Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

p. 509-524In different problems of Elasticity the definition of the optimal geometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.Garcia-Palacios, J.; Castro, C.; Samartin, A. (2009). Optimal boundary geometry in an elasticity problem: a systematic adjoint approach. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654

Relativistic Coulomb scattering of spinless bosons

The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb fields is analyzed in detail with an arbitrary mixing of vector and scalar couplings. It is shown that the partial wave series reduces the scattering amplitude to the closed Rutherford formula exactly when the vector and scalar potentials have the same magnitude, and as an approximation for weak fields. The behavior of the scattering amplitude near the conditions that furnish its closed form is also discussed. Strong suppressions of the scattering amplitude when the vector and scalar potentials have the same magnitude are observed either for particles or antiparticles with low incident momentum. We point out that such strong suppressions might be relevant in the analysis of the scattering of fermions near the conditions for the spin and pseudospin symmetries. From the complex poles of the partial scattering amplitude the exact closed form of bound-state solutions for both particles and antiparticles with different scenarios for the coupling constants are obtained. Perturbative breaking of the accidental degeneracy appearing in a pair of special cases is related to the nonconservation of the Runge-Lenz vector

New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac

Helping America's Dual Language Learners Succeed: A Research-based Agenda for Action

In the fall of 2014, the Heising-Simons and McKnight Foundations provided support for a National Research Summit on the Early Care and Education of Dual Language Learners (DLLs) in Washington, DC. The goal of the two day summit was to engage and extend the established knowledge base accrued by the Center for Early Care and Educational Research Dual Language Learners (CECER-DLL), while simultaneously informing the future potential efforts by the Heising-Simons and McKnight Foundations specific to the early care and education of dual language learners. Day two centered on the presentation of five McKnight-commissioned papers, the topics of which included: Research Based Models and Best Practices for DLLs across PreK - 3rd gradePerspectives on Assessment of DLLs Development & Learning, PreK - 3Human Resource Development and Support for Those Serving DLLsThe Critical Role of Leaderships in Programs Designed for DLLs, PreK - 3Policy Advances & Levers Related to DLLs in PreK - 3rd gradeThe report attempts to provide a short summary and synthesis of the topics covered in these papers and the discussion generated at the National Summit on Early Care and Education of Dual Language Learners. In addition, a set of recommendations are presented for each topic with regard to the implications drawn from these synthesis and of particular relevance to the supporting foundations' future investment considerations related to DLLs

Participación popular y protesta social en el simulacro de Guerra de Independencia en Tonatico, Estado de México

Este trabajo tiene por objetivo analizar una festividad popular que se realiza cada año en el poblado de Tonatico, Estado de México, en forma de simulacro de Guerra de Independencia. En esta festividad se expresa un sentido cultural de rebeldía y sarcasmo que forma parte de los imaginarios colectivos patrios. El trabajo está dividido en cuatro partes. En la primera se intenta desarrollar una breve explicación de las festividades cívicas mexicanas desde el punto de vista de la reciente historiografía de la historia cultural patria. En la segunda se elabora una descripción acerca del origen y trayectoria histórica de las celebraciones cívicas y patrias en nuestro país, además de descubrir tanto su carácter formal y solemne como su aspecto popular. En la tercera se examinan los factores que han permitido una larga continuidad del simulacro en manos de los ciudadanos. Y, finalmente, se analiza el desarrollo del simulacro de Guerra de Independencia sobre una secuencia fotográfica, para mostrar el carácter popular, de irreverencia y protesta social que tiene lugar en Tonatico, el 26 y 27 de septiembre de cada año.Este trabajo tiene por objetivo analizar una festividad popular que se realiza cada año en el poblado de Tonatico, Estado de México, en forma de simulacro de Guerra de Independencia. En esta festividad se expresa un sentido cultural de rebeldía y sarcasmo que forma parte de los imaginarios colectivos patrios. El trabajo está dividido en cuatro partes. En la primera se intenta desarrollar una breve explicación de las festividades cívicas mexicanas desde el punto de vista de la reciente historiografía de la historia cultural patria. En la segunda se elabora una descripción acerca del origen y trayectoria histórica de las celebraciones cívicas y patrias en nuestro país, además de descubrir tanto su carácter formal y solemne como su aspecto popular. En la tercera se examinan los factores que han permitido una larga continuidad del simulacro en manos de los ciudadanos. Y, finalmente, se analiza el desarrollo del simulacro de Guerra de Independencia sobre una secuencia fotográfica, para mostrar el carácter popular, de irreverencia y protesta social que tiene lugar en Tonatico, el 26 y 27 de septiembre de cada año

Relativistic quantum dynamics of scalar bosons under a full vector Coulomb interaction

The relativistic quantum dynamics of scalar bosons in the background of a full vector coupling (minimal plus nonminimal vector couplings) is explored in the context of the Duffin-Kemmer-Petiau formalism. The Coulomb phase shift is determined for a general mixing of couplings and it is shown that the space component of the nonminimal coupling is a {\it sine qua non} condition for the exact closed-form scattering amplitude. It follows that the Rutherford cross section vanishes in the absence of the time component of the minimal coupling. Bound-state solutions obtained from the poles of the partial scattering amplitude show that the time component of the minimal coupling plays an essential role. The bound-state solutions depend on the nonminimal coupling and the spectrum consists of particles or antiparticles depending on the sign of the time component of the minimal coupling without chance for pair production even in the presence of strong couplings. It is also shown that an accidental degeneracy appears for a particular mixing of couplings.Comment: 8 pages, 1 table. arXiv admin note: text overlap with arXiv:1403.603

The Generalized Moyal Nahm and Continuous Moyal Toda Equations

We present in detail a class of solutions to the $4D SU(\infty)$ Moyal Anti Self Dual Yang Mills equations that are related to $reductions$ of the generalized Moyal Nahm quations using the Ivanova-Popov ansatz. The former yields solutions to the ASDYM/SDYM equations for arbitary gauge groups. A further dimensional reduction yields solutions to the Moyal Anti Self Dual Gravitational equations. The Self Dual Yang Mills /Self Dual Gravity case requires a separate study. SU(2) and $SU(\infty)$ (continuous) Moyal Toda equations are derived and solutions to the latter equations in $implicit$ form are proposed via the Lax-Brockett double commutator formalism . An explicit map taking the Moyal heavenly form (after a rotational Killing symmetry reduction) into the SU(2) Moyal Toda field is found. Finally, the generalized Moyal Nahm equations are conjectured that contain the continuous $SU(\infty)$ Moyal Toda equation after a suitable reduction. Three different embeddings of the three different types of Moyal Toda equations into the Moyal Nahm equations are discussed.Comment: Revised TEX file. 31 pages. The Legendre transform between the Moyal heavenly form and the Moyal Toda field is solve