Asteroid Mean Elements: Higher Order and Iterative Theories

Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation; they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step, used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory, resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete, fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements, incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determination of the potential of homogeneous polyhedral bodies using line integrals

For the determination of the potential of irregular inhomogeneous bodies they can be decomposed into (polyhedral) parts of homogeneous density. Efficient formulas for the computation of the gravitational potential (and its first and second derivatives) of homogeneous polyhedral bodies are presented. They are obtained using a transformation of the volume integral into line integrals. The most important property of the solution is that all ten quantities under consideration (potential, 3 components of the gravitation vector, 6 components of the tensor of the second derivatives) can be represented by using only two different line integrals. Furthermore, all coordinate transformations needed in the evaluation are chosen in such a way that they do not appear in the final result. The consequence, favorable for efficient programming, is that the same transcendental expressions along each edge of the polyhedron are needed for all ten quantities; even the same linear combinations of them for individual surfaces are appearing in different formulas. The expressions obtained are probably the simplest possible, which is also reflected in the fact that for the special case of a right rectangular prism they may easily be specialized to the usual well-known formulas. Received 28 Juni 1994; Accepted 13 September 1996     

Periodicity of annual precipitation in different climate regions of Croatia

Summary The periodicity of a 100-year series of annual precipitation over Croatia has been studied by means of power spectrum analysis at 3 stations representing the different climatic regions of Croatia. The annual precipitation variance spectra in the continental lowland (Osijek) and at the north East Adriatic coast (Crikvenica) can be fitted by Markov white noise continuum, but in the transitional region between the Dinaric Alps and the Pannonian lowland (Zagreb-Gri) a non-white noise continuum is necessary. Quasi-periodic oscillations appear in two spectra ranges: short (2.2 and 4.7 years) and medium (25.0 and 33.3 years). These results are compared with those of other authors for other parts of the Europe.With 2 Figures     

Effect of source-varying input data on erosion potential model performance

This paper examines the performance of the Erosion Potential Method (EPM or Gavrilovi?) and the model response to input data variations caused by choosing different sources of information for the same parameter. The research presented addresses the input data uncertainty via an analysis of the two model input parameters (the soil protection coefficient and the soil erodibility coefficient). The parameter uncertainty analysis is performed following two different approaches: uncertainty analyses of both the selected sample size and the entire population are conducted for an erosion assessment case study of the Dubra?ina River catchment, Croatia. The analysis indicated that, when changing the data source, significant changes in the model outcome values can occur (up to 47% for this case study). Future method modifications should consider the mitigation of these two parameters by potentially making structural changes in the model and therefore moderating the effect.     

Statistical Analysis of Water Quality Parameters in Seven Major Serbian Rivers during 2004‒2013 Period

Rivers on territory of the Republic of Serbia can be separated to three sea drainage basins: Black, Adriatic and Aegean. Majority of rivers belong to the Black Sea drainage basin. The Danube is the most important river in Serbia and one of the most important rivers of Europe. All rivers investigated in this paper represent direct or indirect tributaries of the Danube River and as that, they are belonging to the Black Sea drainage basin. In this study, the water quality status and the spatial and temporal trends of seven major rivers in Serbia were assessed through the application of ten parameters of Water Quality Index. Ten year (2004–2013) public database of environmental data was used. Into considerations were taken differences between every river individually and difference between sample positions on every single river. Based on the chemical parameters of water quality, it can be seen that the biggest rivers in Serbia show different values of WQ parameters. The highest WQ value is measured on the Drina River, while the lowest value is measured on the Ju?na Morava and the Tisza River. Analyses of parameters per period of year show that there is a statistically significant difference between values during warm and cold periods.     

Dynamics of rocking podium structures

A rocking podium structure is a class of structures consisting of a superstructure placed on top of a rigid slab supported by free‐standing columns. The free‐standing columns respond to sufficiently strong ground motion excitation by uplifting and rocking. Uplift works as a mechanical fuse that limits the forces transmitted to the superstructure, while rocking enables large lateral displacements. Such ‘soft‐story’ system runs counter to the modern seismic design philosophy but has been used to construct several hundred buildings in countries of the former USSR following Polyakov's rule‐of‐thumb guidelines: (i) that the superstructure behave as a rigid body and (ii) that the maximum lateral displacement of the rocking podium frame be estimated using elastic earthquake displacement response spectra. The objectives of this paper are to present a dynamic model for analysis of the in‐plane seismic response of rocking podium structures and to investigate if Polyakov's rule‐of‐thumb guidelines are adequate for the design of such structures. Examination of the rocking podium structure response to analytical pulse and recorded ground motion excitations shows that the rocking podium structures are stable and that Polyakov's rule‐of‐thumb guidelines produce generally conservative designs. Copyright © 2017 John Wiley & Sons, Ltd.     

