Feynman integrals with tensorial structure in the negative dimensional integration scheme

The negative-dimensional integration method (NDIM) is revealing itself as a very useful technique for computing massless and/or massive Feynman integrals, covariant and noncovanant alike. Up until now however, the illustrative calculations done using such method have been mostly covariant scalar integrals/without numerator factors. We show here how those integrals with tensorial structures also can be handled straightforwardly and easily. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. Toward this end, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerge in the computation of a standard one-loop self-energy diagram. One of the novel and heretofore unsuspected bonuses is that there are degeneracies in the way one can express the final result for the referred Feynman integral.

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Onboard and real-time artificial satellite orbit determination using GPS

An algorithm for real-time and onboard orbit determination applying the Extended Kalman Filter (EKF) method is developed. Aiming at a very simple and still fairly accurate orbit determination, an analysis is performed to ascertain an adequacy of modeling complexity versus accuracy. The minimum set of to-be-estimated states to reach the level of accuracy of tens of meters is found to have at least the position, velocity, and user clock offset components. The dynamical model is assessed through several tests, covering force model, numerical integration scheme and step size, and simplified variational equations. The measurement model includes only relevant effects to the order of meters. The EKF method is chosen to be the simplest real-time estimation algorithm with adequate tuning of its parameters. In the developed procedure, the obtained position and velocity errors along a day vary from 15 to 20 m and from 0.014 to 0.018 m/s, respectively, with standard deviation from 6 to 10 m and from 0.006 to 0.008 m/s, respectively, with the SA either on or off. The results, as well as analysis of the final adopted models used, are presented in this work. © 2013 Ana Paula Marins Chiaradia et al.

Mobilidade asteroidal induzida por encontros próximos com vários asteroides massivos

Pós-graduação em Física - FEG

Análise da estabilidade de sistemas dinâmicos periódicos usando Teoria de Sinha

Pós-graduação em Matemática - IBILCE

Metodologia dos observadores de estado para diagnose de falhas em sistemas contendo elementos finitos de placas de Kirchoff

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

ANALYSIS OF CURVED EDGE PLATES BY THE BOUNDARY-ELEMENT METHOD

The aim of this work is to present a formulation of the boundary element method to analyse elastic and isotropic plates with curved boundaries. In this study the plate boundary is approximated, along each element, by a second degree polynomial relation or by a circular arch, in order to better represent the real boundary. The numerical integration is performed by the self-adaptive coordinate transformation proposed by Telles. The effective shear forces are approximated by concentrated reactions applied at the boundary element nodes, according to the alternative formulation introduced by Paiva. Some examples are presented to demonstrate the better accuracy obtained with the proposed elements.

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)