Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses

Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the Bieche et al. approach.Comment: 11 pages, 5 figures; shortened introduction, extended results; to appear in Physical Review E 7

Gauge and Poincare' Invariant Regularization and Hopf Symmetries

We consider the regularization of a gauge quantum field theory following a modification of the Polchinski proof based on the introduction of a cutoff function. We work with a Poincare' invariant deformation of the ordinary point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and Sadooghi, and show that it yields, through a limiting procedure of the cutoff functions, to a regularized theory, preserving all symmetries at every stage. The new gauge symmetry yields a new Hopf algebra with deformed co-structures, which is inequivalent to the standard one.Comment: Revised version. 14 pages. Incorrect statements eliminate

Subextensive singularity in the 2D ±J\pm J Ising spin glass

The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Similar results are found for $p$ = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation $d \nu = 2 - \alpha$, even though $T_c = 0$. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented.Comment: 13 pages, 7 figures; final version, to appear in J. Stat. Phy

Closed-Loop Manufacturing for Aerospace Industry: An Integrated PLM-MOM Solution to Support the Wing Box Assembly Process

The aim of this research is to provide an example of the importance that integrated Product Lifecycle Management (PLM) and Manufacturing Operation Management (MOM) systems have in realizing the Digital Manufacturing. The research first examines what the Digital Manufacturing involves and then identifies Digital Twin and the related Digital Thread as key elements. PLM and MOM solutions support the Digital Twin and the Digital Thread allowing the exchange of product-related information between the digital manufacturing model and the physical manufacturing execution. A Digital Twin of a wing box and its assembly process is created in PLM by building the bill of material and bill of process. Then it is shown how in MOM system the production phase is facilitated by managing production operations, advanced scheduling and supporting the execution of the processes and how the analysis of the manufacturing performance is possible. The result integrating these systems is to have the right information at the right place at the right time along with the related benefits in terms of costs, time and quality. The activity has been developed in Siemens Industry Software under the European Project AirGreen 2, an integrated research action of the REG IADP (Regional Innovative Aircraft Demonstration Platform) part of the Joint Technical Programme, the steering and coordination of LEONARDO Aircraft. The AirGreen 2 project is an Innovation Action funded by the Clean Sky 2 Joint Undertaking under the European Union\u2019s Horizon 2020 research and innovation programme, under Grant Agreement N\ub0807089 REG IADP)

Error threshold in the evolution of diploid organisms

The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully investigated. In particular, it is shown that dominance can protect the wild-type alleles from the error catastrophe. The analysis is restricted to a diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge

Experimental results of crystal-assisted slow extraction at the SPS

The possibility of extracting highly energetic particles from the Super Proton Synchrotron (SPS) by means of silicon bent crystals has been explored since the 1990's. The channelling effect of a bent crystal can be used to strongly deflect primary protons and eject them from the synchrotron. Many studies and experiments have been carried out to investigate crystal channelling effects. The extraction of 120 and 270 GeV proton beams has already been demonstrated in the SPS with dedicated experiments located in the ring. Presently in the SPS, the UA9 experiment is performing studies to evaluate the possibility to use bent silicon crystals to steer particle beams in high energy accelerators. Recent studies on the feasibility of extraction from the SPS have been made using the UA9 infrastructure with a longer-term view of using crystals to help mitigate slow extraction induced activation of the SPS. In this paper, the possibility to eject particles into the extraction channel in LSS2 using the bent crystals already installed in the SPS is presented. Details of the concept, simulations and measurements carried out with beam are presented, before the outlook for the future is discussed.Comment: 4 pages, 7 figures, submitted to to International Particle Accelerator Conference (IPAC) 2017 in Copenhagen, Denmar