Dynamics of quantum adiabatic evolution algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size $n$. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxilary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap, $g_{\rm min}={\cal O}(n 2^{-n/2})$, corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simulteneous fipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimenssional quantum diffusion in the energy space. This effect provides a general limitation on the power of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.Comment: 32 pages, 5 figures, 3 Appendices; List of additions compare to v.3: (i) numerical solution of the stationary Schroedinger equation for the adiabatic eigenstates and eigenvalues; (ii) connection between the scaling law of the minimum gap with the problem size and the shape of the coarse-grained distribution of the adiabatic eigenvalues at the avoided-crossing poin

Bis[5-(4-bromo­phen­yl)-4-(tert-but­oxy­carbon­yl)pyrrolidine-2-carboxyl­ato]copper(II) dihydrate

In the title compound, [Cu(C16H19BrNO4)2]·2H2O, the CuII ion resides on an inversion centre and is coordinated by two O and two N atoms from two enanti­omeric 5-(4-bromo­phen­yl)-4-(tert-but­oxy­carbon­yl)pyrrolidine-2-carboxyl­ate ligands in a distorted square-planar geometry. The relative stereochemistry of the three stereogenic C atoms in each ligand has been determined. In the crystal, inter­molecular N—H⋯O and O—H⋯O hydrogen bonds link the mol­ecules into layers parallel to the bc plane. The crystal studied was twinned by pseudo­merohedry with twin fractions of 0.719 (3) and 0.281 (3)

2-[(1RS,3RS,3aRS,6aSR)-5-Benzyl-4,6-dioxo-3-phenyl­octa­hydro­pyrrolo­[3,4-c]pyrrol-1-yl]acetamide

In the title compound, C21H21N3O3, the relative stereochemistry of the four stereogenic C atoms has been determined. The dihedral angle between the phenyl rings is 77.63 (7)°. In the crystal, ribbons spread along the a axis are formed by N—H⋯O hydrogen bonds. C—H⋯π inter­actions also occur

Systems of Systems Engineering Thesaurus Approach: From Concept to Realisation

The developing discipline of Systems of Systems Engineering (SoSE) is gaining attention in an increasingly broad range of domains; however, each domain comes with its own set of terms and concepts so that there may be confusion between different domains ostensibly engaged in similar challenges. SoSE is faced with concept multiplicity (one term, more than one concept) and term multiplicity (one concept, more than one term). It is unrealistic to expect long-established domains to simply change ontology to match with other domains, but a means of recognising related concepts and terms across domains and across industrial sectors will enable more rapid progress to be made in the development of SoSE. The approach taken to generating a thesaurus, through which such relationships can be documented, is presented. The approach is essentially consultative among SoSE experts and the current version of the thesaurus is available online. A combination of problem statement definition and logical decomposition has been used; the method is described and application is illustrated using well-known terms

q Dependence of Self-Energy Effects of the Plane Oxygen Vibration in YBa₂Cu₃O₇

We have measured the temperature dependence of the peak position and linewidth of the 42.5 meV phonon branch in a twinned single crystal of YBa2Cu3O7 as a function of wave vector q. In the 100/010 direction in the Brillouin zone, considerable softening and broadening occur below the superconducting transition temperature Tc at some values of q. We observe an order of magnitude smaller softening and no linewidth broadening for q in the 110/110 direction. Possible implications of these findings for the symmetry of the superconducting order parameter are discussed

SensiCut: Material-Aware Laser Cutting Using Speckle Sensing and Deep Learning

Laser cutter users face difficulties distinguishing between visually similar materials. This can lead to problems, such as using the wrong power/speed settings or accidentally cutting hazardous materials. To support users, we present SensiCut, an integrated material sensing platform for laser cutters. SensiCut enables material awareness beyond what users are able to see and reliably differentiates among similar-looking types. It achieves this by detecting materials' surface structures using speckle sensing and deep learning. SensiCut consists of a compact hardware add-on for laser cutters and a user interface that integrates material sensing into the laser cutting workflow. In addition to improving the traditional workflow and its safety1, SensiCut enables new applications, such as automatically partitioning designs when engraving on multi-material objects or adjusting their geometry based on the kerf of the identified material. We evaluate SensiCut's accuracy for different types of materials under different sheet orientations and illumination conditions

