We employ the Green–Kubo(G-K)and Einstein relations to estimate the self-diffusion coefficients(denoted as D_(G)and D_(E),respectively)in two-dimensional(2D)strongly coupled dusty plasmas(SC-DPs)via equilibrium molec...We employ the Green–Kubo(G-K)and Einstein relations to estimate the self-diffusion coefficients(denoted as D_(G)and D_(E),respectively)in two-dimensional(2D)strongly coupled dusty plasmas(SC-DPs)via equilibrium molecular dynamics(EMD)simulations.D_(G)and D_(E)are computed for a broad domain of screening length(κ)and coupling parameters(Γ)along with different system sizes.It is observed that both D_(G)and D_(E)decrease linearly with increasing Г in warm liquid states and increase with increasingκ.In cold liquid states,the Einstein relation accurately predicts D_(E)in 2D SC-DPs because diffusion motion is close to normal diffusion,but the G-K relation provides overestimations of D_(G),because VACF indicates anomalous diffusion;thus,D_(G)is not accurate.Our new simulation outcomes reveal that D_(G)and D_(E)remain independent of system sizes.Furthermore,our investigations demonstrate that at higher temperatures,D_(G)and D_(E)converge,suggesting diffusion motion close to normal diffusion,while at lower temperatures,these two values diverge.We find reasonable agreement by comparing current and existing numerical,theoretical and experimental data.Moreover,when normalizing diffusion coefficients by the Einstein frequency and testing against the universal temperature scaling law,D_(G)deviates from theoretical curves at low temperatures and κ,whereas D_(E)only disagrees with theory at very smallκ(■0.10).These findings provide valuable insight into diagnosing dust component parameters within 2D DP systems and contribute to the broader understanding of diffusion processes in DP environments.展开更多
Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains ...Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains of the sample can be extracted through a bi- exponential fit to the echo intensity attenuation, which allows the precise determination of the tortuosity of the polyethylene particles. Further exploration comes from the measurements with branched polyethylene particles and it was found that the diffusion in polymer phase contributed significantly to the slow component of the exponential decay curve. 2007 Jing Dai Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.展开更多
The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a g...The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.展开更多
1 INTRODUCTIONKnowledge of the basic transport phenomena of ions in an ion exchange membrane isimportant for the application of such a membrane.Various studies on the developmentof mathematical models for predicting a...1 INTRODUCTIONKnowledge of the basic transport phenomena of ions in an ion exchange membrane isimportant for the application of such a membrane.Various studies on the developmentof mathematical models for predicting and correlating membrane transport rate havebeen published in recent years.More exact estimation of the diffusion coefficientshas been the subject of chief concern in many of these papers.For a bi-ionic systemwith the same valence,Sato et al.gave a method for estimating diffusion coefficients展开更多
Self-diffusion coefficients of exponential-six fluids are studied using equilibrium molecular dynamics simulation technique. Mean-square displacements and velocity autocorrelation functions are used to calculate self-...Self-diffusion coefficients of exponential-six fluids are studied using equilibrium molecular dynamics simulation technique. Mean-square displacements and velocity autocorrelation functions are used to calculate self-diffusion coefficients through Einstein equation and Green-Kubo formula. It has been found that simulation results are in good agreement with experimental data for liquid argon which is taken as exponential-six fluid. The effects of density, temperature and steepness factor for repulsive part of exponential-six potential on self-diffusion coefficients are also investigated. The simulation results indicate that the self-diffusion coefficient of exponential-six fluid increases as temperature increases and density decreases. In addition, the larger self-diffusion coefficients are obtained as the steepness factor increases at the same temperature and density condition.展开更多
A new model for self-diffusion coefficients was proposed based oil both the concepts of molecular free volume and activation energy. The unknown parameters of this model were clearly defined and compared with the Chap...A new model for self-diffusion coefficients was proposed based oil both the concepts of molecular free volume and activation energy. The unknown parameters of this model were clearly defined and compared with the Chapman-Enskog model. At the same time a new method for calculating activation energy was devised and applied to the new model. In addition, the free volume was defined by implementing the generic van der Waals equation of state, the radial distribution function of which was obtained by using the Morsali- Goharshadi empirical formula. Under the same conditions, the new model was better than the original free volume model.展开更多
We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with t...We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.展开更多
Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)at...Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.展开更多
The transversal relaxation time, the effective transversal relaxation time and the water self-diffusion coefficient are evaluated during hemoglobin S polymerization. One homogeneous permanent magnet and one inhomogene...The transversal relaxation time, the effective transversal relaxation time and the water self-diffusion coefficient are evaluated during hemoglobin S polymerization. One homogeneous permanent magnet and one inhomogeneous and portable unilateral magnet with a very strong and constant static magnetic field gradient were utilized. The Carr-Purcell-Meiboom-Gill method was used before and after placing the studied samples 24 hours at 36°C to guarantee the polymerization. The transversal relaxation shows two exponents after polymerization supporting the concept of partially polymerized hemoglobin. The effective transversal relaxation time decreases around 40%, which can be explained by the increase of water self-diffusion coefficient 1.8 times as a main value. This result can be explained considering the effects of the agglutination process on the obstruction and hydration effects in a partially polymerized solution.展开更多
In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration,this paper proposes a system-level calibration method for field condition.Firstly,a 42-dimension ...In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration,this paper proposes a system-level calibration method for field condition.Firstly,a 42-dimension Kalman filter is constructed to reduce impact brought by turntable.Then,a biaxial rotation path is designed based on the accelerometer output model,including orthogonal 22 positions and tilt 12 positions,which enhances gravity excitation on nonlinear coefficients of accelerometer.Finally,sampling is carried out for calibration and further experiments.The results of static inertial navigation experiments lasting 4000 s show that compared with the traditional method,the proposed method reduces the position error by about 390 m.展开更多
We evaluate some series with summands involving a single binomial coefficient(^6k 3k).For example,we prove that■Motivated by Galois theory,we introduce the so-called Duality Principle for irrational series of Ramanu...We evaluate some series with summands involving a single binomial coefficient(^6k 3k).For example,we prove that■Motivated by Galois theory,we introduce the so-called Duality Principle for irrational series of Ramanujan’s type or Zeilberger’s type,and apply it to find 26 new irrational series identities.For example,we conjecture that■where ■for any integer d≡0,1 (mod 4) with (d/k) the Kronecker symbol.展开更多
To minimize the calculation errors in the sound absorption coefficient resulting from inaccurate measurements of flow resistivity,a simple method for determining the sound absorption coefficient of soundabsorbing mate...To minimize the calculation errors in the sound absorption coefficient resulting from inaccurate measurements of flow resistivity,a simple method for determining the sound absorption coefficient of soundabsorbing materials is proposed.Firstly,the sound absorption coefficients of a fibrous sound-absorbing material are measured at two different frequencies using the impedance tube method.Secondly,utilizing the empirical formulas for the wavenumber and acoustic impedance in the fibrous material,the flow resistivity and porosity of the sound-absorbing materials are calculated using the MATLAB cycle program.Thirdly,based on the values obtained through reverse calculations,the sound absorption coefficient,the real and the imaginary parts of the acoustic impedance of the sound-absorbing material at different frequencies are theoretically computed.Finally,the accuracy of these theoretical calculations is verified through experiments.The experimental results indicate that the calculated values are basically consistent with the measured values,demonstrating the feasibility and reliability of this method.展开更多
This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the beh...This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.展开更多
The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coeff...The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coefficient.When determining the spherical harmonic coefficients using the least squares method,it is essential to analyze the ordering pattern of these coefficients and their positions(e.g.,indices)in the vector or matrix.A systematic analysis on the type of coefficient arrangement is presented in this paper.Moreover,the index algorithm for each coefficient ordering pattern is provided.Additionally,the structure of the normal equation matrix with different coefficient arrangement patterns is analyzed.Based on the analysis and the algorithm presented in this paper:(1)we can calculate the index of each coefficient in the vector or matrix of the normal equation;(2)we can change the structure of the normal equation matrix of the Earth’s gravity field from one type of coefficient arrangement to another.Furthermore,(3)we can directly combine different structures of the normal equation matrix,calculated from different types of gravity satellite missions,to form combined normal equations.This approach is beneficial for the determination of Earth’s gravitational model using multi-type observation data.展开更多
