In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light...In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GALA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-aresecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.展开更多
The elastic-plastic behavior and failure of pipe-on-pipe impact(p-o-p-i)problem is studied through analytical model and numerical simulation in this paper.The impact of a whipping pipe with one end hinged and the othe...The elastic-plastic behavior and failure of pipe-on-pipe impact(p-o-p-i)problem is studied through analytical model and numerical simulation in this paper.The impact of a whipping pipe with one end hinged and the other end free on a simply-supported target pipe at its midpoint is considered.The analytical model based on tubular beam theory is proposed in the study of the deformation and plastic collapse behavior of pipes impacted on different positions and therefore to obtain the various failure modes depending on the material and structural parameters of the pipes.Numerical simulations using the finite element code MSC-Marc are performed and the results are coincident with the theoretical predictions.展开更多
The research concerns Roman medical galactology, galaktologia iatrike (γαλακτσλσγια ιατρικη), i.e. the ancient knowledge of milk and its by-products in medical procedures as described by Celsus in...The research concerns Roman medical galactology, galaktologia iatrike (γαλακτσλσγια ιατρικη), i.e. the ancient knowledge of milk and its by-products in medical procedures as described by Celsus in his treatise entitled De medicina. The authors elaborate on the sources of Celsus' medical theory of milk, comment on the place of the Roman author's theory against the doctrinal background of other medical writers of the period, demonstrate pharmacological characteristics attributed to milk and milk-obtained products by Celsus, specify main cures in which milk and its by-products were made use of as either simple or compound medicines, give examples of the latter, delineate the progress of the theory on milk's medicinal use, and finally comment on the role of milk and milk-obtained products in the diet of the Mediterranean.展开更多
We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponent...We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.展开更多
In fluid mechanics, there is lack of turbulent flows theory. The theory of laminar flows is also not completed. Therefore, the aim of this paper is to fill in the gaps in the theory of laminar flow. First time in the ...In fluid mechanics, there is lack of turbulent flows theory. The theory of laminar flows is also not completed. Therefore, the aim of this paper is to fill in the gaps in the theory of laminar flow. First time in the history of fluid mechanics, it shows that the value of the boundary Reynolds number, dividing the flows of Newtonian fluids into laminar and turbulent, can be calculated theoretically. The very existence of this boundary has been known to researchers over a century ago, but all knowledge in this area so far comes only from experimental physics. This paper marks a turning point, as it not only explains the theory of the said phenomenon, but also presents the methodology of its analytical description. It should be noted that the said description refers to the type of flow which is best understood by scientists, i.e., steady axially-symmetric laminar flow through a straight-axis duct of a circular cross-section of the radius R under the action of constant natural gravitational forces. This paper comes second in a series of papers aimed at eliminating chaos from fluid mechanics and replacing it with harmony and mathematical order.展开更多
In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction an...In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction and its fast convergence towards an optimal solution. Our proposed method is compared with Newton's method for linear program named lpnew, widely used as an optimization algorithm for classification problems.展开更多
As is generally known, Newton's notion of universal gravitation surpassed various theories of particular gravities in the early modem age, as represented mainly by Kepler and Hooke. In his seminal work Hooke and the ...As is generally known, Newton's notion of universal gravitation surpassed various theories of particular gravities in the early modem age, as represented mainly by Kepler and Hooke. In his seminal work Hooke and the Law of Universal Gravitation: A Reappraisal of a Reappraisal Richard S. Westfall argues that Hooke could not reach beyond the concept of spatially bounded particular gravities, as he deployed the method of analogy between the material principle of congruity and incongruity and the extension of gravitational spheres and their action at a distance. However, the doctrine of universal gravitation does not exclude the nature of particular gravities; it is predicated on the notion of an infinite expansion of individual-gravitational spheres and their uniform nature, namely the mutual and centripetal attraction. In my treatise 1 attempt to reinvestigate the nature and structure of gravitation, as established historically in the framework of Newtonian Classical Mechanics, by a method of structural intuition. It examines how the structural intuition, as represented in the celestial-mechanical intuitions of Hooke and Kepler, could unfold into an innovative process within the context of early modem mechanical philosophy, attaining thus a historical siglaificance and legitimacy as against the prevailing Newtonian method of geometric-mathematical axiomatization of mechanical principles. It also explores the actual demonstrative features of the tidal phenomenon with regard to its lunar- and solar-gravitational causation, which has been considered to date to be an important piece of empirical evidence for the theory of universal gravitation.展开更多
