This paper summarizes the activity of the chosen Polish geodetic research teams in 2015–2018 in the fields of Earth: rotation, dynamics as well as magnetic field. It has been prepared for the needs of the presentation on the 27th International Union of Geodesy and Geodynamics General Assembly, Montreal, Canada. The part concerning Earth rotation is mostly focused on the use of modelling of diurnal and subdiurnal components of Earth rotation by including low frequency components of polar motion and UT1 in the analysis, study of free oscillations in Earth rotation derived from both space-geodetic observations of polar motion and the time variation of the second degree gravitational field coefficients derived from Satellite Laser Ranging (SLR) and Gravity Recovery and Climate Experiment (GRACE) observations, new methods of monitoring of Earth rotation, as well as studies on applications of the Ring Laser Gyroscope (RLG) for direct and continuous measurements of changes in Earth rotation and investigations of the hydrological excitation of polar motion. Much attention was devoted to the GRACE-derived gravity for explaining the influence of surface mass redistributions on polar motion. Monitoring of the geodynamical phenomena is divided into study on local and regional dynamics using permanent observations, investigation on tidal phenomena, as well as research on hydrological processes and sea level variation parts. Finally, the recent research conducted by Polish scientists on the Earth’s magnetic field is described.

Template matching is a process to identify and localize a template image on an original image. Several methods are commonly used for template matching, one of which uses the Fourier transform. This study proposes a modification of the method by adding an improved rotation to the Fourier transform. Improved rotation in this study uses increment rotation and three shear methods for the template image rotation process. The three shear rotation method has the advantage of precise and noisefree rotation results, making the template matching process even more accurate. Based on the experimental results, the use of 10°angle increments has increased template matching accuracy. In addition, the use of three shear rotations can improve the accuracy of template matching by 13% without prolonging the processing time.

This paper deals with an issue of a rotational motion impact on a construction and presents civil engineering applications of a fiber optic rotational seismograph named Fiber-Optic System for Rotational Events & Phenomena Monitoring. It has been designed for a long- term building monitoring and structural rotations’ recording. It is based on the Sagnac effect which enables to detect one-axis rotational motion in a direct way and without any reference system. It enables to detect a rotation component in the wide range of a signal amplitude from 10-8 rad/s to 10 rad/s, as well as a frequency from DC to 1000 Hz. Data presented in this paper show the behavior of a reinforced concrete frame construction on different floors. Several measurements were carried out by placing the applied sensor on different floor levels of a building. The laboratory and in-situ measurements confirmed that Fiber-Optic System for Rotational Events & Phenomena Monitoring is an accurate and suitable device for applications in civil engineering.

This paper presents the summary of research activities carried out in Poland in 2011–2014 in the field of Earth rotation and geodynamics by several Polish research institutions. It contains a summary of works on Earth rotation, including evaluation and prediction of its parameters and analysis of the related excitation data as well as research on associated geodynamic phenomena such as geocentre motion, global sea level change and hydrological processes. The second part of the paper deals with monitoring of geodynamic phenomena. It contains analysis of geodynamic networks of local, and regional scale using space (GNSS and SLR) techniques, Earth tides monitoring with gravimeters and water-tube hydrostatic clinometer, and the determination of secular variation of the Earth’ magnetic field.

The model of the equations of generalized thermoelasticity in a semi-conducting medium with two-temperature is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under Lord-Schulman theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the considered variables. Also some particular cases are discussed in the context of the problem. Numerical results for the considered variables are obtained and illustrated graphically. Comparisons are also made with the results predicted in the absence and presence of rotation as well as two-temperature parameter.

The paper presents a method of measuring the angle of rotation and twist using a tilted fibre Bragg grating

(TFBG) periodic structure with a tilt angle of 6◦, written into a single-mode optical fibre. It has been shown

that the rotation of the sensor by 180◦ causes a change in the transmission coefficient from 0.5 to 0.84 at

a wavelength of 1541.2 nm. As a result of measurements it was determined that the highest sensitivity can

be obtained for angles from 30◦ to 70◦ in relation to the basic orientation. The change in the transmission

spectrum occurs for cladding modes that change their intensity with the change in the polarization of light

propagating through the grating. The same structure can also be used to measure the twist angle. The

possibility of obtaining a TFBG twist by 200◦ over a length of 10 mm has been proved. This makes it

possible to monitor both the angle of rotation and the twist of an optical fibre with the fabricated TFBG.

