Transition to turbulence in pulsating pipe flow

Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, $\alpha$), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low $\alpha$. In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence ("puffs") analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics are dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero $\alpha$ limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number. In the high frequency limit puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing $\alpha$) from the decay dominated (quasi steady) threshold to the steady pipe flow level

Tripartite Entanglement and Quantum Correlation

We provide an analytical solution from the correlators of the generalized $R$-matrix in the 3-qubit pure states. It provides the upper bound to the maximum violation of Mermin's inequality. For a generic 2-qubit pure state, the concurrence characterizes the maximum violation of Bell's inequality from the $R$-matrix. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The $R$-matrix shows the maximum violation of Bell's operator. For a general 3-qubit state, we have five invariant entanglement quantities under local unitary transformations. We show that the five invariant quantities describe the correlation in the generalized $R$-matrix. The violation of Mermin's operator is not a proper diagnosis by observing the dependence for entanglement measures. We then classify 3-qubit quantum states. Each classification quantifies Quantum Entanglement by the total concurrence. In the end, we relate the experiment correlators to Quantum Entanglement.Comment: 14 pages, 4 figures, minor changes, reference change

Non-Locality≠\neqQuantum Entanglement

The unique entanglement measure is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the non-locality. For justification, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only considering one entanglement measure, the numerical result contradicts expectation. Therefore, we conclude ``Non-Locality$\neq$Quantum Entanglement''. We propose the generalized $R$-matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We then demonstrate the evidence by restoring the monotonically increasing result.Comment: 38 pages, 10 figures, minor changes, reference adde

Domain Generalization of 3D Object Detection by Density-Resampling

Point-cloud-based 3D object detection suffers from performance degradation when encountering data with novel domain gaps. To tackle it, the single-domain generalization (SDG) aims to generalize the detection model trained in a limited single source domain to perform robustly on unexplored domains. In this paper, we propose an SDG method to improve the generalizability of 3D object detection to unseen target domains. Unlike prior SDG works for 3D object detection solely focusing on data augmentation, our work introduces a novel data augmentation method and contributes a new multi-task learning strategy in the methodology. Specifically, from the perspective of data augmentation, we design a universal physical-aware density-based data augmentation (PDDA) method to mitigate the performance loss stemming from diverse point densities. From the learning methodology viewpoint, we develop a multi-task learning for 3D object detection: during source training, besides the main standard detection task, we leverage an auxiliary self-supervised 3D scene restoration task to enhance the comprehension of the encoder on background and foreground details for better recognition and detection of objects. Furthermore, based on the auxiliary self-supervised task, we propose the first test-time adaptation method for domain generalization of 3D object detection, which efficiently adjusts the encoder's parameters to adapt to unseen target domains during testing time, to further bridge domain gaps. Extensive cross-dataset experiments covering "Car", "Pedestrian", and "Cyclist" detections, demonstrate our method outperforms state-of-the-art SDG methods and even overpass unsupervised domain adaptation methods under some circumstances.Comment: 14 pages, 6 figure

Experimental and Numerical Analysis of Rock Burst Tendency and Crack Development Characteristics of Tianhu Granite

Rock burst is a serious nonlinear dynamic geological hazard in underground engineering construction. In this paper, a true triaxial unloading rock burst experiment and numerical simulation are carried out on Tianhu granite to investigate the rock burst tendency and crack development characteristics of surrounding rock after excavation. The experiment and numerical simulation process monitored the rock burst stress path to determine the rock burst stress. According to the evolution law of the frequency and amplitude of rock burst acoustic emission monitoring, the shape characteristics of rock burst fragments are analyzed. The rock burst numerical simulation analysis is carried out by the PFC software, and the temporal and spatial evolution law of cracks is obtained. The research results show that the laboratory experiment and numerical simulation of Tianhu granite have rock burst strengths of 163.4 MPa and 161 MPa, respectively, and the average rock burst stress ratio is 8.38, that is, the Tianhu granite has a low rock burst tendency. During the rock burst, the development of tensile cracks will produce flaky debris, and the development of shear cracks will produce lumpy debris. Rock burst will happen when the crack growth rate to be exceeded the unloading crack growth rate; therefore, it can be used as a precursor signal for the occurrence of rock burst

Correlation between the strength of low-temperature T-linear normal-state resistivity and TcT_{\rm c} in overdoped electron-doped cuprate superconductors

