Experimental Study on the Wavelengths of Two-Dimensional and Three-Dimensional Freak Waves

Freak waves are commonly characterized by strong-nonlinearity, and the wave steepness, which is calculated from the wavelength, is a measure of the degree of the wave nonlinearity. Moreover, the wavelength can describe the locally spatial characteristics of freak waves. Generally, the wavelengths of freak waves are estimated from the dispersion relations of Stokes waves. This paper concerns whether this approach enables a consistent estimate of the wavelength of freak waves. The two-(unidirectional, long-crested) and three-dimensional(multidirectional, shortcrested) freak waves are simulated experimentally through the dispersive and directional focusing of component waves, and the wavelengths obtained from the surface elevations measured by the wave gauge array are compared with the results from the linear, 3rd-order and 5th-order Stokes wave theories. The comparison results suggest that the 3rd-order theory estimates the wavelengths of freak waves with higher accuracy than the linear and 5th-order theories. Furthermore, the results allow insights into the dominant factors. It is particularly noteworthy that the accuracy is likely to depend on the wave period, and that the wavelengths of longer period freak waves are overestimated but the wavelengths are underestimated for shorter period ones. In order to decrease the deviation, a modified formulation is presented to predict the wavelengths of two-and three-dimensional freak waves more accurately than the 3rd-order dispersion relation, by regression analysis. The normalized differences between the predicted and experimental results are over 50% smaller for the modified model suggested in this study compared with the 3rd-order dispersion relation.

THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT

In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case.

Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model

In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.

Three-dimensional Computational Fluid Dynamics Modeling of Two-phase Flow in a Structured Packing Column

Characterizing the complex two-phase hydrodynamics in structured packed columns requires a power- ful modeling tool. The traditional two-dimensional model exhibits limitations when one attempts to model the de- tailed two-phase flow inside the columns. The present paper presents a three-dimensional computational fluid dy- namics （CFD） model to simulate the two-phase flow in a representative unit of the column. The unit consists of an CFD calculations on column packed with Flexipak 1Y were implemented within the volume of fluid （VOF） mathe- matical framework. The CFD model was validated by comparing the calculated thickness of liquid film with the available experimental data. Special attention was given to quantitative analysis of the effects of gravity on the hy- drodynamics. Fluctuations in the liquid mass flow rate and the calculated pressure drop loss were found to be quali- tatively in agreement with the experimental observations.

Three-Dimensional Tidal Model and Its Application to Numerical Simulation of Water Quality in Coastal Waters

The turbulence mechanism plays an important part in the mixing process and momentum transfer of turbulence. A three-dimensional Prandtl mixing length tidal model has been developed to simulate tidal flows and water quality. The eddy viscosities and diffusivities are computed from the Prandtl mixing length model. In order to model the water quality of an estuary or coastal area many interdependent processes need to be simulated. These may be conveniently separated into three main groups: transport and mixing processes, biochemical interaction of water quality variables and the utilization and re-cycling of nutrients by living matter. The model simulates full oxygen and nutrient balance, primary productivity and the transport, reaction mechanism and fate of pollutants over tidal time-scales. The model is applied to numerical simulation of tidal flows and water quality in Dalian Bay. The model has been calibrated against a limited data set of historical water quality observations and in general demonstrates excellent agreement with all available data.

Three-Dimensional and Cross-sectional Characteristics of Normal Grain Growth Based on Monte Carlo Simulation

An appropriate Monte Carlo method was developed to simulate the three-dimensional normal grain growth more completely. Comparative investigation on the three-dimensional and the cross-sectional characteristics of normal grain growth was done. It was found that the time exponent of grain growth determined from cross-section exhibits the same rule of increasing slowly with time and approaching the theoretical value n = 0.5 of steadygrain growth as the three-dimensional (3-D) system. From change of the number of grains per unit area with timemeasured in cross-section, the state of 3-D normal grain growth may be predicted. The gtain size distribution incross-section is different from that in 3-D system and can not express the evolution characteristic of the 3-D distribution. Furthermore, there exists statistical connection between the topological parameters in cross-section and thosein three-dimensions.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

The three-dimension model for the rock-breaking mechanism of disc cutter andanalysis of rock-breaking forces

To study the rock deformation with three- dimensional model under rolling forces of disc cutter, by car- rying out the circular-grooving test with disc cutter rolling around on the rock, the rock mechanical behavior under rolling disc cutter is studied, the mechanical model of disc cutter rolling around the groove is established, and the the- ory of single-point and double-angle variables is proposed. Based on this theory, the physics equations and geometric equations of rock mechanical behavior under disc cutters of tunnel boring machine （TBM） are studied, and then the bal- ance equations of interactive forces between disc cutter and rock are established. Accordingly, formulas about normal force, rolling force and side force of a disc cutter are de- rived, and their validity is studied by tests. Therefore, a new method and theory is proposed to study rock- breaking mech- anism of disc cutters.

