The interplay of magnetic and semiconducting properties has been in the focus for more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magne...The interplay of magnetic and semiconducting properties has been in the focus for more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magnetic semiconductor families, including europium chalcogenides, chromium spinels, dilute magnetic semiconductors, dilute ferromagnetic semiconductors and insulators, mentioning also sources of non-uniformities in the magnetization distribution, accounting for an apparent high Curie temperature ferromagnetism in many systems. Our survey is carried out from today's perspective of ferromagnetic and antiferromagnetic spintronics as well as of the emerging fields of magnetic topological materials and atomically thin 2D layers.展开更多
Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger mode...Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.展开更多
Energy dissipation is of fundamental interest and crucial importance in quantum systems. However,whether energy dissipation can emerge without backscattering inside topological systems remains a question. As a hallmar...Energy dissipation is of fundamental interest and crucial importance in quantum systems. However,whether energy dissipation can emerge without backscattering inside topological systems remains a question. As a hallmark, we propose a microscopic picture that illustrates energy dissipation in the quantum Hall(QH) plateau regime of graphene. Despite the quantization of Hall, longitudinal, and two-probe resistances(dubbed as the quantum limit), we find that the energy dissipation emerges in the form of Joule heat. It is demonstrated that the non-equilibrium energy distribution of carriers plays much more essential roles than the resistance on energy dissipation. Eventually, we suggest probing the phenomenon by measuring local temperature increases in experiments and reconsidering the dissipation typically ignored in realistic topological circuits.展开更多
The interaction of band topology and disorder can give rise to intriguing phenomena.One paradigmatic example is the topological Anderson insulator,whose nontrivial topology is induced in a trivial system by disorders....The interaction of band topology and disorder can give rise to intriguing phenomena.One paradigmatic example is the topological Anderson insulator,whose nontrivial topology is induced in a trivial system by disorders.In this study,we investigate the efect of purely non-Hermitian disorders on topological systems using a one-dimensional acoustic lattice with coupled resonators.Specifically,we construct a theoretical framework to describe the non-Hermitian topological Anderson insulator phase solely driven by disordered loss modulation.Then,the complete evolution of non-Hermitian disorder-induced topological phase transitions,from an initial trivial phase to a topological Anderson phase and finally to a trivial Anderson phase,is revealed experimentally using both bulk and edge spectra.Interestingly,topological modes induced by non-Hermitian disorders to be immune to both weak Hermitian and non-Hermitian disorders.These findings pave the way for future research on disordered non-Hermitian systems for novel wave manipulation.展开更多
Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes.Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic ins...Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes.Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator Mn Bi2Te4.We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment,Kerr and Faraday effects occur.Under perpendicular electric field,antiferromagnetic topological insulators(AFMTI)show sharp peaks at the interband transition threshold,whereas trivial insulators show small adjacent positive and negative peaks.Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators.We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr(Faraday)angles and vanishing ellipticity.Under external magnetic moment,AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity.For the qualitative behaviors,AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change.These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.展开更多
We design and present a switchable slow light rainbow trapping(SLRT) state in a strongly coupling topological photonic system made from a magneto-optical photonic crystal waveguide channel. The waveguide channel suppo...We design and present a switchable slow light rainbow trapping(SLRT) state in a strongly coupling topological photonic system made from a magneto-optical photonic crystal waveguide channel. The waveguide channel supports slow light states with extremely small group velocity(vg2.1 × 10-6c), low group-velocity dispersion, and a broadband operation bandwidth(3.60–4.48 GHz, near 22% of bandwidth). These slow light states originate from the strong coupling between two counter propagating topological photonic states. Under a gradient magnetic field, different frequency components of a wave packet are separated and stored at different positions for a long temporal duration with high spatial precision(without crosstalk and overlap between the electric fields of different frequencies) to form SLRT. Besides, these SLRT states can be easily switched among the forbidden state,trapped state, and releasing state by tuning the external magnetic field. The results suggest that the topological photonic state can offer a precise route of spatial-temporal-spectral control upon a light signal and find applications for optical buffers, broadband slow light systems, optical filters, wavelength-division multiplexing, and other optical communication devices.展开更多
