Damping optimization of parameter dependent mechanical systems by rational interpolation

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization criteria based on the \(\mathcal {H}_{2}\) system norm. The objective function is non-convex and the associated optimization problem typically requires a large number of objective function evaluations. We propose an optimization approach that calculates ‘interpolatory’ reduced order models, allowing for significant acceleration of the optimization process. In our approach, we use parametric model reduction (PMOR) based on the Iterative Rational Krylov Algorithm, which ensures good approximations relative to the \(\mathcal {H}_{2}\) system norm, aligning well with the underlying damping design objectives. For the parameter sampling that occurs within each PMOR cycle, we consider approaches with predetermined sampling and approaches using adaptive sampling, and each of these approaches may be combined with three possible strategies for internal reduction. In order to preserve important system properties, we maintain second-order structure, which through the use of modal coordinates, allows for very efficient implementation. The methodology proposed here provides a significant acceleration of the optimization process; the gain in efficiency is illustrated in numerical experiments.     

Interpolatory model reduction of parameterized bilinear dynamical systems

Interpolatory projection methods for model reduction of nonparametric linear dynamical systems have been successfully extended to nonparametric bilinear dynamical systems. However, this has not yet occurred for parametric bilinear systems. In this work, we aim to close this gap by providing a natural extension of interpolatory projections to model reduction of parametric bilinear dynamical systems. We introduce necessary conditions that the projection subspaces must satisfy to obtain parametric tangential interpolation of each subsystem transfer function. These conditions also guarantee that the parameter sensitivities (Jacobian) of each subsystem transfer function are matched tangentially by those of the corresponding reduced-order model transfer function. Similarly, we obtain conditions for interpolating the parameter Hessian of the transfer function by including additional vectors in the projection subspaces. As in the parametric linear case, the basis construction for two-sided projections does not require computing the Jacobian or the Hessian.     

A finiteness theorem for Markov bases of hierarchical models

We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is greater than a computable bound, the Markov bases consist of elements from Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver complexities for all K×2×2×2 tables.     

Novel thiazole‐piperazine derivatives as potential cholinesterase inhibitors

Dementia is a cognitive disorder mostly associated with Alzheimer's disease (AD) in addition to being seen in many other diseases of the central nervous system (CNS). The limited number of drugs is not sufficient to provide adequate improvement to increase the quality of life of patients suffering from this symptom; therefore, all treatment options should be evaluated in detail. In this study, new molecules, [2‐(4‐(2/3/4‐substituted phenyl)piperazin‐1‐yl)‐4‐phenylthiazol‐5‐yl][3/4‐substituted phenyl]methanone derivatives ( 1‐44 ), were obtained and analyzed in terms of their anticholinesterase activities. Kinetic mode and molecular interactions were also evaluated. An enzyme inhibition study was undertaken on acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) using the Ellman method. Maestro program was used in molecular modeling studies. Forty‐four compounds were evaluated on AChE and BChE enzymes at 10^?3 and 10^?4 concentrations. The inhibition concentrations were calculated as 0.268μM to 2.104μM for six compounds ( 4 , 5 , 16 , 27 , 37 , and 38 ) on AChE. Compound 5 including the 4‐methoxy substituent (IC₅₀: 0.268μM) and compound 38 containing the 4‐methoxy and 3‐methyl substituents (IC₅₀: 0.286μM) showed the highest AChE inhibitory activity. They were further examined in terms of hydrogen bonding with Arg296 and Ar‐Ar interaction with Trp286. The activity of compound 5 was also assessed in mixed‐type kinetic mode.     

Unit-cell simulations of damage and failure in PRMMCs

The purpose of this work is damage and failure modeling in multiphase metallic materials via unit-cell simulations and homogenization methods. To this end, we investigate such behaviour in particle-reinforced metal matrix composites (PRMMCs). Taking into account the processes of void nucleation (due, e.g., to particle debonding and/or cracking) and growth, we examine the effect of phase composition, particle sizes and distributions, as well as the nature of the particle/matrix interface, on damage and failure in the unit cell. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High performance AlxGa1−xN-based avalanche photodiodes

We report high performance solar-blind photodetectors with reproducible avalanche gain as high as 820 under ultraviolet illumination. The solar-blind photodetectors have a sharp cut-off around 276 nm. We improved the device performance by designing different epitaxial wafer structure with thinner active multiplication layer. We compare the resulting fabricated devices from these wafers in terms of dark current, photoresponse, avalanche gain performances.     

Utilization of transport efficacy of novel calix[4]arene-embedded polymer inclusion membrane towards trace metals

In this study, 25,27-bis(3-mercaptopropoxyl)-26,28-dihydroxy calix[4]arene was successfully synthesized from the reaction of calix[4]arene-dialkylbromide derivative with thiourea. The structure of 25,27-bis(3-mercaptopropoxyl)-26,28-dihydroxy calix[4]arene was fully characterized using ¹HNMR, ¹³CNMR and elemental analysis techniques. The obtained mercapto-substituted calix[4]arene derivative was employed as an additive material along with cellulose triacetate (CTA) and 2-nitrophenyl octyl ether (o-NPOE) for the preparation of a novel polymer inclusion membrane (C@PIM). The structure and surface morphology of mercapto-substituted calix[4]arene-embedded polymer inclusion membrane was determined using thermogravimetric analysis, scanning electron microscopy and elemental analysis techniques. Donnan dialysis system was also used to assess the transport efficacy of C@PIM towards Pb(II), Zn(II), Cu(II), Ni(II), Cd(II) and Co(II) ions. The results show that new C@PIM exhibited 99% transport efficacy but also selectivity toward Ni(II) and other ions.     

On the lifetime of a random binary sequence

Consider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task (“1”) or the failure of the element (“0”). Initially, m tasks are sent to the system. At the second step, a complex of length m₁ is formed and sent to the system, where m₁ is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of “1” or “0”. We obtain a recursive equation for the expected value of this waiting time random variable.     

Modeling of claim exceedances over random thresholds for related insurance portfolios

Large claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern.     

The behavior of warm standby components with respect to a coherent system

This paper is concerned with a coherent system consisting of active components and equipped with warm standby components. In particular, we study the random quantity which denotes the number of surviving warm standby components at the time of system failure. We represent the distribution of the corresponding random variable in terms of system signature and discuss its potential utilization with a certain optimization problem.