Low Exponent Research Articles

Modified Newton identities

The sums of powers with identical exponents of natural, real, or complex numbers, considered as roots of algebraic equation, are expressed directly through the products of coefficients of that equation, starting from the well-known Newton identities. The final Eq. (6) includes the same power of sum of all numbers ± a sum over all partitions of the exponent. Each term of the last sum is the equation coefficients product with the net power keeping the “dimensionality” of the exponent and having a numerical factor, equal to a proper polynomial coefficient, built of exponents of equation coefficients entering the product. The revers Eq. (43) for equation coefficients is also a sum over all partitions of the same exponent with known numerical coefficients. The entering products are built of “commutators-anticommutators of power of sum and sum of powers” (C-A) of the initial sum addends. The numerous identities Eq. (44) for a C-A with an exponent, exceeding the number of C-A sum terms by 2, and similar C-A-s with lower exponents are established.

The influence of nano/micro sample size on the strain-rate sensitivity of plastic flow in tungsten

The plastic flow characteristics of body centered cubic metals, which is dominated by the motion of screw dislocations, generally exhibits strong strain rate dependence. In-situ scanning electron microscopy compression tests are performed on tungsten (W) single crystal nano and micro pillars, with diameters in the range 100–2000 nm. We demonstrate here that by reducing sample size, the strain rate sensitivity of plastic flow, including not only the yield strength but also the strain burst statistics, is reduced. It is found that the strain rate sensitivity of the flow stress scales with the sample size d as d0.67. Statistical analysis of the strain burst size displays truncated power law scaling with a lower exponent at higher strain rate for micron size pillars. Nano size pillars (<500 nm) show near universal scaling exponent of 1.50±0.07 at all applied strain rates. The strain hardening rate and deformation morphology are found not to be very sensitive to the strain rate. This external pillar sample size effect is further compared with the internal grain size in nanocrystalline W in order to guide the design of new materials by tuning the characteristic length scale (external or grain size)

Large elongations in WE54 magnesium alloy by solute-drag creep controlling the deformation behavior

Solute-drag creep is a diffusion-controlled process that may govern deformation in coarse-grained materials with solute atoms in solution. Elongation-to-failure tensile tests were conducted in a WE54 alloy containing solutes of Y and Nd in the range 25–450 °C. Elongations of more than 150% were observed at high temperatures and a maximum elongation to failure of 312% was determined at 450 °C and 10-2 s-1. Microstructural observations show elongated grains and the presence of dislocation bands after deformation under these conditions. Strain-rate-change tests reveal a range at high temperatures showing low stress exponents. Since grain boundary sliding was discarded as a possible controlling mechanism, the observed low stress exponents, high elongations and elongated grains are attributed to solute-drag creep as the principal deformation mechanism.

STABLE SOLUTIONS TO THE STATIC CHOQUARD EQUATION

This paper is concerned with the static Choquard equation $$\begin{eqnarray}-\unicode[STIX]{x1D6E5}u=\bigg(\frac{1}{|x|^{N-\unicode[STIX]{x1D6FC}}}\ast |u|^{p}\bigg)|u|^{p-2}u\quad \text{in }\mathbb{R}^{N},\end{eqnarray}$$ where $N,p&gt;2$ and $\max \{0,N-4\}&lt;\unicode[STIX]{x1D6FC}&lt;N$. We prove that if $u\in C^{1}(\mathbb{R}^{N})$ is a stable weak solution of the equation, then $u\equiv 0$. This phenomenon is quite different from that of the local Lane–Emden equation, where such a result only holds for low exponents in high dimensions. Our result is the first Liouville theorem for Choquard-type equations with supercritical exponents and $\unicode[STIX]{x1D6FC}\neq 2$.

Cryptocurrency Market Development: Hurst Method

The aim of this work is to study the pricing in the cryptocurrency market and applying cryptocurrencies by the Bank of Russia for its monetary policy. The research objectives are to identify the cyclical nature of price dynamics, to study market maturity and potential risks that have a long-term positive relationship with the financial stability of the cryptocurrency market. The author uses the Hurst method with the Amihud illiquidity measure to study the resistance of four cryptocurrencies (Bitcoin, Litecoin, Ripple and Dash) and their evolution over the past five years. The study results in the author’s conclusion that the cryptocurrency market has entered a new stage of development, which means a reduced possibility to have excess profits when investing in the most liquid cryptocurrencies in the future. However, buying new high-risk tools provides opportunities for speculative income. The author concludes that illiquid cryptocurrencies exhibit strong inverse anti-persistence in the form of a low Hurst exponent. A trend investing strategy may help obtain abnormal profits in the cryptocurrency market. The Bank of Russia could partially apply digital currency to implement monetary policy, which would soften the business cycle and control the inflation. If Russia accepts the law ‘’On Digital Financial Assets’’ and legalizes cryptocurrencies after the economic crisis caused by the COVID-19 pandemic, the Bank of Russia might act as a lender of last resort and offer crypto loans.

