The purpose is to explore the effects of Exercise rehabilitation(ER)on bone mineral density(BMD)of the knee,muscle strength(MS),and physical function(PF)after ACL rupture.Finally,A total of 58 patients were randomized...The purpose is to explore the effects of Exercise rehabilitation(ER)on bone mineral density(BMD)of the knee,muscle strength(MS),and physical function(PF)after ACL rupture.Finally,A total of 58 patients were randomized into 2 groups(Control Group[CON]:conventional treatment,male=16,female=13,age=[31.63±8.01]years;Exercise rehabilitation group[ER]:6-week ER on CON basis,male=17,female=12,age=[31.26±7.07]years).At baseline and 6 weeks,the knee BMD was measured using DEXA,MS and PF measures were recorded by isokinetic strength test,IKDC,Lysholm,and VAS score.T-tests,analysis of variance(ANOVA),and Mann-Whitney tests were used for comparisons.The BMD outcomes:after a 6-week period,the BMD of the CON([1.47±0.24]g·cm^(-2))was significantly lower than that of the ER([1.65±0.37]g·cm^(-2))at lateral condyle of femur(LCF)(p=0.041).MS outcomes:at 6 weeks,the relative peak torque(RPT)of the quadriceps and hamstrings during concentric contractions in ER group were significantly higher than that in CON group(p<0.001,p=0.017).Similarly,during eccentric contractions in ER group,the RPT of the quadriceps and the H/Q ratio revealed significant variations from the CON group(p=0.033,p=0.043).PF outcomes:the IKDC,Lysholm,and VAS scores of the ER group were significantly improved compared to the CON group(p<0.001,p<0.001,p=0.002).The conclusion is that 6 weeks of ER intervention for patients with ACL rupture can effectively delay the decline of BMD in the LCF of the knee joint,and enhance the restoration of MS and PF.This provides guidance for clinical rehabilitation.展开更多
Recently a Hybrid Carrier （HC） scheme based on Weighted-type Fractional Fourier Transform （WFRFT） was proposed and developed, which contains Single Carrier （SC） and Multi-Carrier （MC） synergetie transmission. ...Recently a Hybrid Carrier （HC） scheme based on Weighted-type Fractional Fourier Transform （WFRFT） was proposed and developed, which contains Single Carrier （SC） and Multi-Carrier （MC） synergetie transmission. The wide interest is primarily due to its appealing characteristics, such as the robust performances in different types of selective fading channels and a great deal of potential for secure communications. According to the literatures, the HC signal and SC or MC signal probability distributions are different. In particular, some benefits of this HC scheme are brought by the quasi-Gaussian distribution of WFRFT signals. However, until now researchers have only presented statistic properties through computer simulations, and the accurate expressions of signals are not derived yet. In this paper, we derive the accu- rate and rigorously established closed-form expressions of Probability Density Function （PDF） of WFRFT signal real and imaginary parts with a large number of QPSK subcarriers, and this PDF can describe the behavior of data modulated by WFRFT, avoiding the complex computation for extensive computer simulations. Furthermore, the components of PDF expression are described and analyzed, and it is revealed that the tendency of signal quasi-Gaussian changes with the increasing of the parameter a （a in （0,1]）. To validate the analytical results, extensive simulations have been conducted, showing a very good match between the analytical results and the real situations. The contribution of this paper may be useful to deduce the closed form expressions of Bit Error Ratio （BER）, the Complementary Cumulative Distribution Function （CCDF） of Peak to Average Power Ratio （PAPR）, and other analytical studies which adopt the PDF.展开更多
A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameteri...The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.展开更多
The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear st...The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.展开更多
Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important in...Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.展开更多
The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution ...The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.展开更多
This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density fun...This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.展开更多
Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in...Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.展开更多
We have examined the theoretical implications of combining two main and three auxiliary ligands to form several Ir(Ⅲ)complexes featuring a transition metal as their core atom to identify some appropriate organic ligh...We have examined the theoretical implications of combining two main and three auxiliary ligands to form several Ir(Ⅲ)complexes featuring a transition metal as their core atom to identify some appropriate organic lightemitting diode(OLED)materials.By utilizing electronic structure,frontier molecular orbitals,minimum single-line absorption,triplet excited states,and emission spectral data derived from the density functional theory,the usefulness of these Ir(Ⅲ)complexes,including(piq)_(2)Ir(acac),(piq)_(2)Ir(tmd),(piq)_(2)Ir(tpip),(fpiq)_(2)Ir(acac),(fpiq)_(2)Ir(tmd),and(fpiq)_(2)Ir(tpip),in OLEDs was examined,where piq=1-phenylisoquinoline,fpiq=1-(4-fluorophenyl)isoquinoline,acac=(3Z)-4-hydroxypent-3-en-2-one,tmd=(4Z)-5-hydroxy-2,2,6,6-tetramethylhept-4-en-3-one,and tpip=tetraphenylimido-diphosphonate.These complexes all have low-efficiency roll-off properties,especially(fpiq)_(2)Ir(tpip).Some researchers have successfully synthesized complexes extremely similar to(piq)_(2)Ir(acac)through the Suzuki-Miyaura coupling reaction.展开更多
We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown...We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state twoor higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.展开更多
We study the uncertainties of quantum mechanical observables, quantified by the standard deviation(square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functi...We study the uncertainties of quantum mechanical observables, quantified by the standard deviation(square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions(PDFs) of the uncertainties of arbitrary qubit observables.Based on these PDFs, the uncertainty regions of the observables are characterized by the support of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying stateindependent uncertainty relations. Our results may be generalized to multiple observable cases in higher dimensional spaces.展开更多
The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude an...The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.展开更多
The present work proposes a novel methodology for constructing coarse-grained （CG） models, which aims at minimizing the difference between CG model and the corresponding original system. The difference is defined as...The present work proposes a novel methodology for constructing coarse-grained （CG） models, which aims at minimizing the difference between CG model and the corresponding original system. The difference is defined as a functional of their equilibrium conformationaJ probability densities, then is estimated from equilibrium averages of many independent physical quantities denoted as basis functions. An orthonormalization strategy is adopted to get the independent basis functions from su^ciently preselected interesting physical quantities of the system. Thus the current method is named as probability density matching coarse-graining （PMCG） scheme, which effectively takes into account the overall cha,~acteristics of the original systems to construct CG model, and it is a rtatural improvement of the usual CG scheme wherein some physical quantities are intuitively chosen without considering their correlations. We verify the general PMCG framework in constructing a one-site CG water model from TIP3P model. Both structure of liquids and pressure of the TIP3P water system are found to be well reproduced at the same time in the constructed CG model.展开更多
Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the...Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.展开更多
By adopting stochastic density functional theory(SDFT)and mixed stochastic-deterministic density functional theory(MDFT)methods,we perform first-principles calculations to predict the shock Hugoniot curves of boron(pr...By adopting stochastic density functional theory(SDFT)and mixed stochastic-deterministic density functional theory(MDFT)methods,we perform first-principles calculations to predict the shock Hugoniot curves of boron(pressure P=7.9×10^(3)-1.6×10^(6) GPa and temperature T=25-2800 eV),silicon(P=2.6×10^(3)-7.9×10^(5) GPa and T=21.5-1393 eV),and aluminum(P=5.2×10^(3)-9.0×10^(5) GPa and T=25-1393 eV)over wide ranges of pressure and temperature.In particular,we systematically investigate the impact of different cutoff radii in norm-conserving pseudopotentials on the calculated properties at elevated temperatures,such as pressure,ionization energy,and equation of state.By comparing the SDFT and MDFT results with those of other first-principles methods,such as extended first-principles molecular dynamics and path integral Monte Carlo methods,we find that the SDFT and MDFT methods show satisfactory precision,which advances our understanding of first-principles methods when applied to studies of matter at extremely high pressures and temperatures.展开更多
The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the...The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.展开更多
We propose a new flame index for the transported probability density function(PDF) method. The flame index uses mixing flux projections of Lagrangian particles on mixture fraction and progress variable directions as t...We propose a new flame index for the transported probability density function(PDF) method. The flame index uses mixing flux projections of Lagrangian particles on mixture fraction and progress variable directions as the metrics to identify the combustion mode, with the Burke-Schumann solution as a reference. A priori validation of the flame index is conducted with a series of constructed turbulent partially premixed reactors. It indicates that the proposed flame index is able to identify the combustion mode based on the subgrid mixing information. The flame index is then applied the large eddy simulation/PDF datasets of turbulent partially premixed jet flames. Results show that the flame index separate different combustion modes and extinction correctly. The proposed flame index provides a promising tool to analyze and model the partially premixed flames adaptively.展开更多
Machine learning(ML)has demon-strated significant potential in en-hancing the predictive capabilities of density functional theory methods.In this study,we develop an ML model for correcting B3LYP-D,a density function...Machine learning(ML)has demon-strated significant potential in en-hancing the predictive capabilities of density functional theory methods.In this study,we develop an ML model for correcting B3LYP-D,a density functional approximation that incorporates dispersion correc-tions for non-covalent interactions.This model utilizes semilocal elec-tron density descriptors,and is trained with accurate reference data for both relative and ab-solute energies.Extensive benchmark tests reveal that the ML correction substantially en-hances the generalization ability of the B3LYP-D functional,improving the predictions of at-omization and dissociation energies for complex molecular systems.It retains the accuracy of B3LYP-D in predicting reaction barrier heights and non-covalent interactions while enabling efficient,fully self-consistent field calculations.This work signifies a promising advancement in the development of ML-corrected functionals that surpass the performance of traditional B3LYP-D.展开更多