Dynamic Characteristic Mechanism of Atrial Septal Defect Using Real-Time Three-Dimensional Echocardiography and Evaluation of Right Ventricular Functions

The dynamic characteristics of the area of the atrial septal defect（ASD） were evaluated using the technique of real-time three-dimensional echocardiography（RT 3DE）, the potential factors responsible for the dynamic characteristics of the area of ASD were observed, and the overall and local volume and functions of the patients with ASD were measured. RT 3DE was performed on the 27 normal controls and 28 patients with ASD. Based on the three-dimensional data workstations, the area of ASD was measured at P wave vertex, R wave vertex, T wave starting point, and T wave terminal point and in the T-P section. The right atrial volume in the same time phase of the cardiac cycle and the motion displacement distance of the tricuspid annulus in the corresponding period were measured. The measured value of the area of ASD was analyzed. The changes in the right atrial volume and the motion displacement distance of the tricuspid annulus in the normal control group and the ASD group were compared. The right ventricular ejection fractions in the normal control group and the ASD group were compared using the RT 3DE long-axis eight-plane（LA 8-plane） method. Real-time three-dimensional volume imaging was performed in the normal control group and ASD group（n=30）. The right ventricular inflow tract, outflow tract, cardiac apex muscular trabecula dilatation, end-systolic volume, overall dilatation, end-systolic volume, and appropriate local and overall ejection fractions in both two groups were measured with the four-dimensional right ventricular quantitative analysis method（4D RVQ） and compared. The overall right ventricular volume and the ejection fraction measured by the LA 8-plane method and 4D RVQ were subjected to a related analysis. Dynamic changes occurred to the area of ASD in the cardiac cycle. The rules for dynamic changes in the area of ASD and the rules for changes in the right atrial volume in the cardiac cycle were consistent. The maximum value of the changes in the right atrial volume occurred in the end-systolic period when the peak of the curve appeared. The minimum value of the changes occurred in the end-systolic period and was located at the lowest point of the volume variation curve. The area variation curve for ASD and the motion variation curve for the tricuspid annulus in the cardiac cycle were the same. The displacement of the tricuspid annulus exhibited directionality. The measured values of the area of ASD at P wave vertex, R wave vertex, T wave starting point, T wave terminal point and in the T-P section were properly correlated with the right atrial volume（P〈0.001）. The area of ASD and the motion displacement distance of the tricuspid annulus were negatively correlated（P〈0.05）. The right atrial volumes in the ASD group in the cardiac cycle in various time phases increased significantly as compared with those in the normal control group（P=0.0001）. The motion displacement distance of the tricuspid annulus decreased significantly in the ASD group as compared with that in the normal control group（P=0.043）. The right ventricular ejection fraction in the ASD group was lower than that in the normal control group（P=0.032）. The ejection fraction of the cardiac apex trabecula of the ASD patients was significantly lower than the ejection fractions of the right ventricular outflow tract and inflow tract and overall ejection fraction. The difference was statistically significant（P=0.005）. The right ventricular local and overall dilatation and end-systolic volumes in the ASD group increased significantly as compared with those in the normal control group（P=0.031）. The a RVEF and the overall ejection fraction decreased in the ASD group as compared with those in the normal control group（P=0.0005）. The dynamic changes in the area of ASD and the motion curves for the right atrial volume and tricuspid annulus have the same dynamic characteristics. RT 3DE can be used to accurately evaluate the local and overall volume and functions of the right ventricle. The local and overall volume loads of the right ventricle in the ASD patients increase significantly as compared with those of the normal people. The right ventricular cardiac apex and the overall systolic function decrease.

Clinical Value of Stereoscopic Three-dimensional Echocardiography in Assessment of Atrial Septal Defects: Feasibility and Efficiency

