Cavitation Nuclei Population and Event Rates

To model the processes of cavitation inception, noise and damage, it is necessary to generate a model of the cavitation event rate which can then be coupled with the consequences of the individual events to produce a complete synthesis of the phenomenon. In this paper we describe recent efforts to connect the observed event rates to the measured distributions of cavitation nuclei in the oncoming stream. Comparison are made between the observed event rates and event rates calculated from measured nuclei distributions using an algorithm which includes the dynamics of the nuclei motion and growth. Various complications are explored including the effect of the boundary layer, the relative motion between the nucleus and the liquid, the observable bubble size effect, and the effect of bubble growth on neighboring nuclei. All of these are seen to have important influences on the event rate, and therefore, on cavitation inception and other macroscopic consequences. We demonstrate that it is possible to predict the correct order of magnitude of the event rate when an attempt is made to model the important flow complications

The Micro-Bubble Distribution in the Wake of a Cavitating Circular Cylinder

Bubble nuclei populations in the wake of a circular cylinder under cavitating and noncavitating conditions were measured using a Phase Doppler Anemometry (PDA) system. In addition, the mean velocity defect and the turbulent fluctuations were monitored in order to try to understand the nuclei population dynamics within the flow. At the Reynolds numbers of these experiments (20000->33000) the laminar near-wake is fairly steady and under very limited cavitation conditions nuclei accumulate in this wake so that the population there is several orders of magnitude larger than in the upstream flow. Further downstream the population declines again as nuclei are entrained into the wake. However at fifteen diameters downstream the population is still much larger than in the upstream flow

A hybrid framework for estimating nonlinear functions of quantum states

Estimating nonlinear functions of quantum states, such as the moment \tr(\rho^m), is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the quantum part is constituted by the generalized swap test, and the classical part is realized by postprocessing the result from randomized measurements. This hybrid framework utilizes the partial coherent power of the intermediate-scale quantum processor and, at the same time, dramatically reduces the number of quantum measurements and the cost of classical postprocessing. We demonstrate the advantage of our framework in the tasks of state-moment estimation and quantum error mitigation.Comment: v1:5+17 pages, 9 figures; v2:enhance the presentation, clarify the advantages, especially updates Figure 3 and add Table

Universal entanglement and correlation measure in two-dimensional conformal field theory

We calculate the amount of entanglement shared by two intervals in the ground state of a (1+1)-dimensional conformal field theory (CFT), quantified by an entanglement measure $\mathcal{E}$ based on the computable cross norm (CCNR) criterion. Unlike negativity or mutual information, we show that $\mathcal{E}$ has a universal expression even for two disjoint intervals, which depends only on the geometry, the central charge c, and the thermal partition function of the CFT. We prove this universal expression in the replica approach, where the Riemann surface for calculating $\mathcal{E}$ at each order n is always a torus topologically. By analytic continuation, result of n=1/2 gives the value of $\mathcal{E}$. Furthermore, the results of other values of n also yield meaningful conclusions: The n=1 result gives a general formula for the two-interval purity, which enables us to calculate the Renyi-2 N-partite information for N<=4 intervals; while the $n=\infty$ result bounds the correlation function of the two intervals. We verify our findings numerically in the spin-1/2 XXZ chain, whose ground state is described by the Luttinger liquid.Comment: 5+2 pages, 3+2 figure

Fundamental Limitation on the Detectability of Entanglement

Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponential resources, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to theoretically evaluate the detection capability of entanglement criteria. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double-exponentially. Furthermore, if multi-copy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems.Comment: 16 pages, 7 figure

Analysis of the Tooth Surface Contact Area of a Circular-Arc-Tooth-Trace Cylindrical Gear under Load

To reconstruct the tooth surface of a circular-arc-tooth-trace cylindrical gear (CATT cylindrical gear), a 3D model has been developed and the contact characteristics have been investigated. Based on the development principle and meshing theory, the tooth surface equation, tooth surface curvature equation and tooth surface contact ellipse equation of the CATT cylindrical gear were deduced, and it was proved that the contact was a point contact. Then, the tooth surface was reconstructed and a 3D model was developed. Next, by performing the finite element analysis and meshing impression experiment, it was proved again that the contact is the point contact, and the contact area became an ellipse under loading. Finally, the influences of the design parameters on the contact ellipse were investigated. The general tendency is that the elliptical contact area increases from the tooth root to the gear top; the elliptical contact area decreases when the modulus and the gear tooth number near the tooth root increase and it increases when the modulus and the gear tooth number near the tooth top increase; the elliptical contact area increases when the tooth line radius increases. The elliptical contact area decreases in a cliff-like manner near the tooth top. The research results provide a reference for the design, profile modification and lubrication of the CATT cylindrical gear

Models of Cavitation Event Rates

To model the processes of cavitation inception, noise, and damage, it is necessary to generate a model of the cavitation event rate which can then be coupled with the consequences of the individual events to produce a complete synthesis of the phenomenon. In this paper we describe recent efforts to connect the observed event rates to the measured distributions of cavitation nuclei in the oncoming stream. A comparison is made between the observed event rates and event rates calculated from measured nuclei distributions using an algorithm which includes the dynamics of the nuclei motion and growth. Various complications are explored including the relative motion between the nucleus and the liquid, the effect of the finite bubble size of the growing bubble relative to the dimensions of the low pressure region, and the effect of bubble growth on neighboring nuclei. All of these are seen to have an important influence on the event rate, and therefore, on cavitation inception and other macroscopic consequences. We demonstrate that it is possible to predict the correct order of magnitude of the event rate when an attempt is made to model the important flow complications

Influence of Cutter Errors on Forming Accurate Variable Hyperbolic Circular Arc Tooth Trace Cylindrical Gears

The cutter error is an important factor in the accurate forming of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gears. Also, the study of the relationship between the cutter error and the forming of accurate teeth is beneficial for the gear modification design and the improvement in contact performance. Firstly, based on the principle of forming VH-CATT cylindrical gears, the sources of error in the tooth forming related to accuracy were analysed, including the errors in the cutter position and the cutter geometry, such as the error of rotation around the x-axis g, the error of rotation around the y-axis b, the error of translation along the x-axis Δx, the error of translation along the y-axis Δy, the error of translation along the z-axis Δz, the pressure angle error Δa and the tooth line radius error ΔRT. Next, based on the meshing theory and processing, an ideal tooth surface equation and a tooth surface equation with cutter errors were derived, and the tooth surface reconstruction was done. Then, the gear tooth thickness error was defined to characterize the accuracy of gear forming. Finally, the influences of the cutter error on the tooth thickness error and gear contact were investigated. The study shows that all cutter errors have certain influence on the tooth thickness error, contact area and load distribution; Δx has basically no effect on the gear tooth thickness error; Δx and g make the actual meshing point deviate from the middle section. The study content and the applied methods are helpful in the tooth surface error traceability, the counter-adjustment of the tooth surface processing and the modification design. This study provides also a basis for gear design and load-bearing contact analysis