The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expressio...The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expression for the angular momentum of a system in terms of the angular momenta of its parts is deduced. It is shown that the characteristics of the relative motion depend on the system’s total mass, whereas the characteristics of the individual motions depend on the masses of the two bodies. The reduced energy and angular momentum densities are constants of motion that do not depend on the distribution of the total mass between the two bodies;whereas the energy may vary in absolute value from an infinitesimal to a maximum value which occurs when the two bodies are of equal masses. In correspondence with infinite possible ways to describe the absolute rotational positioning of a two body system, an infinite set of Laplace-Runge-Lenz vectors (LRL) are constructed, all fixing a unique orientation of the orbit relative to the fixed stars. The common expression of LRV vector is an approximation of the actual one. The conditions for nested and intersecting individual orbits of the two bodies are specified. As far as we know, and apart from the law of periods, the laws of equivalent orbits concerning their associated periods, areal velocities, angular velocities, velocities, energies, as well as, the law of total angular momentum, were never considered before.展开更多
The two-body fragmentation dynamics of water isotopologues dications(H_(2)O^(2+),HOD^(2+),and D_(2)O^(2+))induced by200 eV electron impact is investigated.Two fragment ions and an emitted electron are detected in coin...The two-body fragmentation dynamics of water isotopologues dications(H_(2)O^(2+),HOD^(2+),and D_(2)O^(2+))induced by200 eV electron impact is investigated.Two fragment ions and an emitted electron are detected in coincidence,and their momentum vectors are determined by employing a reaction microscope.The complete kinematical information of four two-body fragmentation channels of H^(+)+OH+,H^(+)+OD^(+),D^(+)+OH^(+),and D^(+)+OD+is obtained.By analyzing the projectile energy-loss spectrum,the initial electronic state of the two-body dissociation channel is determined.Upon examining the kinetic energy release(KER)distributions of the four fragmentation channels,a clear difference is found between the two-body fragmentation channel H^(+)+OD+and the other three channels.The isotopic effect in the two-body fragmentation is demonstrated by the analysis of the relative yields of the two-body fragmentation channels originating from different isotopologues,which shows preferential cleavage of the O-H bond over the O-D bond.These results provide deeper insight into the microscopic dynamic mechanisms in water radiolysis.展开更多
A unified tensor-product representation of LaplaceRunge-Lenz（LRL） vector about inversely-quadric and centric-force systems is derived.For a two-body Kepler system under gravitation or Coulomb force,the modified and ...A unified tensor-product representation of LaplaceRunge-Lenz（LRL） vector about inversely-quadric and centric-force systems is derived.For a two-body Kepler system under gravitation or Coulomb force,the modified and unified tensor-product representation of LRL vector is also deduced by using an effective single-body description.Some properties of the vector are numerated and proved.Conservation of this vector is demonstrated in the tensor-product form.The energy formula for a bound-state elliptic orbit is simply derived via a novel approach.For a two-body system,the R-test rules for every kinds of Kepler＇s motion are discussed in detail.展开更多
This paper presents a detailed investigation of unsteady supersonic flows around a typical two-body configuration, which consists of a capsule and a canopy. The cases with different trailing distances between the caps...This paper presents a detailed investigation of unsteady supersonic flows around a typical two-body configuration, which consists of a capsule and a canopy. The cases with different trailing distances between the capsule and canopy are simulated. The objective of this study is to examine the detailed effects of trailing distance on the flow fields and analyze the flow physics of the different flow modes around the parachute-like two-body model. The computational results show unsteady pulsating flow fields in the small trailing distance cases and are in reasonable agree- ment with the experimental data. As the trailing distance increases, this unsteady flow mode takes different forms along with the wake/shock and shock/shock interactions, and then gradually fades away and transits to oscillate mode, which is very different from the former. As the trailing distance keeps increasing, only the capsule wake/canopy shock interaction is present in the flow field around the two-body model, which reveals that the unsteady capsule shock/canopy shock interaction is a key mechanism for the pulsation mode.展开更多
