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By analyzing Newton’s rings, often encountered in interferometry, the parameters of spherical surfaces such as the rings’ center and the curvature radius can be estimated. First, the classical convolutional neural networks, visual geometry group (VGG) network and U-Net, are applied to parameter estimation of Newton’s rings. After these models are trained, the rings’ center and curvature radius can be obtained simultaneously. Compared with previous analysis methods of Newton’s rings, it is shown that the proposed method has higher precision, better immunity to noise, and lower time consumption. For a Newton’s rings pattern of 640 × 480 pixels comprising − 5 d B Gaussian noise or 60% salt-and-pepper noise, the parameters can be estimated by the VGG model in 0.01 s, the error of the rings’ center is less than one pixel, and the error of curvature radius is lower than 0.5%.

Source spectral models developed for strong ground motion simulations are phenomenological models that represent the average effect that the source processes have on near fault ground motion. Their parameters are directly regressed from the observations and often do not have clear meaning for the physics of the source process. We investigate the relation between the kinematic double-corner frequency (DCF) source spectral model JA19_2S (Ji and Archuleta, BSSA, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We derive scaling relations for the low and high corner frequency in terms of static stress drop, dynamic stress drop, fault rupture velocity, fault aspect ratio, and relative hypocenter location. We find that the non-self-similar low corner frequency scaling relation of JA19_2S model for 5.3

The best-known part of Brune’s (1970) spectral model is the single corner f–2 source spectrum. However, Brune noted that a more realistic heterogeneous rupture would have a source displacement spectrum with a low-frequency f–0 segment proportional to seismic momentM0, a segment with f–2 high-frequency decay, and an intermediate f–1 branch that connects the two. This “f–0–f–1–f–2” shape source spectrum features two corner frequencies fC1 and fC2>fC1. Brune (1970) associated the emergence of the fC2 with the partial stress drop over a fault considering a rupture with heterogeneous stress release. Here we introduce two double-corner source spectral models JA19 and JA19_2S for 3.3≤M≤7.3, constrained by stochastic modeling the mean PGA and mean PGV of the NGA West-2 database. JA19 is self-similar. Its two corner frequencies fC1 and fC2 scale with moment magnitude (M) as (1) log(fC1(M))=1.754– 0.5M and (2) log(fC2(M)) = 3.250 – 0.5M. We find that relation (1) is consistent with the known self-similar scaling relations of the rupture duration (Td) where Td= 1/(πfC1). Relation (2) may reflect scaling relation of the average rise time (TR), whereTR ~0.8/fC2. Stochastic simulations using JA19 cannot reproduce the sharp change in magnitude dependence of PGA and PGV at M5.3, suggesting a breakdown of self-similarity. To model this change, JA19_2S is found by perturbing the fC1 scaling relationship in JA19. For JA19_2S: log(fC1(M)) = 1.474 – 0.415M for M≤5.3 and log(fC1(M)) = 2.375 – 0.585M for M>5.3. In both models the relation fC2/fC1>>1 applies. Seismic radiated energy scales withM02fC12fC2. The ratiofC2/fC1 scales not only with the ratio of effective stress drop and static stress drop as Brune (1970) pointed out but also with the fault aspect ratio. The source spectral shape “f–0–f–1–f–2”, originally proposed by Brune (1970), provides a bridge to reconcile the known scaling relationships in source duration, static stress drop, seismic radiated energy, fault aspect ratio, and ground motion parameters within acceptable uncertainties. It also explains why the stress parameter would generally be larger than static stress drop which is related to the lower corner frequency.

