Approximating the Real Structured Stability Radius with Frobenius Norm Bounded Perturbations

We propose a fast method to approximate the real stability radius of a linear dynamical system with output feedback, where the perturbations are restricted to be real valued and bounded with respect to the Frobenius norm. Our work builds on a number of scalable algorithms that have been proposed in recent years, ranging from methods that approximate the complex or real pseudospectral abscissa and radius of large sparse matrices (and generalizations of these methods for pseudospectra to spectral value sets) to algorithms for approximating the complex stability radius (the reciprocal of the $H_\infty$ norm). Although our algorithm is guaranteed to find only upper bounds to the real stability radius, it seems quite effective in practice. As far as we know, this is the first algorithm that addresses the Frobenius-norm version of this problem. Because the cost mainly consists of computing the eigenvalue with maximal real part for continuous-time systems (or modulus for discrete-time systems) of a sequence of matrices, our algorithm remains very efficient for large-scale systems provided that the system matrices are sparse

Jet propulsion without inertia

A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies, and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented, and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e. jetting) surfaces are considered, and the optimal jetting flow profiles at the surface for maximizing the hydrodynamic efficiency are determined computationally. The maximal efficiency which may be achieved by a sphere using such jet propulsion is 12.5%, a significant improvement upon traditional flagella-based means of locomotion at zero Reynolds number. Unlike other swimming mechanisms which rely on the presentation of a small cross section in the direction of motion, the efficiency of a jetting body at low Reynolds number increases as the body becomes more oblate, and limits to approximately 162% in the case of a flat plate swimming along its axis of symmetry. Our results are discussed in the light of slime extrusion mechanisms occurring in many cyanobacteria

Verification of the code to calculate duct flow affected by external magnetic field

In this paper, the authors present the results of software verification for solving magnetohydrodynamic problem in duct exposed to constant magnetic fields. The proposed approach uses the following open source software: OpenFOAM for solving problems of continuum mechanics using the finite volume method, Elmer for solving magnetic field distribution based on the finite element method, and EOF-library for data exchange between these two programs. The verification results were demonstrated by fluid flow in a square duct exposed to constant uniform spanwise magnetic field. The research was carried out with a laminar fluid flow, which makes it similar to the Hartmann's problem. The existing experience of calculating such problems, their verification and application were discussed. The paper provides a brief mathematical description of the proposed solution and basic procedures for implementing the code proposed by the authors. At the first stage of verification, the comparison of fluid velocity distribution results at Hartmann’s numbers equal to 1, 10, 20 and 50 was demonstrated. These results were obtained by means of proposed software, an analytical solution, and a test problem provided by OpenFOAM developers for two-dimensional case. At the second stage of software verification, sufficient convergence of the results was shown for fluid velocity distribution in the three-dimensional case of the Hartmann’s problem compared with the OpenFOAM test problem data and the results obtained by Comsol Multiphisics and ANSYS. As a result, distributions of the fluid flow velocity between Hartmann’s walls were obtained for various study cases: a two-dimensional problem, a three-dimensional problem with electrically insulated walls, and a three-dimensional problem with walls having infinite electrical conductivity. The last stage of the study corresponds to assessing of software performance in comparison with the built-in OpenFOAM solver and commercial software Comsol Multiphysics and ANSYS. It was found that the proposed approach takes more time to calculate these problems than the built-in OpenFOAM solver, but less than Comsol. However, the problem formulation in EOF-library allows solving problems with complex geometry, which is not available in the built-in OpenFOAM solver. In conclusion, analysis of computation performance with parallelization was carried out. It showed significant reducing of computation time with the help of EOF-library in comparison with the commercial software Comsol and ANSYS

Coping with negative stereotypes toward older workers: Organizational and work-related outcomes

The current study aims to test a moderated-mediation model in which occupational selfefficacy determines the indirect effect of negative stereotypes about older workers in the organization both on psychological engagement in the work domain and on attitudes toward development opportunities through identification with the company. The survey involved 1,501 Italian subjects aged over 50 who were employed by a major large-scale retailer. Consistently with the Social Identity Theory and the Social Exchange Theory, results showed that the perception of negative stereotypes about older workers in the organization is associated with low identification with the company and, subsequently, with poor psychological engagement in the work domain and with attitudes indicating very little interest in development opportunities. In addition, this association was found to be stronger in older workers with higher and medium levels of occupational selfefficacy. These findings suggest that organizations should discourage the dissemination of negative stereotypes about older workers in the workplace because they may lead to older workers' disengagement from the work domain and their loss of interest in development opportunities

Position-sensorless control of permanent-magnet-assisted synchronous reluctance motor

The sensorless control of permanent-magnet-assisted synchronous reluctance (PMASR) motors is investigated, in order to conjugate the advantages of the sensorless control with full exploitation of the allowed operating area, for a given inverter. An additional pulsating flux is injected in the d-axis direction at low and zero speed, while it is dropped out, at large speed, to save voltage and additional loss. A flux-observer-based control scheme is used, which includes an accurate knowledge of the motor magnetic behavior. This leads, in general, to good robustness against load variations, by counteracting the magnetic cross saturation effect. Moreover, it allows an easy and effective correspondence between the wanted torque and flux and the set values of the chosen control variables, that is d-axis flux and q-axis current. Experimental verification of the proposed method is given, both steady-state and dynamic performance are outlined. A prototype PMASR motor will be used to this aim, as part of a purposely assembled prototype drive, for light traction application (electric scooter

Bayesian Autoregressive Frailty Models for Inference in Recurrent Events

We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections