This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilt...This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.展开更多
The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are...The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.展开更多
We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we constructed the set of Hamilton-...We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we constructed the set of Hamilton-Jacobi partial differential equations (HJPDEs) within fractional calculus. We formulated the fractional path integral quantization for these systems. A mathematical example is examined with first- and second-class constraints.展开更多
This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exist...This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.展开更多
This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under ...This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.展开更多
In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discus...In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discussed between the uneonstrained minimizers of DGALs on the product space of problem variables and multipliers, and the solutions of the eonstrained problem and the corresponding values of the Lagrange multipliers. The resulting properties indicate more precisely that this class of DGALs is exact multiplier penalty functions. Therefore, a solution of the equslity-constralned problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of a DGAL on the product space of problem variables and multipliers.展开更多
The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of th...The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result.展开更多
The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagr...The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given.Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established.Finally,two examples are given to illustrate the methods and results appear in this paper.展开更多
In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associat...In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.展开更多
Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the...Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the Acetes chinensis in the Lianyungang nearshore licensed fishing area.The Lagrangian frame approaches including the Lagrangian coherent structures theory,Lagrangian residual current,and Lagrangian particle-tracking model were applied to find the transport pathways and aggregation characteristics of Acetes chinensis.There exist some material transport pathways for Acetes chinensis passing through the licensed fishing area,and Acetes chinensis is easy to accumulate in the licensed fishing area.The main mechanism forming this distribution pattern is the local circulation induced by the nonlinear interaction of topography and tidal flow.Both the Lagrangian coherent structure analysis and the particle trajectory tracking indicate that Acetes chinensis in the licensed fishing area come from the nearshore estuary.This work contributed to the adjustment of licensed fishing area and the efficient utilization of fishery resources.展开更多
This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quan...This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result at the end.展开更多
If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geome...If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.展开更多
A fluid-structure interaction approach is proposed in this paper based onNon-Ordinary State-Based Peridynamics(NOSB-PD)and Updated Lagrangian Particle Hydrodynamics(ULPH)to simulate the fluid-structure interaction pro...A fluid-structure interaction approach is proposed in this paper based onNon-Ordinary State-Based Peridynamics(NOSB-PD)and Updated Lagrangian Particle Hydrodynamics(ULPH)to simulate the fluid-structure interaction problem with large geometric deformation and material failure and solve the fluid-structure interaction problem of Newtonian fluid.In the coupled framework,the NOSB-PD theory describes the deformation and fracture of the solid material structure.ULPH is applied to describe the flow of Newtonian fluids due to its advantages in computational accuracy.The framework utilizes the advantages of NOSB-PD theory for solving discontinuous problems and ULPH theory for solving fluid problems,with good computational stability and robustness.A fluidstructure coupling algorithm using pressure as the transmission medium is established to deal with the fluidstructure interface.The dynamic model of solid structure and the PD-ULPH fluid-structure interaction model involving large deformation are verified by numerical simulations.The results agree with the analytical solution,the available experimental data,and other numerical results.Thus,the accuracy and effectiveness of the proposed method in solving the fluid-structure interaction problem are demonstrated.The fluid-structure interactionmodel based on ULPH and NOSB-PD established in this paper provides a new idea for the numerical solution of fluidstructure interaction and a promising approach for engineering design and experimental prediction.展开更多
Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat t...Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.展开更多
Over the past two decades,numerous countries have actively participated in the International Argo Program,working toward the global“OneArgo”goal.China's Argo program has deployed over 500 autonomous profiling fl...Over the past two decades,numerous countries have actively participated in the International Argo Program,working toward the global“OneArgo”goal.China's Argo program has deployed over 500 autonomous profiling floats in the Indo-Pacific,with 55 Beidou(BD)floats,equipped with the Beidou satellite communication system,currently operational.During the operation of the BD float network,we found that in addition to the limitation of floats battery,the loss may also be caused by communication loss due to the floats escaping from the Beidou-2's short message coverage.In this study,float trajectories are simulated using velocity fields from an eddy-resolved resolution Estimating the Circulation and Climate of the Ocean,PhaseⅡ(ECCO2)model and a Lagrangian particle tracking model programmed to represent the vertical motions of profiling floats.The simulations can help to explore both the representativeness and the predictability of profiling float displacements.By deploying a large number of synthetic floats in the Lagrangian particle tracking system,we construct probability density functions(PDFs)of the simulated-float trajectory among key oceans,for example,a joint region of East Indian-South China Sea-Northwest Pacific Ocean(5°–40°N,70°–140°E),which is generally similar to the location of the present BD float network.These statistics can help to estimate the chance of floats drifting into shallow seas(such as the East China Sea)and out of the coverage of the Beidou satellite communication.With this knowledge changes to the future China's Argo observing system could be made.展开更多
We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conse...We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program of Suzhou University of Science and Technology,China(Grant No.SKYCX16 012)
文摘This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China(12272248,11972241)。
文摘The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.
文摘We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we constructed the set of Hamilton-Jacobi partial differential equations (HJPDEs) within fractional calculus. We formulated the fractional path integral quantization for these systems. A mathematical example is examined with first- and second-class constraints.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)the Fund for Fundamental Research of Beijing Institute of Technology (Grant No 20070742005)
文摘This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10772025)the Fund for Fundamental Research of Beijing Institute of Technology
文摘This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.
