A multi-process(fracturing,shut-in and production)multi-phase flow model was derived considering the osmotic pressure,membrane effect,elastic energy and capillary force,to determine the optimal shut-in time after mult...A multi-process(fracturing,shut-in and production)multi-phase flow model was derived considering the osmotic pressure,membrane effect,elastic energy and capillary force,to determine the optimal shut-in time after multi-cluster staged hydraulic fracturing in shale reservoirs for the maximum production.The accuracy of the model was verified by using production data and commercial software.Based on this model and method,a physical model was made based on the inversion of fracture parameters from fracturing pressure data,to simulate the dynamic changes of pore pressure and oil saturation during fracturing,soaking and production,examine effects of 7 factors on the optimal shut-in time,and find out the main factors affecting the optimal shut-in time through orthogonal experiments.With the increase of shut-in time,the increment of cumulative production increases rapidly first and then tended to a stable value,and the shut-in time corresponding to the inflection point of the change was the optimal shut-in time.The optimal shut-in time has a nonlinear negative correlation with matrix permeability,porosity,capillary pressure multiple and fracture length,a nonlinear positive correlation with the membrane efficiency and total volume of injected fluid,and a nearly linear positive correlation with displacement.The seven factors in descending order of influence degree on optimal shut-in time are total volume of injected fluid,capillary force multiple,matrix permeability,porosity,membrane efficiency,salinity of fracturing fluid,fracturing fluid displacement.展开更多
Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for ...Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for shut-in time after horizontal well volume fracturing with the goal of shortening oil breakthrough time and achieving rapid oil breakthrough, and analyzes the influences of permeability, porosity, fracture half-length and fracturing fluid volume on the shut-in time. The oil and water imbibition displacement in the matrix and fractures occurs during the shut-in process of wells after fracturing. If the shut-in time is too short, the oil-water displacement is not sufficient, and the oil breakthrough time is long after the well is put into production. If the shut-in time is too long, the oil and water displacement is sufficient, but the energy dissipation in the formation near the bottom of the well is severe, and the flowing period is short and the production is low after the well is put into production. A rational shut-in time can help shorten the oil breakthrough time, extend the flowing period and increase the production of the well. The rational shut-in time is influenced by factors such as permeability, porosity, fracture half-length and fracturing fluid volume. The shortest and longest shut-in times are negatively correlated with porosity, permeability, and fracture half-length, and positively correlated with fracturing fluid volume. The pilot test in tight oil horizontal wells in the Songliao Basin, NE China, has confirmed that the proposed optimization method can effectively improve the development effect of horizontal well volume fracturing.展开更多
The acquisition of neutron time spectrum data plays a pivotal role in the precise quantification of uranium via prompt fission neutron uranium logging(PFNUL).However,the impact of the detector dead-time effect remains...The acquisition of neutron time spectrum data plays a pivotal role in the precise quantification of uranium via prompt fission neutron uranium logging(PFNUL).However,the impact of the detector dead-time effect remains paramount in the accurate acquisition of the neutron time spectrum.Therefore,it is imperative for neutron logging instruments to establish a dead-time correction method that is not only uncomplicated but also practical and caters to various logging sites.This study has formulated an innovative equation for determining dead time and introduced a dead-time correction method for the neutron time spectrum,called the“dual flux method.”Using this approach,a logging instrument captures two neutron time spectra under disparate neutron fluxes.By carefully selecting specific“windows”on the neutron time spectrum,the dead time can be accurately ascertained.To substantiate its efficacy and discern the influencing factors,experiments were conducted utilizing a deuterium-tritium(D-T)neutron source,a Helium-3(3He)detector,and polyethylene shielding to collate and analyze the neutron time spectrum under varying neutron fluxes(at high voltages).The findings underscore that the“height”and“spacing”of the two windows are the most pivotal influencing factors.Notably,the“height”(fd)should surpass 2,and the“spacing”twd should exceed 200μs.The dead time of the 3 He detector determined in the experiment was 7.35μs.After the dead-time correction,the deviation of the decay coefficients from the theoretical values for the neutron time spectrum under varying neutron fluxes decreased from 12.4%to within 5%.Similarly,for the PFNUL instrument,the deviation in the decay coefficients decreased from 22.94 to 0.49%after correcting for the dead-time effect.These results demonstrate the exceptional efficacy of the proposed method in ensuring precise uranium quantification.The dual flux method was experimentally validated as a universal approach applicable to pulsed neutron logging instruments and holds immense significance for uranium exploration.展开更多
