A remark on the trace-map for the Silver mean sequence

In this work we study the Silver mean sequence based on substitution rules by means of a transfer-matrix approach. Using transfer-matrix method we find a recurrence relation for the traces of general transfer-matrices which characterizes electronic properties of the quasicrystal in question. We also find an invariant of the trace-map.Comment: 5 pages, minor improvements in style and presentation of calculation

Advances in the neurophysiology of magnocellular neuroendocrine cells

© 2020 British Society for Neuroendocrinology Hypothalamic magnocellular neuroendocrine cells have unique electrical properties and a remarkable capacity for morphological and synaptic plasticity. Their large somatic size, their relatively uniform and dense clustering in the supraoptic and paraventricular nuclei, and their large axon terminals in the neurohypophysis make them an attractive target for direct electrophysiological interrogation. Here, we provide a brief review of significant recent findings in the neuroplasticity and neurophysiological properties of these neurones that were presented at the symposium “Electrophysiology of Magnocellular Neurons” during the 13th World Congress on Neurohypophysial Hormones in Ein Gedi, Israel in April 2019. Magnocellular vasopressin (VP) neurones respond directly to hypertonic stimulation with membrane depolarisation, which is triggered by cell shrinkage-induced opening of an N-terminal-truncated variant of transient receptor potential vanilloid type-1 (TRPV1) channels. New findings indicate that this mechanotransduction depends on actin and microtubule cytoskeletal networks, and that direct coupling of the TRPV1 channels to microtubules is responsible for mechanical gating of the channels. Vasopressin neurones also respond to osmostimulation by activation of epithelial Na+ channels (ENaC). It was shown recently that changes in ENaC activity modulate magnocellular neurone basal firing by generating tonic changes in membrane potential. Both oxytocin and VP neurones also undergo robust excitatory synapse plasticity during chronic osmotic stimulation. Recent findings indicate that new glutamate synapses induced during chronic salt loading express highly labile Ca2+-permeable GluA1 receptors requiring continuous dendritic protein synthesis for synapse maintenance. Finally, recordings from the uniquely tractable neurohypophysial terminals recently revealed an unexpected property of activity-dependent neuropeptide release. A significant fraction of the voltage-dependent neurohypophysial neurosecretion was found to be independent of Ca2+ influx through voltage-gated Ca2+ channels. Together, these findings provide a snapshot of significant new advances in the electrophysiological signalling mechanisms and neuroplasticity of the hypothalamic-neurohypophysial system, a system that continues to make important contributions to the field of neurophysiology

PKS B1545-321: Bow shocks of a relativistic jet?

Sensitive, high resolution images of the double-double radio galaxy PKS B1545-321 reveal detailed structure, which we interpret in the light of previous work on the interaction of restarted jets with pre-existing relict cocoons. We have also examined the spectral and polarization properties of the source, the color distribution in the optical host and the environment of this galaxy in order to understand its physical evolution. We propose that the restarted jets generate narrow bow shocks and that the inner lobes are a mixture of cocoon plasma reaccelerated at the bow shock and new jet material reaccelerated at the termination shock. The dynamics of the restarted jets implies that their hot spots advance at mildly relativistic speeds with external Mach numbers of at least 5. The existence of supersonic hot spot Mach numbers and bright inner lobes is the result of entrainment causing a reduction in the sound speed of the pre-existing cocoon. The interruption to jet activity in PKS B1545-321 has been brief - lasting less than a few percent of the lifetime $\sim (0.3-2)\times 10^{8} yr$ of the giant radio source. The host galaxy is located at the boundary of a large scale filamentary structure, and shows blue patches in color distribution indicative of a recent merger, which may have triggered the Mpc-scale radio galaxy.Comment: 26 pages including 1 table and 16 figures. To appear in MNRA

Dynamics and Excitation of Radio Galaxy Emission-Line Regions - I. PKS 2356-61

Results are presented from a programme of detailed longslit spectroscopic observations of the extended emission-line region (EELR) associated with the powerful radio galaxy PKS 2356-61. The observations have been used to construct spectroscopic datacubes, which yield detailed information on the spatial variations of emission-line ratios across the EELR, together with its kinematic structure. We present an extensive comparison between the data and results obtained from the MAPPINGS II shock ionization code, and show that the physical properties of the line-emitting gas, including its ionization, excitation, dynamics and overall energy budget, are entirely consistent with a scenario involving auto-ionizing shocks as the dominant ionization mechanism. This has the advantage of accounting for the observed EELR properties by means of a single physical process, thereby requiring less free parameters than the alternative scheme involving photoionization by radiation from the active nucleus. Finally, possible mechanisms of shock formation are considered in the context of the dynamics and origin of the gas, specifically scenarios involving infall or accretion of gas during an interaction between the host radio galaxy and a companion galaxy.Comment: 35 pages, LaTeX, uses aas2pp4.sty file, includes 9 PostScript figures. Two additional colour plates are available from the authors upon request. Accepted for publication in the Astrophysical Journa

Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories

A fundamental criterion of viability of any gravity theory is existence of a stable ground-state solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary.Comment: A modified and expanded version of a second part of the paper which previously appeared as gr-qc/0702097v1. The first, modified part is now published as gr-qc/0702097v2 and as a separate paper in Class. Qu. Grav. The present paper matches the published versio

A new duality transformation for fourth-order gravity

We prove that for non-linear L = L(R), the Lagrangians L and \hat L give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator is conformally invariant.Comment: 11 pages, LaTeX, no figures. Gen. Relat. Grav. in prin

A complete classification of spherically symmetric perfect fluid similarity solutions

We classify all spherically symmetric perfect fluid solutions of Einstein's equations with equation of state p/mu=a which are self-similar in the sense that all dimensionless variables depend only upon z=r/t. For a given value of a, such solutions are described by two parameters and they can be classified in terms of their behaviour at large and small distances from the origin; this usually corresponds to large and small values of z but (due to a coordinate anomaly) it may also correspond to finite z. We base our analysis on the demonstration that all similarity solutions must be asymptotic to solutions which depend on either powers of z or powers of lnz. We show that there are only three similarity solutions which have an exact power-law dependence on z: the flat Friedmann solution, a static solution and a Kantowski-Sachs solution (although the latter is probably only physical for a1/5, there are also two families of solutions which are asymptotically (but not exactly) Minkowski: the first is asymptotically Minkowski as z tends to infinity and is described by one parameter; the second is asymptotically Minkowski at a finite value of z and is described by two parameters. A complete analysis of the dust solutions is given, since these can be written down explicitly and elucidate the link between the z>0 and z<0 solutions. Solutions with pressure are then discussed in detail; these share many of the characteristics of the dust solutions but they also exhibit new features.Comment: 63 pages. To appear in Physical Review