Combustion performance of composite propellants containing core-shell Al@M(IO3)x metastable composites

Aluminum (Al) has been widely used in solid composite propellants (SCPs) to increase the specific impulse. However, Al always subjects to coalescence, sintering to large agglomerations during combustion of SCPs resulting in larger two-phase flow losses. Herein, core-shell μ-Al@M(IO3)x composites have designed and synthesized as a replacement for micron-sized Al (μ-Al) in the Al/AP/RDX/HTPB propellant with tunable combustion behavior. The results show the thermal reactivity and heat releases of SCP are largely enhanced by using these novel metal-based composites. With the inclusion of μ-Al@EGCG@Fe(IO3)3 (EGCG: Epigallocatechin gallate), the major exothermic peak is reduced by 29.1 °C compared to the reference propellant with a heat release increase up to 5475 J g−1, exceeding that of the reference sample (86 J g−1 higher). The burn rates are increased with the inclusion of μ-Al@(MIO3)x, while the pressure exponent is higher. The SCP-1 (0.3), SCP-2 (0.18) and SCP-4 (0.25) that have relatively low pressure exponent and high burn rates are good candidates for future applications. The major condensed combustion products (CCPs) of these SCPs are Al2O3, Al2.81O3.56N0.44, Al4C3, Al2OC, AlN and C7H18ClN. The agglomeration can be reduced with a minor inclusion of μ-Al@M(IO3)x due to the enhanced interfacial reactions, and the average CCP sizes (0.5 μm for SCP-1 and SCP-4) are even smaller than that of initial μ-Al (1.2 μm).

Dependence of Photoluminescence Emission on Excitation Power and Temperature in Highly Doped 6H- SiC

The excitation power and temperature dependences of photoluminescence (PL) emission in 6H polytype of silicon carbide are investigated extensively. A sublinear power-function dependence of the donor-acceptor pair emission intensity on the excitation power is explained by a rate-equation model. A very low power exponent $(k=0.3)$ in a power-law dependence of PL intensity on the excitation power of $\mathrm{B}$-$\mathrm{N}$ codoped 6H-$\mathrm{Si}\mathrm{C}$ at room temperature indicates that three-particle Auger recombination is the main carrier recombination pathway. Auger recombination in an $\mathrm{Al}$-$\mathrm{N}$ codoped $\mathrm{Si}\mathrm{C}$ does not manifest as strongly as that of the $\mathrm{B}$-$\mathrm{N}$ codoped sample due to high density of ionized impurities which capture the nonequilibrium carriers faster. The ionized impurities form localized potential wells due to their random distribution, which is revealed by a blue shift of the PL band with increasing excitation intensity (approximately 16 meV per decade) and with decreasing temperature. Low-temperature Hall-effect measurement of the $\mathrm{Al}$-$\mathrm{N}$ codoped sample confirms the high density of ionized impurities and significantly reduced ionization energy of dopant states by approximately 53 meV due to the high dopant densities. These results could lead to realization of tunable $\mathrm{Si}\mathrm{C}$-based light sources in severe operating conditions.

Local strain hardening behavior in a dissimilar metal welded joint with buttering layer of ultra-supercritical turbine rotor

Stratified tensile tests were performed to quantitatively investigate strain hardening behavior along a dissimilar metal welded joint (DMWJ) with buttering layer of ultra-supercritical turbine rotor. The results show weld region has lower tensile strength but better strain hardening capacity than base metals (BMs). The buttering layer (BL) exhibits higher strain hardening capacity than weld metal (WM). Two strain hardening exponents were found based on the fitted stress-strain curves using Hollomon equation. The lower exponent is related to the ferrite matrix, whereas the larger exponent is related to the precipitation phase, including martensite, bainite and sorbite. The gradient distribution of strain hardening exponent in heat affected zones (HAZs) is related to the gradient change of tempered martensite and grain size. The strain hardening mismatch in interface is related to the drastic changes in microstructure and amount of carbides. The dislocation cell structure and sub grain were observed after tensile tests, and carbides were elastic during tensile deformation. Kocks–Mecking (K–M) type plots of strain hardening rate versus true stress presented two hardening stages (stages III and IV) in welded joint. More ferrite and finer tempered martensite are conductive to extending the strain hardening period. Local strain hardening parameters play an important role in the accurate evaluation of crack behavior in HAZ and interface.

