The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

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.

Density functional theory study of B- and Si-doped carbons and their adsorption interactions with sulfur compounds

Understanding the adsorption interactions between carbon materials and sulfur compounds has far-reaching impacts,in addition to their well-known important role in energy storage and conversion,such as lithium-ion batteries.In this paper,properties of intrinsic B or Si single-atom doped,and B-Si codoped graphene(GR)and graphdiyne(GDY)were investigated by using density functional theory-based calculations,in which the optimal doping configurations were explored for potential applications in adsorbing sulfur compounds.Results showed that both B or Si single-atom doping and B-Si codoping could substantially enhance the electron transport properties of GR and GDY,improving their surface activity.Notably,B and Si atoms displayed synergistic effects for the codoped configurations,where B-Si codoped GR/GDY exhibited much better performance in the adsorption of sulfurcontaining chemicals than single-atom doped systems.In addition,results demonstrated that,after B-Si codoping,the adsorption energy and charge transfer amounts of GDY with sulfur compounds were much larger than those of GR,indicating that B-Si codoped GDY might be a favorable material for more effectively interacting with sulfur reagents.

Langmuir-Schaefer Film Investigation and Density Functional Theory Band Gap Calculations of Calix[n]arene-Para-Aminobenzoic Acid for Drug Nanosensor Application

Calix[n]arenes was utilized to detect PABA,the primary sunscreen component.This study investigates the interaction of calix[4]arene(C4),calix[6]arene(C6),and PABA using the Langmuir method and first-principle density functional theory(DFT).Using the Langmuir-Schaefer(LS)technique,an ultrathin film composed of calix[n]arenes and their complexes with PABA was deposited on various substrates.Based on the Langmuir study,the PABA molecule was bonded to the lower rims of both C4 and C6 with the host-guest ratio of 1:1.All of the LS films formed were then characterized by ultravioletvisible spectroscopy(UV-Vis),Fourier-transform infrared spectroscopy(FTIR)and carbon,hydrogen,nitrogen,sulfur elemental analyzer(CHNS).The band gap reduction obtained in the DFT study denotes the charge transfer interaction with promising reactivity between the calix[n]arenes and PABA.The sensing of PABA by C4 and C6 is successful based on the formation of bonding between them due to the hosts’effective trapping capacity.The outcomes of this study could be applied to drug delivery systems for future pharmaceutical and medical applications.

Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory

Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data.

Solvent effects on Diels-Alder reaction in ionic liquids:A reaction density functional study

Extensive experimental studies have been performed on the Diels-Alder(DA)reactions in ionic liquids(ILs),which demonstrate that the IL environment can significantly influence the reaction rates and selectivity.However,the underlying microscopic mechanism remains ambiguous.In this work,the multiscale reaction density functional theory is applied to explore the effect of 1-butyl-3-methylimidazolium hexafluorophosphate([BMIM][PF_(6)])solvent on the reaction of cyclopentadiene(CP)with acrolein,methyl acrylate,or acrylonitrile.By analyzing the free energy landscape during the reaction,it is found that the polarization effect has a relatively small influence,while the solvation effect makes both the activation free energy and reaction free energy decrease.In addition,the rearrangement of local solvent structure shows that the cation spatial distribution responds more evidently to the reaction than the anion,and this indicates that the cation plays a dominant role in the solvation effect and so as to affect the reaction rates and selectivity of the DA reactions.

Robustness of the octupole collectivity in 144Ba within the cranking covariant density functional theory in 3D lattice

The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).

Local thermal conductivity of inhomogeneous nano-fluidic films:A density functional theory perspective

Combining the mean field Pozhar-Gubbins(PG)theory and the weighted density approximation,a novel method for local thermal conductivity of inhomogeneous fluids is proposed.The correlation effect that is beyond the mean field treatment is taken into account by the simulation-based empirical correlations.The application of this method to confined argon in slit pore shows that its prediction agrees well with the simulation results,and that it performs better than the original PG theory as well as the local averaged density model(LADM).In its further application to the nano-fluidic films,the influences of fluid parameters and pore parameters on the thermal conductivity are calculated and investigated.It is found that both the local thermal conductivity and the overall thermal conductivity can be significantly modulated by these parameters.Specifically,in the supercritical states,the thermal conductivity of the confined fluid shows positive correlation to the bulk density as well as the temperature.However,when the bulk density is small,the thermal conductivity exhibits a decrease-increase transition as the temperature is increased.This is also the case in which the temperature is low.In fact,the decrease-increase transition in both the small-bulk-density and low-temperature cases arises from the capillary condensation in the pore.Furthermore,smaller pore width and/or stronger adsorption potential can raise the critical temperature for condensation,and then are beneficial to the enhancement of the thermal conductivity.These modulation behaviors of the local thermal conductivity lead immediately to the significant difference of the overall thermal conductivity in different phase regions.

