Multi-point Taylor approximations in one-dimensional linear boundary value problems

We consider second-order linear differential equations in a real interval $I$ with mixed Dirichlet and Neumann boundary data. We consider a representation of its solution by a multi-point Taylor expansion. The number and location of the base points of that expansion are conveniently chosen to guarantee that the expansion is uniformly convergent $\forall x\in I$. We propose several algorithms to approximate the multi-point Taylor polynomials of the solution based on the power series method for initial value problems

A three-point Taylor algorithm for three-point boundary value problems

We consider second-order linear differential equations $\varphi(x)y''+f(x)y'+g(x)y=h(x)$ in the interval $(-1,1)$ with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions given at three points of the interval: the two extreme points $x=\pm 1$ and an interior point $x=s\in(-1,1)$. We consider $\varphi(x)$, $f(x)$, $g(x)$ and $h(x)$ analytic in a Cassini disk with foci at $x=\pm 1$ and $x=s$ containing the interval $[-1,1]$. The three-point Taylor expansion of the solution $y(x)$ at the extreme points $\pm 1$ and at $x=s$ is used to give a criterion for the existence and uniqueness of the solution of the boundary value problem. This method is constructive and provides the three-point Taylor approximation of the solution when it exists. We give several examples to illustrate the application of this technique

The error function in the study of singularly perturbed convection-diffusion problems with discontinuous boundary data

We show the importance of the error function in the approximation of the solution of singularly perturbed convection-diffusion problems with discontinuous boundary conditions. It is observed that the error function (or a combination of them) provides an excellent approximation and reproduces accurately the effect of the discontinuities on the behaviour of the solution at the boundary and interior layers

First order approximation of an elliptic 3D singular perturbation problem

A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is considered. The solution of the problem is written in terms of a double integral. A saddle point analysis is used to obtain a first approximation, which is expressed in terms of a function that can be viewed as a generalization of the complementary error functio

Determination of Network Configuration Considering Inventory Cost in a Supply Chain

AbstractIn this paper we show the importance of applying mathematical optimization when designing the distribution network in a supply chain, specifically in making decisions related location of facilities and inventory management, which are associated with different levels of planning but are closely related.The addressed problem is an extension of the classic capacitated facility location problem. The distinguishing features are: the inventory management, the presence of multiple plants, and the single source constraints in both echelons. A key issue is that demand at each distribution center is a function of the demands at the retailers assigned, which is a random variable whose value is not known at the time of designing the network. We focus on the mathematical modeling of the problem and the evaluation of the performance of the developed models, so, it can be observed the troubles that arise when modeling supply chains that consider different types of decisions

The Error Function in the Study of Singularly Perturbed Convection-Diffusion Problems with Discontinuous Boundary Data

We show the importance of the error function in the approximation of the solution of singularly perturbed convection-diffusion problems with discontinuous boundary conditions. It is observed that the error function (or a combination of them) provides an excellent approximation and reproduces accurately the effect of the discontinuities on the behaviour of the solution at the boundary and interior layers

The decay Z -> neutrino antineutrino photon in the Standard Model

A complete study of the one-loop induced decay Z -> neutrino antineutrino photon is presented within the framework of the Standard Model. The advantages of using a nonlinear gauge are stressed. We have found that the main contributions come from the electric dipole and the magnetic dipole transitions of the Z gauge boson and the neutrino, respectively. We obtain a branching ratio B=7.16E-10, which is about four orders of magnitude smaller than the bound recentely obtained by the L3 collaboration and thus it leaves open a window to search for new physics effects in single-photon decays of the Z boson.Comment: REVTEX,15 pp, 5 eps figures, Approved for publication in Physical Review

Temporal variations of non-volcanic tremor (NVT) locations in the Mexican subduction zone: Finding the NVT sweet spot.

International audienceEpicentral locations of non-volcanic tremors (NVT) in the Mexican subduction zone are determined from the peak of the energy spatial distribution and examined over time. NVT is found to occur persistently at a distance of ∼215 km from the trench, which we term the "Sweet Spot" because this region probably has the proper conditions (i.e., temperature, pressure, and fluid content) for the NVT to occur with minimum shear slip. High-energy NVT episodes are also observed every few months, extending ∼190 km to ∼220 km from the trench with durations of a few weeks. During the 2006 slow slip event (SSE) the duration and the recurrence rate of the NVT episodes increased. Low-energy episodes were also observed, independent from the high-energy episodes, ∼150 km to ∼190 km from the trench during the 2006 SSE. Both the high and low energy episodes were made up of many individual NVT's that had a range of energy-release-rates. However, the highest energy-release-rates of the high-energy episodes were consistently double those of the low-energy episodes and the persistent activity at the Sweet Spot. We suggest that all of the high-energy episodes are evidence of small, short repeat interval SSE. Given this model, the increased recurrence rate of the high-energy NVT episodes during the 2006 long-term SSE implies that short-term SSE's also increase during the SSE and are therefore triggered by the SSE

Propagation inhibition and wave localization in a 2D random liquid medium

Acoustic propagation and scattering in water containing many parallel air-filled cylinders is studied. Two situations are considered and compared: (1) wave propagating through the array of cylinders, imitating a traditional experimental setup, and (2) wave transmitted from a source located inside the ensemble. We show that waves can be blocked from propagation by disorders in the first scenario, but the inhibition does not necessarily imply wave localization. Furthermore, the results reveal the phenomenon of wave localization in a range of frequencies.Comment: Typos in Fiures are correcte

3D electrical resistivity of Gran Canaria island using magnetotelluric data

Gran Canaria, one of the two main islands of the Canary Archipelago off NW Africa, has been volcanically active for at least 15 million years. The island went through several volcanic cycles that varied greatly in composition and extrusive and intrusive activity. The complex orography of the island has excluded extensive land geophysical surveys on the island. A review of the available geophysical information on the island shows that it has been obtained mainly through marine and airborne geophysical surveys. A new dataset comprising 100 magnetotelluric soundings acquired on land has been used to obtain the first 3D electrical resistivity model of the island at crustal scale. The model shows high resistivity values close to the surface in the exposed Tejeda Caldera that extends at depth to the SE cutting the islands in half. Outside the inferred limits of the Tejeda Caldera the 3D model shows low resistivity values that could be explained by hydrothermal alteration at deeper levels and the presence of marine saltwater intrusion at shallower levels near the coast. The presence of unconnected vertical-like structures, with very low resistivity (<10 ohm m) could be associated to small convective cells is confirmed by the sensitivity analysis carried out in the present study. Those structures are the most likely candidates for a detailed analysis in order to determine their geothermal economic potential. A comprehensive review of existing geophysical data and models of Gran Canaria island and their comparison with the new 3D electrical resistivity model is presented.</p