Focusing on the ultralow expansion functionality of the crystalized glass containing the cordierite crystal phase with the molar composition 20.7MgO·20.7Al_(2)O_(3)·51.6SiO_(2)·7.0TiO_(2),we systematica...Focusing on the ultralow expansion functionality of the crystalized glass containing the cordierite crystal phase with the molar composition 20.7MgO·20.7Al_(2)O_(3)·51.6SiO_(2)·7.0TiO_(2),we systematically investigated impacts of thermal treatment protocols on T dependence of coefficients of thermal expansion(CTE).Except for the phase compositions,morphology is identified as another important factor to control the T dependence of CTE.By using X-ray diffraction and scanning electron microscope,various modes of T dependence of CTE for crystallized glasses are ascribed to their different phase compositions and microstructure with finely dispersed nanoparticles.These understanding contributes to the further modification of CTE of the crystalized glass by altering their thermal treatment scenarios.展开更多
Rockfall kinematic characteristics exhibit significant randomness and are influenced by factors such as rock mass properties,slope morphology,impact angle,and slope materials.Accurately determining the key parameters ...Rockfall kinematic characteristics exhibit significant randomness and are influenced by factors such as rock mass properties,slope morphology,impact angle,and slope materials.Accurately determining the key parameters of rockfall movement is critical for understanding motion patterns and effectively preventing and controlling rockfall hazards.In this study,a monitoring system consisting of selfdeveloped inertial navigation equipment,high-speed cameras,and an unmanned aerial vehicle was used to conduct onsite motion tests involving four differently shaped rock specimens on three types of slopes(bedrock,detritus,and clast bedding).The selfdeveloped inertial navigation system integrated a highdynamic-range accelerometer(±400 g)and a shockresistant gyroscope(±4000°/s),capable of robustly collecting data during the test.The data collected from these tests were processed to extract key kinematic parameters such as velocity,trajectory,restitution coefficients,and friction coefficients.The test results demonstrated that the inertial navigation system accurately recorded the acceleration and angular velocity of the rocks during motion,with these measurements closely aligning with the field data.The normal and tangential restitution coefficients were found to be influenced primarily by the slope material and impact angle,with higher normal restitution coefficients observed for low-angle impacts.The normal restitution coefficients ranged from 0.35 to 0.86,whereas the tangential restitution coefficients ranged from 0.46 to 0.91,depending on the slope materials.Additionally,the sliding friction coefficient was calculated to be between 0.66 and 0.78,whereas the rolling friction coefficient for the slab-shaped specimen was determined to be 0.53.These findings provide valuable data for improving the accuracy of rockfall trajectory predictions and the design of protective structures.展开更多
Wind tunnel experiment and CFD(computational fluid dynamics)simulation with LES(large eddy simulation)have been conducted to investigate the characteristics of peak wind force coefficients of porous panels mounted on ...Wind tunnel experiment and CFD(computational fluid dynamics)simulation with LES(large eddy simulation)have been conducted to investigate the characteristics of peak wind force coefficients of porous panels mounted on the roofs of high-rise buildings.First,aerodynamic modelling of porous panels was discussed.The relation between pressure loss coefficient and porosity was obtained.Then,a wind tunnel experiment was conducted to measure the wind forces(net wind pressures)acting on solid and porous panels mounted on the roof of a high-rise building.Because it was difficult to measure the pressures on both sides of thin,porous panel at the same location simultaneously,we proposed to use the roof edge pressures near the panel for the panel’s inside-surface pressures.This experimental method was validated by a CFD simulation reproducing the wind tunnel experiment.The characteristics of peak wind force coefficients of porous panels mounted on the roofs of high-rise buildings were made clear.Finally,positive and negative peak wind force coefficients for designing the rooftop porous panels were proposed.展开更多
In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperat...In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.展开更多
