Optimal bounds with semidefinite programming: an application to stress driven shear flows

We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing schemes, we do not consider the Euler--Lagrange equations for the minimizer. Instead, we use series expansions to formulate a finite dimensional semidefinite program (SDP) whose solution converges to that of the original variational problem. Our formulation accounts for the influence of all modes in the expansion, and the feasible set of the SDP corresponds to a subset of the feasible set of the original problem. Moreover, SDPs can be easily formulated when the fluid is subject to imposed boundary fluxes, which pose a challenge for the traditional methods. We apply this technique to compute rigorous and near-optimal upper bounds on the dissipation coefficient for flows driven by a surface stress. We improve previous analytical bounds by more than 10 times, and show that the bounds become independent of the domain aspect ratio in the limit of vanishing viscosity. We also confirm that the dissipation properties of stress driven flows are similar to those of flows subject to a body force localized in a narrow layer near the surface. Finally, we show that SDP relaxations are an efficient method to investigate the energy stability of laminar flows driven by a surface stress.Comment: 17 pages; typos removed; extended discussion of linear matrix inequalities in Section III; revised argument in Section IVC, results unchanged; extended discussion of computational setup and limitations in Sectios IVE-IVF. Submitted to Phys. Rev.

Exact energy stability of B\'enard-Marangoni convection at infinite Prandtl number

Using the energy method we investigate the stability of pure conduction in Pearson's model for B\'enard-Marangoni convection in a layer of fluid at infinite Prandtl number. Upon extending the space of admissible perturbations to the conductive state, we find an exact solution to the energy stability variational problem for a range of thermal boundary conditions describing perfectly conducting, imperfectly conducting, and insulating boundaries. Our analysis extends and improves previous results, and shows that with the energy method global stability can be proven up to the linear instability threshold only when the top and bottom boundaries of the fluid layer are insulating. Contrary to the well-known Rayleigh-B\'enard convection setup, therefore, energy stability theory does not exclude the possibility of subcritical instabilities against finite-amplitude perturbations.Comment: 11 pages, 2 figures. Preprint submitted to the Journal of Fluid Mechanics. Version 2: minor text and notational changes, added a new appendix A, added detail to Section

Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials

Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares (SSOS) optimization, diagonally dominant sum-of-squares (DSOS) optimization, and scaled diagonally dominant sum-of-squares (SDSOS) optimization. We prove that the set of SSOS polynomials, an inner approximation of the cone of SOS polynomials, strictly contains the spaces of sparse DSOS/SDSOS polynomials. When applicable, therefore, SSOS optimization is less conservative than its DSOS/SDSOS counterparts. Numerical results for large-scale sparse polynomial optimization problems demonstrate this fact, and also that SSOS optimization can be faster than DSOS/SDSOS methods despite requiring the solution of semidefinite programs instead of less expensive linear/second-order cone programs.Comment: 9 pages, 3 figure

Transparency in Port-Hamiltonian-Based Telemanipulation

After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of packet switching scattering-based communication channels

Position Drift Compensation in Port-Hamiltonian Based Telemanipulation

Passivity based bilateral telemanipulation schemes are often subject to a position drift between master and slave if the communication channel is implemented using scattering variables. The magnitude of this position mismatch can be significant during interaction tasks. In this paper we propose a passivity preserving scheme for compensating the position drift arising during contact tasks in port-Hamiltonian based telemanipulation improving the kinematic perception of the remote environment felt by the human operato

Compensation of position errors in passivity based teleoperation over packet switched communication networks

Because of the use of scattering based communication channels, passivity based telemanipulation systems can be subject to a steady state position error between master and slave robots. In this paper, we consider the case in which the passive master and slave sides communicate through a packet switched communication channel (e.g. Internet) and we provide a modification of the slave impedance controller for compensating the steady state position error arising in free motion because of packets loss

Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak-and strong-form finite element solutions

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted

Theocritus and the Bucolic Genre

One of the chapters written by M. Fantuzzi in M. Fantuzzi and R. Hunter, "Tradition and Innovation in Hellenistic poetry" Analysis of the the construction of the genre of "literary mime, and of its sub-genre bucolic poetry. Main emphasis on the idea of "Invention of a tradition" on behalf of Theocritus, and the dynamics between pastoral ideal of hesychia and pains of love both in Theocritus and in the post-Theocritean bucolic poet

Estudio de diferencias en el tratamiento funerario entre distintos grupos etarios en un cementerio del Período Temprano del Noroeste Argentino

