A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in...A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.展开更多
Let there be light-to change the world we want to be!Over the past several decades,and ever since the birth of the first laser,mankind has witnessed the development of the science of light,as light-based technologies ...Let there be light-to change the world we want to be!Over the past several decades,and ever since the birth of the first laser,mankind has witnessed the development of the science of light,as light-based technologies have revolutionarily changed our lives.Needless to say,photonics has now penetrated into many aspects of science and technology,turning into an important and dynamically changing field of increasing interdisciplinary interest.In this inaugural issue of eLight,we highlight a few emerging trends in photonics that we think are likely to have major impact at least in the upcoming decade,spanning from integrated quantum photonics and quantum computing,through topological/non-Hermitian photonics and topological insulator lasers,to AI-empowered nanophotonics and photonic machine learning.This Perspective is by no means an attempt to summarize all the latest advances in photonics,yet we wish our subjective vision could fuel inspiration and foster excitement in scientific research especially for young researchers who love the science of light.展开更多
Artificial microstructures,which allow us to control and change the properties of wave fields through changing the geometrical parameters and the arrangements of microstructures,have attracted plenty of attentions in ...Artificial microstructures,which allow us to control and change the properties of wave fields through changing the geometrical parameters and the arrangements of microstructures,have attracted plenty of attentions in the past few decades.Some artificial microstructure based research areas,such as metamaterials,metasurfaces and phononic topological insulators,have seen numerous novel applications and phenomena.The manipulation of different dimensions(phase,amplitude,frequency or polarization)of wave fields,particularly,can be easily achieved at subwavelength scales by metasurfaces.In this review,we focus on the recent developments of wave field manipulations based on artificial microstructures and classify some important applications from the viewpoint of different dimensional manipulations of wave fields.The development tendency of wave field manipulation from single-dimension to multidimensions provides a useful guide for researchers to realize miniaturized and integrated optical and acoustic devices.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
Over the past decade,topology has emerged as a major branch in broad areas of physics,from atomic lattices to condensed matter.In particular,topology has received significant attention in photonics because light waves...Over the past decade,topology has emerged as a major branch in broad areas of physics,from atomic lattices to condensed matter.In particular,topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials.Simultaneously,photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields.Here,we review recent progress in the growing field of topological photonics in three parts.The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases.The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics.Last,we present recently emerging fields in topological photonics that have not yet been reviewed.This part includes topological degeneracies in nonzero dimensions,unidirectional Maxwellian spin waves,higher-order photonic topological phases,and stacking of photonic crystals to attain layer pseudospin.In addition to the various approaches for realizing photonic topological phases,we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.展开更多
A class of minimal subshifts which display Schweizer-Smital chaos and have zero topotogical entropy is constructed, and it is proved that for a compact system, the positive topological entropy is not generally equival...A class of minimal subshifts which display Schweizer-Smital chaos and have zero topotogical entropy is constructed, and it is proved that for a compact system, the positive topological entropy is not generally equivalent to Schweizer-Smital chaos occurring on the measure centre.展开更多
ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuratio...ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.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.
Recent advances in the research of vortex beams,structured beams carrying orbital angular momentum(OAM),have revolutionized the applications of light beams,such as advanced optical manipulations,high-capacity optical ...Recent advances in the research of vortex beams,structured beams carrying orbital angular momentum(OAM),have revolutionized the applications of light beams,such as advanced optical manipulations,high-capacity optical communications,and super-resolution imaging.Undoubtedly,the methods for generation of a vortex beam and detection of its OAM are of vital importance for the applications of vortex beams.In this review,we first introduce the fundamental concepts of vortex beams briefly and then summarize approaches to generating and detecting the vortex beams separately,from bulky diffractive elements to planar elements.Finally,we make a concise conclusion and outline that is yet to be explored.展开更多
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and the...We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.展开更多
In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spac...In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.展开更多
Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade whil...Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete with ongoing challenges in both theory and experiment. Here we propose to establish a universal non-equilibrium characterization of the equilibrium topological quantum phases classified by integers, and further propose the high-precision dynamical schemes to detect such states. The framework of the dynamical classification theory consists of basic theorems. First, we uncover that classifying a d-dimensional(dD) gapped topological phase of generic multibands can reduce to a(d-1)D invariant defined on so-called band inversion surfaces(BISs), rendering a bulk-surface duality which simplifies the topological characterization. Further, we show in quenching across phase boundary the(pseudo) spin dynamics to exhibit unique topological patterns on BISs, which are attributed to the post-quench bulk topology and manifest a dynamical bulk-surface correspondence. For this the topological phase is classified by a dynamical topological invariant measured from an emergent dynamical spintexture field on the BISs. Applications to quenching experiments on feasible models are proposed and studied, demonstrating the new experimental strategies to detect topological phases with high feasibility. This work opens a broad new direction to classify and detect topological phases by non-equilibrium quantum dynamics.展开更多