We investigate the post-Newtonian parameter 7 and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m2n-2 R -nR to the E...We investigate the post-Newtonian parameter 7 and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m2n-2 R -nR to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ~i in addition to the metric tensor g μ v, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters 9,, we can compare our expressions and results with those in Hohmann and Jarv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F- around their background values.展开更多
Some future space missions measure distances of laser links and angles with unprecedented precision, allowing us to test theories of gravity up to the two-post-Newtonian (2PN) order. Besides, investigation of an int...Some future space missions measure distances of laser links and angles with unprecedented precision, allowing us to test theories of gravity up to the two-post-Newtonian (2PN) order. Besides, investigation of an intermediate-range force has been of considerable interests in gravitational experiments. Inspired by these ideas, within the framework of the scalar-tensor theory with an intermediate- range force, its 2PN approximation is obtained with Chandrasekhar's approach. It includes the 2PN metric and equations of motion for general matter without specific equation of state. The conserved quantities to the 2PN order are isolated with the aid of the energy-momentum complex. We also discuss the prospect of testing and distinguishing the intermediate-range force with the orbital motions of celestial bodies and spaeecrafts.展开更多
This paper provides an OpenMP-based parallel Very Dishonest Newton(VDHN) algorithm with variable step size,running transient stability simulations(TSA) on multi-core computers.Under the framework of simultaneous solut...This paper provides an OpenMP-based parallel Very Dishonest Newton(VDHN) algorithm with variable step size,running transient stability simulations(TSA) on multi-core computers.Under the framework of simultaneous solution method of TSA,the step-size control strategy is used according to the local truncation error theory firstly.Then,computation of the generation units,which is the most time-consuming part of the simulation,is dynamically dispatched to several cores using an α dynamic scheduling scheme to obtain workload balancing based on OpenMP.Due to the convergence of Newton-type iterations,an adaptive Jacobian update control strategy is applied to reduce the sequential part of the simulation and the overhead generated by OpenMP.Several large scale test cases verify the validity and practicability of the proposed parallel algorithm,showing that the proposed approach achieves high speed-up and a considerable reduction in parallel overheads.展开更多
As a continuing investigation of an earlier work that establishes the cofiinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness...As a continuing investigation of an earlier work that establishes the cofiinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 10875171
文摘In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GALA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-aresecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.
基金National Natural Science Foundation of China(No.11032001)
文摘The elastic-plastic behavior and failure of pipe-on-pipe impact(p-o-p-i)problem is studied through analytical model and numerical simulation in this paper.The impact of a whipping pipe with one end hinged and the other end free on a simply-supported target pipe at its midpoint is considered.The analytical model based on tubular beam theory is proposed in the study of the deformation and plastic collapse behavior of pipes impacted on different positions and therefore to obtain the various failure modes depending on the material and structural parameters of the pipes.Numerical simulations using the finite element code MSC-Marc are performed and the results are coincident with the theoretical predictions.
文摘The research concerns Roman medical galactology, galaktologia iatrike (γαλακτσλσγια ιατρικη), i.e. the ancient knowledge of milk and its by-products in medical procedures as described by Celsus in his treatise entitled De medicina. The authors elaborate on the sources of Celsus' medical theory of milk, comment on the place of the Roman author's theory against the doctrinal background of other medical writers of the period, demonstrate pharmacological characteristics attributed to milk and milk-obtained products by Celsus, specify main cures in which milk and its by-products were made use of as either simple or compound medicines, give examples of the latter, delineate the progress of the theory on milk's medicinal use, and finally comment on the role of milk and milk-obtained products in the diet of the Mediterranean.
基金The project supported by National Natural Science Foundation of China under Grant No.19902002
文摘We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.
文摘In fluid mechanics, there is lack of turbulent flows theory. The theory of laminar flows is also not completed. Therefore, the aim of this paper is to fill in the gaps in the theory of laminar flow. First time in the history of fluid mechanics, it shows that the value of the boundary Reynolds number, dividing the flows of Newtonian fluids into laminar and turbulent, can be calculated theoretically. The very existence of this boundary has been known to researchers over a century ago, but all knowledge in this area so far comes only from experimental physics. This paper marks a turning point, as it not only explains the theory of the said phenomenon, but also presents the methodology of its analytical description. It should be noted that the said description refers to the type of flow which is best understood by scientists, i.e., steady axially-symmetric laminar flow through a straight-axis duct of a circular cross-section of the radius R under the action of constant natural gravitational forces. This paper comes second in a series of papers aimed at eliminating chaos from fluid mechanics and replacing it with harmony and mathematical order.