En la dècada de 1920 es va excavar a la localitat de La Ciénaga (vall de Hualfín, Província de Catamarca, Argentina) una zona de necròpolis constituïda per un conjunt de 14 cementiris que dècades més tard va ser datada dins del “Período Temprano” del Nord-oest Argentí (200-600 dC). A partir d'una revisió de l'ampli registre documental d'aquelles excavacions i dels materials recuperats, que avui es conserven al Museu de Ciències Naturals de la Plata, es van analitzar els contextos funeraris d'un d'aquests cementiris, el n º 13, centrant l'estudi en la manera en què els individus van ser enterrats d'acord al grup etari al qual pertanyien. En aquest treball es presenten els resultats obtinguts, on s'ha pogut registrar un tractament diferencial pel que fa a diverses variables vinculades al tipus d'enterrament i als aixovars associats. Es busca així analitzar la conceptualització dins de l'àmbit funerari de diferents categories etàries per part del grup social i de quina manera aquestes diferències es veien materialitzades en els sepulcres.In the decade of the 1920's a necropolis comprising a set of 14 cemeteries was excavated in the site of La Ciénaga (Hualfín Valley, Province of Catamarca, Argentina), which some decades later was dated to the Early Period of Argentine Northwest (200-600 AD). Based on a review of the extensive documentation and the materials recovered from those excavations, which are currently preserved in the Museum of Natural Sciences of La Plata, the funerary contexts of one of these cemeteries (No. 13) were analyzed, studying specially the way in which individuals were buried according to the age group they belonged to. A differential treatment was observed in relation to a number of variables regarding the burial type and the grave goods. In this way, the purpose is to analyze the conceptualization of different age categories in the funerary sphere by the social group and how those differences were materialized in the tombs.En la década de 1920 se excavó en la localidad de La Ciénaga (valle de Hualfín, Provincia de Catamarca, Argentina) una zona de necrópolis constituida por un conjunto de 14 cementerios que décadas más tarde fue datada dentro del Período Temprano del Noroeste Argentino (200-600 d. C. ). A partir de una revisión del amplio registro documental de aquellas excavaciones y de los materiales recuperados, que hoy se conservan en el Museo de Ciencias Naturales de La Plata, se analizaron los contextos funerarios de uno de esos cementerios, el nº 13, haciendo hincapié en el estudio del modo en que los individuos fueron sepultados de acuerdo al grupo etario al que pertenecían. En este trabajo se presentan los resultados obtenidos, habiéndose podido registrar un tratamiento diferencial en cuanto a diversas variables vinculadas al tipo de entierro y a los ajuares asociados. Se busca así indagar sobre la conceptualización dentro del ámbito funerario de distintas categorías etarias por parte del grupo social y de qué manera esas diferencias se veían materializadas en los sepulcros

Estudio de diferencias en el tratamiento funerario entre distintos grupos etarios en un cementerio del Período Temprano del Noroeste Argentino

Jornadas de Jóvenes en Investigación Arqueológica, JIA (3as : 5-7 de mayo 2010 : Universitat Autònoma de Barcelona). Sesión 5. Arqueología de la muerte.En la década de 1920 se excavó en la localidad de La Ciénaga (valle de Hualfín, Provincia de Catamarca, Argentina) una zona de necrópolis constituida por un conjunto de 14 cementerios que décadas más tarde fue datada dentro del Período Temprano del Noroeste Argentino (200-600 d.C.). A partir de una revisión del amplio registro documental de aquellas excavaciones y de los materiales recuperados, que hoy se conservan en el Museo de Ciencias Naturales de La Plata, se analizaron los contextos funerarios de uno de esos cementerios, el nº 13, haciendo hincapié en el estudio del modo en que los individuos fueron sepultados de acuerdo al grupo etario al que pertenecían. En este trabajo se presentan los resultados obtenidos, habiéndose podido registrar un tratamiento diferencial en cuanto a diversas variables vinculadas al tipo de entierro y a los ajuares asociados. Se busca así indagar sobre la conceptualización dentro del ámbito funerario de distintas categorías etarias por parte del grupo social y de qué manera esas diferencias se veían materializadas en los sepulcros.In the decade of the 1920's a necropolis comprising a set of 14 cemeteries was excavated in the site of La Ciénaga (Hualfín Valley, Province of Catamarca, Argentina), which some decades later was dated to the Early Period of Argentine Northwest (200-600 AD). Based on a review of the extensive documentation and the materials recovered from those excavations, which are currently preserved in the Museum of Natural Sciences of La Plata, the funerary contexts of one of these cemeteries (No. 13) were analyzed, studying specially the way in which individuals were buried according to the age group they belonged to. A differential treatment was observed in relation to a number of variables regarding the burial type and the grave goods. In this way, the purpose is to analyze the conceptualization of different age categories in the funerary sphere by the social group and how those differences were materialized in the tombs.En la dècada de 1920 es va excavar a la localitat de La Ciénaga (vall de Hualfín, Província de Catamarca, Argentina) una zona de necròpolis constituïda per un conjunt de 14 cementiris que dècades més tard va ser datada dins del "Período Temprano" del Nord-oest Argentí (200-600 dC). A partir d'una revisió de l'ampli registre documental d'aquelles excavacions i dels materials recuperats, que avui es conserven al Museu de Ciències Naturals de la Plata, es van analitzar els contextos funeraris d'un d'aquests cementiris, el n º 13, centrant l'estudi en la manera en què els individus van ser enterrats d'acord al grup etari al qual pertanyien. En aquest treball es presenten els resultats obtinguts, on s'ha pogut registrar un tractament diferencial pel que fa a diverses variables vinculades al tipus d'enterrament i als aixovars associats. Es busca així analitzar la conceptualització dins de l'àmbit funerari de diferents categories etàries per part del grup social i de quina manera aquestes diferències es veien materialitzades en els sepulcres.