To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)pre...To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.展开更多
During air injection into an oil reservoir,an oxidation reaction generates some heat to raise the reservoir temperature.When the reservoir temperature reaches an ignition temperature,spontaneous ignition occurs.There ...During air injection into an oil reservoir,an oxidation reaction generates some heat to raise the reservoir temperature.When the reservoir temperature reaches an ignition temperature,spontaneous ignition occurs.There is a time delay from the injection to ignition.There are mixed results regarding the feasibility of spontaneous ignition in real-field projects and in laboratory experiments.No analytical model is available in the literature to estimate the oxidation time required to reach spontaneous ignition with heat loss.This paper discusses the feasibility of spontaneous ignition from theoretical points and experimental and field project observations.An analytical model considering heat loss is proposed.Analytical models with and without heat loss investigate the factors that affect spontaneous ignition.Based on the discussion and investigations,we find that it is more difficult for spontaneous ignition to occur in laboratory experiments than in oil reservoirs;spontaneous ignition is strongly affected by the initial reservoir temperature,oil activity,and heat loss;spontaneous ignition is only possible when the initial reservoir temperature is high,the oil oxidation rate is high,and the heat loss is low.展开更多
Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast ele...Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.展开更多
The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of conti...The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,respectively.Using the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels.The steady-state solutions of the Fokker–Planck equation are obtained in exact form.Numerical experiments are provided to support our results under different parameters.展开更多
For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smalle...For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.展开更多
In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary rando...In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.展开更多
The composite time scale(CTS)provides a stable,accurate,and reliable time scale for modern society.The improvement of CTS’s real-time performance will improve its stability,which strengths related applications’perfo...The composite time scale(CTS)provides a stable,accurate,and reliable time scale for modern society.The improvement of CTS’s real-time performance will improve its stability,which strengths related applications’performance.Aiming at this goal,a method achieved by determining the optimal calculation interval and accelerating adjustment stage is proposed in this paper.The determinants of the CTS’s calculation interval(characteristics of the clock ensemble,the measurement noise,the time and frequency synchronization system’s noise and the auxiliary output generator noise floor)are studied and the optimal calculation interval is obtained.We also investigate the effect of ensemble algorithm’s initial parameters on the CTS’s adjustment stage.A strategy to get the reasonable initial parameters of ensemble algorithm is designed.The results show that the adjustment stage can be finished rapidly or even can be shorten to zero with reasonable initial parameters.On this basis,we experimentally generate a distributed CTS with a calculation interval of 500 s and its stability outperforms those of the member clocks when the averaging time is longer than1700 s.The experimental result proves that the CTS’s real-time performance is significantly improved.展开更多
A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploratio...A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.展开更多
Active target time projection chambers are state-of-the-art tools in the field of low-energy nuclear physics and are particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays.The Fu...Active target time projection chambers are state-of-the-art tools in the field of low-energy nuclear physics and are particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays.The Fudan multi-purpose active target time projection chamber(fMeta-TPC)with 2048 channels was developed to studyα-clustering nuclei.This study focused on the photonuclear reaction with a laser Compton scattering gamma source,particularly for the decay of the highly excitedαcluster state.The design of fMeta-TPC is described in this paper.A comprehensive evaluation of its offline performance was conducted using an ultraviolet laser and ^(241)Amαsource.The results showed that the intrinsic angular resolution of the detector was within 0.30°,and the detector had an energy resolution of 6.85%for 3.0 MeVαparticles.The gain uniformity of the detector was approximately 10%(RMS/Mean),as tested by the ^(55)Fe X-ray source.展开更多
