Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.     

The formation and stability of the configuration of the planetary system HD 126611

Recent Doppler velocity measurements have revealed the existence of two planets orbiting the star HD 12661 on medium-eccentricity orbits. The inner planet has a period of 263.6 d and a mass of 2.3 Jupiter masses, and the outer planet has a period of 1444.5d and a mass of 1.57 Jupiter masses. The stability of this system requires the two planets to be in a state of mean-motion orbit resonances. By numerical method we have studied the orbit migration and stability of the system in its early ages under the action of the proto-stellar disk, and calculated the probabilities of the planets being captured into the mean -motion resonances during their migrations. It is found that at present the two planets are probably situated at the edge of the 11:2 mean-motion resonance and are in chaotic motions. This result may be helpful to clarify the arguments on the present configuration. Besides, it is indicated that very probably, after the formation of the system, the gaseous disk has almost disappeared before the planets migrated to the present configuration.     

Seismic Inference using Genetic Algorithms

A flood of reliable seismic data will soon arrive. The migration to largertelescopes on the ground may free up 4-m class instruments for multi-sitecampaigns, and several forthcoming satellite missions promise to yieldnearly uninterrupted long-term coverage of many pulsating stars. We willthen face the challenge of determining the fundamental properties of thesestars from the data, by trying to match them with the output of ourcomputer models. The traditional approach to this task is to make informedguesses for each of the model parameters, and then adjust them iterativelyuntil an adequate match is found. The trouble is: how do we know that oursolution is unique, or that some other combination of parameters will notdo even better? Computers are now sufficiently powerful and inexpensivethat we can produce large grids of models and simply compare all ofthem to the observations. The question then becomes: what range ofparameters do we want to consider, and how many models do we want tocalculate? This can minimize the subjective nature of the process, but itmay not be the most efficient approach and it may give us a false sense ofsecurity that the final result is correct, when it is really justoptimal. I discuss these issues in the context of recent advances inthe asteroseismological analysis of white dwarf stars.     

CCD photometry inVRI bands of the galactic cluster NGC 2818

bdAbstract The open cluster NGC 2818 containing a planetary nebula has been observed inVRI bands using the CCD system at prime focus of the 2.3-metre Vainu Bappu Telescope. The study extending to starsV ∼ 21 magnitude establishes the distance modulus as(m-M) ₀ = 12.9 ±0.1 for the cluster. Based on the fitting of theoretical isochrones computed for solar metallicity, an age of 5(±1) × 10₈ years has been assigned to the cluster. Association of the planetary nebula with the cluster indicates that the progenitor mass of the planetary nebula on the main sequence is ≥2.5M_⊙ Based on observations obtained with the Vainu Bappu Telescope.     

Correcting systematic effects in a large set of photometric light curves

We suggest a new algorithm to remove systematic effects in a large set of light curves obtained by a photometric survey. The algorithm can remove systematic effects, such as those associated with atmospheric extinction, detector efficiency, or point spread function changes over the detector. The algorithm works without any prior knowledge of the effects, as long as they linearly appear in many stars of the sample. The approach, which was originally developed to remove atmospheric extinction effects, is based on a lower rank approximation of matrices, an approach which has already been suggested and used in chemometrics, for example. The proposed algorithm is especially useful in cases where the uncertainties of the measurements are unequal. For equal uncertainties, the algorithm reduces to the Principal Component Analysis (PCA) algorithm. We present a simulation to demonstrate the effectiveness of the proposed algorithm and we point out its potential, in the search for transit candidates in particular.     

The evolution of binary fractions in globular clusters

We study the evolution of binary stars in globular clusters using a new Monte Carlo approach combining a population synthesis code ( startrack ) and a simple treatment of dynamical interactions in the dense cluster core using a new tool for computing three- and four-body interactions ( fewbody ). We find that the combination of stellar evolution and dynamical interactions (binary–single and binary–binary) leads to a rapid depletion of the binary population in the cluster core. The maximum binary fraction today in the core of a typical dense cluster such as 47 Tuc, assuming an initial binary fraction of 100 per cent, is only ∼ 5–10 per cent. We show that this is in good agreement with recent Hubble Space Telescope observations of close binaries in the core of 47 Tuc, provided that a realistic distribution of binary periods is used to interpret the results. Our findings also have important consequences for the dynamical modelling of globular clusters, suggesting that 'realistic models' should incorporate much larger initial binary fractions than has usually been the case in the past.