Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes qui...Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.展开更多
This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special c...This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.展开更多
The hot compressive deformation behavior of hot isostatically pressed Ti-47.5Al-2Cr-2Nb-0.2W-0.2B alloy using gas atomization powders was systematically investigated and the processing map was obtained in the temperat...The hot compressive deformation behavior of hot isostatically pressed Ti-47.5Al-2Cr-2Nb-0.2W-0.2B alloy using gas atomization powders was systematically investigated and the processing map was obtained in the temperature range of 1323-1473 Kand strain rate range of 0.001-0.5s^（-1）.The calculated activation energy in the above variational ranges of temperature and strain rate possesses a low activation energy value of approximately 365.6kJ/mol based on the constitutive relationship models developed with the Arrhenius-type constitutive model respectively considering the strain rate and deformation temperature.The hot working flow behavior during the deformation process was analyzed combined with the microstructural evolution.Meanwhile,the processing maps during the deformation process were established based on the dynamic material model and Prasad instability criterion under different deformation conditions.Finally,the optimal hot processing window of this alloy corresponding to the wide temperature range of 1353-1453 Kand the low strain rate of 0.001-0.1s^（-1） was obtained.展开更多
Rectisol process is more efficient in comparison with other physical or chemical absorption methods for gas purification. To implement a real time simulation of Rectisol process, thermodynamic model and simulation str...Rectisol process is more efficient in comparison with other physical or chemical absorption methods for gas purification. To implement a real time simulation of Rectisol process, thermodynamic model and simulation strategy are needed. In this paper, a method of modified statistical associated fluid theory with perturbation theory is used to predict thermodynamic behavior of process. As Rectisol process is a highly heat-integrated process with many loops, a method of equation oriented strategy, sequential quadratic programming, is used as the solver and the process converges perfectly. Then analyses are conducted with this simulator.展开更多
Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata w...Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata water bursting, the judgment matrix was found by the expert scoring method, the contribution weights of the influenced factors were given out by the equation analytic process. The thirteen controlling factors and five main controlling factors were put award by analyzing weights, so the result was basically conform to the field practice. The expert scoring method and analytic process can convert the objective fact to the subjective cognition, so it is a method that can turn the qualitative into the quantitative. This can be relative objectively and precisely to study the question of many factors and grey box.展开更多
Hot deformation behavior of an as-extruded duplex structured Mg-9Li-3Al-2.5Sr alloy is investigated via hot compression tests conducted at 200-350℃ with strain rate of 0.001-1 s^-1.The flow behavior of Mg-9Li-3Al-2.5...Hot deformation behavior of an as-extruded duplex structured Mg-9Li-3Al-2.5Sr alloy is investigated via hot compression tests conducted at 200-350℃ with strain rate of 0.001-1 s^-1.The flow behavior of Mg-9Li-3Al-2.5Sr alloy can be described accurately by hyperbolic sine constitutive equation and the average activation energy for deformation is calculated as 143.5 k J/mol.Based on a dynamic materials model,the processing maps of Mg-9Li-3Al-2.5Sr alloy which describe the variation of power dissipation efficiency are constructed as a function of temperature and strain rate.The processing maps exhibit an area of discontinuous dynamic recrystallization occurring at 280-300℃ with strain rate of 0.001-0.01 s^-1,which corresponds to the optimum hot working conditions.展开更多
The high-temperature deformation behavior of a beta Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy was investigated by a Gleeble-1500 D thermal simulator. The height reduction was 50%, corresponding to a true strain of 0.693. Th...The high-temperature deformation behavior of a beta Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy was investigated by a Gleeble-1500 D thermal simulator. The height reduction was 50%, corresponding to a true strain of 0.693. The strain rate ranging from 0.01 to 10.00 s^-1 and the deformation temperature ranging from 800 to 950 ℃ were considered.The flow stress and the apparent activation energy for deformation, along with the constitutive equation, were used to analyze the behavior of the Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy. The processing map was established. The effect of strain rate on the microstructure at 850 ℃ was evaluated.The flow stress-strain curves indicated that the peak flow stresses increased along with an increase in the strain rate and decreased as the deformation temperature increased.Based on the true stress-true strain curves, the constitutive equation was established and followed as the ε= 6.58×10-（10）[sinh（0.0113σ）]-（3.44）exp（-245481.3/RT）. The processing map exhibited the ＂unsafe＂ region at the strain rate of10 s^-1 and the temperature of 850 ℃,and the rest region was ＂safe＂. The deformation microstructure demonstrated that both dynamic recovery（DRV） and dynamic recrystallization（DRX） existed during deformation. At the lower strain rate of 0.01 s^-1, the main deformation mechanism was the DRV, and the DRX was the dominant deformation mechanism at the higher strain rate of 1.00 s^-1.展开更多
