Topological description of periodic structures of an asymmetric nonlinear oscillator

The bifurcation structure of periodic solutions of a harmonically driven asymmetric nonlinear oscillator (Rayleigh–Plesset equation, describing bubble dynamics) is examined. The control parameters were the amplitude and frequency of the driving with frequency values higher than the subharmonic resonance frequency of the system. In the investigated parameter region, the endoskeleton of the bifurcation structure, composed by solutions with low periodicities, can be described by an asymmetric Farey-ordering tree. To each periodic domain, a sub-structure can be associated created by period-n tupling processes, whose topology are governed by a two-sided symmetric Farey tree. Higher order sub-structures apparently exhibit self-similar features

The use of Poisson regression in the sociological study of suicide

This paper explains how Poisson regression can be used in studies in which the dependent variable describes the number of occurrences of some rare event such as suicide. After pointing out why ordinary linear regression is inappropriate for treating dependent variables of this sort, we go on to present the basic Poisson regression model and show how it fits in the broad class of generalized linear models. Then we turn to discussing a major problem of Poisson regression known as overdispersion and suggest possible solutions, including the correction of standard errors and negative binomial regression. The paper ends with a detailed empirical example, drawn from our own research on suicide

Two-Parameter Bifurcation Analysis for the Seeking of High Amplitude Oscillation of a Periodically Driven Gas Bubble in Glycerine

The dynamics of a harmonically driven spherical gas/vapour bubble has been studied intensely in the last decades. The collapse of a bubble induce extreme conditions, such as high pressure and temperature or even shock waves. The ultrasonic technology exploit these conditions in various fields of industry, for example, ultrasonic pasteurization, alteration of the viscosity of thixotropic fluids, production of new kind of copolymers, or in cancer therapy. The present study intends to aid the applications through the numerical investigation of a harmonically excited spherical gas bubble placed in the highly viscous glycerine. We seek parameter regions where the bubble wall velocities as high as possible, perhaps even higher than the sound speed in the liquid domain. Such kind of high amplitude, collapse-like radial oscillations are difficult to find due to the very high viscosity, which is approximately three orders of magnitude greater than of water. The two investigated parameters were the pressure amplitude and the frequency of the harmonic forcing. The applied model was the Keller—Miksis equation, which is a second order nonlinear ordinary differential equation, describing the bubble wall motion and taking into account liquid compressibility as a first order approximation

Energy Dissipation and Chemical Yield of an Ultrasound Driven Single Bubble

A detailed parameter study is made of chemically active spherical bubbles. The calculations apply an up-to-date chemical mechanism for pure oxygen initial content, taking into account pressure dependency, duplication of chemical reactions, and proper third-body efficiency coefficients. The chemical yield is defined as the amount of substance at the maximum bubble radius, and the dissipated power is approached in a relatively new method. The parameter study focuses on finding the parameter combinations where maximum yield and maximum energy efficiency arise for various chemical species (O3, OH radical, H2 and H2O2). Results show that the locations of maximum yield and efficiency points differ significantly, depending on the chemical species. Usually, neither chemical yield nor efficiency values arise at maximum pressure amplitude and minimum driving frequency (as one would presumably expect)

Condition Monitoring of Centrifugal Pumps Based on Pressure Measurements

The purpose of the present study is the investigation of condition of centrifugal pumps via pressure signals. Instead of vibration measurement on the housings that is widely used in industry, our method is based on pressure signal measurement on the pressure side of the pump. Fourier transforming such a signal can get us to make conclusions about the behavior of the pump. By changing the operating point along a characteristic curve, we can create waterfall diagrams that provide useful information about the pump at constant rotational speed. For example, it is possible to differentiate the mechanical and the hydrodynamical effects predicting the occurrence of many constructional failures (such as unbalance, angular misalignment, bearing misalignment, motor instability, etc.); thus, preventing heavy damage of the equipment