Periodic orbits and non-integrability of Armbruster-Guckenheimer-Kim potential

In this paper we study the periodic orbits of the Hamiltonian system with the Armburster-Guckenheimer Kim potential and its C1 non-integrability in the sense of Liouville-Arnold.

Dinâmica não linear e controle de um sistema vibratório modelado com memória de forma e, excitado por fontes de energia do tipo ideal e não ideal

Pós-graduação em Engenharia Mecânica - FEB

Equações diferenciais implícitas com descontinuidade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de ciclos limites em uma classe de equações diferenciais descontínuas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamical changes from harmonic vibrations of a limited power supply driving a Duffing oscillator

The harmonic oscillations of a Duffing oscillator driven by a limited power supply are investigated as a function of the alternative strength of the rotor. The semi-trivial and non-trivial solutions are derived. We examine the stability of these solutions and then explore the complex behaviors associated with the bifurcations sequences. Interestingly, a 3D diagram provides a global view of the effects of alternate strength on the appearance of chaos and hyperchaos on the system.

Bayesian adaptive designs for drug combinations in early phase clinical trials

Treating patients with combined agents is a growing trend in cancer clinical trials. Evaluating the synergism of multiple drugs is often the primary motivation for such drug-combination studies. Focusing on the drug combination study in the early phase clinical trials, our research is composed of three parts: (1) We conduct a comprehensive comparison of four dose-finding designs in the two-dimensional toxicity probability space and propose using the Bayesian model averaging method to overcome the arbitrariness of the model specification and enhance the robustness of the design; (2) Motivated by a recent drug-combination trial at MD Anderson Cancer Center with a continuous-dose standard of care agent and a discrete-dose investigational agent, we propose a two-stage Bayesian adaptive dose-finding design based on an extended continual reassessment method; (3) By combining phase I and phase II clinical trials, we propose an extension of a single agent dose-finding design. We model the time-to-event toxicity and efficacy to direct dose finding in two-dimensional drug-combination studies. We conduct extensive simulation studies to examine the operating characteristics of the aforementioned designs and demonstrate the designs' good performances in various practical scenarios.^

Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.

An efficient numerical method for compressible flows of a real gas using arithmetic averaging

An efficient numerical method is presented for the solution of the Euler equations governing the compressible flow of a real gas. The scheme is based on the approximate solution of a specially constructed set of linearised Riemann problems. An average of the flow variables across the interface between cells is required, and this is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual square root averaging. The scheme is applied to a test problem for five different equations of state.

Method of Averaging for Impulsive Differential Inclusions

AMS subject classification: Primary 49N25, Secondary 49J24, 49J25.

A nanopore-based stochastic detection method: Single molecule characterisation of nanoparticles using ()- hemolysin

Dissertation presented to obtain the Ph.D degree in Chemistry.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

General method to determine replica symmetry breaking transitions

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

The binding energies of deformed even-even nuclei have been analyzed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner-Kirkwood ̄h expansion up to fourth order, instead of the usual Strutinsky averaging scheme, to compute the shell corrections in a deformed Woods-Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with Z 8 and N 8, we find an rms deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the finite range droplet model of Moller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth-order Wigner-Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth-order to the second-order corrections behaves in a very regular manner as a function of the asymmetry parameter I=(N−Z)/A. This allows us to absorb the fourth-order corrections into the second-order contributions to the binding energy, which enables us us to simplify and speed up the calculation of deformed nuclei.