In order to optimize the deformation processing, the hot deformation behavior of Co-Cr-Mo-Cu （here- after named as Co-Cu） alloy was studied in this paper at a deformation temperature range of 950-1150 ℃ and a strai...In order to optimize the deformation processing, the hot deformation behavior of Co-Cr-Mo-Cu （here- after named as Co-Cu） alloy was studied in this paper at a deformation temperature range of 950-1150 ℃ and a strain rate range of 0.008-5 s^-1. Based on the true stress-true strain curves, a constitutive equation in hyperbolic sin function was established and a hot processing map was drawn. It was found that the flow stress of the Co-Cu alloy increased with the increase of the strain rate and decreased with the increase of the deforming temperature. The hot processing map indicated that there were two unstable regions and one well-processing region. The microstructure, the hardness distribution and the electro- chemical properties of the hot deformed sample were investigated in order to reveal the influence of the hot deformation. Microstructure observation indicated that the grain size increased with the increase of the deformation temperature but decreased with the increase of the strain rate. High temperature and low strain rate promoted the crystallization process but increased the grain size, which results in a reduction in the hardness. The hot deformation at high temperature （1100-1150 ℃） would reduce the corrosion resistance slightly. The final optimized deformation process was： a deformation temperature from 1050to 1100 ℃, and a strain rate from 0.008 to 0.2 s^-1, where a completely recrystallized and homogeneously distributed microstructure would be obtained.展开更多
Isothermal hot compression tests on the as-cast high-Cr ultra-super-critical rotor steel with columnar grains were carried out in the temperature range from 1223 to 1523Kand at strain rates from 0.001 to 1s^（-1）.The...Isothermal hot compression tests on the as-cast high-Cr ultra-super-critical rotor steel with columnar grains were carried out in the temperature range from 1223 to 1523Kand at strain rates from 0.001 to 1s^（-1）.The compression direction was parallel to the longitudinal direction of columnar grains.The constitutive equation based on Arrhenius model was presented,and the processing maps based on the dynamic material model were developed,correlating with microstructure observation.The main softening mechanism was dynamic recovery at 1223 Kunder strain rates from 0.1to 1s^（-1）,whereas it was dynamic recrystallization under other deformation conditions.The constitutive equation modified by strain compensation reasonably predicted the flow stresses.The processing maps and microstructure evolution mechanism schematic indicated that the optimum hot working parameters lay in the zone defined by the temperature range from 1423 to 1473Kand the strain rate range from 0.001 to 1s^（-1）.展开更多
By means of a stochastic model suggested in this paper for the systems with local non-equilibrium excited thermal fluctuations,the famous Shannon entropy is extended to include the heat conduction processes controlled...By means of a stochastic model suggested in this paper for the systems with local non-equilibrium excited thermal fluctuations,the famous Shannon entropy is extended to include the heat conduction processes controlled externally by boundary constraints of constant temperature gradients at two sides.Meanwhile,using the description of master equation for the continuous Markov processes a balance equation of stochastic entropy production valid for one dimension gaseous heat conduction systems with high values of Prandtl number has been also established.Based on it,a general expression for both the stochastic entropy production and the entropy production of fluctuations have been further deduced by theΩ-expansions.In this formalism,all kinds of stochastic contributions to the dissipation from the non-equilibrium thermal fluctuation and internal noise turn explicit.展开更多
The coupled equation method （CEM） has been applied to investigating the resonance structures for the ground state 1s^22s^ 2S of the neutral lithium from the first threshold up to 64.5 eV. Resonance structures of ato...The coupled equation method （CEM） has been applied to investigating the resonance structures for the ground state 1s^22s^ 2S of the neutral lithium from the first threshold up to 64.5 eV. Resonance structures of atomic lithium due to single excitations of the ls and 2s electrons are studied by infinite-order calculations in detail. The effect of spin-orbit splitting is also included for some of the low-lying ls2snp（↑↓） resonance, and the influence of the interference between 1s^2s^3 Snp .↓ and 1s2s^ 1 Snp ↑ states on the resonance structure has been confirmed theoretically. The results show that the presented technique can give the reasonable resonance structures very well in photoionization processes.展开更多