Stereoscopic three-dimensional echocardiography（S-3DE） is a novel displaying technol-ogy based on real-time 3-dimensional echocardiography （RT-3DE）. Our study was to evaluate the feasibility and efficiency of S-3DE in the diagnosis of atrial septal defect （ASD） and its use in the guidance for transcatheter ASD occlusion. Twelve patients with secundum ASD underwent RT-3DE examination and 9 of the 12 were subjected to transcatheter closure of ASD. Stereoscopic vision was generated with a high-performance volume renderer with red-green stereoscopic glasses. S-3DE was compared with standard RT-3D display for the assessment of the shape, size, and the surrounding tis-sues of ASD and for the guidance of ASD occlusion. The appearance rate of coronary sinus and the mean formation time of the IVC, SVC were compared. Our results showed that S-3DE could measure the diameter of ASD accurately and there was no significant difference in the measurements between S-3DE and standard 3D display （2.89±0.73 cm vs 2.85±0.72 cm, P〉0.05; r=0.96, P〈0.05）. The appearance of coronary sinus for S-3DE was higher as compared with the standard 3D display （93.3% vs 100%）. The mean time of the IVC, SVC for S-3DE monitor was slightly shorter than that of the standard 3D display （11.0±3.8 s vs 10.3±3.6 s, P〉0.05）. The mean completion time of interven-tional procedure was shortened with S-3DE display as compared with standard 3D display （17.3±3.1 min vs 23.0±3.9 min, P〈0.05）. Stereoscopic three-dimensional echocardiography could improve the visualization of three-dimensional echocardiography, facilitate the identification of the adjacent structures, decrease the time required for interventional manipulation. It may be a feasible, safe, and efficient tool for guiding transcatheter septal occlusion or the surgical interventions.

Three-Dimensional Measurement and Reconstruction of Fabric Drape Shape

This paper introduces a new method of measuring the three-dimensional drape shape of fabrics with structural light. First, we apply parallel annular structural light to form light and shade alternating contour stripes on the surface of fabrics. We then collect the images of contour stripes using Charge Coupled Device (CCD). Subsequently, we process the images to identify the contour stripes and edges of fabrics, and obtain the fabric contour lines of curved surfaces. Finally, we apply three-dimensional curved surface modeling method based on a network of polar coordinates, and reconstruct the three-dimensional drape shape of fabrics. Experiments show that our method is effective in testing and reconstructing three-dimensional drape shape of fabrics.

Inversion of source mechanism of 1989 Loma Prieta earthquake by three-dimensional FEM Green's function

Based on three-dimensional joint finite element, this paper discusses the theory and methodology about inversionof geodetic data. The FEM and inversion formula is given in detail; also a related code is developed. By use of theGreen's function about 3-D FEM, we invert geodetic measurementS of coseismic deformation of the 1989 Ms=7. 1Loma Prieta earthquake to datermine itS source mechanism. The result indicates that the slip on the fault plane isvery heterogeneous. The maximum slip and shear stress are located about 10 kin to northwest of the eathquakesource, the stress drop is about more than 1 MPa.

Three-Dimensional Bursting Phenomena in Meander Channel

Experiments were conducted in a U-shaped open-channel flume with the intention of investigating the bursting phenomena in the meander channel. The experimental results of the secondary flow fields and the Reynolds shear stress distributions show that the velocity and velocity fluctuation in the transverse direction are not negligible. Moreover, the bursting process is investigated using the three-dimensional quadrant analysis, which is more accurate than using the traditional two-dimensional quadrant analysis for the meandering channel. It is obtained from the experimental results that the internal group of events occurs more frequently than the external group, particularly the internal ejection and internal sweep events. In addition, the transition probabilities of the movements, which are defined as the changes of events from the current situation to the next situation in a time series, show that the stable organizations of events are the most possible movements, whereas the cross organizations of events have the least possible movements.

A three-dimensional digital visualization model of cervical nerves in a healthy person

Three-dimensional reconstruction nerve models are classically obtained from two-dimensional images of ＂visible human＂ frozen sections. However, because of the flexibility of nerve tissues and small color differences compared with surrounding tissues, the integrity and validity of nerve tissues can be impaired during milling. Thus, in the present study, we obtained two-dimensional data from a healthy volunteer based on continuous CT angiography and magnetic resonance myelography. Semi-automatic segmentation and reconstruction were then conducted at different thresholds in different tissues using Mimics software. Small anatomical structures such as muscles and cervical nerves were reconstructed using the medical computer aided design module. Three-dimensional digital models of the cervical nerves and their surrounding structures were successfully developed, which allowed visualization of the spatial relation of anatomical structures with a strong three-dimensional effect, distinct appearance, clear distribution, and good continuity, precision, and integrality. These results indicate the validity of a three-dimensional digital visualization model of healthy human cervical nerves, which overcomes the disadvantages of milling, avoids data loss, and exhibits a realistic appearance and three-dimensional image.