An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy

An inverse optimization strategy was developed to determine the single crystal properties from experimental results of the mechanical behavior of polycrystals. The polycrystal behavior was obtained by means of the finite element simulation of a representative volume element of the microstructure in which the dominant slip and twinning systems were included in the constitutive equation of each grain. The inverse problem was solved by means of the Levenberg-Marquardt method, which provided an excellent fit to the experimental results. The iterative optimization process followed a hierarchical scheme in which simple representative volume elements were initially used, followed by more realistic ones to reach the final optimum solution, leading to important reductions in computer time. The new strategy was applied to identify the initial and saturation critical resolved shear stresses and the hardening modulus of the active slip systems and extension twinning in a textured AZ31 Mg alloy. The results were in general agreement with the data in the literature but also showed some differences. They were partially explained because of the higher accuracy of the new optimization strategy but it was also shown that the number of independent experimental stress-strain curves used as input is critical to reach an accurate solution to the inverse optimization problem. It was concluded that at least three independent stress-strain curves are necessary to determine the single crystal behavior from polycrystal tests in the case of highly textured Mg alloys

Development of an On-board Failure Diagnostics and Prognostics System for Solid Rocket Booster

We develop a case breach model for the on-board fault diagnostics and prognostics system for subscale solid-rocket boosters (SRBs). The model development was motivated by recent ground firing tests, in which a deviation of measured time-traces from the predicted time-series was observed. A modified model takes into account the nozzle ablation, including the effect of roughness of the nozzle surface, the geometry of the fault, and erosion and burning of the walls of the hole in the metal case. The derived low-dimensional performance model (LDPM) of the fault can reproduce the observed time-series data very well. To verify the performance of the LDPM we build a FLUENT model of the case breach fault and demonstrate a good agreement between theoretical predictions based on the analytical solution of the model equations and the results of the FLUENT simulations. We then incorporate the derived LDPM into an inferential Bayesian framework and verify performance of the Bayesian algorithm for the diagnostics and prognostics of the case breach fault. It is shown that the obtained LDPM allows one to track parameters of the SRB during the flight in real time, to diagnose case breach fault, and to predict its values in the future. The application of the method to fault diagnostics and prognostics (FD&P) of other SRB faults modes is discussed

Prediction of Ionic Cr (VI) Extraction Efficiency in Flat Sheet Supported Liquid Membrane Using Artificial Neural Networks (ANNs)

ABSTRACT:Artificial neural networks (ANNs) are computer techniques that attempt to simulate the functionality and decision-making processes of the human brain. In the past few decades, artificial neural networks (ANNs) have been extensively used in a wide range of engineering applications. There are only a few applications in liquid membrane process. The objective of this research was to develop artificial neural networks (ANNs) model to estimate Cr (VI) extraction efficiency in feed phase.Data set (413 experiment records) were obtained from a laboratory scale experimental study. Various combinations of experimental data, namely % (w/w) extractant Alamine 336 concentration in membrane phase, stirring speed in feed and stripping phase, flat sheet support type, stripping phase NaOH concentration, feed phase pH, diluents type, % (w/w) diluents concentration, polymer support type, extractant type, and time are used as inputs into the ANN so as to evaluate the degree of effect of each of these variables on Cr (VI) extraction efficiency in feed phase. The results of the ANN model is compared with multiple linear regression model (MLR). Mean square error (MSE), average absolute relative error (AARE) and coefficient of determination (R 2 ) statistics are used as comparison criteria for the evaluation of the model performances. Based on the comparisons, it was found that the ANN model could be employed successfully in estimating the Cr (VI) extraction efficiency