The microstructure,mechanical properties,and the effects of sliding distance and material removal mechanism on two-body abrasive wear behaviour of hypereutectic Al-Si-Si C composite and its matrix alloy were investiga...The microstructure,mechanical properties,and the effects of sliding distance and material removal mechanism on two-body abrasive wear behaviour of hypereutectic Al-Si-Si C composite and its matrix alloy were investigated.The hypereutectic Al-Si-Si C composite was prepared by stir casting route.The hardness,ultimate tensile strength and yield strength of the composite are increased by 17%,38%,and 30%respectively compared with those of the matrix alloy,while the elongation of the composite is decreased by 48%compared with that of the matrix alloy.The wear rate of the materials is increased with increasing the abrasive size and the applied load and does not vary with the sliding distance.The wear surfaces and wear debris of the materials were characterized by high-resolution field emission scanning electron microscopy(HR FESEM)and wear mechanism was analyzed for low and high load regimes.展开更多
This work investigated the influence of two types of mooring systems on the hydrodynamic performance of a two-body floating wave energy converter(WEC). It also investigated the effects of the physical parameters of th...This work investigated the influence of two types of mooring systems on the hydrodynamic performance of a two-body floating wave energy converter(WEC). It also investigated the effects of the physical parameters of the mooring system on the amount of extractable power from incident waves in the frequency domain. The modeled converter comprised a floating body(a buoy), a submerged body with two mooring systems, and a coupling system for two bodies. The coupling system was a simplified power take-off system that was modeled by a linear spring-damper model. The tension leg mooring system could drastically affect the heave motion of the submerged body of the model and increase relative displacement between the two bodies. The effects of the stiffness parameter of the mooring system on power absorption exceeded those of the pretension tendon force.展开更多
The mathematic calculation on two--body wear of austenitic manganese steel has been performed by means of the elastic contact theory,stress interferometer and SEM.Stress distribution in contacted area was calculated a...The mathematic calculation on two--body wear of austenitic manganese steel has been performed by means of the elastic contact theory,stress interferometer and SEM.Stress distribution in contacted area was calculated and the mechanism on two--body wear has been investigated through numerical quadrature.Results show that two--body wear is mainly plowing wear the cracks of abrasive dust originates from the region between 0.2αand 0.5α(αis radius of contacted round).Driving force to make crack extension along y axis is T_(yzmax)and extension direction is 45°with horizon.Driving forces to make crack extension along x axis is alternativeσ_x and T_(yzmax),the direction of crack extension is 37°with horizon.展开更多
It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects...It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects,a new general system theory is developed based on a new ontology of ether and minds as the fundamental existences in the world.The two-body problem is the simplest model in mechanics and in this paper,it is re-examined by using our new general system theory.It is found that the current description of the classical full two-body problem is inappropriate since the observer and the measurement apparatus have not been explicitly considered.After considering these,it is actually a three-body problem while only the special case of the Kepler problem is the two-body problem.By introducing the concepts of psychic force and psychic field,all the possible movement states in the two-body problem can be explained within the framework of classical mechanics.There is no need to change the meanings of many fundamental concepts,such as time,space,matter,mass,and energy as done in quantum mechanics and relativity theory.This points out a new direction for the unification of different theories.展开更多
A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed.Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-...A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed.Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.展开更多
A local momentum(LM) approximation applicable to semi-relativistic two-body repulsive interactions is presented. It assumes negligible variations in the(vector-type) potential. A Woods–Saxon barrier with a rectangula...A local momentum(LM) approximation applicable to semi-relativistic two-body repulsive interactions is presented. It assumes negligible variations in the(vector-type) potential. A Woods–Saxon barrier with a rectangularlike shape is studied in some detail. The LM-approximation gives exact results within the semi-relativistic framework for rectangular barrier interactions in(1+1) dimensions. Further approximations of the local momentum approach leads to the two-body approximation of Ikhdair & Sever, known since the early 90's as the spinless Salpeter equation approximating the Bethe–Salpeter equation. LM-and GS-results indicate significant two-body effects. Results obtained from the(single-mass) Dirac equation are similar for certain two-body mass combinations.展开更多
