Molecular simulation study of the microstructures and properties of pyridinium ionic liquid[HPy][BF_(4)]mixed with acetonitrile

The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

Structure complexity is the primary driver of functional diversity in the temperate forests of northeastern China

Background:Assessing functional diversity to identify its spatial patterns and drivers is an important step towards understanding the adaptive capacity of ecosystems to environmental change. However, until now, these mechanisms were poorly understood in the temperate forests of northeastern China, which prevented the development of new management methods aimed at increasing functional trait diversity and thus ecological resilience.Methods:In this study, we mapped functional diversity distributions using a Kriging Interpolation Method. A specific random forest model approach was adopted to test the importance ranking of 18 variables in explaining the spatial variation of functional diversity. Three piecewise structural equation models (pSEMs) with forest types as random effects were constructed for testing the direct effects of climate, and the indirect effects of stand structure on functional diversity across the large study region. Specific causal relationships in each forest type were also examined using 15 linear structural equation models.Results:Although environmental filtering by climate is important, stand structure explains most of the functional variation of the forest ecosystems in northeastern China. Our study thus only partially supports the stressdominance hypothesis. Several abundant species determine most of the functional diversity, which supports the mass ratio hypothesis.Conclusions:Our results suggest that forest management aimed at increasing structural complexity can contribute to increased functional diversity, especially regarding the mixing of coniferous and broad-leaved tree species.

Extreme value distributions of mixing two sequences with different MDA＇s

Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.

QCD Predictions for Spin Dependence of Parton Distributions

We introduce the polarized valon distributions to describe the spin dependence of parton distributions.The polarized valon distributions in the proton and polarized parton distributions inside the valon can help to obtain polarized parton distribution in a proton. In order to be able to obtain the spin contribution of sea quarks, we need to improve the valon model We employ the Bernstein polynomial averages to obtain the unknown parameters which exist in our calculations. Our results for the polarized proton structure function, xg1p, are in good agreement with the experimental data for some values of Q2.

Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.

Load distributions of some classic DHTs

The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.

Effects of Landau damping and collision on stimulated Raman scattering with various phase-space distributions

Stimulated Raman scattering(SRS)is one of the main instabilities affecting success of fusion ignition.Here,we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations.The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated,which is consistent with our theoretical analysis quantitatively.Maxwellian distribution,flattened distribution,and bi-Maxwellian distribution are studied in detail,which represent three typical stages of SRS.We also demonstrate the effects of plateau width,hot-electron fraction,hot-to-cold electron temperature ratio,and collisional damping on the Landau damping and growth rate.They gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.

More general results on mixed extreme value distributions

The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz（x） does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.

A class of not max-stable extreme value distributions

The sequences {Zi , 1≤i≤n}, n≥1 have multi-nomial distribution among i.i.d. random variables {X1, , i≥1}, {X2, , ,n i i i≥1}, …, {Xm , i≥1}. The extreme value distribution GZ(x) of this particular triangular array of i.i.d. random variables Z1, , Z2, , …, ,i n n r ?1 Zn is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) GZ (x) = ,n ∏Φα Ai(x)×Φαr (x); i i=1 r ?1 r?1 ii) GZ (x) = ∏Ψα Ai(x)×Ψαr (x); iii) GZ (x) = ∏Λ Ai(λix)×Λ(x), r≥2, 0<α1≤α2≤…≤αr and λi∈(0,1] for i, 1≤i≤r?1 which occur if i i=1 i=1 Fj, …, Fm belong to the same MDA.

Single point velocity distributions in homogeneous isotropic turbulence

The starting point for this paper lies in the results obtained by Tatsumi （2004） for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi （2004） leads to an exact ＂analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view, and obtains a new complete set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier-Stokes equations are presented. The comparison with former theory was also made. The origin of non-Caussian character could be deduced from the above exact solutions.

Intrinsic Rationale of Functional Distribution and Quantitative Distribution--International Experience and Reference of Income Distribution

The issue of income distribution in the modern sense emerged with the creation of the capitalist mode of production-a process characterized by income gaps, at first widening, then narrowing, and widening once again. In the classical economic stage featuring dual economy, income distribution was dominated by capital due to scarce capital and cheap labor, which led to widening income gaps. Entering the neoclassical economic stage, income distribution was dominated by the game between capital and labor due to diminishing marginal return to capital and relatively scarce labor, which led to the growing share of labor compensation and narrowing income gaps. Yet since the 1970s, the deepening of financialization of capital has once again magnified the effect of capital-dominated income distribution, which, together with working class polarization, led to another round of widening income gaps. An observation of the long-term evolution of world economic development and income distribution gives us a clearer view on the intrinsic rationale of change in income distribution: The mode of production determines the mode of distribution and functional distribution shares intrinsic consistency with quantitative distribution.