Topological phases in non-Hermitian systems have become fascinating subjects recently.In this paper,we attempt to classify topological phases in 1D interacting non-Hermitian systems.We begin with the non-Hermitian gen...Topological phases in non-Hermitian systems have become fascinating subjects recently.In this paper,we attempt to classify topological phases in 1D interacting non-Hermitian systems.We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger(SSH)model and discuss its many-body topological Berry phase,which is well defined for all interacting quasi-Hermitian systems(non-Hermitian systems that have real energy spectrum).We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts.Finally,we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts.Thus,we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.展开更多
We study the disorder-induced phase transition in two-dimensional non-Hermitian systems.First,the applicability of the noncommutative geometric method(NGM)in non-Hermitian systems is examined.By calculating the Chern ...We study the disorder-induced phase transition in two-dimensional non-Hermitian systems.First,the applicability of the noncommutative geometric method(NGM)in non-Hermitian systems is examined.By calculating the Chern number of two different systems(a square sample and a cylindrical one),the numerical results calculated by NGM are compared with the analytical one,and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction.Then,we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect.For the square sample,the stability of the non-Hermitian Chern insulator under disorder is confirmed.Significantly,we obtain a nontrivial topological phase induced by disorder.This phase is understood as the topological Anderson insulator in non-Hermitian systems.Finally,the disordered phase transition in the cylindrical sample is also investigated.The clean non-Hermitian cylindrical sample has three phases,and such samples show more phase transitions by varying the disorder strength:(1)the normal insulator phase to the gapless phase,(2)the normal insulator phase to the topological Anderson insulator phase,and(3)the gapless phase to the topological Anderson insulator phase.展开更多
Non-Hermitian topological systems,by combining the advantages of topological robustness and sensitivity induced by nonHermiticity,have recently emerged and attracted much research interest.Here,we propose a device bas...Non-Hermitian topological systems,by combining the advantages of topological robustness and sensitivity induced by nonHermiticity,have recently emerged and attracted much research interest.Here,we propose a device based on the topological coupler in elastic waves with non-Hermiticity,which contains two topological domain walls and four ports.In this device,topological robustness routes the transmission of waves,while non-Hermiticity controls the gain or loss of waves as they propagate.These mechanisms result in continuous and quantitative control of the energy distribution ratio of each port.A nonHermitian Hamiltonian is introduced to reveal the coupling mechanism of the topological coupler,and a scattering matrix is proposed to predict the energy distribution ratio of each port.The proposed topological coupler,which provides a new paradigm for the non-Hermitian topological systems,can be employed as a sensitive beam splitter or a coupler switch.Moreover,the topological coupler has potential applications in information processing and logic operation in elastic circuits or networks,and the paradigm also applies to other classical systems.展开更多
The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant...The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant Euler-Lagrange equations. The invariance is obtained subsequently by investigating the invariance of time variation in the system, and then the relation between the related Hamiltonian and electromagnetic energy density is investigated. Canonical equations are obtained eventually. The electrodynamic interpretation on dissipative electromagnetic systems is revealed.展开更多
It is known that metric transitivity implies topological transitivity. But, the converseremains to be an open question. In 1946 and 1973, M. Morse made a conjecture that thisconverse theorem was probably true for anal...It is known that metric transitivity implies topological transitivity. But, the converseremains to be an open question. In 1946 and 1973, M. Morse made a conjecture that thisconverse theorem was probably true for analytic systems or systems with some degree ofanalytic regularity. In this paper, we disprove the Morse' conjecture for almost every-where analytic C^(∞)-flows on n-dimensional manifolds (n≥2), and prove the validity of theMorse conjecture for analytic flows on T^2.展开更多
Materials,where charge carriers have a linear energy dispersion,usually exhibit a strong nonlinear optical response in the absence of disorder scattering.This nonlinear response is particularly interesting in the tera...Materials,where charge carriers have a linear energy dispersion,usually exhibit a strong nonlinear optical response in the absence of disorder scattering.This nonlinear response is particularly interesting in the terahertz frequency region.We present a theoretical and numerical investigation of charge transport and nonlinear effects,such as the high harmonic generation in topological materials including Weyl semimetals(WSMs)and α-T_(3)systems.The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix.We show that the nonlinear response is strongly dependent on temperature and topological parameters,such as the Weyl point(WP)separation b and Berry phase ФB.A finite spectral gap opening can further modify the nonlinear effects.Under certain parameters,universal behaviors of both the linear and nonlinear response can be observed.Coupled with experimentally accessible critical field values of 10^(4)-10^(5) V=m,our results provide useful information on developing nonlinear optoelectronic devices based on topological materials.展开更多