The theorem obtained by Liao was not true (see [2]). So, this paper presents some criteria of global robust stability for interval Hopfield neural networks with time delay. The methods to judge the robust stability ar...The theorem obtained by Liao was not true (see [2]). So, this paper presents some criteria of global robust stability for interval Hopfield neural networks with time delay. The methods to judge the robust stability are practical and easily verifiable.展开更多
A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more...A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.展开更多
By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]...By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].展开更多
The observation of topological edge states(TESs) revolutionized our understanding of scattering and propagation of electromagnetic(EM) waves. Supported by topological robustness, the TES at the interface between trivi...The observation of topological edge states(TESs) revolutionized our understanding of scattering and propagation of electromagnetic(EM) waves. Supported by topological robustness, the TES at the interface between trivial and non-trivial insulators was not reflected from the structural disorders and imperfections. Recently topological photonic crystals(PhCs) were demonstrated to obtain remarkable one-way propagation of the TES, having the advantages of lossless propagation, dense integration, and high fabrication tolerance over conventional PhCs. Nevertheless, the lack of reversible switching of TES possesses significant limitations in helicity/spin filtering and tunable photonic devices. We proposed a topological PhC based on a prototypical phase-change material, Ge2 Sb2 Te5(GST225) to solve the problem. We find that at a particular frequency, the TES within the structure can be reversibly switched between "on"and "off" by transiting the GST225 structural state between amorphous and crystalline. Moreover, the topology of the PhC was maintained since the tuning of TES was achieved by varying the refractive index of GST225 instead of the structural geometry. This provides a continuous change of the spectral position of the photonic bandgap and TES by gradually crystallising the GST225. We show that the phase change of GST225 from amorphous to crystalline and vice versa can be engineered in nanoseconds. Our proof of concept may offer a platform for dynamically tuning the TESs that might otherwise be challenging to attain in photonic systems. We expect it to have potential applications for photonic devices in topological optical circuits and scatter-free one-way light propagation.展开更多
A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be ob...A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.展开更多
In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo...In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.展开更多
基金The project supported by State Key Laboratory of Structural Analyses of Industrial Equipment
文摘A concept of the independent-continuous topological variable is proposed to establish its corresponding smooth model of structural topological optimization. The method can overcome difficulties that are encountered in conventional models and algorithms for the optimization of the structural topology. Its application to truss topological optimization with stress and displacement constraints is satisfactory, with convergence faster than that of sectional optimizations.
基金support from the National Key R&D Program of China under Grant(No.2017YFA0303800).MS acknowledges support from the Israel Science Foundation.
文摘Let there be light-to change the world we want to be!Over the past several decades,and ever since the birth of the first laser,mankind has witnessed the development of the science of light,as light-based technologies have revolutionarily changed our lives.Needless to say,photonics has now penetrated into many aspects of science and technology,turning into an important and dynamically changing field of increasing interdisciplinary interest.In this inaugural issue of eLight,we highlight a few emerging trends in photonics that we think are likely to have major impact at least in the upcoming decade,spanning from integrated quantum photonics and quantum computing,through topological/non-Hermitian photonics and topological insulator lasers,to AI-empowered nanophotonics and photonic machine learning.This Perspective is by no means an attempt to summarize all the latest advances in photonics,yet we wish our subjective vision could fuel inspiration and foster excitement in scientific research especially for young researchers who love the science of light.
基金This work was supported by the National Key Research and Development Program of China(2016YFA0301102 and 2017YFA0303800)the National Natural Science Fund for Distinguished Young Scholar(11925403)+2 种基金the National Natural Science Foundation of China(11974193,91856101,and 11774186)Natural Science Foundation of Tianjin for Distinguished Young Scientists(18JCJQJC45700)the China Postdoctoral Science Foundation(2020M680851).
文摘Artificial microstructures,which allow us to control and change the properties of wave fields through changing the geometrical parameters and the arrangements of microstructures,have attracted plenty of attentions in the past few decades.Some artificial microstructure based research areas,such as metamaterials,metasurfaces and phononic topological insulators,have seen numerous novel applications and phenomena.The manipulation of different dimensions(phase,amplitude,frequency or polarization)of wave fields,particularly,can be easily achieved at subwavelength scales by metasurfaces.In this review,we focus on the recent developments of wave field manipulations based on artificial microstructures and classify some important applications from the viewpoint of different dimensional manipulations of wave fields.The development tendency of wave field manipulation from single-dimension to multidimensions provides a useful guide for researchers to realize miniaturized and integrated optical and acoustic devices.
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financially supported by the National Research Foundation(NRF)grants(NRF-2019R1A2C3003129,CAMM-2019M3A6B3030637,NRF-2019R1A5A8080290,NRF-2018M3D1A1058997)funded by the Ministry of Science and ICT(MSIT)of the Korean governmentthe Global Ph.D.fellowship(NRF-2017H1A2A1043204)funded by the Ministry of Education of the Korean government.
