Passing through resonance of the unbalanced rotor with self-balancing device

The slow dynamics of unbalanced rotors with a passive self-balancing system are investigated considering the interaction of the mechanical system with a limited power engine. The slow dynamics equations are obtained using the averaging technique for partially strongly damped systems. Stationary system configurations, different types of nonstationary solutions while passing through resonance, and areas of stability and attraction are investigated.

Differentiation of kinematics of the Dnister HPP-1 dam (based on the data of GNSS monitoring of spatial displacements)

The purpose of study is to generalize the vertical displacements of the GNSS network of spatial monitoring of the Dnister HPP-1 dam for the differentiation of its kinematics as well as to evaluate the impact of short-term geodynamic processes in the region. Object of study. The object of the study is the monitoring of the Dniester HPP-1 dam according to the GNSS network data of the stationary system for monitoring the spatial displacement of structures (SSMSDS) of the Dniester HPP-1. The basis of the Dnister SSMSDS are two base GNSS stations additionally equipped with a robotic total station, which are installed on a strong foundation and located at a distance of several hundred meters from the dam. There are control points equipped with a GNSS receiver, antenna and an angle reflector with a 3600 viewing angle on the crest of the dam. The results of GNSS measurements are transmitted to the Leica GNSS Spider software, which processes and determines the coordinates of the base and control points. The GEOMOS software performs a joint estimation of GNSS results and linear-angular measurements. Methodology. To generalize the displacements of GNSS stations of Dnister HPP-1 the method of statistical analysis of time series is used. Authors examine the covariance interrelationships between all GNSS stations of the stationary system for monitoring the spatial displacement of structures (SSMSDS) of the Dnister HPP-1, which are placed on the dam based on the results of measurements from 1.07.2017 to 31.03.2021. For the selected periods of anomalous short-term displacements, the average values of covariance for each GNSS station are calculated. Results. During the period from 1.07.2017 to 31.03.2021 and according to the results of covariance interrelation for most GNSS stations, 3 epochs of anomalous altitude displacements are established (T = 2017.8 ± 0.1, T = 2019.0 ± 0.1, T = 2019.4 ± 0.1). Based on the covariance analysis, it was found that for periods of anomalous vertical displacements, the kinematics of the GNSS station MP01 differs significantly from the kinematics of GNSS stations MP02-MP05. The kinematics of GNSS-stations MP02-MP05 is constant, which indicates the anomalous movement of the unit on which the GNSS-station MP01 is installed in relation to the other blocks of the dam of the Dnister HPP-1. Scientific novelty and practical significance. Authors proposed the method for studying the geodynamics possesses of large industrial areas covered by a network of GNSS stations. Based on the GNSS measurements the periods of anomalous displacement are reveled and further search for spatial kinematic interrelationships between pair of GNSS stations is established. The developed methodology can be used to differentiate the kinematics of structural elements with installed GNSS stations such as engineering structures, industrial areas, geodynamic polygons.

ON A BOUNDARY VALUE PROBLEM FOR ONE OVERDETERMINED SYSTEM IN A HALF-PLANE

This paper considers a boundary value problem for an overdetermined system of equations in a half-plane. This problem arises in particular when solving a stationary system of the two-velocity hydrodynamics with one pressure and homogeneous divergent conditions and the Dirichlet boundary conditions for two phase velocities, as well as in problems of electrodynamics. The generalized solution to a stationary system of the two-velocity hydrodynamics in the case of two-dimensional unbounded domains, for instance, in a half-plane, has a significant difference from the three-dimensional case. Namely, in the two-dimensional case for the velocities it is impossible to satisfy the pre-set conditions at infinity and the condition of boundedness at infinity is imposed. In this case, the medium is considered to be homogeneous, and the energy dissipation occurs due to the shear viscosities of the phases of the subsystems, and other effects are not discussed in this paper. The mass transfer occurs due to the mass force. With an appropriate choice of functional spaces, the existence and uniqueness of a generalized solution with an appropriate stability estimate has been proved.

The importance of ecosystem adaptation on hydrological model predictions in response to climate change

To predict future hydrological behavior in a changing world, often use is made of models calibrated on past observations, disregarding that hydrological systems, hence model parameters, will change as well. Yet, ecosystems likely adjust their root-zone storage capacity, which is the key parameter of any hydrological system, in response to climate change. In addition, other species might become dominant, both under natural and anthropogenic influence. In this study, we propose a top-down approach, which directly uses projected climate data to estimate how vegetation adapts its root-zone storage capacity at the catchment scale in response to changes in magnitude and seasonality of hydro-climatic variables. Additionally, the Budyko characteristics of different dominant ecosystems in sub-catchments are used to simulate the hydrological behavior of potential future land-use change, in a space-for-time exchange. We hypothesize that changes in the predicted hydrological response as a result of 2 K global warming are more pronounced when explicitly considering changes in the sub-surface system properties induced by vegetation adaptation to changing environmental conditions. We test our hypothesis in the Meuse basin in four scenarios designed to predict the hydrological response to 2 K global warming in comparison to current-day conditions using a process-based hydrological model with (a) a stationary system, i.e. no changes in the root-zone storage capacity of vegetation and historical land use, (b) an adapted root-zone storage capacity in response to a changing climate but with historical land use, and (c, d) an adapted root-zone storage capacity considering two hypothetical changes in land use from coniferous plantations/agriculture towards broadleaved forest and vice-versa. We found that the larger root-zone storage capacities (+34 %) in response to a more pronounced seasonality with drier summers under 2 K global warming strongly alter seasonal patterns of the hydrological response, with an overall increase in mean annual evaporation (+4 %), a decrease in recharge (−6 %) and a decrease in streamflow (−7 %), compared to predictions with a stationary system. By integrating a time-dynamic representation of changing vegetation properties in hydrological models, we make a potential step towards more reliable hydrological predictions under change.