The slip and static stress drop of the 2015 M-w 7.8 Gorkha, Nepal earthquake has been studied using its excellent near-source static observations and a newly developed finite fault inversion algorithm with an average stress drop constraint. A series of nonlinear inversions with different target stress drops are conducted to search for the solution that not only most accurately fits the geodetic data, but also has an energy-based stress drop, (Delta) over bar tau(E), matching the target value. Our result reveals that the misfit to the geodetic data gradually decreases when the (Delta) over bar tau(E) of the inverted slip model increases from 2 to 7MPa; but becomes nearly constant when (Delta) over bar tau(E) further increases. Hence, only the lower bound of (Delta) over bar tau(E), that is, (Delta) over bar tau(min)(E) (similar to 7 MPa), of the Gorkha earthquake can be constrained with near-fault geodetic measurements, consistent with our previous study using just far-field seismic data. The upper bound of (Delta) over bar tau(E) can be constrained with an extra constraint on the maximum local stress drop. An artificial upper bound can also be reached if using a large subfault size to represent the source. The lower bound of (Delta) over bar tau(E) leads to the lower bound of the apparent available energy and the upper bound of the radiation efficiency (eta(R), 0.09-0.15), though the latter is also sensitive to the determination of the radiated seismic energy. We find that the lower eta(R) and the reported high rupture velocity (80-93 per cent shear wave speed) can be reconciled by considering the aspect ratio of the dominant slip patch. We recommend using (Delta) over bar tau(min)(E) to replace various slip smoothing constraints to stabilize the finite fault inversion because of its clear physical meaning.

In this letter, we analyze the mutual information of the $\infty $ -PAM constellation in additive white Gaussian noise channel, where $\infty $ -PAM is the extreme case of $M$ -ary PAM of large alphabet size. Under moderate to high signal-to-noise ratio (SNR), we present a simple approximation for the mutual information and find that the shaping loss of $\infty $ -PAM with respect to Gaussian signaling is about $({1}/{2})\log ({\pi \mathrm {e} }/{6})+ ({1}/{2})\log (1 + \mathrm {SNR}^{-1}) - 0.52\,\,\mathrm {SNR}^{-({1}/{2})}$ ; while in low SNR, we find that the shaping loss is negligible. By combining the results above, we present a simple analytical expression that closely approximates the mutual information of $\infty $ -PAM for arbitrary SNR.

To shed light on the deuteron radius puzzle we analyze the theoretical uncertainties of the nuclear structure corrections to the Lamb shift in muonic deuterium. We find that the discrepancy between the calculated two-photon exchange correction and the corresponding experimentally inferred value by Pohl et al. [1] remain. The present result is consistent with our previous estimate, although the discrepancy is reduced from 2.6 $\sigma$ to 2 $\sigma$. The error analysis includes statistic as well as systematic uncertainties stemming from the use of nucleon-nucleon interactions derived from chiral effective field theory at various orders. We therefore conclude that nuclear theory uncertainty is more likely not the source of the discrepancy., Comment: updated according to referee's comments

The spatial correlation of a multidimensional force produced by different aircraft components is an important factor that affects the structural vibration of aircraft. To predict the structural response by external forces with a certain phase difference, determined by the spatial correlation of external forces, an analytical method based on structural response integration is developed and adopted. The characteristics of the external forces, especially the phase difference of the structural vibration, are investigated to reduce structural vibration by utilizing the spatial correlation of the external forces. Additionally, to suppress structural vibration by a propagation wavefield, corresponding to complex flow excitation, the developed integration method is used to estimate the accuracy of the propagation wavefield replaced by concentrated forces. Finally, a measurement is designed and performed, which further reveals the spatial correlation effect of the external forces on the structural vibration.

Vortex-ring cavitation occurs when the pressure inside a torus-shaped core of a vortex ring falls below the vapor pressure of the ambient liquid. By generating a vapor bubble in a rigid tube, a toroidal cavity can be produced outside the tube. The pulsation and propagation behaviors of vortex-ring cavitation are studied using a high-speed video camera and a hydrophone. The experimental results show that the cavity continues to oscillate with a period that depends heavily on the maximal cross-section radius of the cavity and circulation of the vortex flow, under the influence of the surrounding vortex flow field. It is also shown that the cross-radial oscillation of the toroidal cavity can be measured both by a high-speed camera and hydrophone. Moreover, three different methods for estimating the circulation are compared to propose an accurate model of toroidal cavity oscillation. The phenomenon of a toroidal cavity impinging on a fixed wall is also investigated.

We study the ^99Be ground-state energy with non-local \alpha nαn and \alpha \alphaαα potentials derived from Cluster Effective Field Theory. The short-distance dependence of the interaction is regulated with a momentum cutoff. The potential parameters are fitted to reproduce the scattering length and effective range. We implement such potential models in a Non-Symmetrized Hyperspherical Harmonics (NSHH) code in momentum space. In addition we calculate ground-state energies of various alpha nuclei. Work is in progress on a calculation of the photodisintegration of ^99Be with the Lorentz Integral Transform (LIT) method.

