The relaxation methods have served as very efficient tools for solving linear system and have many important applications in the field of science and engineering.In this paper,we study an efficient relaxation method b...The relaxation methods have served as very efficient tools for solving linear system and have many important applications in the field of science and engineering.In this paper,we study an efficient relaxation method based on the well-known Gauss-Seidel iteration method.Theoretical analysis shows our method can converge to the unique solution of the linear system.In addition,our method is applied to solve the saddle point problem and Page Rank problem,and the numerical results show our method is more powerful than the existent relaxation methods.展开更多
By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxa...By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxation methods such as multisplitting AOR-Newton method, multisplitting AOR-chord method and multisplitting AOR-Steffensen method, etc.. Furthermore,a general convergence theorem for the nonlinear multisplitting AOR-type methods and the local convergence for the multisplitting AOR-Newton method are discussed in detail.A lot of numerical tests show that our new methods are feasible and satisfactory.展开更多
Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive d...Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.展开更多
We establish the convergence theories of the symmetric relaxation methods for the system of linear equations with symmetric positive definite coefficient matrix, and more generally, those of the unsymmetric relaxation...We establish the convergence theories of the symmetric relaxation methods for the system of linear equations with symmetric positive definite coefficient matrix, and more generally, those of the unsymmetric relaxation methods for the system of linear equations with positive definite matrix.展开更多
In this paper we propose some waveform relaxation (WR) methods for solving large systems of initial value problems. Nonlinear ODEs, linear ODEs, semi-explicit DAEs and linear DAEs are discussed. The accuracy increase ...In this paper we propose some waveform relaxation (WR) methods for solving large systems of initial value problems. Nonlinear ODEs, linear ODEs, semi-explicit DAEs and linear DAEs are discussed. The accuracy increase for WR methods is investigated.展开更多
This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-co...This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.展开更多
Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set up.This class of methods not ...Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set up.This class of methods not only includes all the existing relaxation methods for the linear complementarity problems,but also yields a lot of novel ones in the sense of multisplitting.We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H matrix with positive diagonal elements.展开更多
This study explores free convective heat transfer in an electrically conducting nanofluid flow over a moving semi-infinite flat plate under the influence of an induced magnetic field and viscous dissipation.The veloci...This study explores free convective heat transfer in an electrically conducting nanofluid flow over a moving semi-infinite flat plate under the influence of an induced magnetic field and viscous dissipation.The velocity and magnetic field vectors are aligned at a distance from the plate.The Spectral Relaxation Method(SRM)is used to numerically solve the coupled nonlinear partial differential equations,analyzing the effects of the Eckert number on heat and mass transfer.Various nanofluids containing Cu,Ag,Al_(2)O_(3),and TiO_(2) nanoparticles are examined to assess how external magnetic fields influence fluid behavior.Key parameters,including the nanoparticle volume fraction ϕ,magnetic parameter M,magnetic Prandtl number Prm,and Eckert number Ec,are evaluated for their impact on velocity,induced magnetic field,and heat transfer.Results indicate that increasing the magnetic parameter reduces velocity and magnetic field components in alumina-water nanofluids,while a higher nanoparticle volume fraction enhances the thermal boundary layer.Greater viscous dissipation(Ec)increases temperature,and Al_(2)O_(3) nanofluids exhibit higher speeds than Cu,Ag,and TiO_(2) due to density differences.Silver-water nanofluids,with their higher density,move more slowly.The SRM results closely align with those from Maple,confirming the method’s accuracy.展开更多
In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-m...In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.展开更多
The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical ...The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.展开更多
In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the me...In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.展开更多
The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent m...The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.展开更多
The purpose is to accurately predict the performance of foil bearing and achieve accurate results in the design of foil bearing structure.A new type of foil bearing with surface microstructure is used as experimental ...The purpose is to accurately predict the performance of foil bearing and achieve accurate results in the design of foil bearing structure.A new type of foil bearing with surface microstructure is used as experimental material.First,the lubrication mechanism of elastic foil gas bearing is analyzed.Then,the numerical solution process of the static bearing capacity and friction torque is analyzed,including the discretization of the governing equation of rarefied gas pressure based on the non-dimensional modified Reynolds equation and the over relaxation iteration method,the grid planning within the calculation range,the static solution of boundary parameters and static solution of the numerical process.Finally,the solution program is analyzed.The experimental data in National Aeronautics and Space Administration(NASA)public literature are compared with the simulation results of this exploration,so as to judge the accuracy of the calculation process.The results show that under the same static load,the difference between the minimum film thickness calculated and the test results is not obvious;when the rotor speed of the bearing is 60000 r/min,the influence of the boundary slip effect increases with the increase of the micro groove depth on the flat foil surface;when the eccentricity or the micro groove depth of the bearing increases,the bearing capacity will be strengthened.When the eccentricity is 6µm and 14µm,the viscous friction torque of the new foil bearing increases significantly with the increase of the depth of the foil micro groove,but when the eccentricity is 22µm,the viscous friction torque does not change with the change of the depth of the foil micro groove.It shows that the bearing capacity and performance of foil bearing are improved.展开更多