A novel trilinear decomposition algorithm:Three-dimension non-negative matrix factorization

Non-negative matrix factorization （NMF） is a technique for dimensionality reduction by placing non-negativity constraints on the matrix. Based on the PARAFAC model, NMF was extended for three-dimension data decomposition. The three-dimension nonnegative matrix factorization （NMF3） algorithm, which was concise and easy to implement, was given in this paper. The NMF3 algorithm implementation was based on elements but not on vectors. It could decompose a data array directly without unfolding, which was not similar to that the traditional algorithms do, It has been applied to the simulated data array decomposition and obtained reasonable results. It showed that NMF3 could be introduced for curve resolution in chemometrics.

Neutron-induced single event upset simulation in Geant4 for three-dimensional die-stacked SRAM

Three-dimensional integrated circuits(3D ICs)have entered into the mainstream due to their high performance,high integration,and low power consumption.When used in atmospheric environments,3D ICs are irradiated inevitably by neutrons.In this paper,a 3D die-stacked SRAM device is constructed based on a real planar SRAM device.Then,the single event upsets(SEUs)caused by neutrons with different energies are studied by the Monte Carlo method.The SEU cross-sections for each die and for the whole three-layer die-stacked SRAM device is obtained for neutrons with energy ranging from 1 MeV to 1000 MeV.The results indicate that the variation trend of the SEU cross-section for every single die and for the entire die-stacked device is consistent,but the specific values are different.The SEU cross-section is shown to be dependent on the threshold of linear energy transfer(LETth)and thickness of the sensitive volume(Tsv).The secondary particle distribution and energy deposition are analyzed,and the internal mechanism that is responsible for this difference is illustrated.Besides,the ratio and patterns of multiple bit upset(MBU)caused by neutrons with different energies are also presented.This work is helpful for the aerospace IC designers to understand the SEU mechanism of 3D ICs caused by neutrons irradiation.

AN EXAMPLE OF THREE-DIMENSIONALPROGRESSIVE SLOPE FAILURE

In fact, the failure of any slope takes place progressively, but the progressive failure mechanism has not been emphasized sufficently in the present stability analysis of slopes. This paper provides an example of the progressive slope failure which took place at Pingzhuang west surface coal mine and was numbered the 26th slide. The three-dimensional reliability model for progressive slope failure is used to study the failure process of the 26th slide. The outcomes indicate that the progressive failure is indeed the failure mechanism of the slide.

Hydrogen-bonded Three-Dimensional Networks Encapsulating One-dimensional Covalent Chains: [Cu(3-ampy)(H_2O)_4](SO_4)·(H_2O) (3-ampy = 3-Aminopyridine)

A three-dimensional complex [Cu（3-ampy）（HEO）4]（SO4）·（H2O） （3-ampy = 3-amino- pyridine） has been synthesized. Crystallographic data： C5H16CuN2O9S, Mr = 343.80, triclinic, space group P1, a = 7.675（2）, b = 8.225（3）, c = 10.845（3）A, α= 86.996（4）, β = 76.292（4）, γ= 68.890（4）°, V = 620.0（3）A^3, Z = 2, Dc = 1.841 g/cm^3, F（000） = 354 and μ = 1.971 mm^-1. The structure was refined to R = 0.0269 and wR = 0.0659 for 1838 observed reflections （I 〉 2a（/））. The structure consists of [Cu（3-ampy）（H2O）4]^2＋ cations, SO4^2- anions and lattice water molecules. 3-Ampy acting as a bidentate bridging ligand generates a 1D covalent chain. A supramolecular 2D framework is formed through π-π stacking of pyridine rings. The lattice water molecules and SO4^2- anions are located between the adjacent 2D frameworks. The hydrogen bonding interactions from lattice water molecules and SO4^2- anions to coordinate water extend the 2D framework into a 3D network.

Creative Teaching + Creative Class = Creative Products + Additional Value—A Case Study of Course Reform of Three-dimension Structure

The teaching model of "creative Teaching + creative class = creative products + additional value" was proposed, so as to cultivate students' design creativity and practical ability by changing teaching concepts and curriculum of Three-dimension Structure, and using new materials for spatial creativity training. This paper acclaims that only if the traditional teaching concepts of Three-dimension Structrue are abandoned, students' specialty fully used, the teaching effect will be improved effectively.

THE THREE-DIMENSIONAL FUNDAMENTAL SOLUTION TO STOKES FLOW IN THE OBLATE SPHEROIDAL COORDINATES WITH APPLICATIONS TO MULTIPLES SPHEROID PROBLEMS

A new three-dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb's solution into expressions in terms Of the oblate spheroidal coordinates. These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids. The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three-dimensional problems were completely avoided. The examples demonstrate that present approach is highly accurate, consistently stable and computationally efficient. The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere. For the first time, the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions. The generality of this approach was illustrated by two problems of three spheroids.