It is aimed to describe the nucleus of \(^9\)Be in an \(\alpha \)-\(\alpha \)-neutron cluster model, where the \(\alpha \)-\(\alpha \) and \(\alpha \)-neutron interactions are determined via an effective field theory (EFT) for halo nuclei (halo-EFT). Here, only the \(\alpha \)-\(\alpha \) case is discussed more detailed and hence results are given for \(\alpha \)-\(\alpha \) phase shifts and for the ground-state energy of \(^{12}\)C as a three \(\alpha \) cluster. The calculation of the \(^{12}\)C wave function is made via an expansion on nonsymmetrized hyperspherical harmonics (NSHH) in momentum space.

The charge radius of the deuteron (D), was recently determined to three times the precision compared with previous measurements using the measured Lamb shift in muonic deuterium (\(\mu \)D). However, the \(\mu \)D value is 5.6 \(\sigma \) smaller than the world averaged CODATA-2014 value (Pohl R et al. (2016) Science 353:669 [1]). To shed light on this discrepancy we analyze the uncertainties of the nuclear structure calculations of the Lamb shift in \(\mu \)D and conclude that nuclear theory uncertainty is not likely to be the source of the discrepancy.

Nuclear structure effects to the Lamb shift in light muonic atoms are driven by the two-photon exchange contribution, whose evaluation relies significantly on nuclear theory. Using ab initio calculations, we have studied nuclear structure effects in several light muonic atoms, including \(\mu ^{2,3}\mathrm {H}\) and \(\mu ^{3,4}\mathrm {He}^+\) [1, 2, 3, 4, 5]. The two-photon exchange is associated with nuclear electromagnetic sum rules. The calculation was done with the implementation of state-of-the-art nuclear potentials, derived either phenomenologically or from chiral effective field theory. The statistical and systematic uncertainties from nuclear theory were analyzed by potential-model comparison, and by using power-counting and parameter-optimization techniques, that have been developed in chiral effective field theory. High precision of the ab initio results is crucial for accurately extracting nuclear charge radii in muonic atom spectroscopy.

We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory. We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron. We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift. We also discuss the impact of relativistic and other higher-order effects. We find agreement with previous calculations and explain the accuracy of our calculation., Comment: 26 pages, 6 figures, 1 table

We compute the momentum-space probability density of ${}^6$He at leading order in Halo EFT. In this framework, the ${}^6$He nucleus is treated as a three-body problem with a ${}^4$He core ($c$) and two valence neutrons ($n$). This requires the $nn$ and $nc$ t-matrices as well as a $cnn$ force as input in the Faddeev equations. Since the $nc$ t-matrix corresponds to an energy-dependent potential, we consider the consequent modifications to the standard normalization and orthogonality conditions. We find that these are small for momenta within the domain of validity of Halo EFT. In this regime, the ${}^6$He probability density is regulator independent, provided the cutoff is significantly above the EFT breakdown scale., Comment: 34 pages, 3 figures, version to appear in Few-Body Systems. Further explanations and discussions added, typos corrected, results unchanged

We present benchmark calculations of Zemach moments and radii of $^{2,3}\mathrm{H}$ and $^{3,4}\mathrm{He}$ using various few-body methods. Zemach moments are required to interpret muonic atom data measured by the CREMA collaboration at the Paul Scherrer Institute. Conversely, radii extracted from spectroscopic measurements can be compared with ab initio computations, posing stringent constraints on the nuclear model. For a given few-body method, different numerical procedures can be applied to compute these quantities. A detailed analysis of the numerical uncertainties entering the total theoretical error is presented. Uncertainties from the few-body method and the calculational procedure are found to be smaller than the dependencies on the dynamical modeling and the single nucleon inputs, which are found to be $\ensuremath{\lesssim}2%$. When relativistic corrections and two-body currents are accounted for, the calculated moments and radii are in very good agreement with the available experimental data.

