A comparison between different optimization criteria for tuned mass dampers design

Tuned mass sampers (TMDs) are widely used strategies for vibration control in many engineering applications, so that many TMD optimization criteria have been proposed till now. However, they normally consider only TMD stiffness and damping as design variables and assume that the tuned mass is a pre-selected value. In this work a more complete approach is proposed and then also TMD mass ratio is optimized. A standard single degree of freedom system is investigated to evaluate TMD protection efficiency in case of excitation at the support. More precisely, this model is used to develop two different optimizations criteria which minimize the main system displacement or the inertial acceleration. Different environmental conditions described by various characterizations of the input, here modelled by a stationary filtered stochastic process, are considered. Results show that all solutions obtained considering also the mass of the TMD as design variable are more efficient if compared with those obtained without it. However, in many cases these solutions are inappropriate because the optimal TMD mass is greater than real admissible values in practical technical applications for civil and mechanical engineering. Anyway, one can deduce that there are some interesting indications for applications in some actual contexts. In fact, the results show that there are some ranges of environmental parameters ranges where results attained by the displacement criterion are compatible with real applications requiring some percent of main system mass. Finally, the present research gives promising indications for complete TMD optimization application in emerging technical contexts, as micromechanical devices and nano resonant beams.     

Legendre spectral method for the fractional Bratu problem

In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some spectral collocation methods. Some illustrative examples are also given to show the validity and applicability of this method, and the obtained results are compared with the existing studies to highlight its high efficiency and neglectable error.     

Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods

This paper deals with the modelling of pedestrian dynamics at the entry of a metro station by means of the thermostatted kinetic theory framework. Specifically, the model depicts the time evolution of the pedestrian dynamics at the turnstiles under no panic conditions. The modelling of the microscopic interactions is based on the stochastic game theory and reflects the decision dynamics of the turnstiles pursued by pedestrians. A qualitative analysis is addressed to the equilibrium solutions by means of the classical stability theory of perturbations. Numerical simulations aim at showing the emerging behaviours captured by the model. In particular the model validation is obtained by performing a sensitivity analysis on the parameters and on the initial conditions. Further refinements and research perspective, including the modelling under panic conditions, are discussed in the last section of the paper.     

Small values of signed harmonic sums

For every $\tau \in \mathbb{R}$ and every integer N, let ${\mathfrak{m}}_N(\tau )$ be the minimum of the distance of τ from the sums ${\sum }_{n=1}^N{s}_n/n$, where $s_1,\dots ,s_n\in \{?1,+1\}$. We prove that ${\mathfrak{m}}_N(\tau )<\exp ?(?C{(\log ?N)}^2)$, for all sufficiently large positive integers N (depending on C and τ), where C is any positive constant less than $1/\log ?4$.     

RBFOpt: an open-source library for black-box optimization with costly function evaluations

We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the solution methodology implemented in the open-source library RBFOpt, available on COIN-OR. The algorithm is based on the Radial Basis Function method originally proposed by Gutmann (J Glob Optim 19:201–227, 2001.  https://doi.org/10.1023/A:1011255519438), which builds and iteratively refines a surrogate model of the unknown objective function. The two main methodological contributions of this paper are an approach to exploit a noisy but less expensive oracle to accelerate convergence to the optimum of the exact oracle, and the introduction of an automatic model selection phase during the optimization process. Numerical experiments show that RBFOpt is highly competitive on a test set of continuous and mixed-integer nonlinear unconstrained problems taken from the literature: it outperforms the open-source solvers included in our comparison by a large amount, and performs slightly better than a commercial solver. Our empirical evaluation provides insight on which parameterizations of the algorithm are the most effective in practice. The software reviewed as part of this submission was given the Digital Object Identifier (DOI)  https://doi.org/10.5281/zenodo.597767.     

Monotone thematic factorizations of matrix functions

We continue the study of the so-called thematic factorizations of admissible very badly approximable matrix functions. These factorizations were introduced by V.V. Peller and N.J. Young for studying superoptimal approximation by bounded analytic matrix functions. Even though thematic indices associated with a thematic factorization of an admissible very badly approximable matrix function are not uniquely determined by the function itself, R.B. Alexeev and V.V. Peller showed that the thematic indices of any monotone non-increasing thematic factorization of an admissible very badly approximable matrix function are uniquely determined. In this paper, we prove the existence of monotone non-decreasing thematic factorizations for admissible very badly approximable matrix functions. It is also shown that the thematic indices appearing in a monotone non-decreasing thematic factorization are not uniquely determined by the matrix function itself. Furthermore, we show that the monotone non-increasing thematic factorization gives rise to a great number of other thematic factorizations.     

