Kinetic energy(KE) functional is crucial to speed up density functional theory calculation. However, deriving it accurately through traditional physics reasoning is challenging. We develop a generally applicable KE fu...Kinetic energy(KE) functional is crucial to speed up density functional theory calculation. However, deriving it accurately through traditional physics reasoning is challenging. We develop a generally applicable KE functional estimator for a one-dimensional (1D) extended system using a machine learning method. Our end-to-end solution combines the dimensionality reduction method with the Gaussian process regression, and simple scaling method to adapt to various 1D lattices. In addition to reaching chemical accuracy in KE calculation, our estimator also performs well on KE functional derivative prediction. Integrating this machine learning KE functional into the current orbital free density functional theory scheme is able to provide us with expected ground state electron density.展开更多
In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that d...In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.展开更多
This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has be...This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has been reduced to a simple form. So we have dealt with the small perturbation problem of the almost periodic system.展开更多
In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case ...In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.展开更多
It is proposed that the observed Higgs Boson at the LHC is the Standard Model Higgs boson that adopts the existence of the hidden lepton condensate. The hidden lepton is in the forbidden lepton family, outside of the ...It is proposed that the observed Higgs Boson at the LHC is the Standard Model Higgs boson that adopts the existence of the hidden lepton condensate. The hidden lepton is in the forbidden lepton family, outside of the three lepton families of the Standard Model. Being forbidden, a single hidden lepton cannot exist alone;so it must exist in the lepton condensate as a composite of μ’ and μ’± hidden leptons and their corresponding antileptons. The calculated average mass of the hidden lepton condensate is 128.8 GeV in good agreements with the observed 125 or 126 GeV. The masses of the hidden lepton condensate and all elementary particles including leptons, quarks, and gauge bosons are derived from the periodic system of elementary particles. The calculated constituent masses are in good agreement with the observed values by using only four known constants: the number of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the mass of Z boson, and the fine structure constant.展开更多
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same prop...This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.展开更多
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con...We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.展开更多
Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing el...Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing electro-gravimagnetic waves. The two classes of solutions of this biquaternionic wave equation have been investigated, generated by scalar potentials (pulsars) and vectorial potentials (spinors). Their asymptotic properties are considered, on the base of which they are classified into heavy (boson) and light (lepton) elementary particles. The biquaternion representation of the hydrogen atom is given. The periodic system of elements is produced, which is built on the principle of the musical structure of a simple gamma.展开更多
The purpose of this article is to propose a new design for the periodic table of elements. The new design is based on a three-dimensional (3D) model of the gastropod shell structure and presents a mechanism of the for...The purpose of this article is to propose a new design for the periodic table of elements. The new design is based on a three-dimensional (3D) model of the gastropod shell structure and presents a mechanism of the formation of elements that reflects the laws of nature that guide the formation of the gastropod shell, electron orbitals, and element structure. The author also identifies challenges associated with the current standard periodic table, such as the positions of hydrogen, helium, lanthanides, and actinides. The author’s research is a response to the IUPAC’s request, dating back to 2016, to settle unresolved disputes surrounding the current standard periodic table. Hence, the author proposes the “Gastropod Shell Model”, which presents the periodic system in 2D and 3D snail shells based on a hypothesized unifying principle guiding the formation of elements: the universal unified theory that considers the spiral and vortex forms as the bridge between energy and matter. The author was able to position hydrogen, helium, lanthanides, and actinides uniquely in their proposed periodic system to solve problems associated with their positions in the standard periodic table. Readers will be interested in uncovering the “hypothesized unifying principle guiding the formation of elements”.展开更多