Analysis of Surface Crack using Various Crack Growth Models

This research focusing on fatigue crack growth experiment and assessments of fatigue crack growth model. Fatigue has been considered as the most important phenomena in the engineering problems. It has been found to occur in every engineering field. Many methods were introduced to overcome fatigue problem. One of it is fatigue crack growth prediction models. Fatigue crack growth model prediction can determine the residual life of the mechanical component. Fatigue crack growth is an important parameter in engineering. It may begin from undamaged area and propagate afterwards. In this case, a mechanical component condition before an unstable crack still can be used until fatigue. With the study of fatigue crack growth, it can predict the crack life of the component and can reduce cost to repair the component. In this thesis, primary objective is to develop, test and provide computational fracture mechanics model that emphasized an uncertainties quantification for surface crack. Fracture and failure study that has been promoted by S-version finite element method is focus on the analysis of the surface-crack problem. In this project, a few limitations of the study have been implemented as to present a specific scope of the investigation. Both fatigue crack growth model is considered; Paris law model and modified Forman model. The specimen in this analysis is aluminium al 2024 T3. The effect of load on the fatigue crack growth rate is investigated on aluminium 2024 T3. It is concluded that modified Forman has a low exponent compared to the Paris law. Further the crack growth prediction based on modified Forman is lower than Paris law. Paris law only can predict the crack in the region II while modified Forman can predict the crack in region II and III. After finish setup the project based on the instruction, the project is proceeded and the data is collected. The result is analysed based on the objective by using data collected from the project. After that, conclusion is made based on the result of the project.

Avalanches and mixing behavior of porous 316L stainless steel under tension

The investigation of acoustic emission (AE) reveals mixing of avalanche processes in porous 316L stainless steel. One avalanche mechanism relates to the movement of dislocations, the other to crack propagation. Both mechanisms occur under different external tensions: small tension dislodges dislocations while crack propagation occurs at much higher tension close to the mechanical failure point. In an intermediate overlap regime, both effects occur simultaneously. The avalanche related power laws show a mixing behavior where the higher avalanche exponents form an upper limit for the mixing curve and the lower exponent is approached asymptotically for strong AE signals. The power law probability distribution functions, show a characteristic upwards bend near the crossover between the two mechanisms. The three regimes, namely, the dislocation movement, mixing, and crack propagation, are confirmed by other avalanche characteristics: the sparseness of the AE spectra, the avalanche exponents of energy, amplitude, and duration. Only the crack propagation follows mean field predictions, while the dislocation movements (in confined spaces) deviates significantly from mean field behavior with much greater exponents than those predicted in this approximation. We demonstrate that apparent deviations from scale invariance are, in reality, the result of two superimposed avalanche processes whereby each of them remains scale invariant. The seeming deviations from scale invariance are actually superposition effects.

Fatigue crack propagation behaviour of carboxyl-terminated polybutadiene solid rocket propellants

The fatigue crack growth behavior of composite solid carboxyl-terminated polybutadiene (CTPB) base propellants from a two stage-rocket has been analyzed. Both motors presented similar compositional percentage of the different constituents but while the booster motor presented aluminum as fuel and fine oxidizer particles, the sustainer motor presented nitroguanidine as fuel and coarse rigid inorganic particles. The fracture characterization revealed that the critical energy release rate values obtained from the grains of the booster motor were higher than those computed from the sustainer motor. The fatigue crack growth behavior of the propellant grains under study was comparable to that shown in rubber and the fatigue crack growth curves obtained from the booster motor were below those from the sustainer motor. The micromechanism of failure in both motors was microvoid nucleation and growth till the formation of a macro-crack capable of subcritical advancement. In the grains from the booster motor, the nucleation and progression of damage occurred through the matrix with fracture surfaces plain and with no trace of oxidizer particles. Instead, in the propellant grains from the sustainer motor, the damage was generated in the particle–binder interface and the progression occurred along these interfaces leading to an abrupt fracture surface with discernible oxidizer particles. The mechanism of failure in the booster motor led to a better fatigue crack growth behavior and the irregular crack advancement in the sustainer motor implied a lower exponent of the crack growth rate to the energy release rate power law.