A comprehensive understanding of exact seismic P-wave reflection and transmission(R/T)coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration....A comprehensive understanding of exact seismic P-wave reflection and transmission(R/T)coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration.Nonetheless,scant attention has been devoted in previous literature to the investigation of stress-dependent exact R/T coefficients in horizontal transversely isotropic(HTI)media,characterized by a horizontal symmetry axis,at such interfaces.Addressing this scholarly gap,we present exact R/T coefficient formulations specifically tailored to an imperfectly welded contact interface separating two HTI media under the influence of in-situ horizontal stress.We begin by deriving the equation of motion for a stressed HTI medium,utilizing the theoretical framework of acoustoelasticity to examine the impact of in-situ horizontal stress on the overarching elastic properties of HTI media.Precise boundary conditions are then established at the imperfectly welded contact interface by applying generalized stress-strain relationships and linear-slip theory,with the influence of in-situ horizontal stress on the interface further explored through the linear-slip model.By integrating these elements with the seismic wave displacement equation,we derive exact R/T coefficient formulations applicable to an imperfectly welded contact interface between two HTI media.Numerical analyses are conducted to elucidate the effects of in-situ horizontal stress on critical parameters such as rock density,seismic wave velocity,Thomsen-type anisotropy parameters,R/T coefficients,and seismic reflection responses at the imperfectly welded contact interface.Furthermore,the proposed formulations are frequency-dependent,with the imperfectly welded contact interface acting as a frequency-selective filter for both reflected and transmitted waves.Notably,under conditions of sufficiently large incident angles,the sensitivity of R/T coefficients to key influencing factors increases significantly.The derived R/T coefficient formulations and the accompanying numerical results offer valuable insights for fracture characterization,stress-dependent parameter inversion,and in-situ stress detection.展开更多
The present paper investigates the methods for estimating the maximum(positive)and the minimum(negative)peak wind force coefficients on domed free roofs based on the quasi-steady theory and the peak factor method,in w...The present paper investigates the methods for estimating the maximum(positive)and the minimum(negative)peak wind force coefficients on domed free roofs based on the quasi-steady theory and the peak factor method,in which the experimental results obtained from our previous studies(2019,2025)are used.Focus is on the distributions of the peak wind force coefficients along the centerline parallel to the wind direction considering that domed free roof is an axisymmetric body.Empirical formulas are provided to the distributions of mean wind force coefficient,RMS(root mean square)fluctuating wind force coefficient and peak factors as a function of the rise/span ratio of the roof and the turbulence intensity of the approach flow in the along-wind direction at the mean roof height.The proposed methods are validated by the experimental results for the peak wind force coefficients.The methods would provide useful information to structural engineers when estimating the design wind loads on cladding/components of domed free roofs.展开更多
基金support of the Fundamental Research Funds for the Central Universities of China(Grant No.2019ZDPY16).
文摘We employ the Green–Kubo(G-K)and Einstein relations to estimate the self-diffusion coefficients(denoted as D_(G)and D_(E),respectively)in two-dimensional(2D)strongly coupled dusty plasmas(SC-DPs)via equilibrium molecular dynamics(EMD)simulations.D_(G)and D_(E)are computed for a broad domain of screening length(κ)and coupling parameters(Γ)along with different system sizes.It is observed that both D_(G)and D_(E)decrease linearly with increasing Г in warm liquid states and increase with increasingκ.In cold liquid states,the Einstein relation accurately predicts D_(E)in 2D SC-DPs because diffusion motion is close to normal diffusion,but the G-K relation provides overestimations of D_(G),because VACF indicates anomalous diffusion;thus,D_(G)is not accurate.Our new simulation outcomes reveal that D_(G)and D_(E)remain independent of system sizes.Furthermore,our investigations demonstrate that at higher temperatures,D_(G)and D_(E)converge,suggesting diffusion motion close to normal diffusion,while at lower temperatures,these two values diverge.We find reasonable agreement by comparing current and existing numerical,theoretical and experimental data.Moreover,when normalizing diffusion coefficients by the Einstein frequency and testing against the universal temperature scaling law,D_(G)deviates from theoretical curves at low temperatures and κ,whereas D_(E)only disagrees with theory at very smallκ(■0.10).These findings provide valuable insight into diagnosing dust component parameters within 2D DP systems and contribute to the broader understanding of diffusion processes in DP environments.
基金This work was supported by the National Natural Science Foundation of China （No. 20490205 and No. 20406017） ； CSC-DAAD （PPP2004） project.
文摘Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains of the sample can be extracted through a bi- exponential fit to the echo intensity attenuation, which allows the precise determination of the tortuosity of the polyethylene particles. Further exploration comes from the measurements with branched polyethylene particles and it was found that the diffusion in polymer phase contributed significantly to the slow component of the exponential decay curve. 2007 Jing Dai Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.
基金supported by the National Natural Science Foundation of China(Grant Nos.11032003 and 11221202)the National Basic Research Program of China(Grant No.2010CB731600)
文摘The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.