Metal-organic framework(MOF) has been widely applied in photocatalysis, which is significant for addressing energy crises and environmental issues. Based on density functional theory calculations,the performances of C...Metal-organic framework(MOF) has been widely applied in photocatalysis, which is significant for addressing energy crises and environmental issues. Based on density functional theory calculations,the performances of Cu-BTC, a copper-based MOF, and its derivatives Cu TM-BTC via the substitution of transition metal(TM) elements at the Cu site for photocatalytic overall water splitting(POWS) have been studied. POWS of Cu-BTC suffers from the sluggish hydrogen evolution reaction due to the large overpotential of 2.02 V and limited solar utilization due to a wide HOMO-LUMO gap of 4.11 e V. Via TM substitution, the HOMO-LUMO gap narrows but still satisfies the redox potentials when taken 3d-TM of Cr, Fe, Co or Ni, 4d-TM of Rh or Pd, or 5d-TM of Re or Pt into consideration, benefiting for the light absorption. Furthermore, Cr and Re could serve as active sites for hydrogen evolution with remarkably lowered overpotentials of 0.79 V and 0.28 V, respectively;similarly, oxygen evolution activities could be enhanced by Fe, Co and Rh because of their reduced overpotentials which are less than 0.5 V. Therefore,our findings pave guidance for designing Cu-BTC derivatives in overall water splitting.展开更多
基金provided by the Joint Fund for Regional Innovation and Development(U23A20471)Beijing Natural Science Foundation(L242161,L241073,and 7232354)。
文摘The purpose is to explore the effects of Exercise rehabilitation(ER)on bone mineral density(BMD)of the knee,muscle strength(MS),and physical function(PF)after ACL rupture.Finally,A total of 58 patients were randomized into 2 groups(Control Group[CON]:conventional treatment,male=16,female=13,age=[31.63±8.01]years;Exercise rehabilitation group[ER]:6-week ER on CON basis,male=17,female=12,age=[31.26±7.07]years).At baseline and 6 weeks,the knee BMD was measured using DEXA,MS and PF measures were recorded by isokinetic strength test,IKDC,Lysholm,and VAS score.T-tests,analysis of variance(ANOVA),and Mann-Whitney tests were used for comparisons.The BMD outcomes:after a 6-week period,the BMD of the CON([1.47±0.24]g·cm^(-2))was significantly lower than that of the ER([1.65±0.37]g·cm^(-2))at lateral condyle of femur(LCF)(p=0.041).MS outcomes:at 6 weeks,the relative peak torque(RPT)of the quadriceps and hamstrings during concentric contractions in ER group were significantly higher than that in CON group(p<0.001,p=0.017).Similarly,during eccentric contractions in ER group,the RPT of the quadriceps and the H/Q ratio revealed significant variations from the CON group(p=0.033,p=0.043).PF outcomes:the IKDC,Lysholm,and VAS scores of the ER group were significantly improved compared to the CON group(p<0.001,p<0.001,p=0.002).The conclusion is that 6 weeks of ER intervention for patients with ACL rupture can effectively delay the decline of BMD in the LCF of the knee joint,and enhance the restoration of MS and PF.This provides guidance for clinical rehabilitation.
基金supported by the National Natural Science Foundation General Program of China(No.61201146)the National Basic Research Program of China(2013CB329003)the Fundamental Research Funds for the Central Universities(HIT.NSRIF.2015022)
文摘Recently a Hybrid Carrier （HC） scheme based on Weighted-type Fractional Fourier Transform （WFRFT） was proposed and developed, which contains Single Carrier （SC） and Multi-Carrier （MC） synergetie transmission. The wide interest is primarily due to its appealing characteristics, such as the robust performances in different types of selective fading channels and a great deal of potential for secure communications. According to the literatures, the HC signal and SC or MC signal probability distributions are different. In particular, some benefits of this HC scheme are brought by the quasi-Gaussian distribution of WFRFT signals. However, until now researchers have only presented statistic properties through computer simulations, and the accurate expressions of signals are not derived yet. In this paper, we derive the accu- rate and rigorously established closed-form expressions of Probability Density Function （PDF） of WFRFT signal real and imaginary parts with a large number of QPSK subcarriers, and this PDF can describe the behavior of data modulated by WFRFT, avoiding the complex computation for extensive computer simulations. Furthermore, the components of PDF expression are described and analyzed, and it is revealed that the tendency of signal quasi-Gaussian changes with the increasing of the parameter a （a in （0,1]）. To validate the analytical results, extensive simulations have been conducted, showing a very good match between the analytical results and the real situations. The contribution of this paper may be useful to deduce the closed form expressions of Bit Error Ratio （BER）, the Complementary Cumulative Distribution Function （CCDF） of Peak to Average Power Ratio （PAPR）, and other analytical studies which adopt the PDF.
