Steady shocks around black holes produced by sub-keplerian flows with negative energy

We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas onto a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since keplerian disks have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. We give a simple procedure to obtain analytically the position of the shocks. The comparison of the analytical results with the data of 1D and 2D axisymmetric numerical simulations confirms that the shocks form and are stable.Comment: 5 pages, 5 figures, accepted by MNRAS on 10 November 200

Zeros of Dedekind zeta functions under GRH

Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $[T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.Comment: Some misprints corrected, simplified proof for a lemma. This version will appear in Mathematics of Computatio

Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH

Let \psi_\K be the Chebyshev function of a number field \K. Under GRH we prove an explicit upper bound for |\psi_\K(x)-x| in terms of the degree and the discriminant of \K. The new bound improves significantly on previous known results.Comment: Some misprints corrected. This is the final version which will appear in Mathematics of Computatio

Hydrodynamic Simulations of Oscillating Shock Waves in a Sub-Keplerian Accretion Flow Around Black Holes

We study the accretion processes on a black hole by numerical simulation. We use a grid based finite difference code for this purpose. We scan the parameter space spanned by the specific energy and the angular momentum and compare the time-dependent solutions with those obtained from theoretical considerations. We found several important results (a) The time dependent flow behaves close to a constant height model flow in the pre-shock region and a flow with vertical equilibrium in the post-shock region. (c) The infall time scale in the post-shock region is several times higher than the free-fall time scale. (b) There are two discontinuities in the flow, one being just outside of the inner sonic point. Turbulence plays a major role in determining the locations of these discontinuities. (d) The two discontinuities oscillate with two different frequencies and behave as a coupled harmonic oscillator. A Fourier analysis of the variation of the outer shock location indicates higher power at the lower frequency and lower power at the higher frequency. The opposite is true when the analysis of the inner shock is made. These behaviours will have implications in the spectral and timing properties of black hole candidates.Comment: 19 pages, 13 figures, 1 Table MNRAS (In press

Visual illusions: An interesting tool to investigate developmental dyslexia and autism spectrum disorder

A visual illusion refers to a percept that is different in some aspect from the physical stimulus. Illusions are a powerful non-invasive tool for understanding the neurobiology of vision, telling us, indirectly, how the brain processes visual stimuli. There are some neurodevelopmental disorders characterized by visual deficits. Surprisingly, just a few studies investigated illusory perception in clinical populations. Our aim is to review the literature supporting a possible role for visual illusions in helping us understand the visual deficits in developmental dyslexia and autism spectrum disorder. Future studies could develop new tools – based on visual illusions – to identify an early risk for neurodevelopmental disorders

The free energy landscape of GABA binding to a pentameric ligand-gated ion channel and its disruption by mutations

Pentameric ligand-gated ion channels (pLGICs) of the Cys-loop superfamily are important neuroreceptors that mediate fast synaptic transmission. They are activated by the binding of a neurotransmitter, but the details of this process are still not fully understood. As a prototypical pLGIC, here we choose the insect resistance to dieldrin (RDL) receptor, involved in the resistance to insecticides, and investigate the binding of the neurotransmitter GABA to its extracellular domain at the atomistic level. We achieve this by means of $\mu$-sec funnel-metadynamics simulations, which efficiently enhance the sampling of bound and unbound states by using a funnel-shaped restraining potential to limit the exploration in the solvent. We reveal the sequence of events in the binding process, from the capture of GABA from the solvent to its pinning between the charged residues Arg111 and Glu204 in the binding pocket. We characterize the associated free energy landscapes in the wild-type RDL receptor and in two mutant forms, where the key residues Arg111 and Glu204 are mutated to Ala. Experimentally these mutations produce non-functional channels, which is reflected in the reduced ligand binding affinities, due to the loss of essential interactions. We also analyze the dynamical behaviour of the crucial loop C, whose opening allows the access of GABA to the binding site, while its closure locks the ligand into the protein. The RDL receptor shares structural and functional features with other pLGICs, hence our work outlines a valuable protocol to study the binding of ligands to pLGICs beyond conventional docking and molecular dynamics techniques.Comment: accepted (May 2016); 27 pages, 6 figures, Table of contents graphic, Journal of Chemical Theory and Computation (2016

Ab initio simulations of accretion disks instability

We show that accretion disks, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behavior has been obtained by performing a set of time-dependent 2D SPH simulations of accretion disks with different values of alpha and accretion rate. In this study, to avoid any influence of the initial disk configuration, we produced the disks injecting matter from an outer edge far from the central object. The period of oscillations is 2 - 50 s respectively for the two cases, and the variation amplitude of the disc luminosity is 10^38 - 10^39 erg/s. An explanation of this luminosity behavior is proposed in terms of limit cycle instability: the disk oscillates between a radiation pressure dominated configuration (with a high luminosity value) and a gas pressure dominated one (with a low luminosity value). The origin of this instability is the difference between the heat produced by viscosity and the energy emitted as radiation from the disk surface (the well-known thermal instability mechanism). We support this hypothesis showing that the limit cycle behavior produces a sequence of collapsing and refilling states of the innermost disk region.Comment: 11 pages, 15 Postscript figures, uses natbib.sty, accepted for publication in MNRA