A panel method free-wake code for aeroelastic rotor predictions

A panel method free-wake model to analyse the rotor flapping is presented. The aerodynamic model consists of a panel method, which takes into account the three-dimensional rotor geometry, and a free-wake model, to determine the wake shape. The main features of the model are the wake division into a near-wake sheet and a far wake represented by a single tip vortex, and the modification of the panel method formulation to take into account this particular wake description. The blades are considered rigid with a flap degree of freedom. The problem solution is approached using a relaxation method, which enforces periodic boundary conditions. Finally, several code validations against helicopter and wind turbine experimental data are performed, showing good agreement

Integrability of second-order Lagrangians admitting a first-order Hamiltonian formalism

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) necessary and sufficient conditions for the Poincaré–Cartan form of a second-order Lagrangian on an arbitrary fibred manifold p : E → N to be projectable onto J 1 E are explicitly determined; ii) for each of such Lagrangians, a first-order Hamiltonian formalism is developed and a new notion of regularity is introduced; iii) the variational problems of this class defined by regular Lagrangians areprovedtobeinvolutive

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

A continuous model for quasinilpotent operators.

A classical result due to Foias and Pearcy establishes a discrete model for every quasinilpotent operator acting on a separable, infinite-dimensional complex Hilbert space HH . More precisely, given a quasinilpotent operator T on HH , there exists a compact quasinilpotent operator K in HH such that T is similar to a part of K⊕K⊕⋯⊕K⊕⋯K⊕K⊕⋯⊕K⊕⋯ acting on the direct sum of countably many copies of HH . We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0C0 -semigroups of quasinilpotent operators.

Real time optimization in chemical process: evaluation of strategies, improvements and industrial application.

The increasing economic competition drives the industry to implement tools that improve their processes efficiencies. The process automation is one of these tools, and the Real Time Optimization (RTO) is an automation methodology that considers economic aspects to update the process control in accordance with market prices and disturbances. Basically, RTO uses a steady-state phenomenological model to predict the process behavior, and then, optimizes an economic objective function subject to this model. Although largely implemented in industry, there is not a general agreement about the benefits of implementing RTO due to some limitations discussed in the present work: structural plant/model mismatch, identifiability issues and low frequency of set points update. Some alternative RTO approaches have been proposed in literature to handle the problem of structural plant/model mismatch. However, there is not a sensible comparison evaluating the scope and limitations of these RTO approaches under different aspects. For this reason, the classical two-step method is compared to more recently derivative-based methods (Modifier Adaptation, Integrated System Optimization and Parameter estimation, and Sufficient Conditions of Feasibility and Optimality) using a Monte Carlo methodology. The results of this comparison show that the classical RTO method is consistent, providing a model flexible enough to represent the process topology, a parameter estimation method appropriate to handle measurement noise characteristics and a method to improve the sample information quality. At each iteration, the RTO methodology updates some key parameter of the model, where it is possible to observe identifiability issues caused by lack of measurements and measurement noise, resulting in bad prediction ability. Therefore, four different parameter estimation approaches (Rotational Discrimination, Automatic Selection and Parameter estimation, Reparametrization via Differential Geometry and classical nonlinear Least Square) are evaluated with respect to their prediction accuracy, robustness and speed. The results show that the Rotational Discrimination method is the most suitable to be implemented in a RTO framework, since it requires less a priori information, it is simple to be implemented and avoid the overfitting caused by the Least Square method. The third RTO drawback discussed in the present thesis is the low frequency of set points update, this problem increases the period in which the process operates at suboptimum conditions. An alternative to handle this problem is proposed in this thesis, by integrating the classic RTO and Self-Optimizing control (SOC) using a new Model Predictive Control strategy. The new approach demonstrates that it is possible to reduce the problem of low frequency of set points updates, improving the economic performance. Finally, the practical aspects of the RTO implementation are carried out in an industrial case study, a Vapor Recompression Distillation (VRD) process located in Paulínea refinery from Petrobras. The conclusions of this study suggest that the model parameters are successfully estimated by the Rotational Discrimination method; the RTO is able to improve the process profit in about 3%, equivalent to 2 million dollars per year; and the integration of SOC and RTO may be an interesting control alternative for the VRD process.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

[Lecture notes]

Notes from lectures at the New York Institute for mathematics and mechanics?

Submanifolds of dimension n-1 in [epsilon]n̳ with normals satisfying a Lipschitz condition.

"Paper written under Contract Nonr. 58304."

Lehrbuch der höhern Geometrie, in analytischer Darstellung.

Mode of access: Internet.

Traité d'analyse /

t. 1. Intégrales simples et multiples. Lʼéquation de Laplace et ses applications. Développments in séries. Applications géométriques du calcul infinitésimal.

Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

Determination of the Pu autoionizing level angular momenta by a multistep excitation with linearly polarized laser light

The modified polarization spectroscopy method was applied for determination of angular momenta of autoionizing states of Pu in multistep resonance ionization processes. In comparison with the known one, our method does not require circular polarization at all, only linear polarizations are needed. This simplicity was reached using a three-dimensional excitation geometry. Angular momenta of nine new autoionizing ²⁴²Pu states were determined. The method suggested could be applied for efficiency improvement in multistep RIMS applications as well as for the odd-even isotope separation for elements with a J = 0 ground state (Pu, Yb, Sm etc.).