AN APPLICATION OF TOPOLOGICAL ANALYSIS TO STUDYING THE THREE-DIMENSIONAL FLOW IN CASCADES;PART I—TOPOLOGICAL RULES FOR SKIN-FRICTION LINES AND SECTION STREAMLINES

Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are (1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in eachpitch range; (2) for an annular or straight cascade with no-clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch; (3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes; (4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles; (5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.

AN APPLICATION OF TOPOLOGICAL METHOD TO ANALYSING THE THREE-DIMENSIONAL FLOW IN CASCADES(Ⅱ)-TOPOLOGICAL ANALYSIS ON THE VECTOR FIELD PATTERNS OF SKINFRICTIONS AND SECTION STREAMLINES

With an application of topological analysis,in this paper the skin-friction line patterns on compressor and turbine cascade surfaces are depicted and the streamline patterns of the secondary flow fields in the cross-section of a curved pipe and a turbine cascade are drawn under given conditions.In addition the structures of vortices within three-dimensional viscous flow fields in cascades are analysed.

Modification of the Hybridization Gap by Twisted Stacking of Quintuple Layers in a Three-Dimensional Topological Insulator Thin Film

Twisting the stacking of layered materials leads to rich new physics. A three-dimensional topological insulator film hosts two-dimensional gapless Dirac electrons on top and bottom surfaces, which, when the film is below some critical thickness, will hybridize and open a gap in the surface state structure. The hybridization gap can be tuned by various parameters such as film thickness and inversion symmetry, according to the literature. The three-dimensional strong topological insulator Bi(Sb)Se(Te) family has layered structures composed of quintuple layers(QLs) stacked together by van der Waals interaction. Here we successfully grow twistedly stacked Sb_2Te_3 QLs and investigate the effect of twist angels on the hybridization gaps below the thickness limit. It is found that the hybridization gap can be tuned for films of three QLs, which may lead to quantum spin Hall states.Signatures of gap-closing are found in 3-QL films. The successful in situ application of this approach opens a new route to search for exotic physics in topological insulators.

Three-Dimensional Ocean Sensor Networks:A Survey

The past decade has seen a growing interest in ocean sensor networks because of their wide applications in marine research,oceanography,ocean monitoring,offshore exploration,and defense or homeland security.Ocean sensor networks are generally formed with various ocean sensors,autonomous underwater vehicles,surface stations,and research vessels.To make ocean sensor network applications viable,efficient communication among all devices and components is crucial.Due to the unique characteristics of underwater acoustic channels and the complex deployment environment in three dimensional(3D) ocean spaces,new efficient and reliable communication and networking protocols are needed in design of ocean sensor networks.In this paper,we aim to provide an overview of the most recent advances in network design principles for 3D ocean sensor networks,with focuses on deployment,localization,topology design,and position-based routing in 3D ocean spaces.

Grain size distribution and topology in 3D grain growth simulation with large-scale Monte Carlo method

Three-dimensional normal grain growth was appropriately simulated using a Potts model Monte Carlo algorithm. The quasi-stationary grain size distribution obtained from simulation agreed well with the experimental result of pure iron. The Weibull function with a parameter β=2.77 and the Yu-Liu function with a parameter v =2.71 fit the quasi-stationary grain size distribution well. The grain volume distribution is a function that decreased exponentially with increasing grain volume. The distribution of boundary area of grains has a peak at S/〈S〉=0.5, where S is the boundary area of a grain and 〈S〉 is the mean boundary area of all grains in the system. The lognormal function fits the face number distribution well and the peak of the face number distribution is f=10. The mean radius off-faced grains is not proportional to the face number, but appears to be related by a curve convex upward. In the 2D cross-section, both the perimeter law and the Aboav-Weaire law are observed to hold.