基金Supported by the Post-doctoral Foundation of China
文摘1 INTRODUCTIONKnowledge of the basic transport phenomena of ions in an ion exchange membrane isimportant for the application of such a membrane.Various studies on the developmentof mathematical models for predicting and correlating membrane transport rate havebeen published in recent years.More exact estimation of the diffusion coefficientshas been the subject of chief concern in many of these papers.For a bi-ionic systemwith the same valence,Sato et al.gave a method for estimating diffusion coefficients
基金Supported by the National Natural Science Foundation of China(No.29736170).
文摘Self-diffusion coefficients of exponential-six fluids are studied using equilibrium molecular dynamics simulation technique. Mean-square displacements and velocity autocorrelation functions are used to calculate self-diffusion coefficients through Einstein equation and Green-Kubo formula. It has been found that simulation results are in good agreement with experimental data for liquid argon which is taken as exponential-six fluid. The effects of density, temperature and steepness factor for repulsive part of exponential-six potential on self-diffusion coefficients are also investigated. The simulation results indicate that the self-diffusion coefficient of exponential-six fluid increases as temperature increases and density decreases. In addition, the larger self-diffusion coefficients are obtained as the steepness factor increases at the same temperature and density condition.
文摘A new model for self-diffusion coefficients was proposed based oil both the concepts of molecular free volume and activation energy. The unknown parameters of this model were clearly defined and compared with the Chapman-Enskog model. At the same time a new method for calculating activation energy was devised and applied to the new model. In addition, the free volume was defined by implementing the generic van der Waals equation of state, the radial distribution function of which was obtained by using the Morsali- Goharshadi empirical formula. Under the same conditions, the new model was better than the original free volume model.
基金supported by the National Natural Science Foundation of China (Grant No. 51076128)the National High Technology Research and Development Program of China (Grant No. 2009AA05Z107)
文摘We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.
文摘Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.
文摘The transversal relaxation time, the effective transversal relaxation time and the water self-diffusion coefficient are evaluated during hemoglobin S polymerization. One homogeneous permanent magnet and one inhomogeneous and portable unilateral magnet with a very strong and constant static magnetic field gradient were utilized. The Carr-Purcell-Meiboom-Gill method was used before and after placing the studied samples 24 hours at 36°C to guarantee the polymerization. The transversal relaxation shows two exponents after polymerization supporting the concept of partially polymerized hemoglobin. The effective transversal relaxation time decreases around 40%, which can be explained by the increase of water self-diffusion coefficient 1.8 times as a main value. This result can be explained considering the effects of the agglutination process on the obstruction and hydration effects in a partially polymerized solution.
基金supported by the National Natural Science Foundation of China(42276199).
文摘In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration,this paper proposes a system-level calibration method for field condition.Firstly,a 42-dimension Kalman filter is constructed to reduce impact brought by turntable.Then,a biaxial rotation path is designed based on the accelerometer output model,including orthogonal 22 positions and tilt 12 positions,which enhances gravity excitation on nonlinear coefficients of accelerometer.Finally,sampling is carried out for calibration and further experiments.The results of static inertial navigation experiments lasting 4000 s show that compared with the traditional method,the proposed method reduces the position error by about 390 m.
基金Supported by the National Natural Science Foundation of China(Grant No.12371004)。
文摘We evaluate some series with summands involving a single binomial coefficient(^6k 3k).For example,we prove that■Motivated by Galois theory,we introduce the so-called Duality Principle for irrational series of Ramanujan’s type or Zeilberger’s type,and apply it to find 26 new irrational series identities.For example,we conjecture that■where ■for any integer d≡0,1 (mod 4) with (d/k) the Kronecker symbol.
基金National Natural Science Foundation of China(No.51705545)。
文摘To minimize the calculation errors in the sound absorption coefficient resulting from inaccurate measurements of flow resistivity,a simple method for determining the sound absorption coefficient of soundabsorbing materials is proposed.Firstly,the sound absorption coefficients of a fibrous sound-absorbing material are measured at two different frequencies using the impedance tube method.Secondly,utilizing the empirical formulas for the wavenumber and acoustic impedance in the fibrous material,the flow resistivity and porosity of the sound-absorbing materials are calculated using the MATLAB cycle program.Thirdly,based on the values obtained through reverse calculations,the sound absorption coefficient,the real and the imaginary parts of the acoustic impedance of the sound-absorbing material at different frequencies are theoretically computed.Finally,the accuracy of these theoretical calculations is verified through experiments.The experimental results indicate that the calculated values are basically consistent with the measured values,demonstrating the feasibility and reliability of this method.
