Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D

We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on the use of Green's third identity and local Taylor-like interpolations of density functions in terms of harmonic polynomials. The proposed technique effectively regularizes the singularities present in boundary integral operators and layer potentials, and recasts the latter in terms of integrands that are bounded or even more regular, depending on the order of the density interpolation. The resulting boundary integrals can then be easily, accurately, and inexpensively evaluated by means of standard quadrature rules. A variety of numerical examples demonstrate the effectiveness of the technique when used in conjunction with the classical trapezoidal rule (to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type quadrature rule (to integrate over surfaces given as unions of non-overlapping quadrilateral patches) in three-dimensions

Signatures of rocky planet engulfment in HAT-P-4. Implications for chemical tagging studies

Aims. To explore the possible chemical signature of planet formation in the binary system HAT-P-4, by studying abundance vs condensation temperature Tc trends. The star HAT-P-4 hosts a planet detected by transits while its stellar companion does not have any detected planet. We also study the Lithium content, which could shed light on the problem of Li depletion in exoplanet host stars. Conclusions. The exoplanet host star HAT-P-4 is found to be ~0.1 dex more metal rich than its companion, which is one of the highest differences in metallicity observed in similar systems. This could have important implications for chemical tagging studies, disentangling groups of stars with a common origin. We rule out a possible peculiar composition for each star as lambda Boo, delta Scuti or a Blue Straggler. The star HAT-P-4 is enhanced in refractory elements relative to volatile when compared to its stellar companion. Notably, the Lithium abundance in HAT-P-4 is greater than in its companion by ~0.3 dex, which is contrary to the model that explains the Lithium depletion by the presence of planets. We propose a scenario where, at the time of planet formation, the star HAT-P-4 locked the inner refractory material in planetesimals and rocky planets, and formed the outer gas giant planet at a greater distance. The refractories were then accreted onto the star, possibly due to the migration of the giant planet. This explains the higher metallicity, the higher Lithium content, and the negative Tc trend detected. A similar scenario was recently proposed for the solar twin star HIP 68468, which is in some aspects similar to HAT-P-4. We estimate a mass of at least Mrock ~ 10 Mearth locked in refractory material in order to reproduce the observed Tc trends and metallicity.Comment: 5 pages, 6 figures, A&A Letters accepte

High-precision analysis of binary stars with planets. I. Searching for condensation temperature trends in the HD 106515 system

We explore the probable chemical signature of planet formation in the remarkable binary system HD 106515. The A star hosts a massive long-period planet with 9 MJup detected by radial velocity. We also refine stellar and planetary parameters by using non-solar-scaled opacities when modeling the stars. Methods. We carried out a simultaneous determination of stellar parameters and abundances, by applying for the first time non-solar-scaled opacities in this binary system, in order to reach the highest possible precision. Results. The stars A and B in the binary system HD 106515 do not seem to be depleted in refractory elements, which is different when comparing the Sun with solar-twins. Then, the terrestrial planet formation would have been less efficient in the stars of this binary system. Together with HD 80606/7, this is the second binary system which does not seem to present a (terrestrial) signature of planet formation, and hosting both systems an eccentric giant planet. This is in agreement with numerical simulations, where the early dynamical evolution of eccentric giant planets clear out most of the possible terrestrial planets in the inner zone. We refined the stellar mass, radius and age for both stars and found a notable difference of 78% in R compared to previous works. We also refined the planet mass to mp sini = 9.08 +/- 0.20 MJup, which differs by 6% compared with literature. In addition, we showed that the non-solar-scaled solution is not compatible with the classical solar-scaled method, and some abundance differences are comparable to NLTE or GCE effects specially when using the Sun as reference. Then, we encourage the use of non-solar-scaled opacities in high-precision studies such as the detection of Tc trends.[abridged]Comment: 9 pages, 10 figures, A&A accepted. arXiv admin note: text overlap with arXiv:1507.0812

Stability of moving solitons in trans-polyacetylene in an electric field

In this work we study the dynamics and stability of charged solitons in trans-polyacetylene (tPA), and revisit the issue of the stability of these non-linear excitations under the effect of an external electric field applied parallel to the polymer. Using the formalism of the Su-Schrieffer-Heeger (SSH) model, we solve the coupled dynamical equations for electrons and classical nuclei at the mean-field level and in the regime of low external electric field $E$, where the dynamics of the moving soliton is adiabatic. Analyzing observable quantities in real space and frequency space, we identify the microscopic mechanisms triggering the dynamical instabilities of the soliton. In addition, we put forward the definition of a proper quantitative measure of its stability, an issue which to the best of our knowledge has remained an open question. Besides its intrinsic interest from the fundamental point of view, our work might be relevant for the design of novel organic electronic devices based on soliton-mediated transport.Comment: 14 pages, 9 figures, 1 appendi