In the present article, we introduced a new model of the equations of general ized thermoelasticity for unbounded orthotropic body containing a cylindrical cavity. We applied this model in the context of generalized thermoelasticity with phase-lags under the effect of rotation. In this case, the thermal conductivity of the material is considered to be variable. In addition, the cylinder surface is traction free and subjected to a uniform unit step temperature. Using the Laplace transform technique, the distributions of the temperature, displacement, radial stress and hoop stress are determined. A detailed analysis of the effects of rotation, phase-lags and the variability thermal conductivity parameters on the studied fields is discussed. Numerical results for the studied fields are illustrated graphically in the presence and absence of rotation.

Receiver function provides the signature of sharp seismic discontinuities and the information about the shear wave (S−wave) velocity distribution beneath the seismic station. This information is very valuable in areas where any or few reflection and/or refraction studies are available and global and/or regional models give only rough information about the seismic velocities. The data recorded by broadband seismic stations have been analysed to investigate the crustal and upper mantle structure of the Svalbard Archipelago. Svalbard Archipelago is a group of islands located in Arctic, at the north−western part of the Barents Sea continental platform, which is bordered to the west and to the north by passive continental margins. The new procedure of parameterization and selection of receiver functions (RFs) has been proposed. The back−azimuthal sections of RF show a strong variation for the HSPB and KBS stations. Significant amplitudes of transversal component of RF (T−RF) for the HSPB station indicate a shallow dipping layer towards the southwest. The structure of the crust beneath the SPITS array seems to be less heterogeneous, with very low amplitudes of converted phase comparing to the KBS and HSPB stations. Forward modelling by trial−and−error method shows a division of the crust into 3–4 layers beneath all stations and layering of the uppermost mantle beneath the SPITS array and the HSPB stations. The thickness of the mantle transition zone is larger for western part of archipelago and smaller for eastern part comparing to iasp91 model.

A proper description of ground motions generated by seismic and paraseismic events requires gathering data of six components of seismic waves. T hree of them, the so called translational waves, are well researched and identified. Unfortunately, until recently, the remaining three components named as rotational waves were generally estimated with the use of indirect methods based on theoretical calculations. T his was related mostly with the lack of proper instruments for the recording of rotational seismic waves. T hus, rotational waves were not fully recognized thus far. Recently, several types of advanced instruments for direct measurements of rotation were invented. Based on the measurements of strong ground motions it was indicated that the amplitude of the rotational components in close distances from the seismic source can be significantly larger than expected. Apart from this, there is still a lack of analyses considering the characteristic of rotational seismic waves generated by induced seismic events. In this paper, the results of preliminary measurements of rotational motions generated by induced seismic waves were presented. Ground movements related with mining tremors were analyzed in terms of amplitude, frequency and duration.

The formation of optimal crop rotations is virtually unsolvable from the standpoint of the classical methodology of experimental research. Here, we deal with a mathematical model based on expert estimates of “predecessor-crop” pairs’ efficiency created for the conditions of irrigation in the forest-steppe of Ukraine. Solving the problem of incorporating uncertainty assessments into this model, we present new models of crop rotations’ economic efficiency taking into account irrigation, application of fertilisers, and the negative environmental effect of nitrogen fertilisers’ introduction into the soil. For the considered models we pose an optimisation problem and present an algorithm for its solution that combines a gradient method and a genetic algorithm. Using the proposed mathematical tools, for several possible scenarios of water, fertilisers, and purchase price variability, the efficiency of growing corn as a monoculture in Ukraine is simulated. The proposed models show a reduction of the profitability of such a practice when the purchase price of corn decreases below 0.81 EUR∙kg ^–1 and the price of irrigation water increases above 0.32 EUR∙m ^–3 and propose more flexible crop rotations. Mathematical tools developed in the paper can form a basis for the creation of decision support systems that recommend optimal crop rotation variations to farmers and help to achieve sustainable, profitable, and ecologically safe agricultural production. However, future works on the actualisation of the values of its parameters need to be performed to increase the accuracy.

