A novel chaos control strategy for discrete-time Brusselator models

This article deals with the dynamical analysis of discrete-time Brusselator models. Euler’s forward and nonstandard difference schemes are implemented for discretization of Brusselator system. We investigate the local dynamics related to equilibria of both discrete-time models. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. A novel chaos control method is implemented in order to control chaos in discrete-time Brusselator models under the influence of flip and Hopf bifurcations. Numerical simulations are provided to illustrate theoretical discussion and effectiveness of newly introduced chaos control strategy.     

Analytical performance of glucometers in a tertiary care hospital

Point-of-care (POC) testing of glucose (glucometers) represents a convenient alternative to monitor glycemia since the measurement procedure is performed without delay after sampling of the capillary blood, thereby avoiding the metabolism by the blood cells of glucose present in plasma. Likely because of sample instability, there is no proficiency test provider in Brazil for this type of POC sample. In this context, this study aimed to evaluate the analytical performance of glucometers used in a tertiary care hospital. The glucometers used were the Accu-Chek Performa^® model from Roche Diagnostics, which use the principle of amperometry. The reference method was the reaction with modified hexokinase/glucose-6-phosphate in a Dimension^® device. The stability evaluation of the control samples showed that it can be performed up to 90 min after the collection of whole blood samples. In the two rounds performed, only one result of the 17 glucometers evaluated was out of the threshold of two standard deviation. Thus, this method for control of glucometers met the expectations and enabled comparing the glucometers in a hospital. Given the current quality guidelines, daily internal quality control of glucometers is recommended, besides at least two annual comparisons between the results of the glucometers and the reference method and one EQA every 3 months.     

Further Implications of the Bessis–Moussa–Villani Conjecture

We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function is the Laplace transform of a positive measure supported on [0,∞].     

Effect of boundary representation on viscous,separated flows in a discontinuous-Galerkin Navier–Stokes solver

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier–Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.     

Classical and quantum effects in spatially modulated optical parametric oscillators

We study the effects of transverse spatial modulations in a multimode degenerate optical parametric oscillator. Intracavity photonic crystals allow us to tune the instability threshold and improve entanglement above threshold. Here we compare such results with the case in which the modulation is in the injected field profile.     

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.