Polynomials of Degree-Based Indices for Three-Dimensional Mesh Network

In order to study the behavior and interconnection of network devices,graphs structures are used to formulate the properties in terms of mathematical models.Mesh network(meshnet)is a LAN topology in which devices are connected either directly or through some intermediate devices.These terminating and intermediate devices are considered as vertices of graph whereas wired or wireless connections among these devices are shown as edges of graph.Topological indices are used to reflect structural property of graphs in form of one real number.This structural invariant has revolutionized the field of chemistry to identify molecular descriptors of chemical compounds.These indices are extensively used for establishing relationships between the structure of nanotubes and their physico-chemical properties.In this paper a representation of sodium chloride(NaCl)is studied,because structure of NaCl is same as the Cartesian product of three paths of length exactly like a mesh network.In this way the general formula obtained in this paper can be used in chemistry as well as for any degree-based topological polynomials of three-dimensional mesh networks.

A New Eight-connected Three-dimensional Network Based on a Tetranuclear Zinc Cluster Building Block

One interesting coordination polymer, [Zn2（1,2,4-BTC）（OH）（H2O）2]2·2H2O 1, has been synthesized from 1,2,4-BTC （1,2,4-BTC = 1,2,4-bentricarboxylate） under hydrothermal conditions and characterized by elemental analyses, IR, TG and single-crystal X-ray diffraction. Complex I crystallizes in triclinic, space group P^-1, with a = 6.5200（13）, b = 9,0600（18）, c = 10.968（2） A^°, α = 111.55（3）, β = 92.07（3）,γ= 95.03（3）°, C9H10O10Zn2, Mr = 408.91, V= 598.7（2） A^°^3, Dc = 2.268 g/cm^3, F（000） = 408 and Z = 2. X-ray diffraction analysis reveals that complex 1 is a three-dimensional network built from tetranuclear Zn（Ⅱ） building unit. In this complex, the Zn4 unit is an eight-connected knot, while 1,2,4-BTC a four-connected knot. This results in a CaF2 topology. To the best of our knowledge, such Zn4 unit is the first 8-connected building block built from asymmetry ligand.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

Topological approach of liver segmentation based on 3D visualization technology in surgical planning for split liver transplantation

BACKGROUND Split liver transplantation(SLT)is a complex procedure.The left-lateral and right tri-segment splits are the most common surgical approaches and are based on the Couinaud liver segmentation theory.Notably,the liver surface following right trisegment splits may exhibit different degrees of ischemic changes related to the destruction of the local portal vein blood flow topology.There is currently no consensus on preoperative evaluation and predictive strategy for hepatic segmental necrosis after SLT.AIM To investigate the application of the topological approach in liver segmentation based on 3D visualization technology in the surgical planning of SLT.METHODS Clinical data of 10 recipients and 5 donors who underwent SLT at Shenzhen Third People’s Hospital from January 2020 to January 2021 were retrospectively analyzed.Before surgery,all the donors were subjected to 3D modeling and evaluation.Based on the 3D-reconstructed models,the liver splitting procedure was simulated using the liver segmentation system described by Couinaud and a blood flow topology liver segmentation(BFTLS)method.In addition,the volume of the liver was also quantified.Statistical indexes mainly included the hepatic vasculature and expected volume of split grafts evaluated by 3D models,the actual liver volume,and the ischemia state of the hepatic segments during the actual surgery.RESULTS Among the 5 cases of split liver surgery,the liver was split into a left-lateral segment and right trisegment in 4 cases,while 1 case was split using the left and right half liver splitting.All operations were successfully implemented according to the preoperative plan.According to Couinaud liver segmentation system and BFTLS methods,the volume of the left lateral segment was 359.00±101.57 mL and 367.75±99.73 mL,respectively,while that measured during the actual surgery was 397.50±37.97 mL.The volume of segment IV(the portion of ischemic liver lobes)allocated to the right tri-segment was 136.31±86.10 mL,as determined using the topological approach to liver segmentation.However,during the actual surgical intervention,ischemia of the right tri-segment section was observed in 4 cases,including 1 case of necrosis and bile leakage,with an ischemic liver volume of 238.7 mL.CONCLUSION 3D visualization technology can guide the preoperative planning of SLT and improve accuracy during the intervention.The simulated operation based on 3D visualization of blood flow topology may be useful to predict the degree of ischemia in the liver segment and provide a reference for determining whether the ischemic liver tissue should be removed during the surgery.