In this study,a multisensor system consisting of 23 potentiometric sensors was applied for long-term online measurements in outlet flow of the water treatment plant.Within 1 month of continuous measurements,the data s...In this study,a multisensor system consisting of 23 potentiometric sensors was applied for long-term online measurements in outlet flow of the water treatment plant.Within 1 month of continuous measurements,the data set of more than 295,000 observations was acquired.The processing of this dataset with conventional chemometric tools was cumbersome and not very informative.Topological data analysis(TDA)was recently suggested in chemometric literature to deal with large spectroscopic datasets.In this research,we explore the opportunities of TDA with respect to multisensor data with only 23 variables.It is shown that TDA allows for convenient data visualization,studying the evolution of water quality during the measurements and tracking the periodical structure in the data related to the water quality depending on the time of the day and the day of the week.TDA appears to be a valuable tool for multisensor data exploration.展开更多
The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what des...The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.展开更多
By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions, we prove the existence of positive solution of the problem.
基金supported by the Foundation for Polish Science through the IRA Programme financed by EU within SG OP Programmesupport by the Austrian Science Foundation-FWF (P31423 and P26830)the Austrian Exchange Service (OAD) Project PL-01/2017
文摘The interplay of magnetic and semiconducting properties has been in the focus for more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magnetic semiconductor families, including europium chalcogenides, chromium spinels, dilute magnetic semiconductors, dilute ferromagnetic semiconductors and insulators, mentioning also sources of non-uniformities in the magnetization distribution, accounting for an apparent high Curie temperature ferromagnetism in many systems. Our survey is carried out from today's perspective of ferromagnetic and antiferromagnetic spintronics as well as of the emerging fields of magnetic topological materials and atomically thin 2D layers.
基金supported by the National Key Research and Development Program of China(Grant No.2016YFA0301800)the National Natural Science Foundation of China(Grant Nos.11704367,11904109,91636218)+2 种基金the National Natural Science Foundation of China(Grant Nos.U1830111,and U1801661)the Key-Area Research and Development Program of GuangDong Province(Grant No.2019B030330001)the Key Program of Science and Technology of Guangzhou(Grant No.201804020055)。
文摘Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.
基金supported by the National Key R&D Program of China (2019YFA0308403, and 2022YFA1403700)the Innovation Program for Quantum Science and Technology (2021ZD0302400)+2 种基金the National Natural Science Foundation of China (12350401, 12304052, 12374034, and 11921005)the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB28000000)funded by China Postdoctoral Science Foundation (BX20220005)。
文摘Energy dissipation is of fundamental interest and crucial importance in quantum systems. However,whether energy dissipation can emerge without backscattering inside topological systems remains a question. As a hallmark, we propose a microscopic picture that illustrates energy dissipation in the quantum Hall(QH) plateau regime of graphene. Despite the quantization of Hall, longitudinal, and two-probe resistances(dubbed as the quantum limit), we find that the energy dissipation emerges in the form of Joule heat. It is demonstrated that the non-equilibrium energy distribution of carriers plays much more essential roles than the resistance on energy dissipation. Eventually, we suggest probing the phenomenon by measuring local temperature increases in experiments and reconsidering the dissipation typically ignored in realistic topological circuits.
基金supported by the National Key Research&Development Program of China(Grant Nos.2022YFA1404400,and 2022YFA1404403)the National Natural Science Foundation of China(Grant No.92263208)the Fundamental Research Funds for the Central Universities。
文摘The interaction of band topology and disorder can give rise to intriguing phenomena.One paradigmatic example is the topological Anderson insulator,whose nontrivial topology is induced in a trivial system by disorders.In this study,we investigate the efect of purely non-Hermitian disorders on topological systems using a one-dimensional acoustic lattice with coupled resonators.Specifically,we construct a theoretical framework to describe the non-Hermitian topological Anderson insulator phase solely driven by disordered loss modulation.Then,the complete evolution of non-Hermitian disorder-induced topological phase transitions,from an initial trivial phase to a topological Anderson phase and finally to a trivial Anderson phase,is revealed experimentally using both bulk and edge spectra.Interestingly,topological modes induced by non-Hermitian disorders to be immune to both weak Hermitian and non-Hermitian disorders.These findings pave the way for future research on disordered non-Hermitian systems for novel wave manipulation.