The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff （TOV） equations for hydrostatic equilibrium assuming the electron gas to be non-interacting....The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff （TOV） equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of 1.4562 M is modified to 1.4166 M in the general relativistic case for 4He （and 12 6C） white dwarfs. Using the same general relativistic treatment, the critical mass for 56 26Fe white dwarfs is obtained as 1.2230 M. In addition, departure from the ideal degenerate equation of state （EoS） is accounted for by considering Salpeter＇s EoS along with the TOV equation, yielding slightly lower values for the critical masses, namely 1.4081 M for 4He, 1.3916M for 12C and 1.1565M for 56 26Fe white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that 4 2He and 12 6C white dwarfs are stable against neutronization with the critical values of 1.4081 M and 1.3916 M, respectively. However, the critical masses for 16 8O, 20 10Ne, 24 12Mg, 28 14Si,32 16S and 56 26Fewhite dwarfs are 26Fe white lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.展开更多
In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent...In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property,generalizing a few known findings in the literature.The study is ended with many examples.展开更多
We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of re...We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.展开更多
In this paper,we will define the quantum Gaussian processes based on ordinary Gaussian processes by means of reproducing kernel Hilbert spaces,and investigate the relation between their stochastic properties. Particul...In this paper,we will define the quantum Gaussian processes based on ordinary Gaussian processes by means of reproducing kernel Hilbert spaces,and investigate the relation between their stochastic properties. Particularly,we are interested in Brownian bridges and quantum Ornstein Uhlenbeck processes.We are even able to construct each of them in two different ways:to construct quantum processes based on ordinary Brownian bridges(Ornstein-Uhlenbeck processes resp.)or to solve the quantum S.D.E. driven by quantum Brownian motions. But essentially they are the same.展开更多
We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting ...We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.展开更多
We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative...We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51205286,51275348)
文摘Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.
基金Supported by the Foundation of Suzhou Science and Technology University
文摘This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.
基金the financial supports from the National Natural Science Foundation of China(Grant Nos.51301157 and 51434007)the National High Technology Research and Development Program of China 863 Program(Grant No.2013AA031103)
文摘The hot compressive deformation behavior of hot isostatically pressed Ti-47.5Al-2Cr-2Nb-0.2W-0.2B alloy using gas atomization powders was systematically investigated and the processing map was obtained in the temperature range of 1323-1473 Kand strain rate range of 0.001-0.5s^（-1）.The calculated activation energy in the above variational ranges of temperature and strain rate possesses a low activation energy value of approximately 365.6kJ/mol based on the constitutive relationship models developed with the Arrhenius-type constitutive model respectively considering the strain rate and deformation temperature.The hot working flow behavior during the deformation process was analyzed combined with the microstructural evolution.Meanwhile,the processing maps during the deformation process were established based on the dynamic material model and Prasad instability criterion under different deformation conditions.Finally,the optimal hot processing window of this alloy corresponding to the wide temperature range of 1353-1453 Kand the low strain rate of 0.001-0.1s^（-1） was obtained.
基金Supported by the National Basic Research Program of China(2013CB733600)
文摘Rectisol process is more efficient in comparison with other physical or chemical absorption methods for gas purification. To implement a real time simulation of Rectisol process, thermodynamic model and simulation strategy are needed. In this paper, a method of modified statistical associated fluid theory with perturbation theory is used to predict thermodynamic behavior of process. As Rectisol process is a highly heat-integrated process with many loops, a method of equation oriented strategy, sequential quadratic programming, is used as the solver and the process converges perfectly. Then analyses are conducted with this simulator.
文摘Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata water bursting, the judgment matrix was found by the expert scoring method, the contribution weights of the influenced factors were given out by the equation analytic process. The thirteen controlling factors and five main controlling factors were put award by analyzing weights, so the result was basically conform to the field practice. The expert scoring method and analytic process can convert the objective fact to the subjective cognition, so it is a method that can turn the qualitative into the quantitative. This can be relative objectively and precisely to study the question of many factors and grey box.