The recently observed an intimate link between the nature of the strange metallic normal-state and superconductivity in the overdoped electron-doped cuprate superconductors is calling for an explanation. Here the intrinsic correlation between the strength of the low-temperature linear-in-temperature normal-state resistivity and superconducting transition temperature $T_{\rm c}$ in the overdoped electron-doped cuprate superconductors is studied within the framework of the kinetic-energy-driven superconductivity. On the one hand, the main ingredient is identified into a electron pairing mechanism involving {\it the spin excitation}, and then $T_{\rm c}$ has a dome-like shape doping dependence with the maximal $T_{\rm c}$ that occurs at around the optimal electron doping. On the other hand, in the normal-state above $T_{\rm c}$, the low-temperature linear-in-temperature normal-state resistivity in the overdoped regime arises from the momentum relaxation due to the electron umklapp scattering mediated by {\it the same spin excitation}. This {\it same spin excitation} that governs both the electron umklapp scattering responsible for the low-temperature linear-in-temperature normal-state resistivity and electron pairing responsible for superconductivity naturally generates a correlation between the strength of the low-temperature linear-in-temperature normal-state resistivity and $T_{\rm c}$ in the overdoped regime.Comment: 12 pages, 6 figures. arXiv admin note: text overlap with arXiv:2211.0308

T-linear resistivity in the strange-metal phase of cuprate superconductors due to umklapp scattering from a spin excitation

The strange-metal phase of cuprate superconductors exhibits a linear in temperature resistivity, however, the origin of this remarkable anomaly is still not well understood. Here the linear temperature dependence of the electrical resistivity in the strange-metal phase of cuprate superconductors is investigated from the underdoped to overdoped regimes. The momentum dependence of the transport scattering rate arising from the umklapp scattering between electrons by the exchange of the spin excitation is derived and employed to calculate the electrical resistivity by making use of the Boltzmann equation. It is shown that the antinodal umklapp scattering leads to the linear in temperature resistivity in the low-temperature with the temperature linear coefficient that decreases with the increase of the doping concentration, however, the nodal umklapp scattering induces a deviation from the linear in temperature resistivity in the far lower temperature, and then the quadratic in temperature resistivity in the far lower temperature is generated by both the antinodal and nodal umklapp scattering. The theory also shows that the same spin excitation that acts like a bosonic glue to hold the electron pairs together also mediates scattering of electrons in the strange-metal phase of cuprtae superconductors responsible for the linear in temperature resistivity and the associated electronic structure.Comment: 16 pages, 11 figure

Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent (GD) to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of GD depends linearly, and sometimes even quadratically, on the condition number of the low-rank object, and therefore, GD slows down painstakingly when the problem is ill-conditioned. This chapter introduces a new algorithmic approach, dubbed scaled gradient descent (ScaledGD), that provably converges linearly at a constant rate independent of the condition number of the low-rank object, while maintaining the low per-iteration cost of gradient descent for a variety of tasks including sensing, robust principal component analysis and completion. In addition, ScaledGD continues to admit fast global convergence to the minimax-optimal solution, again almost independent of the condition number, from a small random initialization when the rank is over-specified in the presence of Gaussian noise. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization without hurting generalization.Comment: Book chapter for "Explorations in the Mathematics of Data Science - The Inaugural Volume of the Center for Approximation and Mathematical Data Analytics". arXiv admin note: text overlap with arXiv:2104.1452

Rethinking Pseudo-LiDAR Representation

The recently proposed pseudo-LiDAR based 3D detectors greatly improve the benchmark of monocular/stereo 3D detection task. However, the underlying mechanism remains obscure to the research community. In this paper, we perform an in-depth investigation and observe that the efficacy of pseudo-LiDAR representation comes from the coordinate transformation, instead of data representation itself. Based on this observation, we design an image based CNN detector named Patch-Net, which is more generalized and can be instantiated as pseudo-LiDAR based 3D detectors. Moreover, the pseudo-LiDAR data in our PatchNet is organized as the image representation, which means existing 2D CNN designs can be easily utilized for extracting deep features from input data and boosting 3D detection performance. We conduct extensive experiments on the challenging KITTI dataset, where the proposed PatchNet outperforms all existing pseudo-LiDAR based counterparts. Code has been made available at: https://github.com/xinzhuma/patchnet.Comment: ECCV2020. Supplemental Material attache