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FourPhonon is a computational package that can calculate four-phonon scattering rates in crystals. It is built within ShengBTE framework, which is a well-recognized lattice thermal conductivity solver based on Boltzmann transport equation. An adaptive energy broadening scheme is implemented for the calculation of four-phonon scattering rates. In analogy with $thirdorder.py$ in ShengBTE, we also provide a separate python script, $Fourthorder.py$, to calculate fourth-order interatomic force-constants. The extension module preserves all the nice features of the well-recognized lattice thermal conductivity solver ShengBTE, including good parallelism and straightforward workflow. In this paper, we discuss the general theory, program design, and example calculations on Si, BAs and $\mathrm{LiCoO_2}$.

Face recognition is an important yet challenging problem in computer vision. A major challenge in practical face recognition applications lies in significant variations between profile and frontal faces. Traditional techniques address this challenge either by synthesizing frontal faces or by pose invariant learning. In this paper, we propose a novel method with Lie algebra theory to explore how face rotation in the 3D space affects the deep feature generation process of convolutional neural networks (CNNs). We prove that face rotation in the image space is equivalent to an additive residual component in the feature space of CNNs, which is determined solely by the rotation. Based on this theoretical finding, we further design a Lie Algebraic Residual Network (LARNet) for tackling pose robust face recognition. Our LARNet consists of a residual subnet for decoding rotation information from input face images, and a gating subnet to learn rotation magnitude for controlling the strength of the residual component contributing to the feature learning process. Comprehensive experimental evaluations on both frontal-profile face datasets and general face recognition datasets convincingly demonstrate that our method consistently outperforms the state-of-the-art ones., Comment: Accepted by ICML 2021

Mrk~231 is the closest radio-quiet quasar known and one of the most luminous infrared galaxies in the local Universe. It is characterised by the co-existence of a radio jet and powerful multi-phase multi-scale outflows, making it an ideal laboratory to study active galactic nucleus (AGN) feedback. We analyse the multi-epoch very long baseline interferometry data of Mrk~231 and estimate the jet head advance speed to be $\lesssim0.013\ c$, suggesting a sub-relativistic jet flow. The jet position angle changes from $-113^\circ$ in the inner parsec to $-172^\circ$ at a projected distance of 25 parsec. The jet structure change might result from either a jet bending following the rotation of the circum-nuclear disc or the projection of a helical jet on the plane of the sky. In the large opening angle ($\sim60^\circ$) cone, the curved jet interacts with the interstellar medium and creates wide-aperture-angle shocks which subsequently dissipate a large portion of the jet power through radiation and contribute to powering the large-scale outflows. The low power and bent structure of the Mrk~231 jet, as well as extensive radiation dissipation, are consistent with the obstruction of the short-length jet by the host galaxy's environment., Comment: 8 pages, 3 figures. Acceptance for publication in MNRAS

In this paper, we consider the multiplicity and asymptotics of standing waves with prescribed mass $\int_{{\mathbb{R}^N}} {{u}^2}=a^2$ to the energy critical half-wave \begin{equation}\label{eqA0.1} \sqrt{-\Delta}u=\lambda u+\mu|u|^{q-2} u+|u|^{2^*-2}u,\ \ u\in H^{1/2}(\R^N), \end{equation} where $N\!\geq\! 2$, $a\!>\!0$, $q \!\in\!\big(2,2+\frac{2}{N}\big)$, $2^*\!=\!\frac{2N}{N-1}$ and $\lambda\!\in\!\R$ appears as a Lagrange multiplier. We show that \eqref{eqA0.1} admits a ground state $u_a$ and an excited state $v_a$, which are characterised by a local minimizer and a mountain-pass critical point of the corresponding energy functional. Several asymptotic properties of $\{u_a\}$, $\{v_a\}$ are obtained and it is worth pointing out that we get a precise description of $\{u_a\}$ as $a\!\to\! 0^+$ without needing any uniqueness condition on the related limit problem. The main contribution of this paper is to extend the main results in J. Bellazzini et al. [Math. Ann. 371 (2018), 707-740] from energy subcritical to energy critical case. Furthermore, these results can be extended to the general fractional nonlinear Schr\"{o}dinger equation with Sobolev critical exponent, which generalize the work of H. J. Luo-Z. T. Zhang [Calc. Var. Partial Differ. Equ. 59 (2020)] from energy subcritical to energy critical case.