In this paper,the covert age of information(CAoI),which characterizes the timeliness and covertness performance of communication,is first investigated in the short-packet covert communication with time modulated retro...In this paper,the covert age of information(CAoI),which characterizes the timeliness and covertness performance of communication,is first investigated in the short-packet covert communication with time modulated retrodirective array(TMRDA).Specifically,the TMRDA is designed to maximize the antenna gain in the target direction while the side lobe is sufficiently suppressed.On this basis,the covertness constraint and CAoI are derived in closed form.To facilitate the covert transmission design,the transmit power and block-length are jointly optimized to minimize the CAoI,which demonstrates the trade-off between covertness and timelessness.Our results illustrate that there exists an optimal block-length that yields the minimum CAoI,and the presented optimization results can achieve enhanced performance compared with the fixed block-length case.Additionally,we observe that smaller beam pointing error at Bob leads to improvements in CAoI.展开更多
The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is ac...The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS's long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser(averaging time longer than ~10~5s).Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.展开更多
We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third ord...We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.展开更多
基金Supported by the National Natural Science Foundation of China Joint Fund Project(U1562217,U21B2701)。
文摘A multi-process(fracturing,shut-in and production)multi-phase flow model was derived considering the osmotic pressure,membrane effect,elastic energy and capillary force,to determine the optimal shut-in time after multi-cluster staged hydraulic fracturing in shale reservoirs for the maximum production.The accuracy of the model was verified by using production data and commercial software.Based on this model and method,a physical model was made based on the inversion of fracture parameters from fracturing pressure data,to simulate the dynamic changes of pore pressure and oil saturation during fracturing,soaking and production,examine effects of 7 factors on the optimal shut-in time,and find out the main factors affecting the optimal shut-in time through orthogonal experiments.With the increase of shut-in time,the increment of cumulative production increases rapidly first and then tended to a stable value,and the shut-in time corresponding to the inflection point of the change was the optimal shut-in time.The optimal shut-in time has a nonlinear negative correlation with matrix permeability,porosity,capillary pressure multiple and fracture length,a nonlinear positive correlation with the membrane efficiency and total volume of injected fluid,and a nearly linear positive correlation with displacement.The seven factors in descending order of influence degree on optimal shut-in time are total volume of injected fluid,capillary force multiple,matrix permeability,porosity,membrane efficiency,salinity of fracturing fluid,fracturing fluid displacement.
基金Supported by China National Major Project of Science and Technology(2016ZX05046-004)PetroChina Major Project of Science and Technology(2017B-4905)PetroChina Jilin Oilfield Company Major Project of Science and Technology(JY21A2-12).
文摘Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for shut-in time after horizontal well volume fracturing with the goal of shortening oil breakthrough time and achieving rapid oil breakthrough, and analyzes the influences of permeability, porosity, fracture half-length and fracturing fluid volume on the shut-in time. The oil and water imbibition displacement in the matrix and fractures occurs during the shut-in process of wells after fracturing. If the shut-in time is too short, the oil-water displacement is not sufficient, and the oil breakthrough time is long after the well is put into production. If the shut-in time is too long, the oil and water displacement is sufficient, but the energy dissipation in the formation near the bottom of the well is severe, and the flowing period is short and the production is low after the well is put into production. A rational shut-in time can help shorten the oil breakthrough time, extend the flowing period and increase the production of the well. The rational shut-in time is influenced by factors such as permeability, porosity, fracture half-length and fracturing fluid volume. The shortest and longest shut-in times are negatively correlated with porosity, permeability, and fracture half-length, and positively correlated with fracturing fluid volume. The pilot test in tight oil horizontal wells in the Songliao Basin, NE China, has confirmed that the proposed optimization method can effectively improve the development effect of horizontal well volume fracturing.