In this paper,we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods,which can be viewed as an extension of the classic Krasnosel'skii-Mann iteration and Banach-P...In this paper,we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods,which can be viewed as an extension of the classic Krasnosel'skii-Mann iteration and Banach-Picard contraction.As applications,we derive the linear convergence of the generalized proximal point algorithm and the relaxed forward-backward splitting method in a simple and elegant way.展开更多
A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the...A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.展开更多
This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the meth...This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the methods with others＇ and then makes some modifications and finally, examples illustrating the applicability of the proposed methods are given.展开更多
Objectives: To assess respiratory elastance and resistive properties in patients with autoimmune liver disorders using the passive relaxation expiration technique and compare findings to a group of patients with non-a...Objectives: To assess respiratory elastance and resistive properties in patients with autoimmune liver disorders using the passive relaxation expiration technique and compare findings to a group of patients with non-autoimmune liver disease and control subjects. These findings were then related to control of ventilation and gas exchange. A secondary objective was to assess respiratory muscle strength and gas exchange and their relation to respiratory mechanics. Methods: Measurements included respiratory elastance and resistance using the passive relaxation method. Pulmonary function, gas exchange and control of ventilation were assessed using standard methods. Results: a) Compared to control subjects, Ers in patients with liver disease was on average 50% greater than in controls;b) mean respiratory resistance, expressed as the respiratory constants, K<sub>1</sub> and K<sub>2</sub> in the Rohrer relationship, Pao/V’ = K<sub>1</sub> + K<sub>2</sub>V’, was not different from control resistance;c) mean maximal inspiratory and maximal expiratory pressures averaged 36% and 55% of their respective control values;d) inspiratory occlusion pressure in 0.1 sec (P<sub>0.1</sub>) was increased and negatively associated with FVC;and e) increases in P<sub>0.1</sub>, mean inspiratory flow (Vt/Ti) and presence of respiratory alkalosis confirmed the increase in ventilatory drive. Despite inspiratory muscle weakness in patients, P<sub>0.1</sub>/Pimax averaged 5-fold higher than in control subjects. Conclusions: Despite inspiratory muscle weakness and a V’<sub>E</sub> similar to that in normal subjects, central drive is increased in patients with chronic liver disease. The increase in ventilatory drive is related to smaller lung volumes and weakly associated with increase in respiratory elastance. Findings confirm that P<sub>0.1</sub> is a reliable measure of central drive and is an approach that can be used in the evaluation of control of ventilation in patients with chronic liver disease.展开更多
In this paper, the problem of an unsteady free convection of MHD nanofluid flow past a semi-infinite vertical rotating plate embedded in a porous medium subject to a first-order chemical reaction has been studied nume...In this paper, the problem of an unsteady free convection of MHD nanofluid flow past a semi-infinite vertical rotating plate embedded in a porous medium subject to a first-order chemical reaction has been studied numerically. The fluid flow has been mathematically modelled under the assumption that the viscosity of the fluid is temperature dependent. The governing dimensional partial differential equations were transformed into their equivalence non-dimensional form using a suitable variable. The resulting nonlinear partial differential equations were solved numerically using the bivariate interpolated spectral relaxation method (BI-SRM). The impacts of our physical parameters on the velocity components, temperature, concentration, and axial components of the induced magnetic field, as well as skin friction, are investigated using graphical and tabular forms. This establishes that as the rotation parameter increases, the secondary velocity field is rising, however when the Reynolds magnetic number increases, the opposite pattern is demonstrated.展开更多
Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qu...Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qualities. Firstly, we take into account the relation among tasks and build the single task nonlinear optimal model with a set of platform constraints. The Lagrange relaxation method and the pruning strategy are used to solve the model. Secondly, this paper presents optimization-based planning algorithms for efficiently allocating platforms to multiple tasks. To achieve the balance of the resource assignments among tasks, the m-best assignment algorithm and the pair-wise exchange(PWE)method are used to maximize multiple tasks completion qualities.Finally, a series of experiments are designed to verify the superiority and effectiveness of the proposed model and algorithms.展开更多
In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is pre...In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11871136,11801382,11971092)the Fundamental Research Funds for the Central Universities(Grant No.DUT19LK06)。
文摘The relaxation methods have served as very efficient tools for solving linear system and have many important applications in the field of science and engineering.In this paper,we study an efficient relaxation method based on the well-known Gauss-Seidel iteration method.Theoretical analysis shows our method can converge to the unique solution of the linear system.In addition,our method is applied to solve the saddle point problem and Page Rank problem,and the numerical results show our method is more powerful than the existent relaxation methods.
