This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear comb...This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.展开更多
A signal pre-treatment algorithm based on combination of 3-dimension system identification and Kalman filtering estimation（3DSKE）is proposed.The aim of designing the 3DSKE algorithm is to reduce errors caused by ran...A signal pre-treatment algorithm based on combination of 3-dimension system identification and Kalman filtering estimation（3DSKE）is proposed.The aim of designing the 3DSKE algorithm is to reduce errors caused by random noise,but leave the systematical errors caused by signal source remained to be solved by a special method.The 3DSKE algorithm is especially suitable for time series of pure measured data without dynamic equation and on-line real-time execution.The simulated result shows that the 3DSKE algorithm can help the basic theoretic calculation to realize feasible,stable,fast,high accurate and auto-executing computing process for the navigation applications.展开更多
In the recent years,dielectric elastomers（DEs） have become the most popular actuators owing to their special properties such as large deformation,light weight,flexibility,and chemical and biological compatibility in...In the recent years,dielectric elastomers（DEs） have become the most popular actuators owing to their special properties such as large deformation,light weight,flexibility,and chemical and biological compatibility in the field of soft material[1].A DE consists of a polymer film sandwiched between two compliant electrodes.展开更多
Topological defects and smooth excitations determine the properties of systems showing collective order.We introduce a generic non-singular field theory that comprehensively describes defects and excitations in system...Topological defects and smooth excitations determine the properties of systems showing collective order.We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with O(n)broken rotational symmetry.Within this formalism,we explore fast events,such as defect nucleation/annihilation and dynamical phase transitions where the interplay between topological defects and non-linear excitations is particularly important.To highlight its versatility,we apply this formalism in the context of Bose-Einstein condensates,active nematics,and crystal lattices.展开更多
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity.In this work,we report on the description of continuous elast...Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity.In this work,we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale.Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions,which can be generally provided by atomistic modeling or experiments.The magnitude and phase of these amplitudes,together with the continuous description of strains,are able to characterize crystal rotations,lattice deformations,and dislocations.Moreover,combined with the so-called amplitude expansion of the phase-field crystal model,they provide a suitable tool for bridging microscopic to macroscopic scales.This study enables the in-depth analysis of elasticity effects for macroscale and mesoscale systems taking microscopic details into account.展开更多
文摘This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.
基金Supported by the National Natural Science Foundation of China(61174220)the Project of Beijing Municipal Education Commission(KM201210028002)Weapon Equipment Development Project(9140A09050313BQ01127)
文摘A signal pre-treatment algorithm based on combination of 3-dimension system identification and Kalman filtering estimation（3DSKE）is proposed.The aim of designing the 3DSKE algorithm is to reduce errors caused by random noise,but leave the systematical errors caused by signal source remained to be solved by a special method.The 3DSKE algorithm is especially suitable for time series of pure measured data without dynamic equation and on-line real-time execution.The simulated result shows that the 3DSKE algorithm can help the basic theoretic calculation to realize feasible,stable,fast,high accurate and auto-executing computing process for the navigation applications.
基金supported by the National Key R&D Program of China(Grant No.2016YFB0200700)the National Natural Science Foundation of China(Grant Nos.11372025,11572024,and 11432002)the Defense Industrial Technology Development Program(Grant Nos.JCKY2013601B,JCKY2013205B,and JCKY2016205C)
文摘In the recent years,dielectric elastomers（DEs） have become the most popular actuators owing to their special properties such as large deformation,light weight,flexibility,and chemical and biological compatibility in the field of soft material[1].A DE consists of a polymer film sandwiched between two compliant electrodes.
文摘Topological defects and smooth excitations determine the properties of systems showing collective order.We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with O(n)broken rotational symmetry.Within this formalism,we explore fast events,such as defect nucleation/annihilation and dynamical phase transitions where the interplay between topological defects and non-linear excitations is particularly important.To highlight its versatility,we apply this formalism in the context of Bose-Einstein condensates,active nematics,and crystal lattices.
基金M.S.acknowledges the support of the Postdoctoral Research Fellowship awarded by the Alexander von Humboldt FoundationA.V.acknowledges support from the German Research Foundation under Grant no.Vo899/20 within SPP 1959K.R.E.acknowledges financial support from the National Science Foundation under Grant No.DMR1506634.
文摘Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity.In this work,we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale.Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions,which can be generally provided by atomistic modeling or experiments.The magnitude and phase of these amplitudes,together with the continuous description of strains,are able to characterize crystal rotations,lattice deformations,and dislocations.Moreover,combined with the so-called amplitude expansion of the phase-field crystal model,they provide a suitable tool for bridging microscopic to macroscopic scales.This study enables the in-depth analysis of elasticity effects for macroscale and mesoscale systems taking microscopic details into account.