文摘In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discussed between the uneonstrained minimizers of DGALs on the product space of problem variables and multipliers, and the solutions of the eonstrained problem and the corresponding values of the Lagrange multipliers. The resulting properties indicate more precisely that this class of DGALs is exact multiplier penalty functions. Therefore, a solution of the equslity-constralned problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of a DGAL on the product space of problem variables and multipliers.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10972031)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result.
基金National Natural Science Foundations of China(Nos.11572212,11272227)Innovation Program for Postgraduate of Suzhou University of Science and Technology,China(No.SKCX15_062)
文摘The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given.Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established.Finally,two examples are given to illustrate the methods and results appear in this paper.
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.
基金the National Natural Science Foundation of China(No.31802297)。
文摘Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the Acetes chinensis in the Lianyungang nearshore licensed fishing area.The Lagrangian frame approaches including the Lagrangian coherent structures theory,Lagrangian residual current,and Lagrangian particle-tracking model were applied to find the transport pathways and aggregation characteristics of Acetes chinensis.There exist some material transport pathways for Acetes chinensis passing through the licensed fishing area,and Acetes chinensis is easy to accumulate in the licensed fishing area.The main mechanism forming this distribution pattern is the local circulation induced by the nonlinear interaction of topography and tidal flow.Both the Lagrangian coherent structure analysis and the particle trajectory tracking indicate that Acetes chinensis in the licensed fishing area come from the nearshore estuary.This work contributed to the adjustment of licensed fishing area and the efficient utilization of fishery resources.
基金Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 09CX04018A)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2011AM012)the Postgraduate's Innovation Foundation of China University of Petroleum (East China) (Grant No. CXYB11-12)
文摘This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result at the end.
文摘If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.
基金open foundation of the Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanicsthe Open Foundation of Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment.
文摘A fluid-structure interaction approach is proposed in this paper based onNon-Ordinary State-Based Peridynamics(NOSB-PD)and Updated Lagrangian Particle Hydrodynamics(ULPH)to simulate the fluid-structure interaction problem with large geometric deformation and material failure and solve the fluid-structure interaction problem of Newtonian fluid.In the coupled framework,the NOSB-PD theory describes the deformation and fracture of the solid material structure.ULPH is applied to describe the flow of Newtonian fluids due to its advantages in computational accuracy.The framework utilizes the advantages of NOSB-PD theory for solving discontinuous problems and ULPH theory for solving fluid problems,with good computational stability and robustness.A fluidstructure coupling algorithm using pressure as the transmission medium is established to deal with the fluidstructure interface.The dynamic model of solid structure and the PD-ULPH fluid-structure interaction model involving large deformation are verified by numerical simulations.The results agree with the analytical solution,the available experimental data,and other numerical results.Thus,the accuracy and effectiveness of the proposed method in solving the fluid-structure interaction problem are demonstrated.The fluid-structure interactionmodel based on ULPH and NOSB-PD established in this paper provides a new idea for the numerical solution of fluidstructure interaction and a promising approach for engineering design and experimental prediction.
基金support from the National Natural Science Foundations of China(Nos.11972267 and 11802214)the Open Foundation of the Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics and the Open Foundation of Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment.
文摘Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.
基金The National Natural Science Foundation of China under contract Nos 42106022 and 42106024the National Key Research and Development Program of China under contract No.2021YFC3101502+2 种基金the Fund of Laoshan Laboratory under contract No.LSKJ202201500the Fund of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)under contract No.SML2021SP102the Fund of Chinese Academy of Sciences under contract Nos 133244KYSB20190031,183311KYSB20200015,and SCSIO202201。
文摘Over the past two decades,numerous countries have actively participated in the International Argo Program,working toward the global“OneArgo”goal.China's Argo program has deployed over 500 autonomous profiling floats in the Indo-Pacific,with 55 Beidou(BD)floats,equipped with the Beidou satellite communication system,currently operational.During the operation of the BD float network,we found that in addition to the limitation of floats battery,the loss may also be caused by communication loss due to the floats escaping from the Beidou-2's short message coverage.In this study,float trajectories are simulated using velocity fields from an eddy-resolved resolution Estimating the Circulation and Climate of the Ocean,PhaseⅡ(ECCO2)model and a Lagrangian particle tracking model programmed to represent the vertical motions of profiling floats.The simulations can help to explore both the representativeness and the predictability of profiling float displacements.By deploying a large number of synthetic floats in the Lagrangian particle tracking system,we construct probability density functions(PDFs)of the simulated-float trajectory among key oceans,for example,a joint region of East Indian-South China Sea-Northwest Pacific Ocean(5°–40°N,70°–140°E),which is generally similar to the location of the present BD float network.These statistics can help to estimate the chance of floats drifting into shallow seas(such as the East China Sea)and out of the coverage of the Beidou satellite communication.With this knowledge changes to the future China's Argo observing system could be made.
基金support by Fondazione Cariplo and Fondazione CDP(Italy)under the project No.2022-1895.
文摘We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.