Radiative cooling has recently revived due to its significant potential as an environmentally friendly cooling technology. However, the design of particle-matrix cooling nanocomposites was generally carried out via tedious trial-and-error approaches, and the atomistic physics for efficient radiative cooling was not well understood. In this work, we identify the atomistic metrics of Barium Sulfate (BaSO$_4$) nanocomposite, which is an ultra-efficient radiative cooling material, using a predictive first-principles approach coupled with Monte Carlo simulations. Our results show that BaSO$_4$-acrylic nanocomposites not only attain high total solar reflectance of 92.5% (0.28 - 4.0 um), but also simultaneously demonstrate high normal emittance of 96.0% in the sky window region (8 - 13 um), outperforming the commonly used $\alpha$-quartz ($\alpha$-SiO$_2$). We identify two pertinent characters of ultra-efficient radiative cooling paints: i) a balanced band gap and refractive index, which enables strong scattering while negating absorption in the solar spectrum, and ii) a sufficient number of infrared-active optical resonance phonon modes resulting in abundant Reststrahlen bands and high emissivity in the sky window. The first principles approach and the resulted physical insights in this work pave the way for further search of ultra-efficient radiative cooling materials., Comment: 5 pages, 4 figures

Context. The derived physical parameters for young HII regions are normally determined assuming the emission region to be optically thin. However, this assumption is unlikely to hold for young HII regions such as hyper-compact HII(HCHII) and ultra-compact HII(UCHII) regions and leads to the underestimation of their properties. This can be overcome by fitting the SEDs over a wide range of radio frequencies. Aims. The two primary goals of this study are (1) to determine the physical properties of young HII regions from radio SEDs in the search for potential HCHII regions, and (2) to use these physical properties to investigate their evolution. Method. We used the Karl G. Jansky Very Large Array (VLA) to observe the X-band and K-band with angular resolutions of ~1.7" and ~0.7", respectively, toward 114 HII regions with rising-spectra between 1-5 GHz. We complement our observations with VLA archival data and construct SEDs in the range of 1-26 GHz and model them assuming an ionization-bounded HII region with uniform density. Results. Our sample has a mean electron density of ne=1.6E4cm^{-3}, diameter diam=0.14pc, and emission measure EM = 1.9E7pc*cm^{-6}. We identify 16 HCHII region candidates and 8 intermediate objects between the classes of HCHII and UCHII regions. The ne, diam, and EM change as expected, but the Lyman continuum flux is relatively constant over time. We find that about 67% of Lyman-continuum photons are absorbed by dust within these HII regions and the dust absorption fraction tends to be more significant for more compact and younger HII regions. Conclusion. Young HII regions are commonly located in dusty clumps; HCHII regions and intermediate objects are often associated with various masers, outflows, broad radio recombination lines, and extended green objects, and the accretion at the two stages tends to be quickly reduced or halted., Comment: 28pages, 55 figures, 8 tables. Accepted by A&A; Appendix figures are available at the website (https://doi.org/10.5281/zenodo.4293684)

Four-dimensional (4D) printing of shape memory polymer (SMP) imparts time responsive properties to 3D structures. Here, we explore 4D printing of a SMP in the submicron length scale, extending its applications to nanophononics. We report a new SMP photoresist based on Vero Clear achieving print features at a resolution of ~300 nm half pitch using two-photon polymerization lithography (TPL). Prints consisting of grids with size-tunable multi-colours enabled the study of shape memory effects to achieve large visual shifts through nanoscale structure deformation. As the nanostructures are flattened, the colours and printed information become invisible. Remarkably, the shape memory effect recovers the original surface morphology of the nanostructures along with its structural colour within seconds of heating above its glass transition temperature. The high-resolution printing and excellent reversibility in both microtopography and optical properties promises a platform for temperature-sensitive labels, information hiding for anti-counterfeiting, and tunable photonic devices.