文摘Over the past decade,topology has emerged as a major branch in broad areas of physics,from atomic lattices to condensed matter.In particular,topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials.Simultaneously,photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields.Here,we review recent progress in the growing field of topological photonics in three parts.The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases.The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics.Last,we present recently emerging fields in topological photonics that have not yet been reviewed.This part includes topological degeneracies in nonzero dimensions,unidirectional Maxwellian spin waves,higher-order photonic topological phases,and stacking of photonic crystals to attain layer pseudospin.In addition to the various approaches for realizing photonic topological phases,we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.
文摘A class of minimal subshifts which display Schweizer-Smital chaos and have zero topotogical entropy is constructed, and it is proved that for a compact system, the positive topological entropy is not generally equivalent to Schweizer-Smital chaos occurring on the measure centre.
基金supported by the National Natural Science Foundation of China(10472003)Beijing Natural Science(3002002)+1 种基金Beijing Educational Committee Foundations(KM200410005019)Suspensofled by American MSC Company.
文摘ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.
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.
基金supported by the National Natural Science Foundation of China (Nos. 11874102 and 12174047)Sichuan Province Science and Technology Support Program (No. 2020JDRC0006)Fundamental Research Funds for the Central Universities (No. ZYGX2019J102)
文摘Recent advances in the research of vortex beams,structured beams carrying orbital angular momentum(OAM),have revolutionized the applications of light beams,such as advanced optical manipulations,high-capacity optical communications,and super-resolution imaging.Undoubtedly,the methods for generation of a vortex beam and detection of its OAM are of vital importance for the applications of vortex beams.In this review,we first introduce the fundamental concepts of vortex beams briefly and then summarize approaches to generating and detecting the vortex beams separately,from bulky diffractive elements to planar elements.Finally,we make a concise conclusion and outline that is yet to be explored.
基金Supported by NNSF of China(Grant Nos.11371339,11431012,11401362,11471125)NSF of Guangdong province(Grant No.S2013040014084)
文摘We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
文摘In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.
基金supported by the National Key Research and Development Program of China (2016YFA0301604)National Natural Science Foundation of China (11574008 and 11761161003)the Thousand-Young-Talent Program of China
文摘Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete with ongoing challenges in both theory and experiment. Here we propose to establish a universal non-equilibrium characterization of the equilibrium topological quantum phases classified by integers, and further propose the high-precision dynamical schemes to detect such states. The framework of the dynamical classification theory consists of basic theorems. First, we uncover that classifying a d-dimensional(dD) gapped topological phase of generic multibands can reduce to a(d-1)D invariant defined on so-called band inversion surfaces(BISs), rendering a bulk-surface duality which simplifies the topological characterization. Further, we show in quenching across phase boundary the(pseudo) spin dynamics to exhibit unique topological patterns on BISs, which are attributed to the post-quench bulk topology and manifest a dynamical bulk-surface correspondence. For this the topological phase is classified by a dynamical topological invariant measured from an emergent dynamical spintexture field on the BISs. Applications to quenching experiments on feasible models are proposed and studied, demonstrating the new experimental strategies to detect topological phases with high feasibility. This work opens a broad new direction to classify and detect topological phases by non-equilibrium quantum dynamics.
基金This paper was supported in part by the National Natural Science Foundation of China under Grant 10171072.
文摘The theorem obtained by Liao was not true (see [2]). So, this paper presents some criteria of global robust stability for interval Hopfield neural networks with time delay. The methods to judge the robust stability are practical and easily verifiable.
文摘A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.
文摘By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].
基金supported by International Science&Technology Cooperation Program of China(2015DFG12630)Program for Liaoning Excellent Talents in University(LJQ2015021)
文摘The observation of topological edge states(TESs) revolutionized our understanding of scattering and propagation of electromagnetic(EM) waves. Supported by topological robustness, the TES at the interface between trivial and non-trivial insulators was not reflected from the structural disorders and imperfections. Recently topological photonic crystals(PhCs) were demonstrated to obtain remarkable one-way propagation of the TES, having the advantages of lossless propagation, dense integration, and high fabrication tolerance over conventional PhCs. Nevertheless, the lack of reversible switching of TES possesses significant limitations in helicity/spin filtering and tunable photonic devices. We proposed a topological PhC based on a prototypical phase-change material, Ge2 Sb2 Te5(GST225) to solve the problem. We find that at a particular frequency, the TES within the structure can be reversibly switched between "on"and "off" by transiting the GST225 structural state between amorphous and crystalline. Moreover, the topology of the PhC was maintained since the tuning of TES was achieved by varying the refractive index of GST225 instead of the structural geometry. This provides a continuous change of the spectral position of the photonic bandgap and TES by gradually crystallising the GST225. We show that the phase change of GST225 from amorphous to crystalline and vice versa can be engineered in nanoseconds. Our proof of concept may offer a platform for dynamically tuning the TESs that might otherwise be challenging to attain in photonic systems. We expect it to have potential applications for photonic devices in topological optical circuits and scatter-free one-way light propagation.
基金The project supported by the State Key Laboratory for Structural Analysis of Industrial Equipment,Dalian University of Technology.
文摘A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.
文摘In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.