The full counting statistics of electron transport through two parallel quantum dots with antiparallel magnetic fluxes is investigated as a probe to detect the topological quantum-phase coherence （TQPC）, which resul...The full counting statistics of electron transport through two parallel quantum dots with antiparallel magnetic fluxes is investigated as a probe to detect the topological quantum-phase coherence （TQPC）, which results in the characteristic oscillation of the zero-frequency cumulants including the shot noise and skewness. We show explicitly the phase transition of cumulant spectrum-patterns induced by the topology change of electron path-loops while the pattern period, which depends only on the topology （or Chern number）, is robust against the variation of Coulomb interaction and interdot coupling strengths. Most importantly we report for the first time on a new type of TQPC, which is generated by the two- particle interaction and does not exist in the single-particle wave function interference. Moreover, the accurately quantized peaks of Fano-factor spectrum, which characterize the super- and sub-Poissonian shot noises, are of fundamental importance in technical applications similar to the superconducting quantum interference device.展开更多
This study proposed a wave power system with two coaxial floating cylinders of different diameters and drafts.Wavebob’s conceptual design has been adopted in the wave power system.In this study,a basic analysis of th...This study proposed a wave power system with two coaxial floating cylinders of different diameters and drafts.Wavebob’s conceptual design has been adopted in the wave power system.In this study,a basic analysis of the wave energy extraction by the relative motion between two floats is presented.The maximum power absorption was studied theoretically under regular wave conditions,and the effects of both linear and constant damping forces on the power take-off(PTO)were investigated.A set of dynamic equations describing the floats’displacement under regular waves and different PTOs are established.A time-domain numerical model is developed,considering the PTO parameter and viscous damping,and the optimal PTO damping and output power are obtained.With the analysis of estimating the maximum power absorption,a new estimation method called Power Capture Function(PCF)is proposed and constructed,which can be used to predict the power capture under both linear and constant PTO forces.Based on this,energy extraction is analyzed and optimized.Finally,the performance characteristics of the two-body power system are concluded.展开更多
Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been ...Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been developed. However, the interactions among the constituent particles are still difficult to model precisely. Especially, contact conditions, which vary with material properties and circumstances, are difficult to formulate. In this study, a computational model for simulating adhesive particles on contact in a many-particle system is proposed. The interaction between the particles was represented by a two-body repulsive force that depends on the distance between particles and an additional adhesive force at the contact point. A phase-field variable was introduced to express the surface of each particle, and the adhesive force was formulated using the phase-field distribution. As a result, the adhesion of particles was properly expressed. For a mono-particle system, neighboring particles adhered and uniformly aggregated, while for a dual-particle system, several characteristic patterns were obtained depending on the initial arrangement of the particles. Repulsive contact was also considered as a specific case, and the corresponding results were obtained.展开更多
A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In ...A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) m<sub>r</sub> = m<sub>1</sub>m<sub>2</sub>/(m<sub>1</sub>+m<sub>2</sub>) orbiting around the total mass m = m<sub>1</sub>+m<sub>2</sub> situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters g<sub>μν</sub> (m<sub>1</sub>, m<sub>2</sub>, R, a<sub>1</sub>, a<sub>2</sub>), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.展开更多
Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubatio...Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.展开更多
The primary sensor of astronomy observation satellite （AOS） is mounted on a gimbal base which connects directly with the satellite platform and has two degrees of freedom. Attitude control for AOS with a swinging se...The primary sensor of astronomy observation satellite （AOS） is mounted on a gimbal base which connects directly with the satellite platform and has two degrees of freedom. Attitude control for AOS with a swinging sensor will be highlighted in this paper. Due to the non-negligible mass and length of the sensor, the internal motion between the satellite and the sensor will change the attitude, the position of center of mass and moment of inertia of the SYSTEM （consists of the satellite and the sen- sor）. According to moment of momentum theorem, a rigid two-body dynamic model is derived, which can he used to determine the inertial tensor of the SYSTEM. Modulating the satellite＇s present and desired quaternions results in quasi-Euler angles and normalizing these resultant parameters can ensure that the channel corresponding to each quasi-Euler angle is in the charge of each component of the control torque. Based on the normalized quasi-Euler angles, a switching attitude control law is proposed. With the control law, the corresponding phase trajectory will slide along the switching surface to the origin （corresponding to the desired states）. Simulation results show that the satellite can be controlled perfectly by thrusters with the proposed control law, even in the case of structural asymmetry and serious coupling between the control channels.展开更多