基金the financial support from the National Natural Science Foundation(Project No.51601024)the National Key Research and Development plan(Project No.2016YFB0700403)+1 种基金the Chongqing Research Program of Basic Research and Frontier Technology(Project No.cstc2016jcyj A0418)the Fundamental Research Funds for the Central Universities(Project No.106112015CDJXY130011 and No.CDJZR14130007)
文摘Hot deformation behavior of an as-extruded duplex structured Mg-9Li-3Al-2.5Sr alloy is investigated via hot compression tests conducted at 200-350℃ with strain rate of 0.001-1 s^-1.The flow behavior of Mg-9Li-3Al-2.5Sr alloy can be described accurately by hyperbolic sine constitutive equation and the average activation energy for deformation is calculated as 143.5 k J/mol.Based on a dynamic materials model,the processing maps of Mg-9Li-3Al-2.5Sr alloy which describe the variation of power dissipation efficiency are constructed as a function of temperature and strain rate.The processing maps exhibit an area of discontinuous dynamic recrystallization occurring at 280-300℃ with strain rate of 0.001-0.01 s^-1,which corresponds to the optimum hot working conditions.
基金financially supported by the.National Natural Science Foundation of China (No.51401027)the China Postdoctoral Science Foundation Funded Project (No.2016M591040)
文摘The high-temperature deformation behavior of a beta Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy was investigated by a Gleeble-1500 D thermal simulator. The height reduction was 50%, corresponding to a true strain of 0.693. The strain rate ranging from 0.01 to 10.00 s^-1 and the deformation temperature ranging from 800 to 950 ℃ were considered.The flow stress and the apparent activation energy for deformation, along with the constitutive equation, were used to analyze the behavior of the Ti-3.0 Al-3.5 Cr-2.0 Fe-0.1 B alloy. The processing map was established. The effect of strain rate on the microstructure at 850 ℃ was evaluated.The flow stress-strain curves indicated that the peak flow stresses increased along with an increase in the strain rate and decreased as the deformation temperature increased.Based on the true stress-true strain curves, the constitutive equation was established and followed as the ε= 6.58×10-（10）[sinh（0.0113σ）]-（3.44）exp（-245481.3/RT）. The processing map exhibited the ＂unsafe＂ region at the strain rate of10 s^-1 and the temperature of 850 ℃,and the rest region was ＂safe＂. The deformation microstructure demonstrated that both dynamic recovery（DRV） and dynamic recrystallization（DRX） existed during deformation. At the lower strain rate of 0.01 s^-1, the main deformation mechanism was the DRV, and the DRX was the dominant deformation mechanism at the higher strain rate of 1.00 s^-1.
基金financially supported by the National Natural Science Foundation of China (Nos. 81071262, 31271024 and 31470930)the Funding from Northeastern University ("985 program", Nos. N141008001 and LZ2014018), China
文摘In order to optimize the deformation processing, the hot deformation behavior of Co-Cr-Mo-Cu （here- after named as Co-Cu） alloy was studied in this paper at a deformation temperature range of 950-1150 ℃ and a strain rate range of 0.008-5 s^-1. Based on the true stress-true strain curves, a constitutive equation in hyperbolic sin function was established and a hot processing map was drawn. It was found that the flow stress of the Co-Cu alloy increased with the increase of the strain rate and decreased with the increase of the deforming temperature. The hot processing map indicated that there were two unstable regions and one well-processing region. The microstructure, the hardness distribution and the electro- chemical properties of the hot deformed sample were investigated in order to reveal the influence of the hot deformation. Microstructure observation indicated that the grain size increased with the increase of the deformation temperature but decreased with the increase of the strain rate. High temperature and low strain rate promoted the crystallization process but increased the grain size, which results in a reduction in the hardness. The hot deformation at high temperature （1100-1150 ℃） would reduce the corrosion resistance slightly. The final optimized deformation process was： a deformation temperature from 1050to 1100 ℃, and a strain rate from 0.008 to 0.2 s^-1, where a completely recrystallized and homogeneously distributed microstructure would be obtained.