A primer on triangle functions II

In Saminger-Platz and Sempi (Aequationes Math 76:201–240, 2008) we presented an overview of concepts, facts and results on triangle functions based on the notions of t-norm, copula, (generalized) convolution, semicopula, quasi-copula. Here, we continue our presentation. In particular, we treat the concept of duality and study a few important cases of functional equations and inequalities for triangle functions like, e.g., convolution, Cauchy’s equation, dominance, and Jensen convexity.     

Matrix‐valued Szegő polynomials and quantum random walks

We consider quantum random walks (QRW) on the integers, a subject that has been considered in the last few years in the framework of quantum computation. We show how the theory of CMV matrices gives a natural tool to study these processes and to give results that are analogous to those that Karlin and McGregor developed to study (classical) birth‐and‐death processes using orthogonal polynomials on the real line. In perfect analogy with the classical case, the study of QRWs on the set of nonnegative integers can be handled using scalar‐valued (Laurent) polynomials and a scalar‐valued measure on the circle. In the case of classical or quantum random walks on the integers, one needs to allow for matrix‐valued versions of these notions. We show how our tools yield results in the well‐known case of the Hadamard walk, but we go beyond this translation‐invariant model to analyze examples that are hard to analyze using other methods. More precisely, we consider QRWs on the set of nonnegative integers. The analysis of these cases leads to phenomena that are absent in the case of QRWs on the integers even if one restricts oneself to a constant coin. This is illustrated here by studying recurrence properties of the walk, but the same method can be used for other purposes. The presentation here aims at being self‐contained, but we refrain from trying to give an introduction to quantum random walks, a subject well surveyed in the literature we quote. For two excellent reviews, see [1, 9]. See also the recent notes [20]. © 2009 Wiley Periodicals, Inc.     

Investigation of the influence of spacer arm on the structural evolution of affinity ligands supported on agarose

The influence of the spacer arm on the interaction between agarose and a supported ligand was investigated through molecular dynamics for a combination of several spacers. The spacers differ for degree of hydrophobicity, length, and chemical composition, which was varied through insertion of thio, ether, and CH(2) groups. Agarose was modeled through a modified Glycam force field, whose parameters were determined through ab initio calculations. The structural model of agarose used for the calculations was obtained through MD studies of the conformational evolution of several agarose single and double helixes. The simulations showed that a modification of the spacer properties could determine a change of the stable structure of the ligand with respect to the support. In particular, if the spacer is hydrophilic and rigid, the favored structure is with extended spacer and solvated ligand. Either increasing the spacer length, and thus its flexibility, or decreasing its solvation free energy, which corresponds to diminishing its affinity for water, rapidly leads to a conformational change in which the ligand adsorbs on agarose. Interestingly, we found that if the spacer is long and hydrophilic, a third metastable structure, in which the spacer is sandwiched between the ligand and agarose, is possible. Simulations of several ligands adsorbed on neighboring sites on agarose showed that if the support is not held fixed through restraints, the interaction force between vicinal ligands is sufficient to determine a major conformational change of the system.     

Phase diagram of pentacene growth on Au(110)

We studied the growth of pentacene (C22H14) on the Au(110) surface by means of He atom scattering and Synchrotron X-ray photoemission. We found that two-dimensional commensurate growth only occurs in the monolayer range for a substrate temperature, T(s), higher than approximately 370 K. Larger amounts of deposited molecules forms three-dimensional uncorrelated clusters on the wetting layer. The desorption of second layer molecules occurs at T(s) > or = 420 K. The highest coverage ordered phase displays a (6 x 8) symmetry and corresponds to the saturation coverage at T(s) = 420 K. The (3 x 6) symmetry phase, recently reported for a multilayer planar film [Ph. Guaino, et al. Appl. Phys. Lett. 2004, 85, 2777], is only found at a coverage slightly lower than the (6 x 8) one. The (3 x 6) phase corresponds to the saturation coverage of the first layer at T(s) = 470 K.