Ditroid is a directed version of matroid. In this paper we investigate transversal theory of ditroids. Directed versions of Rado-Hall and Edmonds-Fulkerson theorems are obtained. Our results provide partial answers to...Ditroid is a directed version of matroid. In this paper we investigate transversal theory of ditroids. Directed versions of Rado-Hall and Edmonds-Fulkerson theorems are obtained. Our results provide partial answers to two questions raised by L. Qi.展开更多
In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and ...In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.展开更多
The aim of this paper is to study abundant semigroups which are disjoint unions of multiplicative adequate tranversals. After obtaining some properties of such semigroup, we prove that a semigroup is a disjoint union ...The aim of this paper is to study abundant semigroups which are disjoint unions of multiplicative adequate tranversals. After obtaining some properties of such semigroup, we prove that a semigroup is a disjoint union of multiplicative adequate transversals if and only if it is isomorphic to the direct product of a rectangular band and an adequate semigroup.展开更多
In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which...In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which satisfies some conditions is a quasiideal adequate transversal.展开更多
A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semi...A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.展开更多
A class of weakly U-abundant semigroups satisfying the congruence condition （C） is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particu...A class of weakly U-abundant semigroups satisfying the congruence condition （C） is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particular, the class of weakly U-abundant semigroups satisfying the congruence condition （C） with Ehresmann transversals is studied. After giving some properties of U-abundant semigroups with Ehresmann transversals, we establish some characterization theorems for such semigroups. Our results may be regarded as an extension of the work of Blyth, McAlister and McFadden in regular semigroups and that of El-Qallali, Guo and Chen in abundant semigroups.展开更多
For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of ...For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component parts I, S° and Λ. The structure of images of this type of semigroups is also presented.展开更多
It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular...It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.展开更多
Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discus...Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.展开更多
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this paper, we give some characterizations for the normality of H in G. As a consequence we get a very short and elementary ...Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this paper, we give some characterizations for the normality of H in G. As a consequence we get a very short and elementary proof of the main theorem of a paper of Lal and Shukla, which avoids the use of the classification of finite simple groups. Further, we study the isotopy between the transversals in some groups and determine the number of isotopy classes of transversals of a subgroup of order 2 in D2p, the dihedral group of order 2p, where p is an odd prime and the isotopism classes are formed with respect to induced right loop structures.展开更多
In this paper,a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed.The classes of this complete congruence which are intervals are discussed and their least and...In this paper,a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed.The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.展开更多
Let S be a locally inverse semigroup with an inverse transversal S°.In this paper,we construct an amenable partial order on S by an R-cone.Conversely,every amenable partial order on S can be constructed in this w...Let S be a locally inverse semigroup with an inverse transversal S°.In this paper,we construct an amenable partial order on S by an R-cone.Conversely,every amenable partial order on S can be constructed in this way.We give some properties of a locally inverse semigroup with a Clifford transversal.In particular,if S is a locally inverse semigroup with a Clifford transversal,then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.展开更多
Research on the mechanical–electrical properties is crucial for designing and preparing high-temperature superconducting(HTS)cables.Various winding core structures can influence the mechanical–electrical behavior of...Research on the mechanical–electrical properties is crucial for designing and preparing high-temperature superconducting(HTS)cables.Various winding core structures can influence the mechanical–electrical behavior of cables,but the impact of alterations in the winding core structure on the mechanical–electrical behavior of superconducting cables remains unclear.This paper presents a 3D finite element model to predict the performance of three cables with different core structures when subjected to transverse compression and axial tension.The three cables analyzed are CORC(conductor-on-round-core),CORT(conductor-on-round-tube),and HFRC(conductor-on-spiral-tube).A parametric analysis is carried out by varying the core diameter and inner-to-outer diameter ratio.Results indicate that the CORT cable demonstrates better performance in transverse compression compared to the CORC cable,aligning with experimental data.Among the three cables,the HFRC cables exhibit the weakest resistance to transverse deformation.However,the HFRC cable demonstrates superior tensile deformation resistance compared to the CORT cable,provided that the transverse compression properties are maintained.Finite element results also show that the optimum inner-to-outer diameter ratios for achieving the best transverse compression performance are approximately 0.8 for CORT cables and 0.6 for HFRC cables.Meanwhile,the study explores the effect of structural changes in HTS cable winding cores on their electromagnetic properties.It recommends utilizing small tape gaps,lower frequencies,and spiral core construction to minimize eddy losses.The findings presented in this paper offer valuable insights for the commercialization and practical manufacturing of HTS cables.展开更多
