Analytical Dirac-Hartree-Fock-Slater screening function for atoms (Z=1-92)

An analytical approximation, depending on five parameters, for the atomic screening function is proposed. The corresponding electrostatic potential takes a simple analytical form (superposition of three Yukawa potentials) well suited to most practical applications. Parameters in the screening function, determined by an analytical fitting procedure to Dirac-Hartree-Fock-Slater (DHFS) self-consistent data, are given for Z=1¿92. The reliability of this analytical approach is demonstrated by showing that (a) Born cross sections for elastic scattering of fast charged particles by the present analytical field and by the DHFS field practically coincide and (b) one-electron binding energies computed from the independent-particle model with our analytical field (corrected for exchange and electrostatic self-interaction) agree closely with the DHFS energy eigenvalues.

Bernoulli correction to viscous losses: Radial flow between two parallel discs

For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in density. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution

Analytical expressions for the flame front speed in the downward combustion of thin solid fuels and comparison to experiments

We derive analytical expressions for the propagation speed of downward combustion fronts of thin solid fuels with a background flow initially at rest. The classical combustion model for thin solid fuels that consists of five coupled reaction-convection-diffusion equations is here reduced into a single equation with the gas temperature as the single variable. For doing so we apply a two-zone combustion model that divides the system into a preheating region and a pyrolyzing region. The speed of the combustion front is obtained after matching the temperature and its derivative at the location that separates both regions.We also derive a simplified version of this analytical expression expected to be valid for a wide range of cases. Flame front velocities predicted by our analyticalexpressions agree well with experimental data found in the literature for a large variety of cases and substantially improve the results obtained from a previous well-known analytical expression

Determinación de sistemas de flujo regionales y locales en las depresiones tectónicas del Baix Empordà y La Selva (NE de España) en base a datos hidroquímicos e isotópicos

The Baix Empordà-Selva-Gavarres aquifer system is related to the fault set that created the tectonic basins of Empordà and Selva areas (NE Spain) during the Neogene. In this work, we describe groundwater hydrogeological, hydrochemical and isotopical (3H, δD, δ18O, and the 87Sr/86Sr ratio) characteristics of this system in order to illustrate the relevance of fault zones in groundwater flow-paths and the recharge. In that way, we identify two flow systems, with distinct hydrochemistry and isotopes. A local flow system originates at the Gavarres Range, and it flows towards the basins of the Baix Empordà and Selva, with an approximate residence time of 20 years. Additionally, a regional flow system has only been identified in the Selva basin. This one is related to the main fault zones, as preferential flow paths. Its recharge is located in mountain ranges with higher altitudes, namely the Transversal and Guilleries Ranges, with residence times larger than 50 years. Isotopical data has also shown mixing processes between both flow systems and rainfall recharge while multivariate statistical analysis of principal components has shown the main processes that control hydrochemistry of each flow systems

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus, and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum-rule approach. This solution allows us to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus, and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum-rule approach. This solution allows us to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

Hollow sphere as a detector of gravitational radiation

The most important features of the proposed spherical gravitational wave detectors are closely linked with their symmetry. Hollow spheres share this property with solid ones, considered in the literature so far, and constitute an interesting alternative for the realization of an omnidirectional gravitational wave detector. In this paper we address the problem of how a hollow elastic sphere interacts with an incoming gravitational wave and find an analytical solution for its normal mode spectrum and response, as well as for its energy absorption cross sections. It appears that this shape can be designed having relatively low resonance frequencies (~ 200 Hz) yet keeping a large cross section, so its frequency range overlaps with the projected large interferometers. We also apply the obtained results to discuss the performance of a hollow sphere as a detector for a variety of gravitational wave signals.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Modelling the cooling of concrete by piped water

Piped water is used to remove hydration heat from concrete blocks during construction. In this paper we develop an approximate model for this process. The problem reduces to solving a one-dimensional heat equation in the concrete, coupled with a first order differential equation for the water temperature. Numerical results are presented and the effect of varying model parameters shown. An analytical solution is also provided for a steady-state constant heat generationmodel. This helps highlight the dependence on certain parameters and can therefore provide an aid in the design of cooling systems.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Residual Stress Measurement on a MEMS Structure With High-Spatial Resolution

A new approach to the local measurement of residual stress in microstructures is described in this paper. The presented technique takes advantage of the combined milling-imaging features of a focused ion beam (FIB) equipment to scale down the widely known hole drilling method. This method consists of drilling a small hole in a solid with inherent residual stresses and measuring the strains/displacements caused by the local stress release, that takes place around the hole. In the presented case, the displacements caused by the milling are determined by applying digital image correlation (DIC) techniques to high resolution micrographs taken before and after the milling process. The residual stress value is then obtained by fitting the measured displacements to the analytical solution of the displacement fields. The feasibility of this approach has been demonstrated on a micromachined silicon nitride membrane showing that this method has high potential for applications in the field of mechanical characterization of micro/nanoelectromechanical systems.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Ninety-day oral toxicity studies on two genetically modified maize MON810 varieties in Wistar Han RCC rats (EU 7th Framework Programme project GRACE)

The GMO Risk Assessment and Communication of Evidence (GRACE; www.grace-fp7.eu) project is funded by the European Commission within the 7th Framework Programme. A key objective of GRACE is to conduct 90-day animal feeding trials, animal studies with an extended time frame as well as analytical, in vitro and in silico studies on genetically modified (GM) maize in order to comparatively evaluate their use in GM plant risk assessment. In the present study, the results of two 90-day feeding trials with two different GM maize MON810 varieties, their near-isogenic non-GM varieties and four additional conventional maize varieties are presented. The feeding trials were performed by taking into account the guidance for such studies published by the EFSA Scientific Committee in 2011 and the OECD Test Guideline 408. The results obtained show that the MON810 maize at a level of up to 33 % in the diet did not induce adverse effects in male and female Wistar Han RCC rats after subchronic exposure, independently of the two different genetic backgrounds of the event