Study on Temporal-spatial Distribution of Heavy Rain and Rainstorm in Different Functional Areas of Chongqing

To discuss response ability of five functional areas to rainstorm flood in Chongqing,by taking 8 districts（ counties） as research object,monthly occurrence times of heavy rain and rainstorm in different functional areas over the years and appearance month of the maximum rainfall were conducted statistics. Results showed that frequency distribution of heavy rain in whole year in different functional areas was different,but it was similar in the same functional zone. Temporal-spatial distribution of rainstorm was more independent,and there were different performances in various districts of each functional area. In urban functional core area and urban functional expansion area,rainstorm times was more,and the maximum precipitation was larger. In urban development new district,rainstorm times and the maximum precipitation were relatively smaller in whole Chongqing. In ecological conservation development area of northeast Chongqing,rainstorm duration was longer,and we needed prevention and control during June- September. In ecological protection area of southeast Chongqing,although rainstorm occurrence times was the most in Chongqing,the heavy rainstorm was less.

Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet

This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

Effects of power on ion behaviors in radio-frequency magnetron sputtering of indium tin oxide(ITO)

This study delves into ion behavior at the substrate position within RF magnetron discharges utilizing an indium tin oxide(ITO)target.The positive ion energies exhibit an upward trajectory with increasing RF power,attributed to heightened plasma potential and initial emergent energy.Simultaneously,the positive ion flux escalates owing to amplified sputtering rates and electron density.Conversely,negative ions exhibit broad ion energy distribution functions(IEDFs)characterized by multiple peaks.These patterns are clarified by a combination of radiofrequency oscillation of cathode voltage and plasma potential,alongside ion transport time.This elucidation finds validation in a one-dimensional model encompassing the initial ion energy.At higher RF power,negative ions surpassing 100 e V escalate in both flux and energy,posing a potential risk of sputtering damages to ITO layers.

Experimental studies of H_(2)/Ar plasma in a cylindrical inductive discharge with an expansion region

The electrical parameters of H_(2)/Ar plasma in a cylindrical inductive discharge with an expansion region are investigated by a Langmuir probe,where Ar fractions range from 0%to 100%.The influence of gas composition and pressure on electron density,the effective electron temperature and the electron energy probability functions(EEPFs)at different spatial positions are present.In driver region,with the introduction of a small amount of Ar at 0.3 Pa,there is a rapid increase in electron density accompanied by a decrease in the effective electron temperature.Additionally,the shape of the EEPF transitions from a three-temperature distribution to a bi-Maxwellian distribution due to an increase in electron-electron collision.However,this phenomenon resulting from the changes in gas composition vanishes at 5 Pa due to the prior depletion of energetic electrons caused by the increase in pressure during hydrogen discharge.The EEPFs for the total energy in expansion region is coincident to these in the driver region at 0.3 Pa,as do the patterns of electron density variation between these two regions for differing Ar fractions.At 5 Pa,as the discharge transitions from H_(2)to Ar,the EEPFs evolved from a bi-Maxwellian distribution with pronounced low energy electrons to a Maxwellian distribution in expansion region.This evolve may be attributed to a reduction in molecular vibrational excitation reactions of electrons during transport and the transition from localized electron dynamics in hydrogen discharge to non-localized electron dynamics in argon discharge.In order to validate the experimental results,we use the COMSOL simulation software to calculate electrical parameters under the same conditions.The evolution and spatial distribution of the electrical parameters of the simulation results agree well with the trend of the experimental results.

Approximating the Radial Distribution Function of the Electron in a Hydrogen Atom by a Normal Distribution Suggests That Magnetic Confinement Fusion Would Be Less Energy Efficient than Inertial Confinement Fusion

Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.

Simulation of Haloxylon Ammodendron Stand Basic Diameter Structure Based on Fuzzy Distribution Function

Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting according to the consistency between the characteristics of Fuzzy distribution function and the distribution series of cumulative percentage of stand base diameter, and the fitting precision and effect of Fuzzy distribution function were discussed. The root mean square error RMSE and determination coefficient R2 values showed that Fuzzy-Γ1, Fuzzy-Γ2, Fuzzy-Γ3, Fuzzy-Γ4 had good fitting performance, among which Fuzzy-Γ1 had relatively high fitting precision, and its parameters were closely related to stand age and density, Fuzzy-Γ2 distribution function was the second, and Fuzzy-Γ4 distribution function had the worst fitting effect. By introducing a parameter c from the similarity of four distribution function formulas, a generalized Fuzzy distribution function Fuzzy-Γ5 is obtained. This function shows the highest fitting accuracy. Most of the values of parameter c are near 1 or 2, which shows that the diameter distribution is mainly approximate to Fuzzy-Γ1 and Fuzzy-Γ2.