基金sponsored by Major State Basic Research Development Program of China(No.2011CB012900)National Natural Science Foundation of China(No.51374144)
文摘Isothermal hot compression tests on the as-cast high-Cr ultra-super-critical rotor steel with columnar grains were carried out in the temperature range from 1223 to 1523Kand at strain rates from 0.001 to 1s^（-1）.The compression direction was parallel to the longitudinal direction of columnar grains.The constitutive equation based on Arrhenius model was presented,and the processing maps based on the dynamic material model were developed,correlating with microstructure observation.The main softening mechanism was dynamic recovery at 1223 Kunder strain rates from 0.1to 1s^（-1）,whereas it was dynamic recrystallization under other deformation conditions.The constitutive equation modified by strain compensation reasonably predicted the flow stresses.The processing maps and microstructure evolution mechanism schematic indicated that the optimum hot working parameters lay in the zone defined by the temperature range from 1423 to 1473Kand the strain rate range from 0.001 to 1s^（-1）.
文摘By means of a stochastic model suggested in this paper for the systems with local non-equilibrium excited thermal fluctuations,the famous Shannon entropy is extended to include the heat conduction processes controlled externally by boundary constraints of constant temperature gradients at two sides.Meanwhile,using the description of master equation for the continuous Markov processes a balance equation of stochastic entropy production valid for one dimension gaseous heat conduction systems with high values of Prandtl number has been also established.Based on it,a general expression for both the stochastic entropy production and the entropy production of fluctuations have been further deduced by theΩ-expansions.In this formalism,all kinds of stochastic contributions to the dissipation from the non-equilibrium thermal fluctuation and internal noise turn explicit.
基金This work was supported by the Natural Science Foundation of Yantai Normal University under Grant No.22270301 and L20072804.
文摘The coupled equation method （CEM） has been applied to investigating the resonance structures for the ground state 1s^22s^ 2S of the neutral lithium from the first threshold up to 64.5 eV. Resonance structures of atomic lithium due to single excitations of the ls and 2s electrons are studied by infinite-order calculations in detail. The effect of spin-orbit splitting is also included for some of the low-lying ls2snp（↑↓） resonance, and the influence of the interference between 1s^2s^3 Snp .↓ and 1s2s^ 1 Snp ↑ states on the resonance structure has been confirmed theoretically. The results show that the presented technique can give the reasonable resonance structures very well in photoionization processes.
文摘The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff （TOV） equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of 1.4562 M is modified to 1.4166 M in the general relativistic case for 4He （and 12 6C） white dwarfs. Using the same general relativistic treatment, the critical mass for 56 26Fe white dwarfs is obtained as 1.2230 M. In addition, departure from the ideal degenerate equation of state （EoS） is accounted for by considering Salpeter＇s EoS along with the TOV equation, yielding slightly lower values for the critical masses, namely 1.4081 M for 4He, 1.3916M for 12C and 1.1565M for 56 26Fe white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that 4 2He and 12 6C white dwarfs are stable against neutronization with the critical values of 1.4081 M and 1.3916 M, respectively. However, the critical masses for 16 8O, 20 10Ne, 24 12Mg, 28 14Si,32 16S and 56 26Fewhite dwarfs are 26Fe white lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.
文摘In this study,we are interested in stochastic differential equations driven by GLévy processes.We illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property,generalizing a few known findings in the literature.The study is ended with many examples.
基金supported by National Natural Science Foundation of China (Grant Nos. 61573217,11471192 and 11626142)the National High-Level Personnel of Special Support Program,the Chang Jiang Scholar Program of Chinese Education Ministry+2 种基金the Natural Science Foundation of Shandong Province (Grant Nos. JQ201401 and ZR2016AB08)the Colleges and Universities Science and Technology Plan Project of Shandong Province (Grant No. J16LI55)the Fostering Project of Dominant Discipline and Talent Team of Shandong University of Finance and Economics
文摘We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.
文摘In this paper,we will define the quantum Gaussian processes based on ordinary Gaussian processes by means of reproducing kernel Hilbert spaces,and investigate the relation between their stochastic properties. Particularly,we are interested in Brownian bridges and quantum Ornstein Uhlenbeck processes.We are even able to construct each of them in two different ways:to construct quantum processes based on ordinary Brownian bridges(Ornstein-Uhlenbeck processes resp.)or to solve the quantum S.D.E. driven by quantum Brownian motions. But essentially they are the same.
基金Supported by National Natural Science Foundation of China(Grant No.11126052)
文摘We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.
文摘We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.
