Unraveling the origin of higher success probabilities in quantum annealing versus semi-classical annealing

Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a soluble, simple initial Hamiltonian adiabatically to the ground state of the designated final Hamiltonian. Here we explore whether and when a full quantum representation of the dynamics leads to higher probability to end up in the desired ground when compared to a classical mean field approximation. As simple but nontrivial example we target the ground state of interacting bosons trapped in a tight binding lattice with small local defect by turning on long range interactions. Already two atoms in four sites interacting via two cavity modes prove complex enough to exhibit significant differences between the full quantum model and a mean field approximation for the cavity fields mediating the interactions. We find a large parameter region of highly successful quantum annealing, where the semi-classical approach largely fails. Here we see strong evidence for the importance of entanglement to end close to the optimal solution. The quantum model also reduces the minimal time for a high target occupation probability. Surprisingly, in contrast to naive expectations that enlarging the Hilbert space is beneficial, different numerical cut-offs of the Hilbert space reveal an improved performance for lower cut-offs, i.e. an nonphysical reduced Hilbert space, for short simulation times. Hence a less faithful representation of the full quantum dynamics sometimes creates a higher numerical success probability in even shorter time. However, a sufficiently high cut-off proves relevant to obtain near perfect fidelity for long simulations times in a single run. Overall our results exhibit a clear improvement to find the optimal solution based on a quantum model versus simulations based on a classical field approximation.

Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem

In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on the multilevel discretization. The objective is to avoid solving large-scale equations especially the large-scale Steklov eigenvalue problem whose computational cost increases exponentially. The proposed algorithm transforms the Steklov eigenvalue problem into a series of linear boundary value problems, which are defined in a multigrid space sequence, and a series of small-scale Steklov eigenvalue problems in a coarse correction space. Furthermore, we use the local defect-correction technique to divide the large-scale boundary value problems into small-scale subproblems. Through our proposed algorithm, we avoid solving large-scale Steklov eigenvalue problems. As a result, our proposed algorithm demonstrates significantly improved the solving efficiency. Additionally, we conduct numerical experiments and a rigorous theoretical analysis to verify the effectiveness of our proposed approach.

Resonant Airborne Acoustic Emission for Nondestructive Testing and Defect Imaging in Composites

A new version of an acoustic emission mode which is different from its traditional counterpart is discussed in view of applications for nondestructive testing. It is based on the effect of acoustic waves generation from the defect area in ambient air by local standing wave vibration developed in this area at the defect resonant frequency. Another approach which does not require preliminary knowledge of local defect-resonance frequency is one that uses wideband acoustic activation by a noise-like input signal. The acoustic emission field from the defect area is a “fingerprint” of the radiation source, and thus is applicable to defect detection and imaging. This enables the use of commercial microphone scanning for detecting and imaging various defects in composites. An improvement in the acoustic-emission scanning mode based on a multiple-axis robot is studied to applications to complex shape components. A rapid, full-field imaging of the acoustic-emission field is implemented by means of an array of microphones (acoustic camera). Numerous case studies validate the potential of the resonant acoustic-emission modes for integration in the defect imaging system based on inexpensive, fully acoustic instrumental components.

Corrosion behavior of X80 pipeline steel local defect pits under static liquid film

In this work, the corrosion electrochemical information under different thicknesses of liquid film was tested. The local corrosion development process of X80 steel under different thicknesses of liquid film was studied by combining the detection and analysis of scale and the matrix corrosion morphology. The corrosion was studied by EIS. The composition and microstructures of corrosion scale at different locations were detected by EDS and SEM, and the metal matrix was detected by 3D topography technology to analyze the local corrosion. The results show that a liquid film with a thickness greater than or equal to 1 mm has no effect on the mechanism of the corrosion process, but has a control effect on the corrosion rate and the time of each stage in corrosion. The corrosion process can be divided into two stages: in the early stage, the concentration of ions inside and outside ADP is the same, so the corrosion is uniform; in the later stage, due to the influence of CO2 dissolution and mass transfer distance, the cathodic reaction is mainly outside ADP and the anodic reaction is mainly inside ADP. In addition, corrosion acidification occurs in ADP, which enhances the corrosion process in ADP.

The interplay of supercoiling and thymine dimers in DNA

Thymine dimers are a major mutagenic photoproduct induced by UV radiation. While they have been the subject of extensive theoretical and experimental investigations, questions of how DNA supercoiling affects local defect properties, or, conversely, how the presence of such defects changes global supercoiled structure, are largely unexplored. Here we introduce a model of thymine dimers in the oxDNA forcefield, and validate it by comparison to melting experiments and structural measurements of the thymine dimer induced bend angle. We performed extensive molecular dynamics simulations of double-stranded DNA as a function of external twist and force. Compared to undamaged DNA, the presence of a thymine dimer lowers the supercoiling densities at which plectonemes and bubbles occur. For biologically relevant supercoiling densities and forces, thymine dimers can preferentially segregate to the tips of the plectonemes, where they enhance the probability of a localized tip-bubble. This mechanism increases the probability of highly bent and denatured states at the thymine dimer site, which may facilitate repair enzyme binding. Thymine dimer-induced tip-bubbles also pin plectonemes, which may help repair enzymes to locate damage. We hypothesize that the interplay of supercoiling and local defects plays an important role for a wider set of DNA damage repair systems.

Методи діагностування дефектів деталей авіаційних двигунів з композиційних матеріалів

The key priority in improving the technical and economic performance of gas turbine engines lays in the use of new composite materials. The use of composites in the components of critical load-carrying structures operating under static and dynamic loads during long service lives determines the need to predict the component lives. Also, in order to increase the safety of engine operation and improve the parts manufacturing process, timely defect detection in such structures is of great importance. This article is devoted to the detection of the composite parts defects and damages that occur at different stages of manufacturing and operation. The aim is to investigate the existing methods of non-destructive testing of composite materials, describe their functional concept, and determine the field of their application. The article considers acoustic, thermal, optical, and radiation testing methods. Among the acoustic methods, the phased array method is selected as the most informative and multipurpose. The acoustic emission method is also selected; it will allow real-time monitoring of defect growth during testing. Out of thermal methods, the vibrothermography method was selected as the most advanced among the thermographic sub-methods. It allows using the phenomenon of local defect resonance and thus ensures effective defect detection. Shearography is selected for investigation out of optical methods. The special aspects of the use of X-ray methods are considered through the example of X-ray computed tomography. It is concluded that the approach combining several methods can significantly increase the efficiency of defect detecting and help to assess their criticality. Active thermal testing is well suited for fast scanning of large-sized parts and searching for areas of defect accumulation. In the following, local methods, such as impedance, vibrothermography, or one of the ultrasonic, should be used. To measure deformations under static load, it is a good practice to use shearography. To identify progressive defects under static load, it makes sense to use the acoustic emission method.

The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.