Improved Performance of CSD-Grown Y1- x Gd x Ba2Cu3O7-BaHfO3 Nanocomposite Films on Ni5W Substrates

Y1- x Gd x Ba2Cu3O7-BaHfO3 (YGBCO-BHO) nanocomposite films containing 12 mol% BHO nanoparticles and different amounts of Gd, x , were grown by Chemical Solution Deposition (CSD) on Ni5W substrates in order to investigate the impact of the rare-earth stoichiometry on the structure and superconducting properties of these films. For Gd contents x > 0.5, epitaxial YGBCO-BHO films with an approximate thickness of 270 nm self-field critical current density J c at 77 K ∼ 1,5 MA/cm² were obtained. The field dependence of the critical current density J c( B ) shows a much larger accommodation field and lower exponents α in J c ∼ B −α values compared to pristine YBCO films. This is both due to the high amount of individual nanoparticles in the matrix as observed in TEM images and the higher critical temperatures T c. The results show that the CSD is a potential candidate for the preparation of RE BCO films in long-length coated conductors.

Influence of Fluid Viscous Damper on the Dynamic Response of Suspension Bridge under Random Traffic Load

Fluid viscous dampers (FVDs) are widely used in long‐span suspension bridges for earthquake resistance. To analyze efficiently the influences of FVDs on the dynamic response of a suspension bridge under high‐intensity traffic flow, a bridge‐vehicle coupling method optimized by isoparametric mapping and improved binary search in this work was first developed and validated. Afterwards, the traffic flow was simulated on the basis of monitored weigh‐in‐motion data. The dynamic responses of bridge were analyzed by the proposed method under different FVD parameters. Results showed that FVDs could positively affect bridge dynamic response under traffic flow. The maximum accumulative longitudinal girder displacement, longitudinal girder displacement, and longitudinal pylon acceleration decreased substantially, whereas the midspan girder bending moment, pylon bending moment, longitudinal pylon displacement, and suspender force were less affected. The control efficiency of maximum longitudinal girder displacement and accumulative girder displacement reached 33.67% and 57.71%, longitudinal pylon acceleration and girder bending moment reached 31.51% and 7.14%, and the pylon longitudinal displacement, pylon bending moment, and suspender force were less than 3%. The increased damping coefficient and decreased velocity exponent can reduce the bridge dynamic response. However, when the velocity exponent was 0.1, an excessive damping coefficient brought little improvement and may lead to high‐intensity work under traffic flow, which will adversely affect component durability. The benefits of low velocity exponent also reduced when the damping coefficient was high enough, so if the velocity exponent has to be increased, the damping coefficient can be enlarged to fit with the velocity exponent. The installation of FVDs influences dynamic responses of bridge structures in daily operations and this issue warrants investigation. Thus, traffic load should be considered in FVD design because structural responses are perceptibly influenced by FVD parameters.

Numerical modelling of anomalous microseismicity influenced by lithological heterogeneity in longwall top coal caving mining

Mining-induced microseismicity has been extensively used to evaluate the potential for rock bursts and coal and gas outbursts in underground coal mines. In a research project completed a few years ago, it was observed that characteristics of microseismicity around a working longwall panel were fairly consistent over the monitoring period until a lithological heterogeneity zone with a relatively high coal strength was reached. The current research presented in this paper aims at achieving a better understanding of the effect of lithological heterogeneity on microseismic activity in longwall coal mining. The heterogeneous zone inferred from the tomography measurements was first digitalised and implemented into a 3D geomechanical model. A microseismicity modelling approach which combines deterministic stress and failure analysis together with a stochastic fracture slip evaluation was used to simulate the evolution of microseismicity induced by the progressive face advance passing through the heterogeneous zone. The heterogeneity was taken into account by varying the material strength and the fracture attributes of the elements within the high strength zone. Results have shown that both the high rock strength of coal lithotype and low power law scaling exponent of fractures within this zone contribute to the reduction in fitted b values from frequency-magnitude distribution of microseismicity and the increase in fitted Gaussian distribution parameters to the logarithmic event energy. These deviations are believed to result from the combined effects of increased stress drops and slipped fracture sizes when the heterogeneous zone is approached.