The wear process of PTFE coatings sliding against GCr15-bearing steel ball under vacuum conditions was investigated,and the hardness of the PTFE coatings on both sides of wear track was measured. The experimental resu...The wear process of PTFE coatings sliding against GCr15-bearing steel ball under vacuum conditions was investigated,and the hardness of the PTFE coatings on both sides of wear track was measured. The experimental results showed that the friction coefficient of the PTFE coatings increases with the increase of sliding distance under different sliding velocities. And the friction coefficient of the PTFE coatings increases with the increase of sliding distance under different sliding loads. The wear rate of PTFE coatings decreases with the increase of sliding distance. And the majority of the wear produced during the whole wear process of PTFE coatings sliding against GCr-15 steel ball comes from the early period of friction. The hardness of PTFE coatings on both sides of wear track increases as the distance increases and distributes symmetrically around the wear track. Scanning electron microscope( SEM) was utilized to investigate the worn surface of PTFE coating. It was found that the worn surface of PTFE coating is characterized by sever plastic deformation and spalling of the PTFE coating. The edge of wear track is characterized by micro cracking.展开更多
This paper is a review,which focuses on our work,while including an analysis of many works of other researchers in the field of quaternionic regularization.The regular quaternion models of celestial mechanics and astr...This paper is a review,which focuses on our work,while including an analysis of many works of other researchers in the field of quaternionic regularization.The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel(KS)variables and Euler(Rodrigues-Hamilton)parameters are analyzed.These models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point particle.This paper also covers some applications of these models.Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics.However,the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author.More general(compared with the KS equations)quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented.These equations are derived with the assumption that the KS bilinear relation was not satisfied.The main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented,together with regular equations in the KS variables and Euler parameters,derived by the aforementioned theory.We also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters,developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.展开更多
A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
文摘The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expression for the angular momentum of a system in terms of the angular momenta of its parts is deduced. It is shown that the characteristics of the relative motion depend on the system’s total mass, whereas the characteristics of the individual motions depend on the masses of the two bodies. The reduced energy and angular momentum densities are constants of motion that do not depend on the distribution of the total mass between the two bodies;whereas the energy may vary in absolute value from an infinitesimal to a maximum value which occurs when the two bodies are of equal masses. In correspondence with infinite possible ways to describe the absolute rotational positioning of a two body system, an infinite set of Laplace-Runge-Lenz vectors (LRL) are constructed, all fixing a unique orientation of the orbit relative to the fixed stars. The common expression of LRV vector is an approximation of the actual one. The conditions for nested and intersecting individual orbits of the two bodies are specified. As far as we know, and apart from the law of periods, the laws of equivalent orbits concerning their associated periods, areal velocities, angular velocities, velocities, energies, as well as, the law of total angular momentum, were never considered before.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12325406,92261201,12404305,11974272)the Shannxi Province Natural Science Fundamental Research Project(Grant Nos.2023JC-XJ-03 and 23JSQ013)the Fundamental Research Funds for the Central Universities(Grant No.xzy022024040)。
文摘The two-body fragmentation dynamics of water isotopologues dications(H_(2)O^(2+),HOD^(2+),and D_(2)O^(2+))induced by200 eV electron impact is investigated.Two fragment ions and an emitted electron are detected in coincidence,and their momentum vectors are determined by employing a reaction microscope.The complete kinematical information of four two-body fragmentation channels of H^(+)+OH+,H^(+)+OD^(+),D^(+)+OH^(+),and D^(+)+OD+is obtained.By analyzing the projectile energy-loss spectrum,the initial electronic state of the two-body dissociation channel is determined.Upon examining the kinetic energy release(KER)distributions of the four fragmentation channels,a clear difference is found between the two-body fragmentation channel H^(+)+OD+and the other three channels.The isotopic effect in the two-body fragmentation is demonstrated by the analysis of the relative yields of the two-body fragmentation channels originating from different isotopologues,which shows preferential cleavage of the O-H bond over the O-D bond.These results provide deeper insight into the microscopic dynamic mechanisms in water radiolysis.