Realization of a full hierarchical topology in hexagonal bilayer acoustic crystals

Recently, there has been significant research interest in higher-order topological states within artificial lattices, primarily due to their potential for manipulating waves. In this study, we focus on a three-dimensional hexagonal bilayer acoustic crystal with rotation, layer, and translation degrees of freedom. By systematically reducing the crystal symmetries, we realize a full hierarchical structure of the higher-order topological states. This hierarchical progression begins with the valley-induced twodimensional surface state, followed by the one-dimensional hinge state that arises from the topological obstruction, and ultimately culminating in the zero-dimensional corner state resulting from the edge polarization mechanism. Through finite element simulations and numerical calculations of topological invariants, we confirm the topological origins of all these hierarchical states. Moreover, we successfully verified the full hierarchical topology by directly probing the acoustic field within a finitesized three-dimensional sample. This study offers novel perspectives on the fundamental research pertaining to wave modulation and the intelligent control of sound fields.

Topological Studies of Three-dimensional Flows in a High Pressure Compressor Stator Blade Row without and with Boundary Layer Aspiration

This paper presents a numerical study of the flow topologies of three-dimensional （3D） flows in a high pressure compressor stator blade row without and with boundary layer aspiration on the hub wall. The stator blade is representative of the first stage operating under transonic inlet conditions and the blade design encourages development of highly complex 3D flows. The blade has a small tip clearance. The computational fluid dynamics （CFD） studies show progressive increase of hub corner stall with the increase in incidence. Aspiration is implemented on the hub wall via a slot in the comer between the hub wall and the suction surface. The CFD studies show aspiration to be sensitive to the suction flow rate; lower rate leads to very complex flow struc- tures and increased level of losses whereas higher rate renders aspiration effective for control of hub comer separation. The flow topologies are studied by trace of skin friction lines on the walls. The nature of flow can be explained by the topological rules of closed separation. Furthermore, a deeper analysis is done for a particular case with advanced criterion to test the non-degeneracy of critical points in the flow field.

Realization of a three-dimensional photonic topological insulator

With the support by the National Natural Science Foundation of China and Zhejiang University,the research team led by Prof.Chen HongSheng(陈红胜)at Zhejiang University in China,and their coworkers,the Singapore research team led by Prof.Baile Zhang and Prof.Yidong Chong,experimentally realized a three-dimensional photonic topological insulator,which was published in Nature(2019,565:622).

Reconstructing the flux-rope topology using the FOTE method

With high-resolution data of the Magnetospheric Multiscale(MMS) mission, we observe a magnetic flux rope(MFR) in the Earth's magnetosheath. This MFR, showing a clear bipolar variation of the magnetic field in the normal component to local current sheet, contains a strong core field. We use the FOTE method to reconstruct the topology of this MFR and find it is consistent with previous expectation. For the first time, the spiral field and core field of the MFR are both revealed from the FOTE method. Comparing topologies reconstructed at different times, we suggest that the axis of the MFR rotates about 88° at different spatial location. Shape and size of the normal projection to axis vary with the spatial location as well. Inside the MFR, a significant increase of plasma density from 40 to 80 cm^(-3), a sharp decrease of ion temperature from 200 to 50 eV, an enhancement of cold ions and a series of filamentary currents are found.

3D genomic organization in cancers

Background:The hierarchical three-dimensional(3D)architectures of chromatin play an important role in fundamental biological processes,such as cell differentiation,cellular senescence,and transcriptional regulation.Aberrant chromatin 3D structural alterations often present in human diseases and even cancers,but their underlying mechanisms remain unclear.Results:3D chromatin structures(chromatin compartment A/B,topologically associated domains,and enhancerpromoter interactions)play key roles in cancer development,metastasis,and drug resistance.Bioinformatics techniques based on machine learning and deep learning have shown great potential in the study of 3D cancer genome.Conclusion:Current advances in the study of the 3D cancer genome have expanded our understanding of the mechanisms underlying tumorigenesis and development.It will provide new insights into precise diagnosis and personalized treatment for cancers.