Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.     

Stochastic evaluation of simple pairing approaches to reconstruct incomplete rainfall time series

Two-station pairing approaches are routinely used to infill missing information in incomplete rainfall databases. We evaluated the performance of three simple methodologies to reconstruct incomplete time series in presence of variable nonlinear correlation between data pairs. Nonlinearity stems from the statistics describing the marginal peak-over-threshold (POT) values of rainfall events. A Monte Carlo analysis was developed to quantitatively assess expected errors from the use of chronological pairing (CP) with linear and nonlinear regression and frequency pairing (FP). CP is based on a priori selection of regression functions, while FP is based on matching the probability of non-exceedance of an event from one time series with the probability of non-exceedance of a similar event from another time series. We adopted a generalized Pareto (GP) model to describe POT events, and a t-copula algorithm to generate reference nonlinearly correlated pairs of random temporal distributions distributed according with the GP model. The results suggest that the optimal methodology strongly depends on GP statistics. In general, CP seems to provide the lowest errors when GP statistics were similar and correlation became linear; we found that a power-2 function performs well for the selected statistics when the number of missing points is limited. FP outperforms the other methods when POT statistics are different and variables are markedly nonlinearly correlated. Ensemble-based results seem to be supported by the analysis of observed precipitation at two real-world gauge stations.     

Long-term Geomechanical Observation in the Jeroným Mine

Geomechanical measurements have been carried out in the medieval Jeroným Mine since 2001. At first quarterly observation and later also continual monitoring by distributed measurement network were used. The network includes a number of different sensors that have been installed in selected places of underground spaces. There have not been any manifestations documenting dangerous changes of stability during the period of monitoring (2001–2015). The results of accomplished measurements from all convergence profiles confirm the total stability of all underground spaces. However, a number of places have been documented as potentially unstable. Measured values of selected parameters are presented in the paper, namely, movements along fractures, changes of stress tensor and fluctuations in the level of mine water table.     

About Hypothesis of the Superconducting Origin of the Saturn’s Rings

Hypothesis of possible superconductivity of the iced matter of the rings of Saturn (based on the data of Voyager and Pioneer space missions) allow us to explain many phenomena which have not been adequately understood earlier. Introducing into planetary physics force of magnetic levitation of the superconducting iced particle of the rings, which interact with magnetosphere of the planet, becomes to be possible to explain origin, evolution, and dynamics of the rings; to show how the consequent precipitation of the rings’ matter upon the planet was concluded; how the rings began their rotation; how they were compressed by the magnetic field into the thin disc, and how this disc was fractured into hundreds of thousands of separated rings; why in the ring B do exist “spokes”; why magnetic field lines have distortion near by ring F; why there is a variable azimuth brightness of the ring A; why the rings reflected radio waves so efficiently; why exists strong electromagnetic radiation of the rings in the 20.4 kHz–40.2 MHz range and Saturnian kilometric radiation; why there is anomalous reflection of circularly polarized microwaves; why there are spectral anomalies of the thermal radiation of the rings; why the matter of the various rings does not mix but preserves its small-scale color differences; why there is an atmosphere of unknown origin nearby the rings of Saturn; why there are waves of density and bending waves within Saturn’s rings; why planetary rings in the solar system appear only after the Belt of Asteroids (and may be the Belt of Asteroids itself is a ring for the Sun); why our planet Earth has no rings of its own.     

Adaptive particle swarm optimization for optimal orbital elements of binary stars

The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability.     

Exact Bianchi type-II, VIII and IX perfect fluid cosmological models in Saez-Ballester theory of gravitation

Exact Bianchi type-II, VIII and IX cosmological models are obtained in a scalar tensor theory proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) with perfect fluid as a source. Some physical and geometrical properties of the models are studied. It is observed that the models are free from initial singularities and they are expanding with time.     

Stability of equilibrium points in the generalized perturbed restricted three-body problem

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ _c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ _c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.     

Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories.     

The Problem of the Height Dependence of Magnetic Fields in Sunspots

To understand the physics of sunspots, it is important to know the properties of their magnetic field, and especially its height stratification plays a substantial role. There are mainly two methods to assess this stratification, but they yield different magnetic gradients in the photospheric layers. Determinations based on the several spectral lines of different formation heights and the slope of their profiles result in gradients of ?2 to ?3 G?km^?1, or even steeper. This is similar for the total magnetic field strength and for the vertical component of the magnetic field. The other option is to determine the horizontal partial derivatives of the magnetic field, and with the condition \(\operatorname{div} {{\boldsymbol {B}}} = 0\) also the vertical derivative is known. With this method, gradients of ?0.5 G?km^?1 and even shallower are obtained. Obviously, these results do not agree. If chromospheric spectral lines are included, only shallow gradients around ?0.5 G?km^?1 are obtained. Shallow gradients are also found from gyro-resonance measurements in the radio wave range 300?–?2000 GHz.Some indirect methods are also considered, but they cannot clarify the total picture. An analysis of a numerical simulation of a sunspot indicates a shallow gradient over a wide height range, but with slightly steeper gradients in deep layers.Several ideas to explain the discrepancy are also discussed. With no doubts cast on Maxwell’s equations, the first one is to look at the uncertainties of the formation heights of spectral lines, but a wider range of these heights would require an extension of the solar photosphere that is incompatible with observations and the theory of stellar atmospheres. Submerging and rising magnetic flux might play a role in the outer penumbra, if the resolution is too low to separate them, but it is not likely that this effect acts also in the umbra. A quick investigation assuming a spatial small scale structure of sunspots together with twist and writhe of individual flux tubes shows a reduction of the measured magnetic field strength for spectral lines sensitive to a larger height range. However, sophisticated investigations are required to prove that the explanation for the discrepancy lies here, and the problem of the height gradient of the magnetic field in sunspots is still not solved.