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.42175099,42027804,42075073)the Innovative Project of Postgraduates in Jiangsu Province in 2023(Grant No.KYCX23_1319)+3 种基金supported by the National Natural Science Foundation of China(Grant No.42205080)the Natural Science Foundation of Sichuan(Grant No.2023YFS0442)the Research Fund of Civil Aviation Flight University of China(Grant No.J2022-037)supported by the National Key Scientific and Technological Infrastructure project“Earth System Science Numerical Simulator Facility”(Earth Lab)。
文摘The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.
基金the National Natural Science Foundation of China(No.61273127)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(No.12JK0524)
文摘The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.
文摘Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.
基金the National Natural Science Foundation of Chinafor Innovative Research Groups Under Grant No.50621062the National Natural Science Foundation of China forYoung Scholars Under Grant No.10402030
文摘The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.
文摘This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.
文摘Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.
文摘We have examined the theoretical implications of combining two main and three auxiliary ligands to form several Ir(Ⅲ)complexes featuring a transition metal as their core atom to identify some appropriate organic lightemitting diode(OLED)materials.By utilizing electronic structure,frontier molecular orbitals,minimum single-line absorption,triplet excited states,and emission spectral data derived from the density functional theory,the usefulness of these Ir(Ⅲ)complexes,including(piq)_(2)Ir(acac),(piq)_(2)Ir(tmd),(piq)_(2)Ir(tpip),(fpiq)_(2)Ir(acac),(fpiq)_(2)Ir(tmd),and(fpiq)_(2)Ir(tpip),in OLEDs was examined,where piq=1-phenylisoquinoline,fpiq=1-(4-fluorophenyl)isoquinoline,acac=(3Z)-4-hydroxypent-3-en-2-one,tmd=(4Z)-5-hydroxy-2,2,6,6-tetramethylhept-4-en-3-one,and tpip=tetraphenylimido-diphosphonate.These complexes all have low-efficiency roll-off properties,especially(fpiq)_(2)Ir(tpip).Some researchers have successfully synthesized complexes extremely similar to(piq)_(2)Ir(acac)through the Suzuki-Miyaura coupling reaction.
基金Project supported by the Korean Research Foundation of the Korea Government (MEST) (Grant No. 2009-0073081)
文摘We investigate the possibility for two-mode probability density function （PDF） to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state twoor higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.
基金supported by the NSF of China under Grant Nos.11971140,12075159,and 12171044Beijing Natural Science Foundation(Z190005)+1 种基金the Academician Innovation Platform of Hainan Province,and Academy for Multidisciplinary Studies,Capital Normal Universityfunded by Natural Science Foundations of Hubei Province Grant No.2020CFB538。
文摘We study the uncertainties of quantum mechanical observables, quantified by the standard deviation(square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions(PDFs) of the uncertainties of arbitrary qubit observables.Based on these PDFs, the uncertainty regions of the observables are characterized by the support of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying stateindependent uncertainty relations. Our results may be generalized to multiple observable cases in higher dimensional spaces.
基金Project supported by the National Natural Science Foundation of China (Key Program) (No.10332030)the Natural Science Foundation of Guangdong Province of China (No.04011640)
文摘The principal resonance of Duffing random external excitation was investigated. oscillator to combined deterministic and The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.
基金Supported by National Natural Science Foundation of China under Grant No.11175250
文摘The present work proposes a novel methodology for constructing coarse-grained （CG） models, which aims at minimizing the difference between CG model and the corresponding original system. The difference is defined as a functional of their equilibrium conformationaJ probability densities, then is estimated from equilibrium averages of many independent physical quantities denoted as basis functions. An orthonormalization strategy is adopted to get the independent basis functions from su^ciently preselected interesting physical quantities of the system. Thus the current method is named as probability density matching coarse-graining （PMCG） scheme, which effectively takes into account the overall cha,~acteristics of the original systems to construct CG model, and it is a rtatural improvement of the usual CG scheme wherein some physical quantities are intuitively chosen without considering their correlations. We verify the general PMCG framework in constructing a one-site CG water model from TIP3P model. Both structure of liquids and pressure of the TIP3P water system are found to be well reproduced at the same time in the constructed CG model.