文摘In this paper we propose an algorithm based on the BFGS Quasi-Newton method to solve a linear program. The choice of this method is justified by its theoretical efficiency, the ease to determine a descent direction and its fast convergence towards an optimal solution. Our proposed method is compared with Newton's method for linear program named lpnew, widely used as an optimization algorithm for classification problems.
文摘As is generally known, Newton's notion of universal gravitation surpassed various theories of particular gravities in the early modem age, as represented mainly by Kepler and Hooke. In his seminal work Hooke and the Law of Universal Gravitation: A Reappraisal of a Reappraisal Richard S. Westfall argues that Hooke could not reach beyond the concept of spatially bounded particular gravities, as he deployed the method of analogy between the material principle of congruity and incongruity and the extension of gravitational spheres and their action at a distance. However, the doctrine of universal gravitation does not exclude the nature of particular gravities; it is predicated on the notion of an infinite expansion of individual-gravitational spheres and their uniform nature, namely the mutual and centripetal attraction. In my treatise 1 attempt to reinvestigate the nature and structure of gravitation, as established historically in the framework of Newtonian Classical Mechanics, by a method of structural intuition. It examines how the structural intuition, as represented in the celestial-mechanical intuitions of Hooke and Kepler, could unfold into an innovative process within the context of early modem mechanical philosophy, attaining thus a historical siglaificance and legitimacy as against the prevailing Newtonian method of geometric-mathematical axiomatization of mechanical principles. It also explores the actual demonstrative features of the tidal phenomenon with regard to its lunar- and solar-gravitational causation, which has been considered to date to be an important piece of empirical evidence for the theory of universal gravitation.
基金the National Natural Science Foundation of China(Grant Nos.11175077,11575075,and 11647153)the Natural Science Foundation of Liaoning Province in China(Grant No.L201683666)
文摘We investigate the post-Newtonian parameter 7 and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m2n-2 R -nR to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ~i in addition to the metric tensor g μ v, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters 9,, we can compare our expressions and results with those in Hohmann and Jarv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F- around their background values.
基金supported by the National Natural Science Foundation of China(Grant Nos.11473072 and 11103085)the Fundamental Research Program of Jiangsu Province of China(Grant No.BK20131461)
文摘Some future space missions measure distances of laser links and angles with unprecedented precision, allowing us to test theories of gravity up to the two-post-Newtonian (2PN) order. Besides, investigation of an intermediate-range force has been of considerable interests in gravitational experiments. Inspired by these ideas, within the framework of the scalar-tensor theory with an intermediate- range force, its 2PN approximation is obtained with Chandrasekhar's approach. It includes the 2PN metric and equations of motion for general matter without specific equation of state. The conserved quantities to the 2PN order are isolated with the aid of the energy-momentum complex. We also discuss the prospect of testing and distinguishing the intermediate-range force with the orbital motions of celestial bodies and spaeecrafts.
基金supported by the National Natural Science Foundation of China (Grant No. 2012CB215106)the National Basic Research Program of China ("973" Program) (Grant No. 50977082)
文摘This paper provides an OpenMP-based parallel Very Dishonest Newton(VDHN) algorithm with variable step size,running transient stability simulations(TSA) on multi-core computers.Under the framework of simultaneous solution method of TSA,the step-size control strategy is used according to the local truncation error theory firstly.Then,computation of the generation units,which is the most time-consuming part of the simulation,is dynamically dispatched to several cores using an α dynamic scheduling scheme to obtain workload balancing based on OpenMP.Due to the convergence of Newton-type iterations,an adaptive Jacobian update control strategy is applied to reduce the sequential part of the simulation and the overhead generated by OpenMP.Several large scale test cases verify the validity and practicability of the proposed parallel algorithm,showing that the proposed approach achieves high speed-up and a considerable reduction in parallel overheads.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11573015 and J1210039the Innovation Training Project for Undergraduates of Nanjing University,China
文摘As a continuing investigation of an earlier work that establishes the cofiinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System.