文摘By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxation methods such as multisplitting AOR-Newton method, multisplitting AOR-chord method and multisplitting AOR-Steffensen method, etc.. Furthermore,a general convergence theorem for the nonlinear multisplitting AOR-type methods and the local convergence for the multisplitting AOR-Newton method are discussed in detail.A lot of numerical tests show that our new methods are feasible and satisfactory.
基金Subsidized by The Special Funds For Major State Basic Research Projects G1999032803.
文摘Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.
文摘We establish the convergence theories of the symmetric relaxation methods for the system of linear equations with symmetric positive definite coefficient matrix, and more generally, those of the unsymmetric relaxation methods for the system of linear equations with positive definite matrix.
文摘In this paper we propose some waveform relaxation (WR) methods for solving large systems of initial value problems. Nonlinear ODEs, linear ODEs, semi-explicit DAEs and linear DAEs are discussed. The accuracy increase for WR methods is investigated.
文摘This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.
文摘Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set up.This class of methods not only includes all the existing relaxation methods for the linear complementarity problems,but also yields a lot of novel ones in the sense of multisplitting.We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H matrix with positive diagonal elements.
文摘This study explores free convective heat transfer in an electrically conducting nanofluid flow over a moving semi-infinite flat plate under the influence of an induced magnetic field and viscous dissipation.The velocity and magnetic field vectors are aligned at a distance from the plate.The Spectral Relaxation Method(SRM)is used to numerically solve the coupled nonlinear partial differential equations,analyzing the effects of the Eckert number on heat and mass transfer.Various nanofluids containing Cu,Ag,Al_(2)O_(3),and TiO_(2) nanoparticles are examined to assess how external magnetic fields influence fluid behavior.Key parameters,including the nanoparticle volume fraction ϕ,magnetic parameter M,magnetic Prandtl number Prm,and Eckert number Ec,are evaluated for their impact on velocity,induced magnetic field,and heat transfer.Results indicate that increasing the magnetic parameter reduces velocity and magnetic field components in alumina-water nanofluids,while a higher nanoparticle volume fraction enhances the thermal boundary layer.Greater viscous dissipation(Ec)increases temperature,and Al_(2)O_(3) nanofluids exhibit higher speeds than Cu,Ag,and TiO_(2) due to density differences.Silver-water nanofluids,with their higher density,move more slowly.The SRM results closely align with those from Maple,confirming the method’s accuracy.
文摘In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.
基金supported by the National Natural Science Foundation of China(91116013,11372325,and 11111120080)
文摘The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.
文摘In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.
基金Project supported by the Key Science Foundation of Education Department of Sichuan Province of China (No.2003A081)Sichuan Province Leading Academic Discipline Project (No.SZD0406)
文摘The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.
文摘The purpose is to accurately predict the performance of foil bearing and achieve accurate results in the design of foil bearing structure.A new type of foil bearing with surface microstructure is used as experimental material.First,the lubrication mechanism of elastic foil gas bearing is analyzed.Then,the numerical solution process of the static bearing capacity and friction torque is analyzed,including the discretization of the governing equation of rarefied gas pressure based on the non-dimensional modified Reynolds equation and the over relaxation iteration method,the grid planning within the calculation range,the static solution of boundary parameters and static solution of the numerical process.Finally,the solution program is analyzed.The experimental data in National Aeronautics and Space Administration(NASA)public literature are compared with the simulation results of this exploration,so as to judge the accuracy of the calculation process.The results show that under the same static load,the difference between the minimum film thickness calculated and the test results is not obvious;when the rotor speed of the bearing is 60000 r/min,the influence of the boundary slip effect increases with the increase of the micro groove depth on the flat foil surface;when the eccentricity or the micro groove depth of the bearing increases,the bearing capacity will be strengthened.When the eccentricity is 6µm and 14µm,the viscous friction torque of the new foil bearing increases significantly with the increase of the depth of the foil micro groove,but when the eccentricity is 22µm,the viscous friction torque does not change with the change of the depth of the foil micro groove.It shows that the bearing capacity and performance of foil bearing are improved.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1180145511871059+4 种基金11971238)China Postdoctoral Science Foundation(Grant Nos.2019M6634592020T130081)the Applied Basic Project of Sichuan Province(Grant No.2020YJ0111)the Open Project of Key Laboratory of School of Mathematical Sciences,Chongqing Normal University(Grant No.CSSXKFKTM202004)。
文摘In this paper,we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods,which can be viewed as an extension of the classic Krasnosel'skii-Mann iteration and Banach-Picard contraction.As applications,we derive the linear convergence of the generalized proximal point algorithm and the relaxed forward-backward splitting method in a simple and elegant way.