The paper presents a study of Rotary Electrical Discharge Machining (REDM) process. In REDM, simple shaped cylindrical electrodes are used to generate 3D complex shapes. A theoretical model of machining process is described, which takes into consideration the effect of tool electrode wear on machined surface profile. The software for computer simulation of REDM has been developed. In the paper, the effects of machining parameters on shape error of machined surface are discussed. Results of computer simulation have been confirmed in experimental practice. The simulation model for NC contouring REDM may also be applied to solving numerical control problems and optimization of tool electrode path.

Rotational seismology is one of the fastest developing fields of science nowadays with strongly recognized significance. Capability of monitoring rotational ground motions represents a crucial aspect of improving civil safety and efficiency of seismological data gathering. The correct sensing network selection is very important for reliable data acquisition. This paper presents initial data obtained during the international research study which has involved more than 40 various rotational sensors collected in one place. The key novelty of this experiment was the possibility to compare data gathered by completely different rotational sensors during artificially generated ground vibrations. Authors collected data by four interferometric optical fiber sensors, Fiber-Optic System for Rotational Events & Phenomena Monitoring (FOSREM), which are mobile rotational seismographs with a wide measuring range from 10-7 rad/s up to even few rad/s, sensitive only to the rotational component of the ground movement. Presented experimental results show that FOSREMs are competitive in rotational events recording compared with the state-of-the-art rotational sensors but their operation still should be improved.

The contradiction between the restriction of grating manufacturing technology and high-resolution measurement requirements has been the focus of attention. The precision requirement of angle calculation during the digital subdivision processing of a Moiré signal is focused on, the causes of errors in the solution of arcsine function are analysed, and an improved coordinate rotation digital computer (CORDIC)with double-rotation iteration is proposed by discussing the principle of the conventional CORDIC in detail herein. Because the iterative number and data width of the improved CORDIC are limited by the finite digital circuit resources and thus determine the calculation accuracy directly, subsequently the overall quantization error (OQE) of the improved CORDIC is analysed. The approximate error and rounding error of the algorithm are deduced, and the error models of iterative number and data width are established. The validity and application value of the improved CORDIC are proved through simulations and experiments involving a subdividing circuit. The corresponding relation between the approximate error, rounding error and iteration number, as well as the bit width are proved by quantization. The error of subdivision with the improved CORDIC, obtained through a calibration experiment, is within ±0.5′′ and the mean variance is 0.2′′. The results of the research can be applied directly to a digital subdivision system to guide the parameter setting in the iterative process, which is of crucial importance in the quantitative analysis of error separation and error synthesis.

The bridge horizontal swivel system generally adopts a symmetrical structure and uses a spherical hinge structure that can adjust the rotation to complete rotation construction. Because of the complexity of railway lines under bridges, some asymmetrical horizontal swivel systems have been increasingly applied in practical engineering in recent years. This system is more suitable for areas with complex railway lines, reduces the bridge span, and provides better economic benefits. However, it is also extremely unstable. In addition, instability can easily occur under dynamic loads, such as earthquake action and pulsating wind effects. Therefore, it is necessary to study their mechanical behavior. Based on the horizontal swivel system of an 11,000-ton asymmetric continuous girder bridge, the dynamic response of the horizontal swivel system to seismic action was studied using the finite element simulation analysis method. Furthermore, using the Peer database, seismic waves that meet the calculation requirements are screened for time-history analysis and compared to the response spectrum method. The mechanical properties of the structural system during and after rotation were obtained through calculations. During rotation, the seismic response of the structure is greater. To reduce the calculation time cost, an optimization algorithm based on the mode shape superposition method is proposed. The calculation result is 87% that of the time-history analysis, indicating a relatively high calculation accuracy.

