The study of Electromagnetic Compatibility is essential to ensure the harmonious operation of electronic equipment in a shared environment. The basic principles of Electromagnetic Compatibility focus on the ability of...The study of Electromagnetic Compatibility is essential to ensure the harmonious operation of electronic equipment in a shared environment. The basic principles of Electromagnetic Compatibility focus on the ability of devices to withstand electromagnetic disturbances and not produce disturbances that could affect other systems. Imperceptible in most work situations, electromagnetic fields can, beyond certain thresholds, have effects on human health. The objective of the present article is focused on the modeling analysis of the influence of geometric parameters of industrial static converters radiated electromagnetic fields using Maxwell’s equations. To do this we used the analytical formalism for calculating the electromagnetic field emitted by a filiform conductor, to model the electromagnetic radiation of this device in the spatio-temporal domain. The interactions of electromagnetic waves with human bodies are complex and depend on several factors linked to the characteristics of the incident wave. To model these interactions, we implemented the physical laws of electromagnetic wave propagation based on Maxwell’s and bio-heat equations to obtain consistent results. These obtained models allowed us to evaluate the spatial profile of induced current and temperature of biological tissue during exposure to electromagnetic waves generated by this system. The simulation 2D results obtained from computer tools show that the temperature variation and current induced by the electromagnetic field can have a very significant influence on the life of biological tissue. The paper provides a comprehensive analysis using advanced mathematical models to evaluate the influence of electromagnetic fields. The findings have direct implications for workplace safety, potentially influencing standards and regulations concerning electromagnetic exposure in industrial settings.展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.展开更多
Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterativ...Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.展开更多
Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes qui...Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.展开更多
This paper describes geometrical essentials of some iteration methods （e.g. Newton iteration, secant line method, etc.） for solving nonlinear equations and advances some geometrical methods of iteration that are fle...This paper describes geometrical essentials of some iteration methods （e.g. Newton iteration, secant line method, etc.） for solving nonlinear equations and advances some geometrical methods of iteration that are flexible and efficient.展开更多
The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies f...The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.展开更多
This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integr...This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.展开更多
This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were di...This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.展开更多
Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-New...Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.展开更多
In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is ...In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.展开更多
文摘The study of Electromagnetic Compatibility is essential to ensure the harmonious operation of electronic equipment in a shared environment. The basic principles of Electromagnetic Compatibility focus on the ability of devices to withstand electromagnetic disturbances and not produce disturbances that could affect other systems. Imperceptible in most work situations, electromagnetic fields can, beyond certain thresholds, have effects on human health. The objective of the present article is focused on the modeling analysis of the influence of geometric parameters of industrial static converters radiated electromagnetic fields using Maxwell’s equations. To do this we used the analytical formalism for calculating the electromagnetic field emitted by a filiform conductor, to model the electromagnetic radiation of this device in the spatio-temporal domain. The interactions of electromagnetic waves with human bodies are complex and depend on several factors linked to the characteristics of the incident wave. To model these interactions, we implemented the physical laws of electromagnetic wave propagation based on Maxwell’s and bio-heat equations to obtain consistent results. These obtained models allowed us to evaluate the spatial profile of induced current and temperature of biological tissue during exposure to electromagnetic waves generated by this system. The simulation 2D results obtained from computer tools show that the temperature variation and current induced by the electromagnetic field can have a very significant influence on the life of biological tissue. The paper provides a comprehensive analysis using advanced mathematical models to evaluate the influence of electromagnetic fields. The findings have direct implications for workplace safety, potentially influencing standards and regulations concerning electromagnetic exposure in industrial settings.
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.
基金Supported by the National Natural Science Foundation of China(61272300)
文摘Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.
基金Supported by National Natural Science Foundation of China(Grant Nos.51205286,51275348)
文摘Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.
文摘This paper describes geometrical essentials of some iteration methods （e.g. Newton iteration, secant line method, etc.） for solving nonlinear equations and advances some geometrical methods of iteration that are flexible and efficient.
文摘The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.
文摘This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.
文摘This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.
基金Supported by the Natural Science Foundation of China(Grant Nos.11547175,11271008)Supported by the Science and Technology Department of Henan Province(No.182102310978)Supported by the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(Grant Nos.2017GGJS145,2014GGJS-195)
文摘Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.
基金supported by National Natural Science Foundation of China(No.12005141)supported by National Natural Science Foundation of China(No.11805273)+2 种基金supported by the Collaborative Innovation Program of Hefei Science Center,CAS(No.2021HSCCIP019)National MC Energy R&D Program(No.2018YFE0304100)National Natural Science Foundation of China(No.11905220)。
文摘In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.