基金Supported by Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021MA003 and ZR2020MA020).
文摘This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.
基金supported by The National Natural Science Foundation of China(42374004).
文摘The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coefficient.When determining the spherical harmonic coefficients using the least squares method,it is essential to analyze the ordering pattern of these coefficients and their positions(e.g.,indices)in the vector or matrix.A systematic analysis on the type of coefficient arrangement is presented in this paper.Moreover,the index algorithm for each coefficient ordering pattern is provided.Additionally,the structure of the normal equation matrix with different coefficient arrangement patterns is analyzed.Based on the analysis and the algorithm presented in this paper:(1)we can calculate the index of each coefficient in the vector or matrix of the normal equation;(2)we can change the structure of the normal equation matrix of the Earth’s gravity field from one type of coefficient arrangement to another.Furthermore,(3)we can directly combine different structures of the normal equation matrix,calculated from different types of gravity satellite missions,to form combined normal equations.This approach is beneficial for the determination of Earth’s gravitational model using multi-type observation data.
基金Funded by National Natural Science Foundation of China(No.52172007)Jiangsu Science and Technology Innovation Project for Carbon Peaking and Carbon Neutrality(No.BE2022035)。
文摘Focusing on the ultralow expansion functionality of the crystalized glass containing the cordierite crystal phase with the molar composition 20.7MgO·20.7Al_(2)O_(3)·51.6SiO_(2)·7.0TiO_(2),we systematically investigated impacts of thermal treatment protocols on T dependence of coefficients of thermal expansion(CTE).Except for the phase compositions,morphology is identified as another important factor to control the T dependence of CTE.By using X-ray diffraction and scanning electron microscope,various modes of T dependence of CTE for crystallized glasses are ascribed to their different phase compositions and microstructure with finely dispersed nanoparticles.These understanding contributes to the further modification of CTE of the crystalized glass by altering their thermal treatment scenarios.
基金supported by Guizhou Provincial Basic Research Program(Natural Science,Grant No.QKHJC-ZK[2022]YB075)the National Natural Science Foundation of China(Grant No.42067046)+2 种基金the Guizhou Provincial Program on Commercialization of Scientific and Technological Achievements(N0.QKHCG-LH2024-ZD025)the Science and Technology Planning Project of Guiyang City(Grant No.ZKHT[2023]13-10)Undergraduate Training Program for Innovation and Entrepreneurship of Guizhou Province(Project No.S202110657053)。
文摘Rockfall kinematic characteristics exhibit significant randomness and are influenced by factors such as rock mass properties,slope morphology,impact angle,and slope materials.Accurately determining the key parameters of rockfall movement is critical for understanding motion patterns and effectively preventing and controlling rockfall hazards.In this study,a monitoring system consisting of selfdeveloped inertial navigation equipment,high-speed cameras,and an unmanned aerial vehicle was used to conduct onsite motion tests involving four differently shaped rock specimens on three types of slopes(bedrock,detritus,and clast bedding).The selfdeveloped inertial navigation system integrated a highdynamic-range accelerometer(±400 g)and a shockresistant gyroscope(±4000°/s),capable of robustly collecting data during the test.The data collected from these tests were processed to extract key kinematic parameters such as velocity,trajectory,restitution coefficients,and friction coefficients.The test results demonstrated that the inertial navigation system accurately recorded the acceleration and angular velocity of the rocks during motion,with these measurements closely aligning with the field data.The normal and tangential restitution coefficients were found to be influenced primarily by the slope material and impact angle,with higher normal restitution coefficients observed for low-angle impacts.The normal restitution coefficients ranged from 0.35 to 0.86,whereas the tangential restitution coefficients ranged from 0.46 to 0.91,depending on the slope materials.Additionally,the sliding friction coefficient was calculated to be between 0.66 and 0.78,whereas the rolling friction coefficient for the slab-shaped specimen was determined to be 0.53.These findings provide valuable data for improving the accuracy of rockfall trajectory predictions and the design of protective structures.
