Precision of yule-walker methods for the arma spectral model

In this work a new method is proposed of separated estimation for the ARMA spectral model based on the modified Yule-Walker equations and on the least squares method. The proposal of the new method consists of performing an AR filtering in the random process generated obtaining a new random estimate, which will reestimate the ARMA model parameters, given a better spectrum estimate. Some numerical examples will be presented in order to ilustrate the performance of the method proposed, which is evaluated by the relative error and the average variation coefficient.

Modifying the stochastic model to mitigate GPS systematic errors in relative positioning

The GPS observables are subject to several errors. Among them, the systematic ones have great impact, because they degrade the accuracy of the accomplished positioning. These errors are those related, mainly, to GPS satellites orbits, multipath and atmospheric effects. Lately, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique (PLS). In this method, the errors are modeled as functions varying smoothly in time. It is like to change the stochastic model, in which the errors functions are incorporated, the results obtained are similar to those in which the functional model is changed. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method (CLS). In general, the solution requires a shorter data interval, minimizing costs. The method performance was analyzed in two experiments, using data from single frequency receivers. The first one was accomplished with a short baseline, where the main error was the multipath. In the second experiment, a baseline of 102 km was used. In this case, the predominant errors were due to the ionosphere and troposphere refraction. In the first experiment, using 5 minutes of data collection, the largest coordinates discrepancies in relation to the ground truth reached 1.6 cm and 3.3 cm in h coordinate for PLS and the CLS, respectively, in the second one, also using 5 minutes of data, the discrepancies were 27 cm in h for the PLS and 175 cm in h for the CLS. In these tests, it was also possible to verify a considerable improvement in the ambiguities resolution using the PLS in relation to the CLS, with a reduced data collection time interval. © Springer-Verlag Berlin Heidelberg 2007.

Interaction between wave and coastal structure: Validation of two lagrangian numerical models with experimental results marine 2011

Numerical modeling of the interaction among waves and coastal structures is a challenge due to the many nonlinear phenomena involved, such as, wave propagation, wave transformation with water depth, interaction among incident and reflected waves, run-up / run-down and wave overtopping. Numerical models based on Lagrangian formulation, like SPH (Smoothed Particle Hydrodynamics), allow simulating complex free surface flows. The validation of these numerical models is essential, but comparing numerical results with experimental data is not an easy task. In the present paper, two SPH numerical models, SPHysics LNEC and SPH UNESP, are validated comparing the numerical results of waves interacting with a vertical breakwater, with data obtained in physical model tests made in one of the LNEC's flume. To achieve this validation, the experimental set-up is determined to be compatible with the Characteristics of the numerical models. Therefore, the flume dimensions are exactly the same for numerical and physical model and incident wave characteristics are identical, which allows determining the accuracy of the numerical models, particularly regarding two complex phenomena: wave-breaking and impact loads on the breakwater. It is shown that partial renormalization, i.e. renormalization applied only for particles near the structure, seems to be a promising compromise and an original method that allows simultaneously propagating waves, without diffusion, and modeling accurately the pressure field near the structure.

Ergodic crossover in partially self-avoiding stochastic walks

Consider a one-dimensional environment with N randomly distributed sites. An agent explores this random medium moving deterministically with a spatial memory μ. A crossover from local to global exploration occurs in one dimension at a well-defined memory value μ1=log2N. In its stochastic version, the dynamics is ruled by the memory and by temperature T, which affects the hopping displacement. This dynamics also shows a crossover in one dimension, obtained computationally, between exploration schemes, characterized yet by the trajectory size (Np) (aging effect). In this paper we provide an analytical approach considering the modified stochastic version where the parameter T plays the role of a maximum hopping distance. This modification allows us to obtain a general analytical expression for the crossover, as a function of the parameters μ, T, and Np. Differently from what has been proposed by previous studies, we find that the crossover occurs in any dimension d. These results have been validated by numerical experiments and may be of great value for fixing optimal parameters in search algorithms. © 2013 American Physical Society.

Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

Numerical study of the Ginzburg-Landau-Langevin equation: coherent structures and noise perturbation theory

Pós-graduação em Física - IFT

Método do hamiltoniano termodinamicamente equivalente para sistemas de muitos corpos

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

A Numerical Study of the FENE-CR Model Applied to a Jet Flow Problem

The FENE-CR model is investigated through a numerical algorithm to simulate the time-dependent moving free surface flow produced by a jet impinging on a flat surface. The objective is to demonstrate that by increasing the extensibility parameter L, the numerical solutions converge to the solutions obtained with the Oldroyd-B model. The governing equations are solved by an established free surface flow solver based on the finite difference and marker-and-cell methods. Numerical predictions of the extensional viscosity obtained with several values of the parameter L are presented. The results show that if the extensibility parameter L is sufficiently large then the extensional viscosities obtained with the FENE-CR model approximate the corresponding Oldroyd-B viscosity. Moreover, the flow from a jet impinging on a flat surface is simulated with various values of the extensibility parameter L and the fluid flow visualizations display convergence to the Oldroyd-B jet flow results.

Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

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