Preliminary results of laboratory and field tests of fibre optic rotational seismographs designed for rotational seismology are presented. In order to meet new directions of the research in this field, there is clearly a great need for suitable and extremely sensitive wideband sensors. The presented rotational seismographs based on the fibre optic gyroscopes show significant advantages over other sensor technologies when used in the seismological applications. Although the presented results are prepared for systems designed to record strong events expected by the so-called “engineering seismology”, the described system modification shows that it is possible to construct a device suitable for weak events monitoring expected by basic seismological research. The presented sensors are characterized, first and foremost, by a wide measuring range. They detect signals with amplitudes ranging from several dozen nrad/s up to even few rad/s and frequencies from 0.01 Hz to 100 Hz. The performed Allan variance analysis indicates the sensors main parameters: angle random walk in the range of 3 ∙ 10 ⁻⁸ - 2 ∙ 10 ⁻⁷ rad/s and bias instability in the range of 2 ∙ 10 ⁻⁹ - 2 ∙ 10 ⁻⁸ rad/s depending on the device. The results concerning the registration of rotational seismic events by the systems located in Książ Castle, Poland, as well as in the coalmine “Ignacy” in Rybnik, Poland were also presented and analysed.

The aim of performed research was to evaluate weed seedbank in soil under the influence of four different winter wheat tillage systems. Winter wheat was grown in the following cultivation systems: A – monoculture with direct drilling into white clover mulch; B – monoculture with direct drilling into wheat stubble; C – monoculture with conventional tillage; D – crop rotation with conventional tillage. It was shown that pre-sowing wheat tillage had a more considerable effect on weed species and weed seedbank in soil than type of crop rotation. The least seedbank was observed when plough system was replaced by direct drilling. In the soil layer of 0–20 cm, under wheat no-plough tillage, 20.3% less weed diaspores wasfound compared to monoculture with plough tillage and by 40.1% lessthan in crop rotation. The plough tillage increased amount of weed diaspores in the whole plough layer, while direct drilling increased it only in 0–1 cm of soil layer. After direct drilling of wheat into stubble (B) the number of weed diaspores in 1 dcm³ of soil in 0–1 cm layer was over twofold higher than in direct sowing in mulch (A), and threefold higher than in crop rotation (D) and almost six times higher than in wheat monoculture with conventional tillage (C). Dominating weed species in the soil over the types of wheat cultivation systems were: Chenopodium album L., Amaranthus retroflexus L., Apera spica-venti L., Lamium purpureum L., and Viola arvensis Murr.

In this paper, the problem of concentric pervious spheres carrying a fluid sink at their centre and rotating slowly with different uniform angular velocities Ω1. Ω2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists and the torque, rate of dissipated energy is found analytically in the present situation. The expression of torque on inner sphere rotating slowly with uniform angular velocity Ω1, while outer sphere also rotates slowly with uniform angular velocity Ω2, is evaluated. The special cases like, (i) inner sphere is fixed (i.e. Ω1 = 0), while outer sphere rotates with uniform angular velocity Ω2, (ii) outer sphere is fixed (i.e. Ω2 = 0), while inner sphere rotates with uniform angular velocity Ω1, (iii.) inner sphere rotates with uniform angular velocity Ω1, while outer rotates at infinity with angular velocity Ω2; have been deduced. The corresponding variation of torque with respect to sink parameter has been shown via figures. AMS subject classification – 76 D07.

Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

This paper summarizes the activity of the chosen Polish geodetic research teams in 2019–2022 in the fields of the Earth rotation and geodynamics. This publication has been prepared for the needs of the presentation of Polish scientists’ activities on the 28th International Union of Geodesy and Geodynamics General Assembly, Berlin, Germany. The part concerning Earth rotation is mostly focused on the estimation of the geophysical excitation of polar motion using data from Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) missions, and on the improvement of the determination of Earth rotation parameters based on the Satellite Laser Ranging (SLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and Global Navigation Satellite System (GNSS) satellite techniques. The part concerning geodynamics is focused on geodetic time series analysis for geodynamical purposes and monitoring of the vertical ground movements induced by mass transport within the Earth’s system, monitoring of the crustal movements using GNSS and newly applied Interferometric Synthetic Aperture Radar (InSAR), discussing the changes of the landslides and its monitoring using geodetic methods as well as investigations of seismic events and sea-level changes with geodetic methods. Finally, the recent research activities carried out by Polish scientists in the international projects is presented.