Precise transverse emittance assessment in electron beams is crucial for advancing high-brightness beam injectors.As opposed to intricate methodologies that use specialized devices,quadrupole focusing strength scannin...Precise transverse emittance assessment in electron beams is crucial for advancing high-brightness beam injectors.As opposed to intricate methodologies that use specialized devices,quadrupole focusing strength scanning(Q-scanning)techniques offer notable advantages for various injectors owing to their inherent convenience and cost-effectiveness.However,their stringent approximation conditions lead to inevitable errors in practical operation,thereby limiting their widespread application.This study addressed these challenges by revisiting the analytical derivation procedure and investigating the effects of the underlying approximation conditions.Preliminary corrections were explored through a combination of data processing analysis and numerical simulations.Furthermore,based on theoretical derivations,virtual measurements using beam dynamics calculations were employed to evaluate the correction reliability.Subsequent experimental validations were performed at the Huazhong University of Science and Technology injector to verify the effectiveness of the proposed compensation method.Both the virtual and experimental results confirm the feasibility and reliability of the enhanced Q-scanning-based diagnosis for transverse emittance in typical beam injectors operating under common conditions.Through the integration of these corrections and compensations,enhanced Q-scanning-based techniques emerge as promising alternatives to traditional emittance diagnosis methods.展开更多
Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition d...Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.展开更多
Large-angle stimulated Raman scattering(LA-SRS)in a longitudinally inhomogeneous plasma with a transverse density modulation is studied using a three-wave coupled model and numerical simulations.The simulations show t...Large-angle stimulated Raman scattering(LA-SRS)in a longitudinally inhomogeneous plasma with a transverse density modulation is studied using a three-wave coupled model and numerical simulations.The simulations show that the scattering angle of SRS in a longitudinally inhomogeneous plasma can be significantly affected by transverse density modulation.Under transverse density modulation conditions,the laser focuses into underdense regions,owing to the transversely modulated refractive index.The angle of LA-SRS,neither a purely 90° angle side scattering nor purely backscattering,is almost consistent with the specific angle at which the density inhomogeneity vanishes.In modulated plasmas,the nonuniform distribution of laser intensity shifts the regions of scattering and gain compared with those in uniform plasmas,ultimately affecting the laser transmission.SRS is suppressed in weakly modulated regimes,whereas it is enhanced under strong modulation conditions,and a theoretical criterion distinguishing between strong and weak modulation is established.展开更多
Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We ...Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.展开更多
A scheme based on irregular V-shaped silicon nanoantennas is proposed to optimize transverse unidirectional scattering under plane wave irradiation.Traditional methods of designing regular shapes offer fewer parameter...A scheme based on irregular V-shaped silicon nanoantennas is proposed to optimize transverse unidirectional scattering under plane wave irradiation.Traditional methods of designing regular shapes offer fewer parameters and higher search efficiency.However,due to the limitations of regular shapes,it is challenging to meet high-precision design requirements.Irregular shape design allows for a broader range of adjustments,but the complexity of shape parameters leads to lower search efficiency and a higher likelihood of converging to local optima.展开更多
Open channel confluences,where two streams or rivers converge,play a crucial role in hydraulic engineering and river dynamics.These confluences are characterized by complex hydrodynamics influenced by the discharge ra...Open channel confluences,where two streams or rivers converge,play a crucial role in hydraulic engineering and river dynamics.These confluences are characterized by complex hydrodynamics influenced by the discharge ratios of merging water bodies.This study investigated the mixing structure at open channel confluences using three-dimensional numerical modeling.A comprehensive three-dimensional numerical model was developed and validated against a dataset obtained from controlled laboratory experiments.This dataset incorporated three-dimensional time-averaged velocity measurements.The skew-induced and stress-induced equation systems were adopted as the core governing equations,providing a framework for simulating various scenarios.A total of ten different cases were analyzed.The results highlighted the effect of discharge ratios on turbulence,lateral and vertical vorticities,and the distribution of mixing,which intensified with higher magnitudes of discharge ratios.The mixing structure,driven by velocity gradients and vorticity,revealed the significant role of lateral and vertical vorticities in determining hydrodynamic behaviors and mixing distributions at confluences.Specifically,the momentum ratio of incoming flows governed the spatial evolution of mixing processes.This study revealed that the distribution of mixing served as a key indicator for identifying the formation of mid-channel scours.High normalized velocities induced toward the left bank led to the superelevation of the water surface,enhancing the potential for bed material and the formation of significant scour holes beneath the elevated water surface.This novel approach provides a deeper understanding of the mixing patterns at confluences,particularly in scenarios with equilibrated discharge ratios but in different magnitudes.展开更多
文摘Ditroid is a directed version of matroid. In this paper we investigate transversal theory of ditroids. Directed versions of Rado-Hall and Edmonds-Fulkerson theorems are obtained. Our results provide partial answers to two questions raised by L. Qi.