Measuring the 2S–2P Lamb shift in a hydrogen-like muonic atom allows one to extract its nuclear charge radius with a high precision that is limited by the uncertainty in the nuclear structure corrections. The charge radius of the proton thus extracted was found to be 7 σ away from the CODATA value, in what has become the yet unsolved “proton radius puzzle”. Further experiments currently aim at the isotopes of hydrogen and helium: the precise extraction of their radii may provide a hint at the solution of the puzzle. We present the first ab initio calculation of nuclear structure corrections, including the nuclear polarization correction, to the 2S–2P transition in μ He + 3 and μ H 3 , and assess solid theoretical error bars. Our predictions reduce the uncertainty in the nuclear structure corrections to the level of a few percent and will be instrumental to the on-going μ He + 3 experiment. We also support the mirror μ H 3 system as a candidate for further probing of the nucleon polarizabilities and shedding more light on the puzzle.

Recent calculations of nuclear structure corrections to the Lamb shift in light muonic atoms are based on an expansion in a parameter eta, where only terms up to second order are retained. The parameter eta can be shown to be proportional to the square root of the muon/proton mass ratio, so that it is small and the expansion is expected to converge. However, practical implementations show that the eta convergence may be slower than expected. In this work we probe the uncertainties due to this expansion using a different formalism, which is based on a multipole expansion of the longitudinal and transverse response functions and was first introduced by Leidemann and Rosenfelder. We refer to this alternative expansion as the eta-less formalism. We generalize this formalism to account for the cancellation of elastic terms such as the third Zemach moment (or Friar moment) and embed it in a computationally efficient framework. We implement and test this approach in the case of muonic deuterium. The comparison of results in the point nucleon limit for both methods achieve sub-percent agreement. When nucleon form factors are introduced we find a 4% and 2% difference in the third Zemach moment and nuclear polarizability, respectively, compared to the eta-less expansion, indicating that the nucleon form factor approximations should be improved. However, we find that the sum of these terms removes this dependence and the uncertainty due to the eta-expansion and the related second-order approximation in the nucleon form factors amounts only to 0.2% and thus is fully justified in muonic deuterium. This computationally efficient framework paves the way to further studies in light muonic systems with more than two nucleons, where controlling and reducing uncertainties in nuclear structure corrections is key to the experimental efforts of the CREMA collaboration., Comment: 13 pages, 4 figures, 6 tables

A two-mode (de)multiplexer [(DE)MUX] based on a multimode interferometer coupler and a symmetric Y-junction coupler is proposed and demonstrated on an InP substrate. By introducing a phase shifter section with a thickness-detuned core layer, a miniature two-mode (DE)MUX with mode conversion of 100% is designed and demonstrated. Simulation shows that the total length of the device can be as small as 446 $\mu\text{m} $ : much shorter than other mode (DE) MUX in InP materials. Within the entire C-band wavelength range, the calculated insertion loss of the device is less than 0.7 dB, and the crosstalk is below −24 dB. A mode (DE) MUX was fabricated in InP materials, and the mode conversion of the $\text{TE}_{0}$ and $\text{TE}_{1}$ modes were successfully demonstrated.

The measurement of the Lamb shift in muonic hydrogen and the subsequent emergence of the proton-radius puzzle have motivated an experimental campaign devoted to measuring the Lamb shift in other light muonic atoms, such as muonic deuterium and helium. For these systems it has been shown that two-photon exchange nuclear structure corrections are the largest source of uncertainty and consequently the bottleneck for exploiting the experimental precision to extract the nuclear charge radius. Utilizing techniques and methods developed to study electromagnetic reactions in light nuclei, recent calculations of nuclear structure corrections to the muonic Lamb shift have reached unprecedented precision, reducing the uncertainty with respect to previous estimates by a factor of 5 in certain cases. These results will be useful for shedding light on the nature of the proton-radius puzzle and other open questions pertaining to it. Here, we review and update calculations for muonic deuterium and tritium atoms, and for muonic helium-3 and helium-4 ions. We present a thorough derivation of the formalism and discuss the results in relation to other approaches where available. We also describe how to assess theoretical uncertainties, for which the language of chiral effective field theory furnishes a systematic approach that could be further exploited in the future., Comment: 62 pages, 15 figures, 8 tables

We demonstrate the modulation bandwidth enhancement in integrated coupled DFB lasers. The coupling strength of the dual DFB is tunable duo to a SOA sandwiching in the center. The 3-dB bandwidth is increased from 8.6 GHz to 18.7 GHz under mutual injection locking.