文摘Wind tunnel experiment and CFD(computational fluid dynamics)simulation with LES(large eddy simulation)have been conducted to investigate the characteristics of peak wind force coefficients of porous panels mounted on the roofs of high-rise buildings.First,aerodynamic modelling of porous panels was discussed.The relation between pressure loss coefficient and porosity was obtained.Then,a wind tunnel experiment was conducted to measure the wind forces(net wind pressures)acting on solid and porous panels mounted on the roof of a high-rise building.Because it was difficult to measure the pressures on both sides of thin,porous panel at the same location simultaneously,we proposed to use the roof edge pressures near the panel for the panel’s inside-surface pressures.This experimental method was validated by a CFD simulation reproducing the wind tunnel experiment.The characteristics of peak wind force coefficients of porous panels mounted on the roofs of high-rise buildings were made clear.Finally,positive and negative peak wind force coefficients for designing the rooftop porous panels were proposed.
基金supported by the National Natural Science Foundation of China(No.11931013)the Natural Science Foundation of Guangxi Province(No.2022GXNSFDA035078)the Foundamental Research Funds for the Central Universities,CHD(No.300102122115).
文摘In this paper,we consider an initial boundary value problem for the nonhomo-geneous heat-conducting magnetohydrodynamic fuids when the viscosityμ,magnetic dif-fusivity v and heat conductivity k depend on the temperature according to μ(0)=°,k(0)=08,v(0)=07,withα,>0,β≥0.We prove the global existence of a unique strong solution provided that ■ is suitably small.In addition,we also get some results of the large-time behavior and exponential decay estimates.
基金the sponsorship of the National Natural Science Foundation of China(42474172,42130810)the Science and Technology Innovation Program of Hunan Province(2022RC1238)+1 种基金the Natural Science Foundation of Hunan Province(2025JJ20036,2023JJ30663)the Changzhou Science and Technology Support Project(CE20235069)。
文摘A comprehensive understanding of exact seismic P-wave reflection and transmission(R/T)coefficients at imperfectly welded or non-welded contact interfaces holds paramount importance in the realm of seismic exploration.Nonetheless,scant attention has been devoted in previous literature to the investigation of stress-dependent exact R/T coefficients in horizontal transversely isotropic(HTI)media,characterized by a horizontal symmetry axis,at such interfaces.Addressing this scholarly gap,we present exact R/T coefficient formulations specifically tailored to an imperfectly welded contact interface separating two HTI media under the influence of in-situ horizontal stress.We begin by deriving the equation of motion for a stressed HTI medium,utilizing the theoretical framework of acoustoelasticity to examine the impact of in-situ horizontal stress on the overarching elastic properties of HTI media.Precise boundary conditions are then established at the imperfectly welded contact interface by applying generalized stress-strain relationships and linear-slip theory,with the influence of in-situ horizontal stress on the interface further explored through the linear-slip model.By integrating these elements with the seismic wave displacement equation,we derive exact R/T coefficient formulations applicable to an imperfectly welded contact interface between two HTI media.Numerical analyses are conducted to elucidate the effects of in-situ horizontal stress on critical parameters such as rock density,seismic wave velocity,Thomsen-type anisotropy parameters,R/T coefficients,and seismic reflection responses at the imperfectly welded contact interface.Furthermore,the proposed formulations are frequency-dependent,with the imperfectly welded contact interface acting as a frequency-selective filter for both reflected and transmitted waves.Notably,under conditions of sufficiently large incident angles,the sensitivity of R/T coefficients to key influencing factors increases significantly.The derived R/T coefficient formulations and the accompanying numerical results offer valuable insights for fracture characterization,stress-dependent parameter inversion,and in-situ stress detection.
文摘The present paper investigates the methods for estimating the maximum(positive)and the minimum(negative)peak wind force coefficients on domed free roofs based on the quasi-steady theory and the peak factor method,in which the experimental results obtained from our previous studies(2019,2025)are used.Focus is on the distributions of the peak wind force coefficients along the centerline parallel to the wind direction considering that domed free roof is an axisymmetric body.Empirical formulas are provided to the distributions of mean wind force coefficient,RMS(root mean square)fluctuating wind force coefficient and peak factors as a function of the rise/span ratio of the roof and the turbulence intensity of the approach flow in the along-wind direction at the mean roof height.The proposed methods are validated by the experimental results for the peak wind force coefficients.The methods would provide useful information to structural engineers when estimating the design wind loads on cladding/components of domed free roofs.