Study the Structural, Electronic, Optical Properties of CZTS Compound after Doping Ba at Zn Site and Si at Sn Site Using Density Functional Theory (DFT)

The structural, electronic, and optical properties of Cu2Zn1−xBaxSn1−ySiyS4 compounds have been calculated using GGA-PBE function within the framework of Density Functional Theory (DFT). In the present work, lattice parameters remained the same, that is tetragonal crystal structure for 0% and 100% doping concentration. The electronic band gap of Cu2Zn1−xBaxSn1−ySiyS4 compounds has been gradually increased for continuous increment of doping concentration where the highest electronic band gap is 1.117 eV for Cu2BaSiS4 structure. Moreover, the band gap changes from direct to indirect band gap with the increase of doping concentration in the parent compound. The absorption coefficient has been found to be high (> 104 cm−1) in UV-region for all the doping concentration which makes the studied compound as a potential candidate of absorber layer in the UV detector. The theoretical study of the effect of double doping in the CZTS compound is very interesting for improving the quality of it and it would be a reference for the theoretical and experimental researchers.

Calculation of microscopic nuclear level densities based on covariant density functional theory

In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.

Effects of zinc on χ-Fe_(5)C_(2) for carbon dioxide hydrogenation to olefins:Insights from experimental and density function theory calculations

Production of light olefins from CO_(2), the primary greenhouse gases, is of great importance to mitigate the adverse effects of CO_(2) emission on environment and to supply the value-added products from nonpetroleum resource. However, development of robust catalyst with controllable selectivity and stability remains a challenge. Herein, we report that Zn-promoted Fe catalyst can boost the stable and selective production of light olefins from CO_(2). Specifically, the Zn-promoted Fe exhibits a highly stable activity and olefin selectivity over 200 h time-on-stream compared to the unpromoted Fe catalyst, primarily owing to the preservation of active χ-Fe_(5)C_(2) phase. Structural characterizations of the spent catalysts suggest that Zn substantially regulates the content of iron carbide on the surface and suppresses the reoxidation of bulk iron carbide during the reaction. DFT calculations confirm that adsorption of surface carbon atoms and graphene-like carbonaceous species are not thermochemically favored on Zn-promoted Fe catalyst. Carbon deposition by CAC coupling reactions of two surface carbon atoms and dehydrogenation of CH intermediate are also inhibited. Furthermore, the effects of Zn on antioxidation of iron carbide were also investigated. Zn favored the hydrogenation of surface adsorbed oxygen atoms to H_(2)O and the desorption of H_(2)O, which reduces the possibility of surface carbide being oxidized by the chemisorbed oxygen.

Investigation of the structural, electronic and mechanical properties of CaO–SiO_(2) compound particles in steel based on density functional theory

CaO–SiO_(2)compounds compromise one of the most common series of oxide particles in liquid steels, which could significantly affect the service performance of the steels as crack initiation sites. However, the structural, electronic, and mechanical properties of the compounds in CaO–SiO_(2)system are still not fully clarified due to the difficulties in the experiments. In this study, a thorough investigation of these properties of CaO–SiO_(2)compound particles in steels was conducted based on first-principles density functional theory. Corresponding phases were determined by thermodynamic calculation, including gamma dicalcium silicate(γ-C2S), alpha-prime(L) dicalcium silicate(αL′-C2S), alpha-prime(H) dicalcium silicate(αH′-C2S), alpha dicalcium silicate(α-C2S), rankinite(C3S2), hatrurite(C3S), wollastonite(CS), and pseudowollastonite(Ps-CS). The results showed that the calculated crystal structures of the eight phases agree well with the experimental results. All the eight phases are stable according to the calculated formation energies, and γ-C2S is the most stable. O atom contributes the most to the reactivity of these phases. The Young’s modulus of the eight phases is in the range of 100.63–132.04 GPa. Poisson’s ratio is in the range of0.249–0.281. This study provided further understanding concerning the CaO–SiO_(2)compound particles in steels and fulfilled the corresponding property database, paving the way for inclusion engineering and design in terms of fracture-resistant steels.