基金Supported by the National Teaching Team Foundation(202276003)
文摘A unified tensor-product representation of LaplaceRunge-Lenz（LRL） vector about inversely-quadric and centric-force systems is derived.For a two-body Kepler system under gravitation or Coulomb force,the modified and unified tensor-product representation of LRL vector is also deduced by using an effective single-body description.Some properties of the vector are numerated and proved.Conservation of this vector is demonstrated in the tensor-product form.The energy formula for a bound-state elliptic orbit is simply derived via a novel approach.For a two-body system,the R-test rules for every kinds of Kepler＇s motion are discussed in detail.
基金supported by the National Natural Science Foundation of China(No.11702332)
文摘This paper presents a detailed investigation of unsteady supersonic flows around a typical two-body configuration, which consists of a capsule and a canopy. The cases with different trailing distances between the capsule and canopy are simulated. The objective of this study is to examine the detailed effects of trailing distance on the flow fields and analyze the flow physics of the different flow modes around the parachute-like two-body model. The computational results show unsteady pulsating flow fields in the small trailing distance cases and are in reasonable agree- ment with the experimental data. As the trailing distance increases, this unsteady flow mode takes different forms along with the wake/shock and shock/shock interactions, and then gradually fades away and transits to oscillate mode, which is very different from the former. As the trailing distance keeps increasing, only the capsule wake/canopy shock interaction is present in the flow field around the two-body model, which reveals that the unsteady capsule shock/canopy shock interaction is a key mechanism for the pulsation mode.
基金the financial support received to the first author as a scholarship from MHRD,Government of India.
文摘The microstructure,mechanical properties,and the effects of sliding distance and material removal mechanism on two-body abrasive wear behaviour of hypereutectic Al-Si-Si C composite and its matrix alloy were investigated.The hypereutectic Al-Si-Si C composite was prepared by stir casting route.The hardness,ultimate tensile strength and yield strength of the composite are increased by 17%,38%,and 30%respectively compared with those of the matrix alloy,while the elongation of the composite is decreased by 48%compared with that of the matrix alloy.The wear rate of the materials is increased with increasing the abrasive size and the applied load and does not vary with the sliding distance.The wear surfaces and wear debris of the materials were characterized by high-resolution field emission scanning electron microscopy(HR FESEM)and wear mechanism was analyzed for low and high load regimes.
文摘This work investigated the influence of two types of mooring systems on the hydrodynamic performance of a two-body floating wave energy converter(WEC). It also investigated the effects of the physical parameters of the mooring system on the amount of extractable power from incident waves in the frequency domain. The modeled converter comprised a floating body(a buoy), a submerged body with two mooring systems, and a coupling system for two bodies. The coupling system was a simplified power take-off system that was modeled by a linear spring-damper model. The tension leg mooring system could drastically affect the heave motion of the submerged body of the model and increase relative displacement between the two bodies. The effects of the stiffness parameter of the mooring system on power absorption exceeded those of the pretension tendon force.
