Analysis of the exoplanet containing system Kepler-13

We have applied the close binary system analysis program WinFitter, with its physically detailed fitting function, to an intensive study of the complex multiple system Kepler-13 using photometry data from all 13 short cadence quarters downloaded from the NASA Exoplanet Archive (NEA) (http://exoplanetarchive.ipac.caltech.edu). The data-point error of our normalized, phase-sequenced and binned (380 points per bin: 0.00025 phase interval) flux values, at 14 ppm, allows the model’s specification for the mean reference flux level of the system to a precision better than 1 ppm. Our photometrically derived values for the mass and radius of KOI13.01 are \(6.8\pm0.6~\mbox{M}_{\mathrm{J}}\) and \(1.44\pm0.04~\mbox{R}_{\mathrm{J}}\). The star has a radius of \(1.67\pm0.05~\mbox{R}_{\odot}\). Our modelling sets the mean of the orbital inclination \(i\) at \(94.35\pm0.14^{\circ}\), with the star’s mean precession angle \(\phi_{p}\)—\(49.1\pm5.0^{\circ}\) and obliquity \(\theta_{o}\)\(67.9 \pm 3.0^{\circ}\), though there are known ambiguities about the sense in which such angles are measured.Our findings did not confirm secular variation in the transit modelling parameters greater than their full correlated errors, as argued by previous authors, when each quarter’s data was best-fitted with a determinable parameter set without prejudice. However, if we accept that most of the parameters remain the same for each transit, then we could confirm a small but steady diminution in the cosine of the orbital inclination over the 17 quarter timespan. This is accompanied by a slight increase of the star’s precession angle (less negative), but with no significant change in the obliquity of its spin axis. There are suggestions of a history of strong dynamical interaction with a highly distorted planet rotating in a 3:2 resonance with its revolution, together with a tidal lag of \(\sim30~\mbox{deg}\). The mean precessional period is derived to be about 1000 y, but at the present time the motion of the star’s rotation axis appears to be supporting the gravitational torque, rather than providing the balance against it that would be expected over long periods of time.The planet has a small but detectable backwarming effect on the star, which helps to explain the difference in brightness just after transit and just before occultation eclipses. In assessing these findings it is recognized that sources of uncertainty remain, notably with possible inherent micropulsational effects, variations from other components of the multiple star, stellar activity, differential rotation and the neglect of higher order terms (than \(r_{1}^{5}\)) in the fitting function, where \(r_{1}\) is the ratio of the radius of the star to the mean orbital separation of planet and host star.     

Element sets for high-order Poincaré mapping of perturbed Keplerian motion

The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in Celestial Mechanics and Astrodynamics, e.g., to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits using the high-order Taylor expansion of a Poincaré or stroboscopic map. The HOTM is only accurate close to the expansion point and therefore the number of revolutions for which the map is accurate tends to be limited. The proper selection of coordinates is of key importance for improving the performance of the HOTM method. In this paper, we investigate the use of different element sets for expressing the high-order map in order to find the coordinates that perform best in terms of accuracy. A new set of elements is introduced that enables extremely accurate mapping of the state, even for high eccentricities and higher-order zonal perturbations. Finally, the high-order map is shown to be very useful for the determination and study of fixed points and center manifolds of Poincaré maps.     

Explicit stress–strain equations for modeling frictional materials

In this paper, a comprehensive study on simulating the shearing behavior of frictional materials is performed. A set of two explicit equations, describing the relationship among the shear stress ratio and the distortional strain and the volumetric strain, are formulated independently. The equations contain three stress parameters and three strain parameters and another parameter representing the nonuniformity of stress and strain during softening. All the parameters have clear physical significance and can be determined experimentally. It is demonstrated that the proposed equations have the capacity of simulating the complicated shearing behavior of many types of frictional materials including geomaterials. The proposed equations are used to simulate the stress–strain behavior for 27 frictional materials with 98 tests. These materials include soft and stiff clays in both reconstituted and structured states, silicon sands and calcareous sands, silts, compacted fill materials, volcanic soils, decomposed granite soils, cemented soils (both artificially and naturally cemented), partially saturated soils, ballast, rocks, reinforced soils, tire chips, sugar, wheat, and rapeseed. It has been demonstrated that the proposed explicit constitutive equations have the capacity to capture accurately the shearing behavior of frictional materials both qualitatively and quantitatively. A study on model parameters has been performed.     

