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

Extended rotating disks around post-AGB stars

There is a group of binary post-AGB stars that show a conspicuous NIR excess, usually assumed to arise from hot dust in very compact possibly rotating disks. These stars are surrounded by significantly fainter nebulae than the "standard", well studied protoplanetary and planetary nebulae (PPNe, PNe). We present high-sensitivity mm-wave observations of CO lines in 24 objects of this type. CO emission is detected in most observed sources and the line profiles show that the emissions very probably come from disks in rotation. We derive typical values of the disk mass between 1e-3 and 1e-2 Mo, about two orders of magnitude smaller than the (total) masses of "standard" PPNe. The high-detection rate (upper limits being in fact not very significant) clearly confirm that the NIR excess of these stars arises from compact disks in rotation, very probably the inner parts of those found here. Low-velocity outflows are also found in about eight objects, with moderate expansion velocities of ~ 10 km/s, to be compared with the velocities of about 100 km/s often found in "standard" PPNe. Except for two sources with complex profiles, the outflowing gas in our objects represents a minor nebular component. Our simple estimates of the disk typical sizes yields values ~ 0.5 - 1 arcsec, i.e. between 5e15 and 3e16 cm. Estimates of the linear momenta carried by the outflows, which can only be performed in a few well studied objects, also yield moderate values, compared with the linear momenta that can be released by the stellar radiation pressure (contrary, again, to the case of the very massive and fast bipolar outflows in "standard" PPNe, that are strongly overluminous). The mass and dynamics of nebulae around various classes of post-AGB stars differ very significantly, and we can expect the formation of PNe with very different properties.Comment: 19 pages, 26 figure