American Journal of Physics Goes Online

Numerical and experimental study of a double physical pendulum with magnetic interaction

The aim of this work is to evaluate the dynamics of the quasi-zero stiffness vibration isolator, with particular emphasis on the density distribution of Poincare cross-section points for different conditions of the system's excitation. The research was mainly focused on model tests carried out to examine the structures representing the geometry of strange attractors of a quasi-zero stiffness vibration isolator. The analysed mechanical system consists of one main spring and two compensation springs. Energy losses are caused by friction at the connection points of the compensation springs and vibroisolated mass. On the basis of a formulated non-linear mathematical model, the ranges of variation of physical parameters of an external dynamic input for which the system motion is chaotic are identified. Taking into account three selected values of the dynamic input amplitude, a bifurcation diagram and a diagram defining the number of phase stream intersections (NPSI) with the abscissa of the phase plane are generated. Based on the diagrams, a solution is selected. The diagram proposed by us (NPSI) is an alternative method of identifying areas in which the system moves chaotically. The classic Poincare cross-section combined by us with information about the density of point distribution on the trajectory intersection with the control plane serve as a basis for the assessment of evolution of the geometric structure of strange attractors. The evaluation of the density distribution of Poincare cross-section points provides important information regarding the evolution of geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. However, in the area of small changes in the control parameter, the evolution of the attractor’ geometric structure can only be observed by analysing the density of point distribution on the Poincare cross-section by the probability density function (PDF). The areas with the highest density of the Poincare cross-section are usually located in places where the strange attractor is curved. Taking into account the practical application of research results, operational guidelines are formulated.

Evolution of the geometric structure of strange attractors of a quasi-zero stiffness vibration isolator

Theoretical and numerical analysis of regular one-side oscillations in a single pendulum system driven by a magnetic field

Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

Vortex Interactions Subjected to Deformation Flows: A Review

Parametric resonance induced chaos in magnetic damped driven pendulum

The policy of stimulating regional development is based on local potential, one of the main components of which is population: its number, nature of reproduction, structure, and social-economic conditions (employment, standard of living, and so on).The present research aimed to study the issues of Georgia's demographic potential: population dynamics, natural movement, migration, gender and age structure, labour force, and standard of living of the population. The study of the demographic potential of Georgia is a long-term task of the authors, the first geographical object of which is the study area of ​​the present article - eastern Georgia and, in particular, the regions of Kakheti, Mtskheta-Mtianeti, Kvemo Kartli (not including Tbilisi, the capital of Georgia, but including self-governing city Rustavi) and Shida Kartli. The research adopts a geographical approach, focusing on a unified vision of the issue, and studies regional differences. The research results outline the demographic situation in the study area and the modern trends that reflect the peculiarities of the demographic potential of eastern Georgia. These include the following: a) the decline in the absolute number of population has slowed down in the last decade due to reduced emigration; b) according to the latest statistics, in eastern Georgia as a whole, natural increase is negative (-0.4 percent), but higher than the national average (-1.1%); c) the process of population ageing in eastern Georgia has been generally outlined, the dynamics of which are different between the regions - in Kvemo Kartli, due to the relatively high natural increase, it is developing relatively slowly than in other regions; d) the share of women in gender structure is reduced (50.9 percent) compared to the country's average rate (52.3 percent), while in Mtskheta-Mtianeti, contrary to the general rule, The share of men exceeds that of women; d) Georgians make up 75 percent of the ethnic structure of the study region, followed by Azerbaijanis (19.7 percent), the principal part of the latter concentrated in Kvemo Kartli, which, in, turn, determines a number of peculiarities of the demographic behaviour of the population in this region; e) a large part of the population of eastern Georgia is mostly employed in traditional, non-commercial and partly commercial agriculture, due to which a higher share of self-employed (41.6 percent) was registered in the study area compared to the average in the country (31.9 percent); f) unemployment (18 percent of the economically active population), low income and low purchasing power remain the main social-economic issues. In the last decade, as in the whole of Georgia, signs of improvement were noted in the social-economic situation in the study area, though the COVID-19 pandemic partially slowed this trend.

Giorgi Khomeriki

Papers

Parametric resonance induced chaos in magnetic damped driven pendulum

Demographic Issues of Social-Economic Development of Eastern Georgia: Population as a Demographic Potential