文摘The mathematic calculation on two--body wear of austenitic manganese steel has been performed by means of the elastic contact theory,stress interferometer and SEM.Stress distribution in contacted area was calculated and the mechanism on two--body wear has been investigated through numerical quadrature.Results show that two--body wear is mainly plowing wear the cracks of abrasive dust originates from the region between 0.2αand 0.5α(αis radius of contacted round).Driving force to make crack extension along y axis is T_(yzmax)and extension direction is 45°with horizon.Driving forces to make crack extension along x axis is alternativeσ_x and T_(yzmax),the direction of crack extension is 37°with horizon.
基金supported by the“Construction of a Leading Innovation Team”project by the Hangzhou Municipal government,and the startup funding of New-Joined PI of Westlake University with grant number(041030150118).
文摘It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects,a new general system theory is developed based on a new ontology of ether and minds as the fundamental existences in the world.The two-body problem is the simplest model in mechanics and in this paper,it is re-examined by using our new general system theory.It is found that the current description of the classical full two-body problem is inappropriate since the observer and the measurement apparatus have not been explicitly considered.After considering these,it is actually a three-body problem while only the special case of the Kepler problem is the two-body problem.By introducing the concepts of psychic force and psychic field,all the possible movement states in the two-body problem can be explained within the framework of classical mechanics.There is no need to change the meanings of many fundamental concepts,such as time,space,matter,mass,and energy as done in quantum mechanics and relativity theory.This points out a new direction for the unification of different theories.
文摘A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed.Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.
文摘A local momentum(LM) approximation applicable to semi-relativistic two-body repulsive interactions is presented. It assumes negligible variations in the(vector-type) potential. A Woods–Saxon barrier with a rectangularlike shape is studied in some detail. The LM-approximation gives exact results within the semi-relativistic framework for rectangular barrier interactions in(1+1) dimensions. Further approximations of the local momentum approach leads to the two-body approximation of Ikhdair & Sever, known since the early 90's as the spinless Salpeter equation approximating the Bethe–Salpeter equation. LM-and GS-results indicate significant two-body effects. Results obtained from the(single-mass) Dirac equation are similar for certain two-body mass combinations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11075099.11204203,and 11275118)
文摘The full counting statistics of electron transport through two parallel quantum dots with antiparallel magnetic fluxes is investigated as a probe to detect the topological quantum-phase coherence （TQPC）, which results in the characteristic oscillation of the zero-frequency cumulants including the shot noise and skewness. We show explicitly the phase transition of cumulant spectrum-patterns induced by the topology change of electron path-loops while the pattern period, which depends only on the topology （or Chern number）, is robust against the variation of Coulomb interaction and interdot coupling strengths. Most importantly we report for the first time on a new type of TQPC, which is generated by the two- particle interaction and does not exist in the single-particle wave function interference. Moreover, the accurately quantized peaks of Fano-factor spectrum, which characterize the super- and sub-Poissonian shot noises, are of fundamental importance in technical applications similar to the superconducting quantum interference device.
基金financially supported by the National Key R&D Program of China (Grant No. 2018YFB1501904)the Shandong Provincial Key R&D Program (Grant No. 2019JZZY010902)+2 种基金the National Natural Science Foundation of China (Grant No. 52071303)the Joint Project of NSFC-SD (Grant No. U1906228)the Taishan Scholars Program of Shandong Province (Grant No. ts20190914)
文摘This study proposed a wave power system with two coaxial floating cylinders of different diameters and drafts.Wavebob’s conceptual design has been adopted in the wave power system.In this study,a basic analysis of the wave energy extraction by the relative motion between two floats is presented.The maximum power absorption was studied theoretically under regular wave conditions,and the effects of both linear and constant damping forces on the power take-off(PTO)were investigated.A set of dynamic equations describing the floats’displacement under regular waves and different PTOs are established.A time-domain numerical model is developed,considering the PTO parameter and viscous damping,and the optimal PTO damping and output power are obtained.With the analysis of estimating the maximum power absorption,a new estimation method called Power Capture Function(PCF)is proposed and constructed,which can be used to predict the power capture under both linear and constant PTO forces.Based on this,energy extraction is analyzed and optimized.Finally,the performance characteristics of the two-body power system are concluded.