The control of adiabatic dynamics is essential for quantum manipulation.We investigate the effects of both periodic modulating field and linear sweeping field on adiabatic dynamics based on a non-reciprocal Landau-Zen...The control of adiabatic dynamics is essential for quantum manipulation.We investigate the effects of both periodic modulating field and linear sweeping field on adiabatic dynamics based on a non-reciprocal Landau-Zener model with periodic modulation.We obtain adiabatic phase diagrams in the(ω,δ)parameter space,where the adiabatic region is bounded by the modulating frequencyωgreater than a critical valueω_(c) and the non-reciprocal parameterδless than one.The results show that the adiabaticity of the system is not sensitive to the modulating amplitude.We find that the critical modulating frequency can be expressed as a power function of the modulating period number or the sweeping rate.Our findings suggest that one can change the adiabatic region or improve the adiabaticity by adjusting the parameters of both the modulating and the sweeping fields,which provides an effective means to flexibly control the adiabatic dynamics of non-reciprocal systems.展开更多
Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study propo...Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study proposes a novel aperiodic vibration isolation for improving the internal resonances control of the periodic isolator.The mechanism of the internal resonances control by the aperiodic isolator is firstly explained.For comparing the internal resonances suppression effect of the aperiodic isolator with the periodic isolator,a dynamic model combing the rigid machine,the isolator,and the flexible plate is derived through multi subsystem modeling method and transfer matrix method,whose accuracy is verified through the finite element method.The influences of the aperiodicity and damping of the isolator on the vibration isolation performance and internal resonances suppression effect are investigated by numerical analysis.The numerical results demonstrate that vibration attenuation performances of the periodic isolator and aperiodic isolator are greatly over than that of the continuous isolator in middle and high frequencies.The aperiodic isolator opens the stop bandgaps comparing with the periodic isolator where the pass bandgaps are periodically existed.The damping of the isolator has the stop bandgap widening effect on both the periodic isolator and the aperiodic isolator.In addition,a parameter optimization algorithm of the aperiodic isolator is presented for improving the internal resonances control effect.It is shown that the vibration peaks within the target frequency band of the aperiodic isolator are effectively reduced after the optimization.Finally,the experiments of the three different vibration isolation systems are conducted for verifying the analysis work.展开更多
This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system(TPMS-SCS)for the first time.Although these structures exhibit...This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system(TPMS-SCS)for the first time.Although these structures exhibit outstanding physical and mechanical properties,their dynamic and acoustic features have not been reported yet.This study addresses this gap by calculating the sound transmission loss(STL)coefficient within the framework of the wave approach across various architectures,including the primitive(P),Schoen gyroid(G),and wrapped package-graph(IWP)of a TPMS lattice structure.To determine an analytical STL,a third-order approach is used to precisely capture the stress-strain distribution based on the thickness coordinate,thereby providing a simultaneous solution to the general characteristic relations along with fluid-structure coupling.Given the lack of studies for frequency and STL comparisons,the structure is modeled considering a finite element(FE)design,which is a challenging and time-consuming process because of the complex topological TPMS configurations incorporated within a sandwich cylinder.In fact,achieving convincing computational accuracy requires fine mesh discretization,which significantly increases computational costs during vibroacoustic analysis.Using the numerical results from the COMSOL software Multiphysics,the accuracy of the analytical STL spectrum is verified for different configurations,including P,G,and IWP.The effective acoustic specifications of a TPMS-SCS in the frequency domain are examined by the comparison of the STL with that of a simple cylinder of the same mass.In this context,it would also be beneficial to examine the effect of TPMS thickness,which can demonstrate the importance of the present results.The findings of this approach can be beneficial for scholars working on the numerical and analytical sound insulation characteristics of metamaterial-based cylindrical systems.展开更多
In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described...In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described by four component nonlinear evolution equations(NLEEs).On the background of the Jacobian elliptic function,we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem.Then,with the help of the one-fold Darboux transformation and two-fold Darboux transformation,rogue waves on a dn-periodic background and cn-periodic background are derived,respectively.Finally,the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.展开更多
Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkho...Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.展开更多
A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespa...A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespan and an LPT-LS algorithm is proposed.Non-resumable jobs are first scheduled in a machine by the longest processing time（LPT） rule,and then resumable jobs are scheduled by the list scheduling（LS） rule.And the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the resumable jobs（denoted as S2） are discussed.When S2 is longer than the spare time of the machine after the non-resumable jobs are assigned by the LPT rule,it is equal to 1.When S2 falls in between the spare time of the machine by the LPT rule and the optimal schedule rule,it is less than 2.When S2 is less than the spare time of the machine by the optimal schedule rule,it is less than 2.Finally,numerical examples are presented for verification.展开更多
