A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme

Aby Warburg: His Aims and Methods

In this issue of Engramma: Giulia Zanon’s "Zooming Mnemosyne" deals with the use of details in Warburg’s Bilderatlas, Monica Centanni’s "Collateral effects of the “visibile parlare” (Dante, Pg. X, v. 95)" reconstructs the hypothesis of a visual model for the legend of Trajan’s Justice, according to Warburg intuition about it; this contribution is connected of the paper by Filippo Perfetti’s "Dante, Botticelli, and Trajan. An Open Note" where the author investigates how Botticelli could have come to know that the bas-relief of the Arch of Constantine liberatori urbis was related to an episode in Trajan's life”. The focus of this issue is then extended to Warburg's cultural environment. Matilde Sergio’s "Aby Warburg, Walter Benjaming, and the Memory of Images" investigates the influence of Warburg's essay about Luther, on Benjamin's thought, while Dorothee Gelhard’s "Gertrud Bing’s Scientific Beginnings" reconstructs the intellectual history of Bing's doctoral thesis and its influences on Warburgian work. The theme of Warburg’s Denkraum is the focal point of Salvatore Settis’ "Anselm Kiefer's Logic of Inversion": a fundamental overview of Kiefer's Questi scritti, quando verranno bruciati, daranno finalmente un po’ di luce (Andrea Emo) on display at Sala dello Scrutinio in Palazzo Ducale, Venezia from March to October 2022. The third section of the issue is dedicated to new publications and exhibitions. Echoing Settis’ reflection on Denkraum, we present Clio Nicastro’s "La Dialettica del Denkraum in Aby Warburg", published this year for Palermo University Press; an introduction to "Cultural Memories": a series published by Peter Lang and edited by Katia Pizzi. Giacomo Calandra di Roccolino with "Mary Hertz Warburg: Free and Unconventional" reviews the exhibition of the artist Mary Hertz Warburg. The issue closes with the important "Choral Reading of "Il metodo di Aby Warburg" by Kurt W. Forster. L’antico dei gesti. Il futuro della memoria", where Barbara Baert, Victoria Cirlot, Georges Didi-Huberman, Michael Diers, Andrea Pinotti and Ianick Takaes offer us their personal reading of Warburg’s life and thought as they are presented by Forster’s newly translated book, edited by Ronzani editore

CFD modelling of wind turbine airfoil aerodynamics

This paper reports the first findings of an ongoing research programme on wind turbine computational aerodynamics at the University of Glasgow. Several modeling aspects of wind turbine airfoil aerodynamics based on the solution of the Reynoldsaveraged Navier-Stokes (RANS) equations are addressed. One of these is the effect of an a priori method for structured grid adaptation aimed at improving the wake resolution. Presented results emphasize that the proposed adaptation strategy greatly improves the wake resolution in the far-field, whereas the wake is completely diffused by the non-adapted grid with the same number and distribution of grid nodes. A grid refinement analysis carried out with the adapted grid shows that the improvements of flow resolution thus achieved are of a smaller magnitude with respect to those accomplished by adapting the grid keeping constant the number of nodes. The proposed adaptation approach can be easily included in the structured generation process of both commercial and in-house structured mesh generators systems. The study also aims at quantifying the solution inaccuracy arising from not modeling the laminar-to-turbulent transition. It is found that the drag forces obtained by considering the flow as transitional or fully turbulent may differ by 50 %. The impact of various turbulence models on the predicted aerodynamic forces is also analyzed. All these issues are investigated using a special-purpose hyperbolic grid generator and a multi-block structured finitevolume RANS code. The numerical experiments consider the flow field past a wind turbine airfoil for which an exhaustive campaign of steady and unsteady experimental measurements was conducted. The predictive capabilities of the CFD solver are validated by comparing experimental data and numerical predictions for selected flow regimes. The incompressible analysis and design code XFOIL is also used to support the findings of the comparative analysis of numerical RANS-based results and experimental data

Planar Gravitational Corrections For Supersymmetric Gauge Theories

In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N=1 supersymmetric gauge theories admitting a large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.Comment: 20 pages, 4 figure

Composite pulses in Hyper-Ramsey spectroscopy for the next generation of atomic clocks

The next generation of atomic frequency standards based on an ensemble of neutral atoms or a single-ion will provide very stringent tests in metrology, applied and fundamental physics requiring a new step in very precise control of external systematic corrections. In the proceedings of the 8th Symposium on Frequency Standards and Metrology, we present a generalization of the recent Hyper-Ramsey spectroscopy with separated oscillating fields using composites pulses in order to suppress field frequency shifts induced by the interrogation laser itself. Sequences of laser pulses including specific selection of phases, frequency detunings and durations are elaborated to generate spectroscopic signals with a strong reduction of the light-shift perturbation by off resonant states. New optical clocks based on weakly allowed or completely forbidden transitions in atoms, ions, molecules and nuclei will benefit from these generalized Ramsey schemes to reach relative accuracies well below the 10$^{-18}$ level.Comment: accepted as proceedings of the 8th Symposium on Frequency Standards and Metrology (Potsdam Germany, 12-16 october 2015

Synthetic Frequency Protocol in the Ramsey Spectroscopy of Clock Transitions

We develop an universal method to significantly suppress probe-induced shifts in any types of atomic clocks using the Ramsey spectroscopy. Our approach is based on adaptation of the synthetic frequency concept [V. I. Yudin, et al., Phys. Rev. Lett. 107, 030801 (2011)] (previously developed for BBR shift suppression) to the Ramsey spectroscopy with the use of interrogations for different dark time intervals. Universality of the method consists in arbitrariness of the possible Ramsey schemes. However, most extremal results are obtained in combination with so-called hyper-Ramsey spectroscopy [V. I. Yudin, et al., Phys. Rev. A 82, 011804(R) (2010)]. In the latter case, the probe-induced frequency shifts can be suppressed considerably below a fractional level of 10$^{-18}$ practically for any optical atomic clocks, where this shift previously was metrologically significant. The main advantage of our method in comparison with other radical hyper-Ramsey approaches [R. Hobson, et al., Phys. Rev. A 93, 010501(R) (2016); T. Zanon-Willette, et al., Phys. Rev. A 93, 042506 (2016)] consist in much greater efficiency and resistibility in the presence of decoherentization.Comment: 9 pages, 7 figure