基金supported by the National Natural Science Foundation of China(No.51390493)
文摘Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.
基金supported by the National Key R&D Program of China under Grant No.2025YFB3003603the National Natural Science Foundation of China under Grant Nos.12135002 and 12105209.
文摘By adopting stochastic density functional theory(SDFT)and mixed stochastic-deterministic density functional theory(MDFT)methods,we perform first-principles calculations to predict the shock Hugoniot curves of boron(pressure P=7.9×10^(3)-1.6×10^(6) GPa and temperature T=25-2800 eV),silicon(P=2.6×10^(3)-7.9×10^(5) GPa and T=21.5-1393 eV),and aluminum(P=5.2×10^(3)-9.0×10^(5) GPa and T=25-1393 eV)over wide ranges of pressure and temperature.In particular,we systematically investigate the impact of different cutoff radii in norm-conserving pseudopotentials on the calculated properties at elevated temperatures,such as pressure,ionization energy,and equation of state.By comparing the SDFT and MDFT results with those of other first-principles methods,such as extended first-principles molecular dynamics and path integral Monte Carlo methods,we find that the SDFT and MDFT methods show satisfactory precision,which advances our understanding of first-principles methods when applied to studies of matter at extremely high pressures and temperatures.
基金National Science and Technology Major Project of China(No.2016ZX04003001)。
文摘The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.
基金sponsored by King Abdullah University of Science and Technology(KAUST)the National Natural Science Foundation of China(Grant No.91841302)。
文摘We propose a new flame index for the transported probability density function(PDF) method. The flame index uses mixing flux projections of Lagrangian particles on mixture fraction and progress variable directions as the metrics to identify the combustion mode, with the Burke-Schumann solution as a reference. A priori validation of the flame index is conducted with a series of constructed turbulent partially premixed reactors. It indicates that the proposed flame index is able to identify the combustion mode based on the subgrid mixing information. The flame index is then applied the large eddy simulation/PDF datasets of turbulent partially premixed jet flames. Results show that the flame index separate different combustion modes and extinction correctly. The proposed flame index provides a promising tool to analyze and model the partially premixed flames adaptively.
基金supported by the National Natural Science Foundation of China(Nos.22393912,22425301,22373091,22173088)the AI for Science Foundation of Fudan University(No.Fudan X24AI023)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB0450101).
文摘Machine learning(ML)has demon-strated significant potential in en-hancing the predictive capabilities of density functional theory methods.In this study,we develop an ML model for correcting B3LYP-D,a density functional approximation that incorporates dispersion correc-tions for non-covalent interactions.This model utilizes semilocal elec-tron density descriptors,and is trained with accurate reference data for both relative and ab-solute energies.Extensive benchmark tests reveal that the ML correction substantially en-hances the generalization ability of the B3LYP-D functional,improving the predictions of at-omization and dissociation energies for complex molecular systems.It retains the accuracy of B3LYP-D in predicting reaction barrier heights and non-covalent interactions while enabling efficient,fully self-consistent field calculations.This work signifies a promising advancement in the development of ML-corrected functionals that surpass the performance of traditional B3LYP-D.
基金the financial support from National Natural Science Foundation of China (No. 21503097)Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX23_3905)。
文摘Metal-organic framework(MOF) has been widely applied in photocatalysis, which is significant for addressing energy crises and environmental issues. Based on density functional theory calculations,the performances of Cu-BTC, a copper-based MOF, and its derivatives Cu TM-BTC via the substitution of transition metal(TM) elements at the Cu site for photocatalytic overall water splitting(POWS) have been studied. POWS of Cu-BTC suffers from the sluggish hydrogen evolution reaction due to the large overpotential of 2.02 V and limited solar utilization due to a wide HOMO-LUMO gap of 4.11 e V. Via TM substitution, the HOMO-LUMO gap narrows but still satisfies the redox potentials when taken 3d-TM of Cr, Fe, Co or Ni, 4d-TM of Rh or Pd, or 5d-TM of Re or Pt into consideration, benefiting for the light absorption. Furthermore, Cr and Re could serve as active sites for hydrogen evolution with remarkably lowered overpotentials of 0.79 V and 0.28 V, respectively;similarly, oxygen evolution activities could be enhanced by Fe, Co and Rh because of their reduced overpotentials which are less than 0.5 V. Therefore,our findings pave guidance for designing Cu-BTC derivatives in overall water splitting.