In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the soluti...In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.展开更多
One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equati...One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.展开更多
The formation of periodic layered structure in Ni3Si/Zn diffusion couples with Zn in vapor or liquid state was investigated by SEM-EDS, FESEM and XRD. The results show that the diffusion path in solid-liquid reaction ...The formation of periodic layered structure in Ni3Si/Zn diffusion couples with Zn in vapor or liquid state was investigated by SEM-EDS, FESEM and XRD. The results show that the diffusion path in solid-liquid reaction is Ni3Si/（T＋γ）/γ/…T/γ/Ni4Zn12Si3/γ/…Ni4Zn12Si3/γ/Ni4Zn12Si3/δ…/Ni4Zn12Si3/δ/liquid-Zn, and the diffusion path in solid-vapor reaction is Ni3Si/θ/（T＋γ）/γ/…/T/γ/…T/γ/vapor-Zn. With increasing Zn diffusion flux, the diffusion reaction path moves toward the Zn-rich direction, and the distance from the Ni3Si substrate to the periodic layer pair nearest to the interface decreases. In the initial stage of both reactions,γphase nucleates and grows within T matrix phase at first, and then conjuncts together to form a band to reduce the surface energy. Based on the experimental results and diffusion kinetics analysis, the microstructure differences were compared and the formation mechanism of the periodic layered structure in Ni3Si/Zn system was discussed.展开更多
This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence an...This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence and uniqueness and stability of almost periodic solutions of this system.展开更多
Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addresse...Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.展开更多
基金Supported by the Hong Kong Research Grants Council (Project No.GRF16300918)the National Key R&D Program of China(Grant Nos.2016YFA0300603 and 2016YFA0302400)the National Natural Science Foundation of China (Grant No.11774398)。
文摘Kinetic energy(KE) functional is crucial to speed up density functional theory calculation. However, deriving it accurately through traditional physics reasoning is challenging. We develop a generally applicable KE functional estimator for a one-dimensional (1D) extended system using a machine learning method. Our end-to-end solution combines the dimensionality reduction method with the Gaussian process regression, and simple scaling method to adapt to various 1D lattices. In addition to reaching chemical accuracy in KE calculation, our estimator also performs well on KE functional derivative prediction. Integrating this machine learning KE functional into the current orbital free density functional theory scheme is able to provide us with expected ground state electron density.
基金This work was supported by the National Aviation Cooperation Research Foundation of China (No. 10577012)the Chinese Postdoctoral Foundation (No. 2005038311).
文摘In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.
文摘This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has been reduced to a simple form. So we have dealt with the small perturbation problem of the almost periodic system.
文摘In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.
文摘It is proposed that the observed Higgs Boson at the LHC is the Standard Model Higgs boson that adopts the existence of the hidden lepton condensate. The hidden lepton is in the forbidden lepton family, outside of the three lepton families of the Standard Model. Being forbidden, a single hidden lepton cannot exist alone;so it must exist in the lepton condensate as a composite of μ’ and μ’± hidden leptons and their corresponding antileptons. The calculated average mass of the hidden lepton condensate is 128.8 GeV in good agreements with the observed 125 or 126 GeV. The masses of the hidden lepton condensate and all elementary particles including leptons, quarks, and gauge bosons are derived from the periodic system of elementary particles. The calculated constituent masses are in good agreement with the observed values by using only four known constants: the number of the extra spatial dimensions in the eleven-dimensional membrane, the mass of electron, the mass of Z boson, and the fine structure constant.
基金Project supported by the National Natural Science Foundation of China(Grant No19674046)the Cheung Kong Scholars Programme of Chinathe Construct Program of the Key Discipline in Hunan Province,China
文摘This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.
基金supported by the NSFC(12071413)the Guangxi Natural Sci-ence Foundation(2023GXNSFAA026085)the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.
文摘Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing electro-gravimagnetic waves. The two classes of solutions of this biquaternionic wave equation have been investigated, generated by scalar potentials (pulsars) and vectorial potentials (spinors). Their asymptotic properties are considered, on the base of which they are classified into heavy (boson) and light (lepton) elementary particles. The biquaternion representation of the hydrogen atom is given. The periodic system of elements is produced, which is built on the principle of the musical structure of a simple gamma.