Density Functional Theory Study of Marine Polybrominated Diphenyl Ethers in Anaerobic Degradation

Polybrominated diphenyl ethers(PBDEs)are a kind of serious pollutants in the ocean.Biodegradation is considered as an economical and safe way for PBDEs removal and reductive debromination dominates the initial pathway of anaerobic degradation.On the basis of experimental study,Octa-BDE 197,Hepta-BDE 183,Hexa-BDE 153,Penta-BDE 99 and Tetra-BDE 47 were selected as the initial degradation objects,and their debromination degradation were studied using density functional theory.The structures were optimized by Gaussian 09 program.Furthermore,the molecular orbitals and charge distribution were analyzed.All C-Br bond dissociation energies at different positions including ortho,meta and para bromine atoms were calculated and the sequence of debromination was obtained.There is a close relationship between molecular structure,charge,molecular orbital and C-Br bond.All PBDEs exhibited similar debromination pathways with preferential removal of meta and para bromines.

Ultra-deep Removal of Metal Ions from Coal Tar by Complexation:Experimental Studies and Density Functional Theory Simulations

As one of the important aspects of upgrading coal tar,the ultra-deep removal of metal ions via the complexation method was investigated by screening four complexing agents and performing density functional theory(DFT)simulations.Analysis of the compositions and contents of the metallic compounds in the coal tar revealed that the main components were iron and calcium naphthenates.Direct filtration reduced the mechanical impurity content from 0.24%to 0.0752%,indicating that most of the large particles could be easily removed.Among the four complexing agents,namely,acetic acid,oxalic acid,citric acid,and ethylenediaminetetraacetic acid,oxalic acid exhibited the best demetallization performance.The DFT simulations suggested that the high performance of oxalic acid originated from its 1:1 coordination mode,rigid dicarboxyl structure,and greater binding energy.

Direct atomic-level insight into oxygen reduction reaction on size-dependent Pt-based electrocatalysts from density functional theory calculations

Developing novel oxygen reduction reaction(ORR)catalysts with high activity is urgent for proton exchange membrane fuel cells.Herein,we investigated a group of size-dependent Pt-based catalysts as promising ORR catalysts by density functional theory calculations,ranging from single-atom,nanocluster to bulk Pt catalysts.The results showed that the ORR overpotential of these Pt-based catalysts increased when its size enlarged to the nanoparticle scale or reduced to the single-atom scale,and the Pt_(38)cluster had the lowest ORR overpotential(0.46 V)compared with that of Pt_(111)(0.57 V)and single atom Pt(0.7 V).Moreover,we established a volcano curve relationship between the ORR overpotential and binding energy of O*(ΔE_(O*),confirming the intermediate species anchored on Pt38cluster with suitable binding energy located at top of volcano curve.The interaction between intermediate species and Pt-based catalysts were also investigated by the charge distribution and projected density of state and which further confirmed the results of volcano curve.

Hydrogen evolution reaction between small-sized Zr_(n)(n=2–5)clusters and water based on density functional theory

Density functional theory(DFT)is used to calculate the most stable structures of Zr_(n)(n=2-5)clusters as well as the adsorption energy values of Zr_(n)(n=2-5)clusters after adsorbing single water molecule.The results reveal that there is a significant linear relationship between the adsorption energy values and the energy gaps of the Zr_(n)(n=2-5)clusters.Furthermore,the calculations of the reaction paths between Zr_(n)(n=2-5)and single water molecule show that water molecule can react with Zr_(n)(n=2-5)clusters to dissociate,producing hydrogen,and O atoms mix with the clusters to generate Zr_(n)O(n=2-5),all of which are exothermic reactions.According to the released energy,the Zr4 cluster is the most efficient in Zr_(n)(n=2-5)clusters reacting with single water molecule.The natural population analysis(NPA)and density of states(DOS)demonstrate the production of hydrogen and orbital properties in different energy ranges,respectively,jointly forecasting that Zr_(n)O(n=2-5)will probably continue to react with more water molecules.Our findings contribute to better understanding of Zr's chemical reactivity,which can conduce to the development of effective Zr-based catalysts and hydrogen-production methods.