Biases in determining the diet of jumbo squid Dosidicus gigas (D’ Orbigny 1835) (Cephalopoda: Ommastrephidae) off southern-central Chile (34°S–40°S)

The diet of jumbo squid (Dosidicus gigas) off southern-central Chile is described to examine potential biases in the determination of their main prey. Specimens were collected from catches using different fishing gear (jigging, trawl and purse-seine), from July 2003 to January 2004, and from December 2005 to October 2006. The stomach contents were analyzed in terms of frequency of occurrence, number, and weight of prey items and the diet composition was analyzed using Detrended Correspondence Analysis. In the industrial purse-seine fleet for jack mackerel (Trachurus murphyi), the dominant prey of D. gigas was T. murphyi. In the industrial mid-trawl fishery for Patagonian grenadier (Macruronus magellanicus), the dominant species in the diet of D. gigas was M. magellanicus. Similarly, Chilean hake (Merluccius gayi) was the main prey in the diet of D. gigas obtained in the industrial trawl fishery for Chilean hake; and, in both artisanal fisheries (purse-seine for small pelagics and jigging), small pelagic fish and D. gigas were the main prey in the stomach contents of D. gigas. Cannibalism in D. gigas varied between different fleets and probably is related to stress behavior during fishing. The Detrended Correspondence Analysis ordination showed that the main prey in the diet of D. gigas is associated with the target species of the respective fishery. Consequently, biases are associated with fishing gear, leading to an overestimate in the occurrence of the target species in the diet. We recommend analyzing samples from jigging taken at the same time and place where the trawl and purse-seine fleets are operating to avoid this problem, and the application of new tools like stable isotope, heavy metal, and fatty acid signature analyses

General-purpose kernel regularization of boundary integral equations via density interpolation

This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed technique relies on interpolating the density function around the kernel singularity in terms of solutions of the underlying homogeneous PDE, so as to recast singular and nearly singular integrals in terms of bounded (or more regular) integrands. We present here a simple interpolation strategy which, unlike previous approaches, does not entail explicit computation of high-order derivatives of the density function along the surface. Furthermore, the proposed approach is kernel- and dimension-independent in the sense that the sought density interpolant is constructed as a linear combination of point-source fields, given by the same Green's function used in the integral equation formulation, thus making the procedure applicable, in principle, to any PDE with known Green's function. For the sake of definiteness, we focus here on Nystr\"om methods for the (scalar) Laplace and Helmholtz equations and the (vector) elastostatic and time-harmonic elastodynamic equations. The method's accuracy, flexibility, efficiency, and compatibility with fast solvers are demonstrated by means of a variety of large-scale three-dimensional numerical examples

Interaction Parameters of Surfactant Mixtures by Inverse Gas Chromatography

The Inverse Gas Chromatography (IGC) has been used in the measurement of surfactant-surfactant interaction parameters at different percentages and temperatures in cationic surfactant mixtures. Specific retention volume values obtained with different probe solutes in surfactant mixtures could be qualitative tests of the miscibility as those obtained in polymeric materials. The results for systems constitute by cationic surfactant mixtures have been compared. Two phenomenological methodology, Farooque-Deshpande and Huang, for calculate of the interaction parameter have been employed and the results compared with those obtained in polymer mixtures. The results obtained in surfactant mixtures are similar to obtained in polymeric material when both methodologies are compared. We found that the difference between interception calculated values are greater when the slope obtained by Huang methodology to withdraw of the unity.Fil: Arancibia, Eleuterio Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto de Química del Noroeste. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química del Noroeste; ArgentinaFil: Schulz, Pablo Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Química del Sur. Universidad Nacional del Sur. Departamento de Química. Instituto de Química del Sur; ArgentinaFil: Bardavid, Susana M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto de Química del Noroeste. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química del Noroeste; Argentin

A complex-scaled boundary integral equation for time-harmonic water waves

This paper presents a novel boundary integral equation (BIE) formulation for the two-dimensional time-harmonic water-waves problem. It utilizes a complex-scaled Laplace's free-space Green's function, resulting in a BIE posed on the infinite boundaries of the domain. The perfectly matched layer (PML) coordinate stretching that is used to render propagating waves exponentially decaying, allows for the effective truncation and discretization of the BIE unbounded domain. We show through a variety of numerical examples that, despite the logarithmic growth of the complex-scaled Laplace's free-space Green's function, the truncation errors are exponentially small with respect to the truncation length. Our formulation uses only simple function evaluations (e.g. complex logarithms and square roots), hence avoiding the need to compute the involved water-wave Green's function. Finally, we show that the proposed approach can also be used to find complex resonances through a \emph{linear} eigenvalue problem since the Green's function is frequency-independent