文摘Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been developed. However, the interactions among the constituent particles are still difficult to model precisely. Especially, contact conditions, which vary with material properties and circumstances, are difficult to formulate. In this study, a computational model for simulating adhesive particles on contact in a many-particle system is proposed. The interaction between the particles was represented by a two-body repulsive force that depends on the distance between particles and an additional adhesive force at the contact point. A phase-field variable was introduced to express the surface of each particle, and the adhesive force was formulated using the phase-field distribution. As a result, the adhesion of particles was properly expressed. For a mono-particle system, neighboring particles adhered and uniformly aggregated, while for a dual-particle system, several characteristic patterns were obtained depending on the initial arrangement of the particles. Repulsive contact was also considered as a specific case, and the corresponding results were obtained.
文摘A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) m<sub>r</sub> = m<sub>1</sub>m<sub>2</sub>/(m<sub>1</sub>+m<sub>2</sub>) orbiting around the total mass m = m<sub>1</sub>+m<sub>2</sub> situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters g<sub>μν</sub> (m<sub>1</sub>, m<sub>2</sub>, R, a<sub>1</sub>, a<sub>2</sub>), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.
文摘Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.
文摘The primary sensor of astronomy observation satellite （AOS） is mounted on a gimbal base which connects directly with the satellite platform and has two degrees of freedom. Attitude control for AOS with a swinging sensor will be highlighted in this paper. Due to the non-negligible mass and length of the sensor, the internal motion between the satellite and the sensor will change the attitude, the position of center of mass and moment of inertia of the SYSTEM （consists of the satellite and the sen- sor）. According to moment of momentum theorem, a rigid two-body dynamic model is derived, which can he used to determine the inertial tensor of the SYSTEM. Modulating the satellite＇s present and desired quaternions results in quasi-Euler angles and normalizing these resultant parameters can ensure that the channel corresponding to each quasi-Euler angle is in the charge of each component of the control torque. Based on the normalized quasi-Euler angles, a switching attitude control law is proposed. With the control law, the corresponding phase trajectory will slide along the switching surface to the origin （corresponding to the desired states）. Simulation results show that the satellite can be controlled perfectly by thrusters with the proposed control law, even in the case of structural asymmetry and serious coupling between the control channels.
基金Sponsored by the Research Fund for the College Science and Technology Plan of Shandong Province(Grant No.J12LA11)
文摘The wear process of PTFE coatings sliding against GCr15-bearing steel ball under vacuum conditions was investigated,and the hardness of the PTFE coatings on both sides of wear track was measured. The experimental results showed that the friction coefficient of the PTFE coatings increases with the increase of sliding distance under different sliding velocities. And the friction coefficient of the PTFE coatings increases with the increase of sliding distance under different sliding loads. The wear rate of PTFE coatings decreases with the increase of sliding distance. And the majority of the wear produced during the whole wear process of PTFE coatings sliding against GCr-15 steel ball comes from the early period of friction. The hardness of PTFE coatings on both sides of wear track increases as the distance increases and distributes symmetrically around the wear track. Scanning electron microscope( SEM) was utilized to investigate the worn surface of PTFE coating. It was found that the worn surface of PTFE coating is characterized by sever plastic deformation and spalling of the PTFE coating. The edge of wear track is characterized by micro cracking.
基金Project supported by the Russian Foundation for Basic Research(No.19-01-00205)。
文摘This paper is a review,which focuses on our work,while including an analysis of many works of other researchers in the field of quaternionic regularization.The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel(KS)variables and Euler(Rodrigues-Hamilton)parameters are analyzed.These models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point particle.This paper also covers some applications of these models.Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics.However,the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author.More general(compared with the KS equations)quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented.These equations are derived with the assumption that the KS bilinear relation was not satisfied.The main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented,together with regular equations in the KS variables and Euler parameters,derived by the aforementioned theory.We also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters,developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.
文摘A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
