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

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

Prioritized Planning for Target-Oriented Manipulation via Hierarchical Stacking Relationship Prediction

In scenarios involving the grasping of multiple targets, the learning of stacking relationships between objects is fundamental for robots to execute safely and efficiently. However, current methods lack subdivision for the hierarchy of stacking relationship types. In scenes where objects are mostly stacked in an orderly manner, they are incapable of performing human-like and high-efficient grasping decisions. This paper proposes a perception-planning method to distinguish different stacking types between objects and generate prioritized manipulation order decisions based on given target designations. We utilize a Hierarchical Stacking Relationship Network (HSRN) to discriminate the hierarchy of stacking and generate a refined Stacking Relationship Tree (SRT) for relationship description. Considering that objects with high stacking stability can be grasped together if necessary, we introduce an elaborate decision-making planner based on the Partially Observable Markov Decision Process (POMDP), which leverages observations and generates the least grasp-consuming decision chain with robustness and is suitable for simultaneously specifying multiple targets. To verify our work, we set the scene to the dining table and augment the REGRAD dataset with a set of common tableware models for network training. Experiments show that our method effectively generates grasping decisions that conform to human requirements, and improves the implementation efficiency compared with existing methods on the basis of guaranteeing the success rate.Comment: 8 pages, 8 figure

Dynamic modeling and control of a novel XY positioning stage for semiconductor packaging

This paper presents the dynamic modeling and controller design of an XY positioning stage for semiconductor packaging. The XY stage is directly driven by two linear voice coil motors, and motion decoupling between the X and Y axes is realized through a novel flexible decoupling mechanism based on flexure hinges and preloaded spring. Through bond graph method, the dynamic models of X- and Y-axes servomechanisms are established, respectively, and the state space equations are derived. A control methodology is proposed based on force compensations and the performance of the XY stage is investigated by simulations and experimental tests. The results show that the XY stage has good performance. When the reference displacements are defined as 2 mm, the settling time of the X-axis movement is 64 ms, and the overshoot is 0.7%. Y-axis settling time is 62 ms, and the overshoot is 0.8%. X-axis positioning accuracy is 1.85 μm and the repeatability is 0.95 μm. Y-axis positioning accuracy and repeatability are 1.75 μm and 0.9 μm, respectively. In addition, the stage can track linear, circular and complex trajectories very well