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking $^{25,27}_{\Lambda}$Mg and $^{31}_{\Lambda}$Si as examples, we analyse the impurity effects of $\Lambda_s$ and $\Lambda_p$ on the low-lying states of the core nuclei...Comment: 15 pages with 18 figures and 1 table (version to be published in Physical Review C

Long wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Microscopic theory of single-electron tunneling through molecular-assembled metallic nanoparticles

We present a microscopic theory of single-electron tunneling through metallic nanoparticles connected to the electrodes through molecular bridges. It combines the theory of electron transport through molecular junctions with the description of the charging dynamics on the nanoparticles. We apply the theory to study single-electron tunneling through a gold nanoparticle connected to the gold electrodes through two representative benzene-based molecules. We calculate the background charge on the nanoparticle induced by the charge transfer between the nanoparticle and linker molecules, the capacitance and resistance of molecular junction using a first-principles based Non-Equilibrium Green's Function theory. We demonstrate the variety of transport characteristics that can be achieved through ``engineering'' of the metal-molecule interaction.Comment: To appear in Phys. Rev.

Black hole mass and accretion rate of active galactic nuclei with double-peaked broad emission lines

(Abridged) Using an empirical relation between the broad line region size and optical continuum luminosity, we estimated the black hole mass and accretion rate for 135 AGNs with double-peaked broad emission lines in two samples. With black hole masses from $3\times 10^7M_\odot$ to $5\times 10^9M_\odot$, these AGNs have the dimensionless accretion rates (Eddington ratios) between 0.001 and 0.1, and the bolometric luminosity between $10^{43}erg/s$ and $10^{46}erg/s$, both being significantly larger than those of several previously known low-luminosity double-peaked AGNs. The optical-X-ray spectra indices, $\alpha_{OX}$, of these high-luminosity double-peaked AGNs is between 1 and 1.9. Modest correlations of the $\alpha_{OX}$ value with the Eddington ratio and bolometric luminosity indicate that double-peaked AGNs with higher Eddington ratio or higher luminosity tend to have larger $\alpha_{OX}$ value. Therefore we suggested that the accretion process in some high-luminosity double-peaked AGNs is probably different from that of low-luminosity objects where an ADAF-like accretion flow was thought to exist. This is also supported by the presence of possible big blue bumps in the spectra of some double-peaked AGNs with higher Eddington ratios. We noticed that the prototype double-peaked emission line AGN, Arp 102B, may be an ``intermediate'' object between the high and low luminosity double-peaked AGNs. In addition, we found an apparent strong anti-correlation between the peak separation of double-peaked profile and Eddington ratio. If it is real, it may provide us a clue to understand why double-peaked broad emission lines were hardly found in luminous AGNs with Eddington ratio larger than 0.1.Comment: 24 pages, 6 figures, accepted by Ap

Photometric identification of blue horizontal branch stars

We investigate the performance of some common machine learning techniques in identifying BHB stars from photometric data. To train the machine learning algorithms, we use previously published spectroscopic identifications of BHB stars from SDSS data. We investigate the performance of three different techniques, namely k nearest neighbour classification, kernel density estimation and a support vector machine (SVM). We discuss the performance of the methods in terms of both completeness and contamination. We discuss the prospect of trading off these values, achieving lower contamination at the expense of lower completeness, by adjusting probability thresholds for the classification. We also discuss the role of prior probabilities in the classification performance, and we assess via simulations the reliability of the dataset used for training. Overall it seems that no-prior gives the best completeness, but adopting a prior lowers the contamination. We find that the SVM generally delivers the lowest contamination for a given level of completeness, and so is our method of choice. Finally, we classify a large sample of SDSS DR7 photometry using the SVM trained on the spectroscopic sample. We identify 27,074 probable BHB stars out of a sample of 294,652 stars. We derive photometric parallaxes and demonstrate that our results are reasonable by comparing to known distances for a selection of globular clusters. We attach our classifications, including probabilities, as an electronic table, so that they can be used either directly as a BHB star catalogue, or as priors to a spectroscopic or other classification method. We also provide our final models so that they can be directly applied to new data.Comment: To appear in A&A. 19 pages, 22 figures. Tables 7, A3 and A4 available electronically onlin