文摘The purpose of this article is to propose a new design for the periodic table of elements. The new design is based on a three-dimensional (3D) model of the gastropod shell structure and presents a mechanism of the formation of elements that reflects the laws of nature that guide the formation of the gastropod shell, electron orbitals, and element structure. The author also identifies challenges associated with the current standard periodic table, such as the positions of hydrogen, helium, lanthanides, and actinides. The author’s research is a response to the IUPAC’s request, dating back to 2016, to settle unresolved disputes surrounding the current standard periodic table. Hence, the author proposes the “Gastropod Shell Model”, which presents the periodic system in 2D and 3D snail shells based on a hypothesized unifying principle guiding the formation of elements: the universal unified theory that considers the spiral and vortex forms as the bridge between energy and matter. The author was able to position hydrogen, helium, lanthanides, and actinides uniquely in their proposed periodic system to solve problems associated with their positions in the standard periodic table. Readers will be interested in uncovering the “hypothesized unifying principle guiding the formation of elements”.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12375019 and 11974273)。
文摘The control of adiabatic dynamics is essential for quantum manipulation.We investigate the effects of both periodic modulating field and linear sweeping field on adiabatic dynamics based on a non-reciprocal Landau-Zener model with periodic modulation.We obtain adiabatic phase diagrams in the(ω,δ)parameter space,where the adiabatic region is bounded by the modulating frequencyωgreater than a critical valueω_(c) and the non-reciprocal parameterδless than one.The results show that the adiabaticity of the system is not sensitive to the modulating amplitude.We find that the critical modulating frequency can be expressed as a power function of the modulating period number or the sweeping rate.Our findings suggest that one can change the adiabatic region or improve the adiabaticity by adjusting the parameters of both the modulating and the sweeping fields,which provides an effective means to flexibly control the adiabatic dynamics of non-reciprocal systems.
基金supported by the National Key Research and Development Plan of China (Grant No.2023YFB3406302)Guangdong Basic and Applied Basic Research Foundation (Grant No.2024A1515011126)the Key Research and Development Plan of Shanxi (Grant No.2024GH-ZDXM-29)。
文摘Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study proposes a novel aperiodic vibration isolation for improving the internal resonances control of the periodic isolator.The mechanism of the internal resonances control by the aperiodic isolator is firstly explained.For comparing the internal resonances suppression effect of the aperiodic isolator with the periodic isolator,a dynamic model combing the rigid machine,the isolator,and the flexible plate is derived through multi subsystem modeling method and transfer matrix method,whose accuracy is verified through the finite element method.The influences of the aperiodicity and damping of the isolator on the vibration isolation performance and internal resonances suppression effect are investigated by numerical analysis.The numerical results demonstrate that vibration attenuation performances of the periodic isolator and aperiodic isolator are greatly over than that of the continuous isolator in middle and high frequencies.The aperiodic isolator opens the stop bandgaps comparing with the periodic isolator where the pass bandgaps are periodically existed.The damping of the isolator has the stop bandgap widening effect on both the periodic isolator and the aperiodic isolator.In addition,a parameter optimization algorithm of the aperiodic isolator is presented for improving the internal resonances control effect.It is shown that the vibration peaks within the target frequency band of the aperiodic isolator are effectively reduced after the optimization.Finally,the experiments of the three different vibration isolation systems are conducted for verifying the analysis work.
