One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.

On some Properties of Boolean Functions and Their Binary Decision Diagrams

Иво Й. Дамянов - Манипулирането на булеви функции е основнo за теоретичната информатика, в това число логическата оптимизация, валидирането и синтеза на схеми. В тази статия се разглеждат някои първоначални резултати относно връзката между граф-базираното представяне на булевите функции и свойствата на техните променливи.

Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers

Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels. © 2010 The American Physical Society.

Bifurcation and dynamic response analysis of a rotating blade excited by upstream vortices

Acknowledgements The authors acknowledge the projects supported by the National Basic Research Program of China (973 Project)(No. 2015CB057405) and the National Natural Science Foundation of China (No. 11372082) and the State Scholarship Fund of CSC. DW thanks for the hospitality of the University of Aberdeen.

Étude du diagramme de bifurcation d'un système prédateur-proie

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Étude du diagramme de bifurcation d'un système prédateur-proie

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Automated Equation Formulation for Causal Loop Diagrams

The annotation of Business Dynamics models with parameters and equations, to simulate the system under study and further evaluate its simulation output, typically involves a lot of manual work. In this paper we present an approach for automated equation formulation of a given Causal Loop Diagram (CLD) and a set of associated time series with the help of neural network evolution (NEvo). NEvo enables the automated retrieval of surrogate equations for each quantity in the given CLD, hence it produces a fully annotated CLD that can be used for later simulations to predict future KPI development. In the end of the paper, we provide a detailed evaluation of NEvo on a business use-case to demonstrate its single step prediction capabilities.

Studies on terpenes solubility in water and deep eutectic solvents diagrams for biomedical applications

The main objectives of this work are the measurement of terpenes solubility in water at different temperatures, and the formulation of Deep Eutectic Solvents based on choline chloride and polycarboxylic acids, that can be used as hydrotropes of aqueous solutions in terpenes, replacing conventional organic solvents. In this work a new experimental methodology was implemented, using dialysis membranes, for the measurement of terpenes solubility in water. Concerning the deep eutectic diagrams formulation, the determination of the melting points of the eutectic mixtures was performed using a visual method. The method used for determining solubilities was previously validated using a well-studied model compound, toluene. The experimental results of terpenes solubilities in water resulted in a very satisfactory coefficients of variation, always below 6%. The experimental solubility data were analysed and the temperature dependence is also studied in a thermodynamic perspective. The compound with the largest solubility dependence with the temperature is geraniol, while thymol presents the smallest. The phase diagrams of DES formulated were quite satisfactory, presenting always eutectic points below to 373.15 K. For some compositions, the systems composed by choline chloride and lactic, or malonic, or myristic acid were liquid at room temperature. In the case of monocarboxylic acids, eutectic is formed at 60% mol of the acid, to dicarboxylic acid is formed at 50% mol of the acid and for tricarboxylic acid these point is formed at 30% mol of the acid. In the future, it will be important to study the effect of DES as hydrotropes in aqueous solutions of terpenes. Furthermore, it would be interesting to study more terpenes in order to assess the effect of the size of the alkyl chain and the structures of the compounds.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

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.

The manual of chess: containing the elementary principles of the game; illustrated with numerous diagrams, recent games and original problems.

Mode of access: Internet.

Kissing stenting of aortic bifurcation for aorto-iliac obstructive disease: a comparison between bare metal stents and covered stents

INTRODUCTION Aim of this multicentric study:to compare the short-and mid-term results of bare metal stents(BMS)and covered stents(CS)in the Kissing Stent(KS)technique. METHODS Patients undertaking a KS with BMS or CS between January 2017-August 2021 included. Morphological features of plaques were classified as per the extension of calcifications and thrombosis. Every endpoint and outcome was compared in relation to BMS or CS. All patients included received dual anti-platelets DAPT)for at least one month. RESULTS Thirty-four patients enrolled,17 treated with BMS and 17 with CS. Average age 66 years. The 80% of patients were part of TASC C-D categories. DAPT was administered to 82.4%(28/34)of patients with a mean duration of 4.4±1.6 months. Mean follow-up 32.1±17.8 months. Technical Success was 100%. Immediate Clinical Success was reached in 29 cases(85.3%). Immediate and 30-day Clinical Success was higher in CS(64.7% vs 100%, p=.01). Overall Clinical Success at 1-year follow-up was 91.2%,and resulted significantly higher in CS(82.4% vs 100%,p .04). Overall Primary Patency,Assisted Patency,and Secondary Patency at 30 days were 97.1%,97.1%,and 100%,without differences between BMS and CS(94.1% vs 100%,94.1% vs 100%,and 100% vs 100%;p =.7). Two cases(5.9%)of thrombosis were registered,and both occurred within 3 months after the procedure and both in the BMS,without statistical differences with the CS group(11.8% vs 0%,p .48). Both cases of thrombosis occurred in patients who were not treated with dual antiplatelet therapy(33.3% vs 0%,p .027). Survival statistically differed only at the mean follow-up in favour of CS(70.6% and 100%,p .04). CONCLUSIONS The endovascular approach is currently safe and effective in the treatment of AIOD,and KS offers excellent results in particular if performed with CS; however,no statistically significant differences emerged between the two types of stents in terms of patency,reintervention,and complications. DAPT seems to warrant the best results in terms of patency,although there is still no consensus about the ideal duration of administration.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.