基金supported by the National Natural Science Foundation of China(No.42374226)Jiangxi Provincial Natural Science Foundation(Nos.20232BAB201043 and 20232BCJ23006)+2 种基金Nuclear Energy Development Project(20201192-01)National Key Laboratory of Uranium Resource Exploration-Mining and Nuclear Remote Sensing(ECUT)(2024QZ-TD-09)Fundamental Science on Radioactive Geology and Exploration Technology Laboratory(2022RGET20).
文摘The acquisition of neutron time spectrum data plays a pivotal role in the precise quantification of uranium via prompt fission neutron uranium logging(PFNUL).However,the impact of the detector dead-time effect remains paramount in the accurate acquisition of the neutron time spectrum.Therefore,it is imperative for neutron logging instruments to establish a dead-time correction method that is not only uncomplicated but also practical and caters to various logging sites.This study has formulated an innovative equation for determining dead time and introduced a dead-time correction method for the neutron time spectrum,called the“dual flux method.”Using this approach,a logging instrument captures two neutron time spectra under disparate neutron fluxes.By carefully selecting specific“windows”on the neutron time spectrum,the dead time can be accurately ascertained.To substantiate its efficacy and discern the influencing factors,experiments were conducted utilizing a deuterium-tritium(D-T)neutron source,a Helium-3(3He)detector,and polyethylene shielding to collate and analyze the neutron time spectrum under varying neutron fluxes(at high voltages).The findings underscore that the“height”and“spacing”of the two windows are the most pivotal influencing factors.Notably,the“height”(fd)should surpass 2,and the“spacing”twd should exceed 200μs.The dead time of the 3 He detector determined in the experiment was 7.35μs.After the dead-time correction,the deviation of the decay coefficients from the theoretical values for the neutron time spectrum under varying neutron fluxes decreased from 12.4%to within 5%.Similarly,for the PFNUL instrument,the deviation in the decay coefficients decreased from 22.94 to 0.49%after correcting for the dead-time effect.These results demonstrate the exceptional efficacy of the proposed method in ensuring precise uranium quantification.The dual flux method was experimentally validated as a universal approach applicable to pulsed neutron logging instruments and holds immense significance for uranium exploration.
文摘To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.
基金supported by the National Natural Science Foundation of China (No.51974334)Hainan Province Science and Technology Special Fund (ZDYF2022SHFZ107)local efficient reform and development funds for personnel training projects supported by the central government,Heilongjiang Postdoctoral Scientific Research Fund (LBH-Q21012)。
文摘During air injection into an oil reservoir,an oxidation reaction generates some heat to raise the reservoir temperature.When the reservoir temperature reaches an ignition temperature,spontaneous ignition occurs.There is a time delay from the injection to ignition.There are mixed results regarding the feasibility of spontaneous ignition in real-field projects and in laboratory experiments.No analytical model is available in the literature to estimate the oxidation time required to reach spontaneous ignition with heat loss.This paper discusses the feasibility of spontaneous ignition from theoretical points and experimental and field project observations.An analytical model considering heat loss is proposed.Analytical models with and without heat loss investigate the factors that affect spontaneous ignition.Based on the discussion and investigations,we find that it is more difficult for spontaneous ignition to occur in laboratory experiments than in oil reservoirs;spontaneous ignition is strongly affected by the initial reservoir temperature,oil activity,and heat loss;spontaneous ignition is only possible when the initial reservoir temperature is high,the oil oxidation rate is high,and the heat loss is low.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.92150105,11834004,12227807,and 12241407)the Science and Technology Commission of Shanghai Municipality (Grant No.21ZR1420100)。
文摘Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.
基金the Special Project of Yili Normal University(to improve comprehensive strength of disciplines)(Grant No.22XKZZ18)Yili Normal University Scientific Research Innovation Team Plan Project(Grant No.CXZK2021015)Yili Science and Technology Planning Project(Grant No.YZ2022B036).
文摘The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,respectively.Using the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels.The steady-state solutions of the Fokker–Planck equation are obtained in exact form.Numerical experiments are provided to support our results under different parameters.