Radio emission from the high- and super-Eddington accreting active galactic nuclei (AGNs) has various origins: a persistent jet, the magnetized corona and the wind-like outflows. It is now still unclear which is the leading mechanism responsible for the observed radio emission and how the radio emission is related to other characteristic parameters such as the Eddington ratio and black hole mass. In this paper, we present the 5 GHz Very Large Array (VLA) observational results of a sample of 25 extremely high Eddington accreting supermassive black holes (EESBHs, the Eddington ratio close to or above one) from narrow-line Seyfert 1 galaxies, among which 22 sources are detected. Most of EESBHs show a compact radio structure from a few hundred parsecs to one-kiloparsec scale. We estimated the lowest star formation rate surface density required for producing the observed radio emission, and found it is higher than the largest value previously detected in circumnuclear starburst galaxies, implying that the radio emission is from the AGN activity. Along with a comparison sample, we find an overall inverse radio loudness and Eddington ratio correlation ranging from sub- to super-Eddington ratios. The high-Eddington and mildly super-Eddington AGNs (-0.5~0.6) have a flatter radio spectrum, along with its low radio luminosity: L_R/L_X~10^-5, their radio emission is likely dominated by a magnetized corona, and a radiation pressure caused jet is also proposed in this paper., Comment: 17 pages, 8 figures, 5 tables, submitted to ApJ

High-performance actuators are crucial to enable mechanical versatility of lower-limb wearable robots, which are required to be lightweight, highly backdrivable, and with high bandwidth. State-of-the-art actuators, e.g., series elastic actuators (SEAs), have to compromise bandwidth to improve compliance (i.e., backdrivability). In this paper, we describe the design and human-robot interaction modeling of a portable hip exoskeleton based on our custom quasi-direct drive (QDD) actuation (i.e., a high torque density motor with low ratio gear). We also present a model-based performance benchmark comparison of representative actuators in terms of torque capability, control bandwidth, backdrivability, and force tracking accuracy. This paper aims to corroborate the underlying philosophy of "design for control", namely meticulous robot design can simplify control algorithms while ensuring high performance. Following this idea, we create a lightweight bilateral hip exoskeleton (overall mass is 3.4 kg) to reduce joint loadings during normal activities, including walking and squatting. Experimental results indicate that the exoskeleton is able to produce high nominal torque (17.5 Nm), high backdrivability (0.4 Nm backdrive torque), high bandwidth (62.4 Hz), and high control accuracy (1.09 Nm root mean square tracking error, i.e., 5.4% of the desired peak torque). Its controller is versatile to assist walking at different speeds (0.8-1.4 m/s) and squatting at 2 s cadence. This work demonstrates significant improvement in backdrivability and control bandwidth compared with state-of-the-art exoskeletons powered by the conventional actuation or SEA., Comment: 9 pages, 13 figures

This paper presents a new fractional-order normalized Bouc-Wen (BW) (FONBW) model to describe the asymmetric and rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW) model is only efficient for the symmetric and rate-independent hysteresis description, the FONBW model is devoted to characterizing the asymmetric and rate-dependent behaviors of the hysteresis in PEAs by adopting an Nth-order polynomial input function and two fractional operators, respectively. Different from the traditional modified BW models, the proposed FONBW model also eliminates the redundancy of parameters in the CBW model via the normalization processing. By this way, the developed FONBW model has a relatively simple mathematic expression with fewer parameters to simultaneously characterize the asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters are identified by the self-adaptive differential evolution algorithm. To validate the effectiveness of the proposed model, a series of model verification and inverse-multiplicative-structure-based feedforward control experiments are carried out on a PEA system. Results show that the proposed model is superior to the CBW model and traditional modified BW model in modeling accuracy and hysteresis compensation., Comment: 9 pages, 10 figures, submitted to TMech; 10 pages, 11 figures, add two subsections in Section IV; modify Tables I and III, and Figures 9 and 10

We propose a radically different picture for X-shaped radio galaxies compared to existing models as transition objects between cold mode accreting low spinning retrograde black holes and low spinning prograde black holes. The model explains their smaller average black hole masses, their general aversion for cluster compared to isolated environments, the negligible difference in spectral index between primary and secondary jets despite a time difference in their formation, their absence among the most powerful radio quasars and radio galaxies, and their connection to the elusive FRI quasar class, among others. The key to their formation is cold gas accretion onto Schwarzschild black holes., Comment: 15 pages, 8 figures, Accepted for publication in the Astrophysical Journal