Very-small-aperture 3D infrasonic array for volcanic jet observation at Stromboli Volcano

Summary This study tested a very-small-aperture three-dimensional (VSA-3D) infrasonic array. A 3D array is ideal for resolving the back elevation angle (BEL), which has become important in the analysis of volcanic jet noise or geologic flows on steep mountain slopes. Although a VSA infrasonic array, with an aperture as small as a few tens of meters, has recently been shown to have a sufficient resolution of the back azimuth (BAZ) of incident signals, its BEL resolution is considered to be poor. We performed a four-element 3D array experiment with a 20-m aperture and 2-m height at the summit of Stromboli Volcano. We analyzed the direction of arrival (DOA) with the MUSIC algorithm as a function of frequency and conducted a cluster analysis for the estimated DOA–frequency functions of eruption signals. As a result, individual infrasonic signals were successfully related to eruptive vents. We also calculated the standard deviation (STD) of the DOAs in each cluster. Of the observed BAZ-STDs and BEL-STDs, 80 per cent were <2.0° and <4.6°, respectively. A comparison among the array geometries showed that the installation of a sensor above the ground, even at only 2 m, improved the BEL resolution, indicating that the VSA-3D array provides more detailed information about the wavefield than a planar array. The observed signals had higher BELs (−20° to 0°) than the vent direction (−30° to −25°) at 3–6 Hz, although signals above 20 Hz arrived from the vent direction. Our array verified that such DOA deviations were significant by the STD analysis and some tests with synthetic data. We infer that the DOA deviations do not indicate the source location and are caused by topographical diffraction.

Possibilities of Using Frequency Energy Functions in Problems of Dynamics of Machines for Transport and Technological Purposes

New approaches to the evaluation of the dynamic properties of mechanical vibration systems are proposed, which consider as the design schemes for technical objects operating under dynamic vibration loads. The purpose of the study is to develop ideas for the use of frequency energy functions. In this case, the frequency functions represent the ratio of the potential and kinetic energies in a specific form, based on the use of the relations of the coordinates of the system in the stationary mode. The technologies of system analysis and structural mathematical modeling are used. In this approach, the mechanical oscillatory system is correspond with the block diagram of the automatic control system, which is equivalent in dynamic terms. It is proposed to use the analytical apparatus to take into account the features of interpartial relations, to evaluate the specific modes of dynamic interaction of system elements. A method for determining the natural vibration frequencies of the system based on the use of the frequency energy function is proposed. Methodological bases of approaches to solving problems of system dynamics related to the assessment of the influence of system parameters on their frequency properties are developed. The results of computational modeling are presented.

Features of the system concepts of the dynamics of mechanical vibrational structures under asymmetric connections

The paper is devoted to a new approach to the formation of the methodological basis of system analysis in application to problems of the dynamics of mechanical oscillatory systems taking into account the forces of viscous friction. A mechanical oscillatory system with two mass-inertia elements connected to the support surfaces and to each other by elastic-dissipative elements is considered. A method for estimating the free movements of a mechanical oscillatory system is developed based on the characteristics expressed in terms of the parameters of the lever connections between the partial blocks in the form of a gear ratio. Mathematical models are built on the basis of Lagrange formalism, algebraic methods, and the theory of functions of a complex variable. A matrix method is proposed for constructing frequency functions and damping functions for mechanical oscillatory systems with two degrees of freedom based on the ratio of the potential and kinetic energy of the system, taking into account the forces of viscous friction. For a mechanical system in which the connection of elements with a single reference surface is reset, a graphic analytic analysis of the extreme properties of the corresponding frequency functions and damping functions is performed. A topological approach is proposed.

SYSTEM REPRESENTATIONS OF DYNAMIC PROCESSES IN MECHANICAL OSCILLATORY SYSTEMS WITH SPECIAL FEATURES

Рассматриваются подходы в формировании методологического базиса системного анализа колебательных структур на примере упруго-диссипативных механических систем с двумя степенями свободы. Целью исследования является разработка метода оценки свойств механических колебательных систем с учетом сил вязкого трения на основе частотных функций и функции демпфирования в зависимости от коэффициентов форм связности. Для построения математических моделей используется формализм Лагранжа, матричные методы, элементы теории функций комплексной переменной. Представлены понятия частотной функции и функции демпфирования, отражающие особенности соотношения потенциальной, кинетической энергии системы с учетом сил вязкого трения, представленных диссипативной функцией. Разработан метод построения частотной функции и функции демпфирования, отражающих динамические особенности свободных движений с учетом сил трения в зависимости от коэффициента форм связности. На основе полученных общих аналитических выражений частотных функций и функций демпфирования проведен анализ особенных вариантов механических колебательных систем, представляющих интерес на начальном этапе исследования. Разработанный метод построения частотной функции и функции демпфирования может быть использован для отображения динамических форм связности движений механических колебательных систем. Предложенный метод построения частотной функции и функции демпфирования может быть обобщен на механические колебательные системы, рассматриваемые в различных системах координат. Approaches to the formation of a methodological basis for the system analysis of oscillatory structures on the example of elastic-dissipative mechanical systems with two degrees of freedom are considered. The aim of the study is to develop a method for evaluating the properties of mechanical oscillatory systems with account for viscous friction forces based on frequency functions and damping functions depending on the coefficients of connectivity forms. To build mathematical models, we use Lagrange formalism, matrix methods, and elements of the theory of functions of a complex variable. The concepts of the frequency function and the damping function are presented, which reflect the features of the ratio of the potential and kinetic energy of the system, taking into account the viscous friction forces represented by the dissipative function. A method is developed for constructing the frequency function and damping function that reflect the dynamic features of free movements, taking into account the friction forces depending on the coefficient of connectivity forms. Based on the obtained General analytical expressions of frequency functions and damping functions, special variants of mechanical oscillatory systems that are of interest at the initial stage of research are analyzed. The developed method for constructing the frequency function and the damping function can be used to display dynamic forms of connectivity of movements of mechanical oscillatory systems. The proposed method for constructing the frequency function and the damping function can be extended to mechanical oscillatory systems considered in different coordinate systems.

An adaptive Gaussian quadrature for the Voigt function

We evaluate an adaptive Gaussian quadrature integration scheme suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for “full non-LTE” radiation transfer computations, assuming potential deviations of the velocity distribution of massive particles from the usual Maxwell–Boltzmann distribution. A first validation is made with computations of the usual Voigt profile.

Conventional vs. Convolutional Windows for Reduction of Side Lobes

Convolutional windows analysis and performance comparison with traditional windows is main intent of the present paper. Convolutional windows are formed by convoluting the window by itself. These new class of windows are applied to a pseudo-LFM signal designed by using two stage piece wise linear frequency functions. Simulations were performed for the designed LFM signal with both the traditional and convolutional window functions are is observed that the convolutional windows yield better peak to side lobe level ratio (PSLR) values compared to traditional windows.

Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann’s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation–fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.