How fast does tufa grow? Very high-resolution measurement of the tufa growth rate on artificial substrates by the development of a contactless image-based modelling device

Accurate determination of the tufa growth rate (TGR) is required to answer the fundamental geomorphological question of tufa evolution. The TGR has been measured by various direct and indirect methods. One of the most popular direct methods uses modified micro-erosion meter (MEM), which has several drawbacks. Here, we present for the first time a coordinate measuring macro-photogrammetry device (CMD) for monitoring the TGR in a contactless manner. The CMD was applied on 28 limestone plates at 14 locations within the Skradinski buk area, Croatia, and measurements were performed in the laboratory. The TGR was derived from digital tufa high-resolution models (DTHRMs). The accuracy of the device was evaluated using state-of-the-art three-dimensional (3D) scanners and error calculation at checkpoints. Moreover, the precision was evaluated with the split test (n = 5). A total of 74 DTHRMs with a spatial resolution of 0.0236 mm were created. The TGR ranged from 0.327 to 19.302 mm a⁻¹, with an average of 5.771 mm a⁻¹. A higher TGR was observed on the limestone plates near mosses, located in fast and turbulent water rather than in stagnant water. We found that specific micro-environmental factors (e.g. proximity to moss) positively affected tufa growth. Erosion events were observed, as well as the presence of aquatic insect larvae (Simuliidae and Chironomidae), which positively affected tufa growth. The CMD is a precise and accurate device that does not suffer from the drawbacks of the MEM method and has many other advantages. It has a high capability of tufa erosion detection, enables the identification of macroinvertebrates, and multispectral or hyperspectral cameras can be mounted on the device for spectral reflectance analysis of the tufa surface. The CMD can be applied in any study requiring a sub-millimetre data quality and involving the comparison of consecutive 3D models and derivation of various parameters of smaller objects. © 2020 John Wiley & Sons, Ltd.     

Depositional environment and hydrocarbon source potential of the Oligocene Ruslar Formation (Kamchia Depression; Western Black Sea)

The Oligocene Ruslar Formation is a hydrocarbon source rock in the Kamchia Depression, located in the Western Black Sea area. Depositional environment and source potential of the predominantly pelitic rocks were investigated using core and cuttings samples from four offshore wells. In these wells the Ruslar Formation is up to 500 m thick. Based on lithology and well logs, the Ruslar Formation is subdivided from base to top into units I–VI. Dysoxic to anoxic conditions and mesohaline to euhaline salinities prevailed during deposition of the Ruslar Formation. Relatively high oxygen contents occurred during early Solenovian times (lower part of unit II), when brackish surface water favoured nannoplankton blooms and the deposition of bright marls (“Solenovian event”). Anoxic conditions with photic zone anoxia were established during late Oligocene times (units III and IV) and, probably, reflect a basin-wide anoxic event in the Eastern Paratethys during Kalmykian times. Organic carbon content in the Ruslar Formation is up to 3%. Autochthonous aquatic and allochthonous terrigenous biomass contribute to the organic matter. Relatively high amounts of aquatic organic matter occur in the lower part of the Ruslar Formation (units I and II) and in its upper part (unit VI). Diatoms are especially abundant in the lower part of unit VI. The kerogen is of type III and II with HI values ranging from 50 to 400 mgHC/gTOC. Units I and II (Pshekian, lower Solenovian) are characterized by a fair (to good) potential to produce gas and oil, but potential sources for gas and oil also occur in the Upper Oligocene units IV–VI.     

Asteroid long-periodic perturbations: The second order Hamiltonian

The Hamiltonian of the second order with respect to the disturbing mass, as defined in the higher order-higher degree theory of asteroid secular perturbations by Yuasa (1973), is expressed in the heliocentric, ecliptic coordinate system. Errors found in the original paper with terms coming from the principal part of the disturbing function are removed, and corrected values of the coefficients are computed. The importance of second-order perturbations and the improvement in the accuracy of proper element determination, achieved by using the newly-obtained coefficients, are demonstrated. Finally, a table of the secular frequencies as functions of the semimajor axis is given, and compared with the analogous one by Kozai (1979).