基金Supported by the NNSF of China(10961014)Supported by the NSF of Jiangxi ProvinceSupported by the SF of Education Department of Jiangxi Province(GJJ11388)
文摘In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.
基金Supported by the National Natural Science Foundation of China(Grant No.10961014)the Natural Science Foundation of Jiangxi Province(Grant No.2014BAB201009)the Science Foundation of Education Department of Jiangxi Province(Grant No.GJJ11388)
文摘The aim of this paper is to study abundant semigroups which are disjoint unions of multiplicative adequate tranversals. After obtaining some properties of such semigroup, we prove that a semigroup is a disjoint union of multiplicative adequate transversals if and only if it is isomorphic to the direct product of a rectangular band and an adequate semigroup.
基金Supported by National Natural Science Foundation of China（90818020） Supported by Scientific Research Foundation of China Jiliang University（20060810）
文摘In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which satisfies some conditions is a quasiideal adequate transversal.
文摘A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.
基金The research is supported by the Natural Science Foundation of China （11471255, 61672416）, Special Research Fundation of Education Department of Shaanxi Province （15JK1411）, Natural Science Basic Research Project in Shaanxi Province of China （2015JQ1006） and Basic Research Foundation of Xi＇an University of Architecture and Technology （JC1416）.
文摘A class of weakly U-abundant semigroups satisfying the congruence condition （C） is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particular, the class of weakly U-abundant semigroups satisfying the congruence condition （C） with Ehresmann transversals is studied. After giving some properties of U-abundant semigroups with Ehresmann transversals, we establish some characterization theorems for such semigroups. Our results may be regarded as an extension of the work of Blyth, McAlister and McFadden in regular semigroups and that of El-Qallali, Guo and Chen in abundant semigroups.
基金This work is supported by Natural Science Foundation of Guangdong Province
文摘For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component parts I, S° and Λ. The structure of images of this type of semigroups is also presented.
基金supported by National Natural Science Foundation of China (Grant No.10571061)
文摘It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.
文摘Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.
文摘Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this paper, we give some characterizations for the normality of H in G. As a consequence we get a very short and elementary proof of the main theorem of a paper of Lal and Shukla, which avoids the use of the classification of finite simple groups. Further, we study the isotopy between the transversals in some groups and determine the number of isotopy classes of transversals of a subgroup of order 2 in D2p, the dihedral group of order 2p, where p is an odd prime and the isotopism classes are formed with respect to induced right loop structures.
基金Foundation item： the National Natural Science Foundation of China （No. 10571061） the Science Foundation of Guangdong Province （No. 0501332） and the Science Foundation of the Department of Education of Yunnan Province （No. 07C10110）.
文摘In this paper,a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed.The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.
基金the National Natural Science Foundation of China(No.10471112)the Natural Science Foundation of Education Committee of Shaanxi Province(No.07JK413)
文摘Let S be a locally inverse semigroup with an inverse transversal S°.In this paper,we construct an amenable partial order on S by an R-cone.Conversely,every amenable partial order on S can be constructed in this way.We give some properties of a locally inverse semigroup with a Clifford transversal.In particular,if S is a locally inverse semigroup with a Clifford transversal,then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.
基金supported by the National Natural Science Foundation of China(12072136).
文摘Research on the mechanical–electrical properties is crucial for designing and preparing high-temperature superconducting(HTS)cables.Various winding core structures can influence the mechanical–electrical behavior of cables,but the impact of alterations in the winding core structure on the mechanical–electrical behavior of superconducting cables remains unclear.This paper presents a 3D finite element model to predict the performance of three cables with different core structures when subjected to transverse compression and axial tension.The three cables analyzed are CORC(conductor-on-round-core),CORT(conductor-on-round-tube),and HFRC(conductor-on-spiral-tube).A parametric analysis is carried out by varying the core diameter and inner-to-outer diameter ratio.Results indicate that the CORT cable demonstrates better performance in transverse compression compared to the CORC cable,aligning with experimental data.Among the three cables,the HFRC cables exhibit the weakest resistance to transverse deformation.However,the HFRC cable demonstrates superior tensile deformation resistance compared to the CORT cable,provided that the transverse compression properties are maintained.Finite element results also show that the optimum inner-to-outer diameter ratios for achieving the best transverse compression performance are approximately 0.8 for CORT cables and 0.6 for HFRC cables.Meanwhile,the study explores the effect of structural changes in HTS cable winding cores on their electromagnetic properties.It recommends utilizing small tape gaps,lower frequencies,and spiral core construction to minimize eddy losses.The findings presented in this paper offer valuable insights for the commercialization and practical manufacturing of HTS cables.