Stress sensitivity of tight reservoirs and its effect on oil saturation: A case study of Lower Cretaceous tight clastic reservoirs in the Hailar Basin, Northeast China

To analyze stress sensitivity of tight reservoirs and the boundary conditions for oil filling, core samples of tight clastic reservoirs in the Lower Cretaceous Nantun Formation in the Hailar Basin were selected. The measurements include optical observation of thin sections, changes of porosity and permeability under overburden pressure, together with physical simulation experiments of oil filling. The results show that the stress sensitivity coefficient of permeability is a product of two parameters including the power exponent of porosity-permeability and pore compressibility, which reflect the geometric and mechanical characteristics of pores. The stress sensitivity and pore geometry of tight reservoirs of different lithologies vary greatly. Medium-coarse sandstones-conglomerates have relatively small stress sensitivity coefficient and large power exponent of porosity-permeability, indicating stronger anti-compaction, weaker stress sensitivity and dominated fissure-type pores. Fine sandstone with large stress sensitivity coefficient and small power exponent of porosity-permeability, indicating that stress sensitivity is high, and matrix circular/elliptical pores predominate. Oil filling in tight reservoirs displays two pressure gradient points with threshold characteristics (i.e., starting pressure gradient and critical pressure gradient) and two flow characteristics (i.e., low-speed nonlinear seepage and quasi-linear seepage). Only when the actual pressure gradient breaks through the critical pressure gradient into the quasi-linear seepage zone can oil saturation in the tight reservoir reach the lower limit of 30%, attaining higher oil saturation levels gradually during the subsequent filling process. The favorable tight reservoir is characterized by a low stress sensitivity coefficient and a high power exponent of porosity-permeability, and oil exhibits rapid filling characteristics with quasi-linear seepage. Another type of tight reservoir is characterized by a high stress sensitivity coefficient and a low power exponent of porosity-permeability, and oil exhibits slow filling rate with nonlinear seepage. It is therefore difficult in actual geological conditions for such reservoirs to achieve high oil saturation. Increase in oil saturation during the filling process is controlled by a combination of initial permeability, pore geometry, stress sensitivity and the displacement pressure gradient. These factors affect and compensate each other, comprehensively controlling the accumulation of tight oil, and could be used to classify the reservoir types.

Rheological and Structural Properties of Camel Milk/Sweet Potato Starch Gel

The unique composition of camel milk limited its use for fermented products preparation. In this research, camel milk (CAM) or cow milk (COM) was blended with sweet potato starch (SPS). Blends were precooked and the rheological properties of the gel were determined. Since the elastic modulus (G′) was much greater than the viscous modulus (G″), milk + SPS gels are considered viscoelastic. The tan δ of all blends was &lt;1.0, signifying solid-like behavior; however, variations between CAM gels or COM were identified. Unlike COM, CAM was more frequency-dependent at low frequencies (0.1 to 1.0 rad/sec). Gels exhibited shear thinning according to the nonlinear rheological tests. Camel milk exhibited gel hardness much higher than cow milk. Because of the domination of G′ and the low power law exponent, camel milk is expected to present processing complications such as in extrusion cooking.

Sensory perception plays a larger role in foraging efficiency than heavy-tailed movement strategies

Animals must balance their rates of energetic intake and expenditure while foraging. Several mathematical models have been put forward as energetically optimal foraging strategies when the food environment is sparse (i.e., the distance between food patches in the environment is much larger than the distance from which the forager can perceive food). In particular, Lévy walks with a power law exponent approaching 1 are considered optimal for destructive foragers. However, these models have yet to explore the role of sensory perception in foraging success as the distance between food patches approaches the distance from which the forager can perceive food. Here, we used an agent-based modeling approach to address this question. Our results concur that lower values of the power law exponent (i.e. values approaching 1) result in the most food found, but in contrast to previous studies, we note that, in many cases, lower exponents are not optimal when we consider food found per unit distance traveled. For example, higher values of the exponent resulted in comparable or higher foraging success relative to lower values when the forager's range of sensory perception was restricted to an angle ± 30° from its current heading. In addition, we find that sensory perception has a larger effect on foraging success than the power law exponent. These results suggest that a deeper examination of how animals perceive food sources from a distance may affect longstanding assumptions regarding the optimality of Lévy walk foraging patterns, and lend support to the developing theoretical shift towards models that place increasing emphasis on how organisms interact with their environments.

Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes

Abstract We investigate theoretically the nonlinear dynamics and the emergence of chaos in suspended beam micro/nanoelectromechanical (MEMS/NEMS) resonators actuated by two-sided electrodes. Through the analysis of phase diagrams we have found that the system presents a rich and complex nonlinear behavior. Multistability is observed in a significant region of the relevant parameter space, involving periodic and chaotic attractors. Complex and varied routes to chaos were also found. Basins of attraction with strongly intermingled attractors provide further evidence of multistability. The basins are analyzed in greater detail. Their fractal dimensions and uncertainty exponent are calculated using the well known box counting and uncertainty methods. The results for the uncertainty exponent are compared with those obtained with yet another approach, based on the recently proposed basin entropy method. The comparison provides a test for the new approach, which we conclude that is a reliable alternative method of calculation. Very low uncertainty exponents have been obtained, indicating that some basins have extremely intermingled attractors, what may have significant influence in the experimental investigation and practical applications of the resonators. We also conclude that the observation of chaos in this system is favored by lower frequencies of excitation and comparatively small quality factors (larger dissipation).

Extended Regression Models for Predicting the Pumping Capability and Viscous Dissipation of Two-Dimensional Flows in Single-Screw Extrusion.

Generally, numerical methods are required to model the non-Newtonian flow of polymer melts in single-screw extruders. Existing approximation equations for modeling the throughput–pressure relationship and viscous dissipation are limited in their scope of application, particularly when it comes to special screw designs. Maximum dimensionless throughputs of , implying minimum dimensionless pressure gradients for low power-law exponents are captured. We present analytical approximation models for predicting the pumping capability and viscous dissipation of metering channels for an extended range of influencing parameters (, and ) required to model wave- and energy-transfer screws. We first rewrote the governing equations in dimensionless form, identifying three independent influencing parameters: (i) the dimensionless down-channel pressure gradient , (ii) the power-law exponent , and (iii) the screw-pitch ratio . We then carried out a parametric design study covering an extended range of the dimensionless influencing parameters. Based on this data set, we developed regression models for predicting the dimensionless throughput-pressure relationship and the viscous dissipation. Finally, the accuracy of all three models was proven using an independent data set for evaluation. We demonstrate that our approach provides excellent approximation. Our models allow fast, stable, and accurate prediction of both throughput-pressure behavior and viscous dissipation.

Experimental and numerical investigation of cavitating vortical patterns around a Tulin hydrofoil

The objective of this paper is to investigate the cavitating flow patterns around a specific hydrofoil (Tulin hydrofoil) via combined experimental and numerical studies, and to better understand the vortex-cavitation interactions in transient cavitating flows. The experimental studies were carried out in the closed-loop cavitation tunnel, and a high-speed digital camera is applied to document the cavitation patterns. The numerical investigations are performed using a large-eddy simulation method and the Zwart cavitation model. The results showed that the predicted cavity formation and evolution agree well with the experimental observation. With decreasing of the cavitation number, different cavitating flow patterns occur around the hydrofoil, namely inception cavitation (σ = 1.57), vortex cavitation (σ = 1.27), cavitating vortex street (σ = 1.07), cloud cavitation (σ = 0.87), mixture supercavitation (σ = 0.67), and developed supercavitation (σ = 0.54). Especially, the flow structures of vortex cavitation, cavitating vortex street and cloud cavitation were further investigated with the Euler and Lagrangian method. For vortex cavitation, the cavitating vortex forms and sheds at the leading and trailing edge of the foil alternatively, with a pair of asymmetric vortex structures observed. The trailing edge cavitating vortex has a regular vortex shape and a clear boundary between the vortex structures. For cavitating vortex street, vortex shedding process is not independent, instead, the vortex braid between the trailing edge cavitating vortexes and the so called “cat's eye” vortex row can be obviously observed. The center of circulation region is corresponding to low finite-time Lyapunov exponent (FTLE) value, and the bridges of the FTLE is concentrated in the boundary of the vortex structure and curling in the dynamic surrounding of the circulation region. The trajectory of the points well presents the dynamic flow pattern. For cloud cavitation pattern, the cavity develops to cover the entire suction surface, and the cloud cavity sheds downstream periodically.