Spatial Agglomeration and Diffusion of Population Based on a Regional Density Function Approach:A Case Study of Shandong Province in China

Population density functions have long been used to describe the spatial structure of regional population distributions.Several studies have been conducted to examine the population distribution in Shandong Province,China,but few have applied regional density functions to the analysis.Therefore,based on the 2000,2010,and 2020 population censuses,this study used monocentric and polycentric regional density functions to study the characteristics of population agglomeration and diffusion in Shandong.This is followed by an in-depth discussion based on population growth rate data and hot-and cold-spot analyses.The results showed that the Shandong Province population was spatially unevenly distributed.Population growth rates were higher in urban centers and counties,with more significant changes in population size in the eastern coastal areas than in the inland areas.As verified in this study,the logarithmic form of the single-center regional density function R2 was greater than 0.8,which was in line with the population spatial structure of Shandong Province.During the study period,the estimated population density of the regional center and the absolute value of the regional population density gradient both increased,indicating a clear and increasing trend of centripetal agglomeration of regional centers over the study period.Overall,the R2 value of the multicenter region density function was higher than that of the single-center region density function.The polycentric regional density function showed that the population density gradient of some centers had a downward trend,which reflected the spatial development trend of outward diffusion in these centers.Meanwhile,the variation in the estimated population density and the population density gradient exhibited differences in the central population distribution patterns at different levels.

Density functional theory study of influence of impurity on electronic properties and reactivity of pyrite

The electronic property of pyrite supercell containing As,Se,Te,Co or Ni hetero atoms were calculated using density functional theory（DFT）,and the reactivities of pyrite with oxygen and xanthate were discussed by frontier orbital methods.The cell volume expands due to the presence of impurity.Co and Ni mainly affect the bands near Fermi levels,while As mainly affects the shallow and deep valence bands,and Se and Te mainly affect the deep valence bands.Electronic density analysis suggests that there exists a strong covalent interaction between hetero atom and its surrounding atoms.By frontier orbital calculation,it is suggested that As,Co and Ni have greater influence on the HOMO and LUMO of pyrite than Se and Te.In addition,pyrite containing As,Co or Ni is easier to oxidize by oxygen than pyrite containing Se or Te,and pyrite containing Co or Ni has greater interaction with collector.These are in agreement with the observed pyrite practice.

Density functional theory study on natural hydrophobicity of sulfide surfaces

Adsorption of water on sulfide surfaces and natural floatability of sulfide minerals were studied using density functional theory （DFT） method. All computational models were built in a vacuum environment to eliminate the effects of oxygen and other factors. H2O molecule prefers to stay with pyrite and sphalerite surfaces rather than water, whereas for galena, chalcocite, stibnite, and molybdenite, H2O molecule prefers to stay with water rather than the mineral surfaces. On the other hand, pyrite surface favors N2 more than water, while sphalerite surface cannot adsorb N2. These results show that galena, stibnite, chalcocite, and molybdenite are hydrophobic, while sphalerite is hydrophilic. Although pyrite has certain hydrophilicity, it tends to be aerophilic because the reaction of pyrite with H2O is weaker than pyrite with N2. Thus, pyrite, galena, chalcocite, stibnite and molybdenite all have natural floatability.

Density Function Theory Study on Effects of Different Energetic Substituent Groups and Bridge Groups on Performance of Carbon-Linked Ditetrazole 2N-Oxides

Based on the parent tetrazole 2N-oxide, six series of novel carbon-linked ditetrazole 2N- oxides with different energetic substituent groups （-NH2, -Na, -NO2, NF2, -NHNO2） and energetic bridge groups （-CH2-, -CH2-CH2-, -NH-, -N=N-, -NH-NH-） were designed. The overall performance and the effects of different energetic substituent groups and energetic bridge groups on the performance were investigated by density functional theory and electrostatic potential methods. The results showed that most of designed compounds have oxygen balance around zero, high heats of formation, high density, high energy, and acceptable sensitivity, indicating that tetrazole N-oxide is a useful parent energetic compound employed for obtaining high energy compounds, even only combined with some very common energetic substituent groups and bridge groups. Comprehensively considering the effects on energy and sensitivity, the -NO2, -NF2, -NH- and-NH-NH- are appropriate substituent groups for combining tetrozale N-oxide to design new energetic compounds, while -NH2, -Na, -CH2-CH2-, and -N=N- are inappropriate.

Density Functional Study of AunCo （n=1-7）

Cobalt-doped gold clusters AunCo （n=1-7） are systematically investigated for the possible stable geometrical configurations and relative stabilities of the lowest-lying isomers using density-functional theory at B3LYP/LanL2DZ level. Several low-lying isomers were determined, and many of them are in electronic configurations with a high spin multiplicity. The results indicate that the ground-state AunCo（n=1-7） clusters adopt a planar structure except for n=7. The stability trend of the AunCo （n=1-7） clusters shows that the Au2Co clusters are magic cluster with high stability.