文摘This study uses numerical and analytical schemes to consider the wave propagation behavior of a triply periodic minimal surface sandwich cylindrical system(TPMS-SCS)for the first time.Although these structures exhibit outstanding physical and mechanical properties,their dynamic and acoustic features have not been reported yet.This study addresses this gap by calculating the sound transmission loss(STL)coefficient within the framework of the wave approach across various architectures,including the primitive(P),Schoen gyroid(G),and wrapped package-graph(IWP)of a TPMS lattice structure.To determine an analytical STL,a third-order approach is used to precisely capture the stress-strain distribution based on the thickness coordinate,thereby providing a simultaneous solution to the general characteristic relations along with fluid-structure coupling.Given the lack of studies for frequency and STL comparisons,the structure is modeled considering a finite element(FE)design,which is a challenging and time-consuming process because of the complex topological TPMS configurations incorporated within a sandwich cylinder.In fact,achieving convincing computational accuracy requires fine mesh discretization,which significantly increases computational costs during vibroacoustic analysis.Using the numerical results from the COMSOL software Multiphysics,the accuracy of the analytical STL spectrum is verified for different configurations,including P,G,and IWP.The effective acoustic specifications of a TPMS-SCS in the frequency domain are examined by the comparison of the STL with that of a simple cylinder of the same mass.In this context,it would also be beneficial to examine the effect of TPMS thickness,which can demonstrate the importance of the present results.The findings of this approach can be beneficial for scholars working on the numerical and analytical sound insulation characteristics of metamaterial-based cylindrical systems.
基金supported by the National Natural Science Foundation of China(Grant No.12361052)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414)+3 种基金the Fundamental Research Funds for the Inner Mongolia Normal University,China(Grant Nos.2022JBTD007,2022JBXC013)Graduate Students'Research and Innovation Fund of Inner Mongolia Autonomous Region(Grant No.B20231053Z)the Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application(Inner Mongolia Normal University),the Ministry of Education(Grant Nos.2023KFZR01,2023KFZR02)the First-Class Disciplines Project,Inner Mongolia Autonomous Region,China(Grant No.YLXKZX-NSD-001)。
文摘In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described by four component nonlinear evolution equations(NLEEs).On the background of the Jacobian elliptic function,we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem.Then,with the help of the one-fold Darboux transformation and two-fold Darboux transformation,rogue waves on a dn-periodic background and cn-periodic background are derived,respectively.Finally,the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.
文摘Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.
基金The National Natural Science Foundation of China (No.70971022,71271054)the Scientific Research Innovation Project for College Graduates in Jiangsu Province(No.CXLX_0157)the Scientific Research Foundation of the Education Department of Anhui Province(No.2011sk123)
文摘A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespan and an LPT-LS algorithm is proposed.Non-resumable jobs are first scheduled in a machine by the longest processing time（LPT） rule,and then resumable jobs are scheduled by the list scheduling（LS） rule.And the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the resumable jobs（denoted as S2） are discussed.When S2 is longer than the spare time of the machine after the non-resumable jobs are assigned by the LPT rule,it is equal to 1.When S2 falls in between the spare time of the machine by the LPT rule and the optimal schedule rule,it is less than 2.When S2 is less than the spare time of the machine by the optimal schedule rule,it is less than 2.Finally,numerical examples are presented for verification.
基金This work was supported by the Basic Program in Natural Sciences, Vietnam and Thai Research Fund Grant, Thailand
文摘In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.
文摘One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.
基金Projects(51271040,51171031)supported by the National Natural Science Foundation of ChinaProject supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China
文摘The formation of periodic layered structure in Ni3Si/Zn diffusion couples with Zn in vapor or liquid state was investigated by SEM-EDS, FESEM and XRD. The results show that the diffusion path in solid-liquid reaction is Ni3Si/（T＋γ）/γ/…T/γ/Ni4Zn12Si3/γ/…Ni4Zn12Si3/γ/Ni4Zn12Si3/δ…/Ni4Zn12Si3/δ/liquid-Zn, and the diffusion path in solid-vapor reaction is Ni3Si/θ/（T＋γ）/γ/…/T/γ/…T/γ/vapor-Zn. With increasing Zn diffusion flux, the diffusion reaction path moves toward the Zn-rich direction, and the distance from the Ni3Si substrate to the periodic layer pair nearest to the interface decreases. In the initial stage of both reactions,γphase nucleates and grows within T matrix phase at first, and then conjuncts together to form a band to reduce the surface energy. Based on the experimental results and diffusion kinetics analysis, the microstructure differences were compared and the formation mechanism of the periodic layered structure in Ni3Si/Zn system was discussed.
文摘This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence and uniqueness and stability of almost periodic solutions of this system.
基金supported by the National Natural Science Foundation of China (Nos. 60404001 and60774089)
文摘Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.