We investigate the characteristics of a liquid jet ejected from an inclined tube, which is submerged immediately under a free surface. Jets are classified into three regimes: the curtain regime, transition regime, and column regime. In all regimes, the jet trajectories deviate from the standard projectile function. An important reason is that additive liquid is entrained from the bulk. The capillary force also contributes to the deviation in the curtain regime. Models are established to predict the horizontal distance that a jet travels above the free surface in the curtain regime and column regime.

In this paper, a new sparse transmitting and receiving array is designed to improve the joint angle and polarization parameter estimation performance for bistatic electromagnetic vector sensors Multiple-Input Multiple-Output radar. Firstly, large array aperture can be obtained with the aid of the sparse transmitting and receiving array. Then, an effective third-order tensor model is constructed in order to make full use of the multidimensional space-time characteristics of output data after matching filtering. And, the Parallel Factor trilinear alternating least square algorithm is proposed to deal with the constructed third-order tensor model, which can yield closed-form automatically paired two dimensional Direction of Departure and two dimensional Direction of Departure estimation without additional angle pair matching process. Furthermore, two sets of high accuracy rotation invariance relationships corresponding to transmit elevation angle and receive elevation angle can be achieved by using the estimated transmit steering vector matrix and receive steering vector matrix. After the accuracy transmit elevation angle and receive angle are obtained, the corresponding transmitting and receiving azimuth angle, polarization angle and polarization phase difference can be accurately estimated by using the vector-cross-product algorithm. Compared with existing algorithms, the proposed algorithm can avoid high dimensional eigenvalue decomposition and additional parameter matching process. Moreover, the high estimation performance of the proposed can be further guaranteed by using the designed sparse array. Finally, simulation results demonstrate the effectiveness and superiority of the proposed method in terms of estimation accuracy and angle resolution.

We calculate the nuclear structure corrections to the Lamb shift in muonic deuterium by using state-of-the-art nucleon-nucleon potentials derived from chiral effective field theory. Our calculations complement previous theoretical work obtained from phenomenological potentials and the zero range approximation. The study of the chiral convergence order-by-order and the dependence on cutoff variations allows us to improve the estimates on the nuclear structure corrections and the theoretical uncertainty coming from nuclear potentials. This will enter the determination of the nuclear radius from ongoing muonic deuterium experiments at PSI., Comment: 6 pages, 2 figures, 3 tables

Recently, phase cancellation metasurface has caused much attention due to its great capability of realizing radar cross section (RCS) reduction. However, owing to the intrinsic resonance property of the meta-atom, it is still challenging to expand the RCS reduction bandwidth. Here, we present a novel strategy to design ultra-broadband low-scattering metasurface by using the mixed meta-atoms combined with the evolutionary algorithm. The mixed meta-atoms are composed of single-layer or double-layer reflected elements, and the six different unit configurations are adopted to generate various reflection phases over a wide band. The planar array theory combined with particle swarm optimization (PSO) algorithm is employed to obtain the optimal mixed meta-atoms and their arrangement. The proposed low-scattering metasurface can achieve more than 10 dB RCS reduction between 5 and 18 GHz with a fractional bandwidth of 113% under normal incidence for both polarizations. The experimental results agree well with the simulated ones, and its bandwidth of the 10 dB RCS reduction reaches about 105.3%. In addition, our metasurface is still demonstrated to have the wide-angle stability for low-scattering property. The proposed design provides a feasible way to achieve ultra-broadband RCS reduction, which may find potential applications in concealing fields

In the paper, the behavior of the particle acted by the oscillating bubble is studied using a high-speed video camera. The bubble is generated using a very low voltage of 55 V. Images are captured at a speed of 15000 fps (frames per second). It is found that the velocity of the particle is dependent on the liquid viscosity, particle size, and tube diameter. Particle velocity decreases with the increase of the glycron-water mixture viscosity. A model is presented to predict the velocity and verified by experimental results. These observations may be beneficial for the application in medical treatment.