基金supported by the National Natural Science Foundation of China(11201324)the Fok Ying Tuny Education Foundation(141114)the Sichuan Technology Program(2022ZYD0011,2022NFSC1852).
文摘For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.
基金supported by the Shenzhen sustainable development project:KCXFZ 20201221173013036 and the National Natural Science Foundation of China(91746107).
文摘In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.
基金the National Key Research and Development Program of China(Grant No.2021YFA1402102)the National Natural Science Foundation of China(Grant No.62171249)the Fund by Tsinghua University Initiative Scientific Research Program.
文摘The composite time scale(CTS)provides a stable,accurate,and reliable time scale for modern society.The improvement of CTS’s real-time performance will improve its stability,which strengths related applications’performance.Aiming at this goal,a method achieved by determining the optimal calculation interval and accelerating adjustment stage is proposed in this paper.The determinants of the CTS’s calculation interval(characteristics of the clock ensemble,the measurement noise,the time and frequency synchronization system’s noise and the auxiliary output generator noise floor)are studied and the optimal calculation interval is obtained.We also investigate the effect of ensemble algorithm’s initial parameters on the CTS’s adjustment stage.A strategy to get the reasonable initial parameters of ensemble algorithm is designed.The results show that the adjustment stage can be finished rapidly or even can be shorten to zero with reasonable initial parameters.On this basis,we experimentally generate a distributed CTS with a calculation interval of 500 s and its stability outperforms those of the member clocks when the averaging time is longer than1700 s.The experimental result proves that the CTS’s real-time performance is significantly improved.
基金Project supported by the National Natural Science Foun dation of China(Grant No.11274398).
文摘A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.
基金supported by the National Key R&D Program of China(Nos.2022YFA1602402,2020YFE0202001,2023YFA1606900)the National Natural Science Foundation of China(NSFC)(Nos.12235003,11835002,11925502,11705031,12275053,12147101).
文摘Active target time projection chambers are state-of-the-art tools in the field of low-energy nuclear physics and are particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays.The Fudan multi-purpose active target time projection chamber(fMeta-TPC)with 2048 channels was developed to studyα-clustering nuclei.This study focused on the photonuclear reaction with a laser Compton scattering gamma source,particularly for the decay of the highly excitedαcluster state.The design of fMeta-TPC is described in this paper.A comprehensive evaluation of its offline performance was conducted using an ultraviolet laser and ^(241)Amαsource.The results showed that the intrinsic angular resolution of the detector was within 0.30°,and the detector had an energy resolution of 6.85%for 3.0 MeVαparticles.The gain uniformity of the detector was approximately 10%(RMS/Mean),as tested by the ^(55)Fe X-ray source.
文摘In this paper,the covert age of information(CAoI),which characterizes the timeliness and covertness performance of communication,is first investigated in the short-packet covert communication with time modulated retrodirective array(TMRDA).Specifically,the TMRDA is designed to maximize the antenna gain in the target direction while the side lobe is sufficiently suppressed.On this basis,the covertness constraint and CAoI are derived in closed form.To facilitate the covert transmission design,the transmit power and block-length are jointly optimized to minimize the CAoI,which demonstrates the trade-off between covertness and timelessness.Our results illustrate that there exists an optimal block-length that yields the minimum CAoI,and the presented optimization results can achieve enhanced performance compared with the fixed block-length case.Additionally,we observe that smaller beam pointing error at Bob leads to improvements in CAoI.
基金supported in part by the National Natural Science Foundation of China (Grant No.61971259)the National Key R&D Program of China (Grant No.2021YFA1402102)Tsinghua University Initiative Scientific Research Program。
文摘The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS's long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser(averaging time longer than ~10~5s).Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.
基金partially supported by the National Nature Science Foundation of China(12271114)the Guangxi Natural Science Foundation(2023JJD110009,2019JJG110003,2019AC20214)+2 种基金the Innovation Project of Guangxi Graduate Education(JGY2023061)the Key Laboratory of Mathematical Model and Application(Guangxi Normal University)the Education Department of Guangxi Zhuang Autonomous Region。
文摘We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