基金Project supported by the National Natural Science Foundation of China(Grant No.11904062)the Starting Research Fund from Guangzhou University(Grant No.RQ2020076)Guangzhou Basic Research Program,jointed funded by Guangzhou University(Grant No.202201020186)。
文摘Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes.Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator Mn Bi2Te4.We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment,Kerr and Faraday effects occur.Under perpendicular electric field,antiferromagnetic topological insulators(AFMTI)show sharp peaks at the interband transition threshold,whereas trivial insulators show small adjacent positive and negative peaks.Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators.We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr(Faraday)angles and vanishing ellipticity.Under external magnetic moment,AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity.For the qualitative behaviors,AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change.These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.
基金National Natural Science Foundation of China(11434017,11504114)Guangdong Innovative and Entrepreneurial Research Team Program(2016ZT06C594)+3 种基金National Key R&D Program of China(2018YFA0306200)Science and Technology Program of Guangzhou(201904010105)Natural Science Foundation of Guangdong Province,China,2019Fundamental Research Funds for the Central Universities(x2wl-D2191420)
文摘We design and present a switchable slow light rainbow trapping(SLRT) state in a strongly coupling topological photonic system made from a magneto-optical photonic crystal waveguide channel. The waveguide channel supports slow light states with extremely small group velocity(vg2.1 × 10-6c), low group-velocity dispersion, and a broadband operation bandwidth(3.60–4.48 GHz, near 22% of bandwidth). These slow light states originate from the strong coupling between two counter propagating topological photonic states. Under a gradient magnetic field, different frequency components of a wave packet are separated and stored at different positions for a long temporal duration with high spatial precision(without crosstalk and overlap between the electric fields of different frequencies) to form SLRT. Besides, these SLRT states can be easily switched among the forbidden state,trapped state, and releasing state by tuning the external magnetic field. The results suggest that the topological photonic state can offer a precise route of spatial-temporal-spectral control upon a light signal and find applications for optical buffers, broadband slow light systems, optical filters, wavelength-division multiplexing, and other optical communication devices.
基金supported by the National Key Research and Development Program of China (2016YFA0300300)the National Natural Science Foundation of China (NSFC+4 种基金11861161001)NSFC/RGC Joint Research Scheme (N-CUHK427/18)the Science, Technology and Innovation Commission of Shenzhen Municipality (ZDSYS20190902092905285)Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B1515120100Center for Computational Science and Engineering of Southern University of Science and Technology。
文摘Topological phases in non-Hermitian systems have become fascinating subjects recently.In this paper,we attempt to classify topological phases in 1D interacting non-Hermitian systems.We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger(SSH)model and discuss its many-body topological Berry phase,which is well defined for all interacting quasi-Hermitian systems(non-Hermitian systems that have real energy spectrum).We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts.Finally,we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts.Thus,we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.
基金Project supported by the National Basic Research Program of China(Grant No.2019YFA0308403)the National Natural Science Foundation of China(Grant No.11822407)+1 种基金Undergraduate Training Program for Innovation and Entrepreneurship,Soochow University(Grant No.201810285022Z)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China.
文摘We study the disorder-induced phase transition in two-dimensional non-Hermitian systems.First,the applicability of the noncommutative geometric method(NGM)in non-Hermitian systems is examined.By calculating the Chern number of two different systems(a square sample and a cylindrical one),the numerical results calculated by NGM are compared with the analytical one,and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction.Then,we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect.For the square sample,the stability of the non-Hermitian Chern insulator under disorder is confirmed.Significantly,we obtain a nontrivial topological phase induced by disorder.This phase is understood as the topological Anderson insulator in non-Hermitian systems.Finally,the disordered phase transition in the cylindrical sample is also investigated.The clean non-Hermitian cylindrical sample has three phases,and such samples show more phase transitions by varying the disorder strength:(1)the normal insulator phase to the gapless phase,(2)the normal insulator phase to the topological Anderson insulator phase,and(3)the gapless phase to the topological Anderson insulator phase.
