Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components

Harmonic generation at a nonlinear imperfect joint of plates by the S0 Lamb wave incidence

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear spring-type interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity

How to evaluate the adiabatic condition for quantum annealing in an experiment

We propose an experimental method to evaluate the adiabatic condition during quantum annealing. The adiabatic condition is composed of the transition matrix element and the energy gap, and our method simultaneously provides information about these without diagonalizing the Hamiltonian. The key idea is to measure a power spectrum of a time domain signal by adding an oscillating field during quantum annealing, and we can estimate the values of transition matrix element and energy gap from the measurement output. Our results provide a powerful experimental tool to analyze the performance of quantum annealing, which will be essential for solving practical combinatorial optimization problems.Comment: 16 pages, 13 figure

Tumor cell invasion from the marginal sinus into extranodal veins during early-stage lymph node metastasis can be a starting point for hematogenous metastasis

Aim: To investigate whether tumor cells in a lymph node (LN) can invade from the marginal sinus into extranodal veins via vessel branches that communicate with intranodal veins and whether this can be a starting point for hematogenous metastasis at the early stage of LN metastasis.Methods: Vascular and lymphatic networks of LNs in MXH10/Mo-lpr/lpr mice were investigated using three-dimensional micro-computed tomography and histological methods. Flow in the blood vessel networks of LNs was investigated by fluorescence microscopy. Tumor cells were injected into the subiliac LNs of MXH10/Mo-lpr/lpr mice to induce metastasis to the proper axillary LNs. Tumor development in the proper axillary LN was detected using an in vivo bioluminescence imaging system. A two-dimensional image of the proper axillary LN microvasculature was reconstructed using a contrast-enhanced high-frequency ultrasound system.Results: Extranodal veins communicated with intranodal veins via branches that penetrated the capsule, and blood flowed from intranodal veins to extranodal veins. Tumor cells that had metastasized to the marginal sinus invaded these communicating veins to develop hematogenous metastases.Conclusion: Metastatic LNs that would be considered by clinical imaging to be stage N0 can be a starting point for hematogenous metastasis. The study findings highlight the need for the development of novel techniques for the diagnosis and treatment of early-stage LN metastasis, i.e., when standard diagnostic imaging might incorrectly classify the LN as stage N0

Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators

Quantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model in the conventional quantum computing architecture. However, the data reuploding tends to require large amount of quantum resources, which motivates us to find an alternative strategy for realizing the expressive quantum machine learning efficiently. In this paper, we propose quantum machine learning with Kerr-nonlinear Parametric Oscillators (KPOs), as another promising quantum computing device. The key idea is that we use not only the ground state and first excited state but also use higher excited states, which allows us to use a large Hilbert space even if we have a single KPO. Our numerical simulations show that the expressibility of our method with only one mode of the KPO is much higher than that of the conventional method with six qubits. Our results pave the way towards resource efficient quantum machine learning, which is essential for the practical applications in the NISQ era.Comment: 13 pages, 8 figure