Studies on the Application of Steady State Assumption in 1DV Model for the Estimation of Settling Velocity of Suspended Sediments in a Shallow Estuary

Settling velocity is one of the important parameters in sediment transport modeling of estuaries. The methods adopted for its determination vary from theoretical equations to experimental methods. The theoretical equation generally adopted in the 1DV model include assumptions in order to simplify the solution. It is generally assumed that either the condition is steady or the vertical diffusion is negligible. This study evaluated the relative importance of the two assumptions made for the estimation of settling velocity. Two approaches were adopted: unsteady and negligible vertical diffusion (NS-NVD) and steady with vertical diffusion (S-VD) to estimate the settling velocity. The Muthupet Estuary in the Coromandal coast of India was selected for the study. The S-VD approach estimated settling velocity fairly well at the two locations with appreciable vertical diffusion. The NS-NVD approach was observed to be superior for estimating settling velocity at shallow reaches of the estuary having low flow velocity. The calculated settling velocity was further applied in 1DV model to predict the suspended sediment concentration. The S-VD approach predicted suspended sediment concentration at those locations with appreciable vertical diffusion with an R² value of 0.82 against 0.67 for the NS-NVD approach. At the other shallow reach of the estuary with low flow velocity, the NS-NVD approach gave an R² value of 0.822 against 0.71 for the S-VD approach. The vertical diffusion was observed to play a secondary role at those locations which are shallow with a water depth of 0.6 m and with a low flow velocity of the order of 0.01 m/s. The study demonstrated that localized hydrodynamic conditions influence the method adopted for the estimation of settling velocity.     

Exact solution of anisotropic compact stars via mass function

Studying relativistic compact objects is important in modern astrophysics to understand several astrophysical issues. It is therefore natural to ask for an internal structure and physical properties of specific classes of compact stars from astrophysical observations. We obtain a class of new relativistic solutions with anisotropic distribution of matter for compact stars. More specifically, stellar models, described by an anisotropic fluid, establishing a relation between metric potentials and generating a specific form of mass function, are explicitly constructed within the framework of General Relativity. New solutions can be used to model compact objects, which adequately describe compact strange star candidates like SMC X-1, Her X-1 and 4U 1538-52, with observational data taken from Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431:3216, 2013). As a possible astrophysical application the obtained solutions could explain the physics of selfgravitating objects, and might be useful for strong-field regimes where data are currently inadequate.     

Changes in hillslope hydrology in a perched,shallow soil system due to clearcutting and residual biomass removal

Sustainable fuels legislation and volatility in energy prices have put additional pressures on the forestry sector to intensify the harvesting of biomass for “advanced biofuel” production. To better understand how residual biomass removal after harvest affects forest hydrology in relatively low slope terrain, a Before-After-Control-Impact (BACI) study was conducted in the USDA Forest Service's Marcell Experimental Forest, Minnesota, USA. Hydrological measurements were made from 2010–2013 on a forested hillslope that was divided into three treatment blocks, where one block was harvested and residual biomass removed (Biomass Removed), the second was harvested and residual biomass left (Biomass Left), and the last block was left as an Unharvested Control. The pre-harvest period (2 years) was 2010–11 and post-harvest (2 years) was 2012–13. Water table elevation at the upslope and downslope position, subsurface runoff, and soil moisture were measured between May–November. Mixed effect statistical models were used to compare both the before-after and “control” treatment ratios (ratios between harvested hillslopes and the Unharvested Control hillslope). Subsurface runoff significantly increased (p < .05) at both harvested hillslopes but to a greater degree on the Biomass Left hillslope. Greater subsurface runoff volumes at both harvested hillslopes were driven by substantial increases during fall, with additional significant increases during summer on the Biomass Left hillslope. The hydrological connectivity, inferred from event runoff ratios, increased due to harvesting at both hillslopes but only significantly on the Biomass Left hillslope. The winter harvest minimized soil disturbance, resulting in no change to the effective hydraulic conductivity distribution with depth. Thus, the observed hydrological changes were driven by increased effective precipitation and decreased evapotranspiration, increasing the duration that both harvested hillslopes were hydrologically active. The harvesting of residual biomass appears to lessen hydrological connectivity relative to leaving residual biomass on the hillslope, potentially decreasing downstream hydrological impacts of similar forestry operations.     

Grains of Nonferrous and Noble Metals in Iron–Manganese Formations and Igneous Rocks of Submarine Elevations of the Sea of Japan

Iron–manganese formations and igneous rocks of submarine elevations in the Sea of Japan contain overlapping mineral phases (grains) with quite identical morphology, localization, and chemical composition. Most of the grains conform to oxides, intermetallic compounds, native elements, sulfides, and sulfates in terms of the set of nonferrous, noble, and certain other metals (Cu, Zn, Sn, Pb, Ni, Mo, Ag, Pd, and Pt). The main conclusion that postvolcanic hydrothermal fluids are the key sources of metals is based upon a comparison of the data of electron microprobe analysis of iron–manganese formations and igneous rocks dredged at the same submarine elevations in the Sea of Japan.     

Study of some chaotic inflationary models in $$ gravity

In this paper, we discuss an inflationary scenario via scalar field and fluid cosmology for an anisotropic homogeneous universe model in \(f(R)\) gravity. We consider an equation of state which corresponds to a quasi-de Sitter expansion and investigate the effect of the anisotropy parameter for different values of the deviation parameter. We evaluate potential models like linear, quadratic and quartic models which correspond to chaotic inflation. We construct the observational parameters for a power-law model of \(f(R)\) gravity and construct the graphical analysis of tensor–scalar ratio and spectral index which indicates the consistency of these parameters with Planck 2015 data.