基金supported by the Research Grants Council of Hong Kong(Grant Nos.16302218,C6013-18G)support by the National Natural Science Foundation of China(Grant Nos.11574216,61505114)。
文摘Non-Hermitian topological systems,by combining the advantages of topological robustness and sensitivity induced by nonHermiticity,have recently emerged and attracted much research interest.Here,we propose a device based on the topological coupler in elastic waves with non-Hermiticity,which contains two topological domain walls and four ports.In this device,topological robustness routes the transmission of waves,while non-Hermiticity controls the gain or loss of waves as they propagate.These mechanisms result in continuous and quantitative control of the energy distribution ratio of each port.A nonHermitian Hamiltonian is introduced to reveal the coupling mechanism of the topological coupler,and a scattering matrix is proposed to predict the energy distribution ratio of each port.The proposed topological coupler,which provides a new paradigm for the non-Hermitian topological systems,can be employed as a sensitive beam splitter or a coupler switch.Moreover,the topological coupler has potential applications in information processing and logic operation in elastic circuits or networks,and the paradigm also applies to other classical systems.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60601028.
文摘The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant Euler-Lagrange equations. The invariance is obtained subsequently by investigating the invariance of time variation in the system, and then the relation between the related Hamiltonian and electromagnetic energy density is investigated. Canonical equations are obtained eventually. The electrodynamic interpretation on dissipative electromagnetic systems is revealed.
文摘It is known that metric transitivity implies topological transitivity. But, the converseremains to be an open question. In 1946 and 1973, M. Morse made a conjecture that thisconverse theorem was probably true for analytic systems or systems with some degree ofanalytic regularity. In this paper, we disprove the Morse' conjecture for almost every-where analytic C^(∞)-flows on n-dimensional manifolds (n≥2), and prove the validity of theMorse conjecture for analytic flows on T^2.
文摘Materials,where charge carriers have a linear energy dispersion,usually exhibit a strong nonlinear optical response in the absence of disorder scattering.This nonlinear response is particularly interesting in the terahertz frequency region.We present a theoretical and numerical investigation of charge transport and nonlinear effects,such as the high harmonic generation in topological materials including Weyl semimetals(WSMs)and α-T_(3)systems.The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix.We show that the nonlinear response is strongly dependent on temperature and topological parameters,such as the Weyl point(WP)separation b and Berry phase ФB.A finite spectral gap opening can further modify the nonlinear effects.Under certain parameters,universal behaviors of both the linear and nonlinear response can be observed.Coupled with experimentally accessible critical field values of 10^(4)-10^(5) V=m,our results provide useful information on developing nonlinear optoelectronic devices based on topological materials.
基金The authors are grateful to O.Lominoga and Zh.Lyadova from SUE“Vodokanal of St.Petersburg”for their valuable help in organizing the experiments.DK acknowledges financial support from RFBR project#17-33-50101.EL and AL acknowledge partial financial support from the Government of Russian Federation,Grant 08-08.VB thanks the Russian Ministry of Education and Science for support of this work within the framework of the basic part of the state task on the theme:“Adaptive technologies of analytical control based on optical sensors”(Project No.4.7001.2017/BP).
文摘In this study,a multisensor system consisting of 23 potentiometric sensors was applied for long-term online measurements in outlet flow of the water treatment plant.Within 1 month of continuous measurements,the data set of more than 295,000 observations was acquired.The processing of this dataset with conventional chemometric tools was cumbersome and not very informative.Topological data analysis(TDA)was recently suggested in chemometric literature to deal with large spectroscopic datasets.In this research,we explore the opportunities of TDA with respect to multisensor data with only 23 variables.It is shown that TDA allows for convenient data visualization,studying the evolution of water quality during the measurements and tracking the periodical structure in the data related to the water quality depending on the time of the day and the day of the week.TDA appears to be a valuable tool for multisensor data exploration.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171034).
文摘The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.
基金The Project Supported by the National Natural Science Foundation of China (10371066).
文摘By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions, we prove the existence of positive solution of the problem.