基金supported by the National Natural Science Foundation of China(Nos.12341501 and 11905074)。
文摘Precise transverse emittance assessment in electron beams is crucial for advancing high-brightness beam injectors.As opposed to intricate methodologies that use specialized devices,quadrupole focusing strength scanning(Q-scanning)techniques offer notable advantages for various injectors owing to their inherent convenience and cost-effectiveness.However,their stringent approximation conditions lead to inevitable errors in practical operation,thereby limiting their widespread application.This study addressed these challenges by revisiting the analytical derivation procedure and investigating the effects of the underlying approximation conditions.Preliminary corrections were explored through a combination of data processing analysis and numerical simulations.Furthermore,based on theoretical derivations,virtual measurements using beam dynamics calculations were employed to evaluate the correction reliability.Subsequent experimental validations were performed at the Huazhong University of Science and Technology injector to verify the effectiveness of the proposed compensation method.Both the virtual and experimental results confirm the feasibility and reliability of the enhanced Q-scanning-based diagnosis for transverse emittance in typical beam injectors operating under common conditions.Through the integration of these corrections and compensations,enhanced Q-scanning-based techniques emerge as promising alternatives to traditional emittance diagnosis methods.
基金Supported in part by the National Key R&D Program of China(No.2020YFA0712300)NSFC(No.61872353)。
文摘Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.
基金supported by the National Natural Science Foundation of China under Grant Nos.U2430207,12035002,and 12305258by the CAEP Foundation under Grant No.YZJJZQ2023020.
文摘Large-angle stimulated Raman scattering(LA-SRS)in a longitudinally inhomogeneous plasma with a transverse density modulation is studied using a three-wave coupled model and numerical simulations.The simulations show that the scattering angle of SRS in a longitudinally inhomogeneous plasma can be significantly affected by transverse density modulation.Under transverse density modulation conditions,the laser focuses into underdense regions,owing to the transversely modulated refractive index.The angle of LA-SRS,neither a purely 90° angle side scattering nor purely backscattering,is almost consistent with the specific angle at which the density inhomogeneity vanishes.In modulated plasmas,the nonuniform distribution of laser intensity shifts the regions of scattering and gain compared with those in uniform plasmas,ultimately affecting the laser transmission.SRS is suppressed in weakly modulated regimes,whereas it is enhanced under strong modulation conditions,and a theoretical criterion distinguishing between strong and weak modulation is established.
基金supported by the National Natural Science Foundation of China Grant Nos.12450004,12274288the Innovation Program for Quantum Science and Technology Grant No.2021ZD0301900。
文摘Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.
基金supported by the National Natural Science Foundation of China(Nos.62475121 and 62335012)。
文摘A scheme based on irregular V-shaped silicon nanoantennas is proposed to optimize transverse unidirectional scattering under plane wave irradiation.Traditional methods of designing regular shapes offer fewer parameters and higher search efficiency.However,due to the limitations of regular shapes,it is challenging to meet high-precision design requirements.Irregular shape design allows for a broader range of adjustments,but the complexity of shape parameters leads to lower search efficiency and a higher likelihood of converging to local optima.
文摘Open channel confluences,where two streams or rivers converge,play a crucial role in hydraulic engineering and river dynamics.These confluences are characterized by complex hydrodynamics influenced by the discharge ratios of merging water bodies.This study investigated the mixing structure at open channel confluences using three-dimensional numerical modeling.A comprehensive three-dimensional numerical model was developed and validated against a dataset obtained from controlled laboratory experiments.This dataset incorporated three-dimensional time-averaged velocity measurements.The skew-induced and stress-induced equation systems were adopted as the core governing equations,providing a framework for simulating various scenarios.A total of ten different cases were analyzed.The results highlighted the effect of discharge ratios on turbulence,lateral and vertical vorticities,and the distribution of mixing,which intensified with higher magnitudes of discharge ratios.The mixing structure,driven by velocity gradients and vorticity,revealed the significant role of lateral and vertical vorticities in determining hydrodynamic behaviors and mixing distributions at confluences.Specifically,the momentum ratio of incoming flows governed the spatial evolution of mixing processes.This study revealed that the distribution of mixing served as a key indicator for identifying the formation of mid-channel scours.High normalized velocities induced toward the left bank led to the superelevation of the water surface,enhancing the potential for bed material and the formation of significant scour holes beneath the elevated water surface.This novel approach provides a deeper understanding of the mixing patterns at confluences,particularly in scenarios with equilibrated discharge ratios but in different magnitudes.