In this work, steady flow-field and heat transfer through a copper-water nanofluid around a rotating circular cylinder, dissipating uniform heat flux, with a constant non-dimensional rotation rate varying from 0 to 5 was investigated numerically using a finite-volume method for Reynolds numbers from the range 10–40. Furthermore, the range of nanoparticle volume fractions considered is 0–5%. The variation of the local and the average Nusselt numbers with Reynolds number, volume fractions, and rotation rate are presented for the range of conditions. The average Nusselt number is found to increase with increasing the nanoparticle volume fractions and decrease with increasing value of the rotation rate.

This paper presents new results for the dynamic behaviour of fluid around a rotating turbulator in a channel. The turbulator has a propeller form which is placed inside a flat channel. The research was carried out using 3D numerical simulation. The rationale of the experiment was as follows: we put a propeller-turbulator inside a flat channel, and then we insert a water flow inside the channel. The turbulator rotates at a constant and uniform speed. The main points studied here are the effect of the presence of turbulator and its rotational direction on the flow behaviour behind the turbulator. The results showed that the behaviour of flow behind the turbulator is mainly related to the direction of turbulator rotating. Also, the studied parameters affect coefficients of drag force and power number. For example, when the turbulator rotates in the positive direction, the drag coefficient decreases in terms of rotational speed of the turbulator, while the drag coefficient increases in terms of rotational speed when the turbulator rotates in the negative direction.

Straw, particularly cereal straw, is a valuable by-product of crop production, which can be used for various purposes, e.g. as livestock feed and bedding or for making fuels, however it should primarily be retained on farmland in order to prevent soil organic matter (SOM) losses and thus to maintain or improve soil quality. The aim of this study was to analyze effects of the frequency of crop residues (straw) incorporation into the soil on the content of soil organic matter and on crop yields. There were the following experimental treatments: SR – straw of all crop in the rotation removed, S1 – straw of one crop per rotation incorporated, S2 – straw of two crops in the rotation incorporated, and S3 – straw of three crops incorporated into the soil (loamy sand). After 21 years of crop rotation with straw removal (SR) the SOM level in the soil slightly decreased to 14.4 g∙kg ^–1 soil DM, compared to that in 1997 (14.6 g∙kg ^–1). However, when straw of one crop (rape) per rotation was incorporated (S1) the content of SOM increased to 15.0 g∙kg ^-1 soil DM, and to 15.6 and 16.0 g∙kg ^–1 in S2 and S3 treatments respectively. Straw retention had also a beneficial effect on the content of labile fractions of SOM (hot water extractable C and N). Grain yields and yield components of wheat and triticale, and seed yields of rape in the SR treatment were not significantly different from those obtained in S1, S2 and S3 treatments.

This paper presents a method of synthesizing copper powders by electrochemical method with the use of a rotating working electrode. The influence of the rotation speed of the working electrode, the current density, the concentration of copper ions, and the addition of ethylene glycol on the shape, size, and size distribution of the obtained powders were investigated. Properties of the synthesized powders were characterized by scanning electron microscopy (SEM) and X-ray powder diffractometry (XRD). It has been shown that it is possible to obtain copper powders with a size of 1 µm by an electrochemical method using the rotary cathode, in sulphate bath with addition of ethylene glycol as a surfactant. Increasing current density causes a decrease in the average size of the obtained powder particles. The addition of 2.5% of ethylene glycol prevents the formation of dendritic powders. The change in the concentration of copper ions in the range from 0.01 to 0.15 mol/dm3 in the electrolyte did not show any significant effect on the size of obtained particles. However, higher concentrations of copper limiting the presence of dendritic-shape particles. Changing the speed of rotation of the electrode affects both the size and the shape of synthesized copper powder. For the rotational speed of the electrode of 115 rpm, the obtained powders have a size distribution in the range of 0-3 µm and an average particle size of 1 µm. The particles had a polygonal shape with an agglomeration tendency.