基金Fundamental Research Funds for the Central Universities,China(No.2232019D3-38)Shanghai Sailing Program,China(No.22YF1400900)。
文摘A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.
文摘This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the methods with others＇ and then makes some modifications and finally, examples illustrating the applicability of the proposed methods are given.
文摘Objectives: To assess respiratory elastance and resistive properties in patients with autoimmune liver disorders using the passive relaxation expiration technique and compare findings to a group of patients with non-autoimmune liver disease and control subjects. These findings were then related to control of ventilation and gas exchange. A secondary objective was to assess respiratory muscle strength and gas exchange and their relation to respiratory mechanics. Methods: Measurements included respiratory elastance and resistance using the passive relaxation method. Pulmonary function, gas exchange and control of ventilation were assessed using standard methods. Results: a) Compared to control subjects, Ers in patients with liver disease was on average 50% greater than in controls;b) mean respiratory resistance, expressed as the respiratory constants, K<sub>1</sub> and K<sub>2</sub> in the Rohrer relationship, Pao/V’ = K<sub>1</sub> + K<sub>2</sub>V’, was not different from control resistance;c) mean maximal inspiratory and maximal expiratory pressures averaged 36% and 55% of their respective control values;d) inspiratory occlusion pressure in 0.1 sec (P<sub>0.1</sub>) was increased and negatively associated with FVC;and e) increases in P<sub>0.1</sub>, mean inspiratory flow (Vt/Ti) and presence of respiratory alkalosis confirmed the increase in ventilatory drive. Despite inspiratory muscle weakness in patients, P<sub>0.1</sub>/Pimax averaged 5-fold higher than in control subjects. Conclusions: Despite inspiratory muscle weakness and a V’<sub>E</sub> similar to that in normal subjects, central drive is increased in patients with chronic liver disease. The increase in ventilatory drive is related to smaller lung volumes and weakly associated with increase in respiratory elastance. Findings confirm that P<sub>0.1</sub> is a reliable measure of central drive and is an approach that can be used in the evaluation of control of ventilation in patients with chronic liver disease.
文摘In this paper, the problem of an unsteady free convection of MHD nanofluid flow past a semi-infinite vertical rotating plate embedded in a porous medium subject to a first-order chemical reaction has been studied numerically. The fluid flow has been mathematically modelled under the assumption that the viscosity of the fluid is temperature dependent. The governing dimensional partial differential equations were transformed into their equivalence non-dimensional form using a suitable variable. The resulting nonlinear partial differential equations were solved numerically using the bivariate interpolated spectral relaxation method (BI-SRM). The impacts of our physical parameters on the velocity components, temperature, concentration, and axial components of the induced magnetic field, as well as skin friction, are investigated using graphical and tabular forms. This establishes that as the rotation parameter increases, the secondary velocity field is rising, however when the Reynolds magnetic number increases, the opposite pattern is demonstrated.
基金supported by the National Natural Science Foundation of China(61573017 61703425)+2 种基金the Aeronautical Science Fund(20175796014)the Shaanxi Province Natural Science Foundation Research Project(2016JQ6062 2017JM6062)
文摘Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qualities. Firstly, we take into account the relation among tasks and build the single task nonlinear optimal model with a set of platform constraints. The Lagrange relaxation method and the pruning strategy are used to solve the model. Secondly, this paper presents optimization-based planning algorithms for efficiently allocating platforms to multiple tasks. To achieve the balance of the resource assignments among tasks, the m-best assignment algorithm and the pair-wise exchange(PWE)method are used to maximize multiple tasks completion qualities.Finally, a series of experiments are designed to verify the superiority and effectiveness of the proposed model and algorithms.
基金supported by the National Natural Science Foundation (10871179) of China
文摘In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.
