Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.

Second-Order Potentials and Forces for Two-Dimensional Diffraction Problem of Finite Water Depth

-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.

Second-order two-scale analysis and numerical algorithms for the hyperbolic–parabolic equations with rapidly oscillating coefficients

We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.

Effect of Spatial Dimension and External Potential on Joule-Thomson Coefficients of Ideal Bose Gases

Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity,the analytical expressions of the Joule-Thomson coefficient (JTC) for an ideal Bose gas are derived in n-dimensionalpotential. The effect of the spatial dimension and the external potential on the JfC axe discussed, respectively. Theseresults show that: (ⅰ) For the free ideal Bose gas, when n/s ≤ 2 (n is the spatial dimension, s is the momentum indexin the relation between the energy and the momentum), and T →T_C (T_C is the critical temperature), the JTC canobviously improve by means of changing the throttle valve's shape and decreasing the spatial dimension of gases. (ⅱ)For the inhomogeneous external potential, the discriminant △= [1-∏_(i=1)~n (kT/ε_i)^(1/t_i) Γ(1/ti +1)] (κ is the BoltzmannConstant, T is the thermodynamic temperature, ε is the external field's energy), is obtained. The potential makes theJTC increase when △> 0, on the contrary, it makes the JTC decrease when △<0. (ⅲ) In the homogenous strongexternal potential, the JTC gets the maximum on the condition of κT/ε_i<<1.

A VARIATIONAL METHOD FOR COMPUTING POTENTIAL COEFFICIENTS USING DIFFERENT TYPES OF GRAVIMETRIC DATA

In this paper,a variational method is presented for solving theclassical gravimetric,satellite gravimetric and satellite altimetric mixed typeboudary value problem to obtain the potential coefficients.According to thisprinciple,classical gravimetric data（height measured by geometric levelling orheight triangulation）,satellite gravimetric data（height measured by satellitegeodesy technique）and satellite altimetric data can be used jointly to calculate thepotential coefficients.

Estimating aquifer transmissivity using Dar-Zarrouk parameters to delineate groundwater potential zones in Alluri Seetharama Raju District,Andhra Pradesh, India

This study aimed to explore groundwater potential zones in the EGMB of Alluri Seetharama Raju district, Andhra Pradesh, India, for drinking and agriculture purposes. To achieve this goal, 72 Vertical Electrical Soundings(VES) were conducted using the Schlumberger electrode configuration. The resistivity sounding data were analyzed to determine the aquifer thickness, basement depth, Dar-Zarrouk parameters,and aquifer transmissivity. Spatial distribution maps were generated for these parameters to understand the subsurface formation. The analysis revealed a linear groundwater potential zone(8.46 km~2) in the eastern part of the study area, extending in the NNE-SSW direction for 9.6 km. Six VES locations(P24, P27, P29,P30, P33, and P38) in this zone exhibit good potential(>30 m aquifer thickness), while the three VES locations(OP19, P5, and P46) in the central region are recommended for drilling bore wells. Additionally,moderate aquifer thickness(20–30 m) are identified in other VES locations(OP14, OP20, P4, P10, P12,P13, P15, P17, P18, P31, P46, and P50) along streams in the western and central part of the area, which can yield reasonable quantities of water. This information is useful for groundwater exploration and watershed management to meet the demands of tribal population in the study area.

A Multi－Square－Well Potential Model and Its Application in Calculating the Second Virial Coefficient

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Experimental study of sheath potential coefficient in the J-TEXT tokamak

Sheath potential coefficient α is a key parameter, which is used to estimate plasma potential(Vp)for edge plasma physics study. Recently, a series of experiments has been carried out under hydrogen plasmas in the J-TEXT tokamak with swept probe, which is employed for current–voltage(I–V) characteristic measurement. Electron temperature is evaluated from I–V curve by three-parameter fitting method, and the electron energy probability function shows that electron distribution is Maxwellian both outside and inside of last closed flux surface(LCFS). Plasma potential is obtained by crossing point between I–V exponential fitting curve and electron saturation current extrapolating line, which is in good agreement with first derivative probe technique. The α coefficient profile in the vicinity of the LCFS is obtained, which is in the range of 2.1–3, and decreases from outside to inside of LCFS.

Determination of Potential Runoff Coefficient Using GIS and Remote Sensing

Flash floods in arid environments are a major hazard feature to human and to the infrastructure. Shortage of accurate environmental data is main reason for inaccurate prediction of flash flooding characteristics. The curve number (CN) is a hydrologic number used to describe the storm water runoff potential for drainage area. This study introduces an approach to determine runoff coefficient in Jeddah, Saudi Arabia using remote sensing and GIS. Remote sensing and geographic information system techniques were used to obtain and prepare input data for hydrologic model. The land cover map was derived using maximum likelihood classification of a SPOT image. The soil properties (texture and permeability) were derived using the soil maps published my ministry of water and agriculture in Saudi Arabia. These soil parameters were used to classify the soil map into hydrological soil groups (HSG). Using the derived information within the hydrological modelling system, the runoff depth was predicted for an assumed severe storm scenario. The advantages of the proposed approach are simplicity, less input data, one software used for all steps, and its ability to be applied for any site. The results show that the runoff depth is directly proportional to runoff coefficient and the total volume of runoff is more than 136 million cubic meters for a rainfall of 103.6 mm.

A Simple Model for the Calculation of Diffusion Coefficient in a Periodic Potential

Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where the internal noise is a Gaussian white noise, and the basic cell of the periodic potential is composed of a parabolic potential linked with a harmonic potential. When the particles cross the joint point of the potential, a time coarse-graining scheme is used to obtain a simple analytical expression of the probability distribution. The particles drift and diffuse from the first barrier to the second barrier, the passing probability over the second barrier corresponding to the escape rate becomes decrease serves as the long-jump probability. The theoretical result is confirmed by numerical simulation results. The approach can be extended to color noise case.

DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)

After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:

A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Prediction of Infinite Dilution Activity Coefficients of Halogenated Hydrocarbons in Water

Geometrical optimization and electrostatic potential calculations have been performed for a series of halogenated hydrocarbons at the HF/Gen-6d level. A number of electrostatic potentials and the statistically based structural descriptors derived from these electrostatic potentials have been obtained. Multiple linear regression analysis and artificial neural network are employed simultaneously in this paper. The result shows that the parameters derived from electrostatic 2 potentials σtot^2, V s and ∑ Vs^＋, together with the molecular volume （Vine） can be used to express the quantitative structure-infinite dilution activity coefficients （γ^∞） relationship of halogenated hydrocarbons in water. The result also demonstrates that the model obtained by using BFGS quasiNewton neural network method has much better predictive capability than that from multiple linear regression. The goodness of the model has been validated through exploring the predictive power for the external test set. The model obtained via neural network may be applied to predict γ^∞ of other halogenated hydrocarbons not present in the data set.

Prediction of Infinite Dilution Activity Coefficients of Alcohol and Ether Organic Compounds in Water

Based on QSPR of alcohol and ether organic compounds in water,geometrical optimization and electrostatic potential calculations were performed at the HF/6-31G＊ level for 73 alcohol and ether organic compounds.Linear relationships between infinite dilution activity coef-ficient（lnγ∞） of alcohols and ethers in water and theoretical descriptors of the molecular structure were established by multiple regression method.The result shows that the parameters derived from molecular electrostatic potential together with molecular surface area can be preferably used to express the quantitative structure-lnγ∞ relationship of alcohols and ethers in water.This reveals that this model has good predictive capabilities（RCV=0.969）.The molecular electrostatic potential has also been proved to have the general applicability in QSPR model of alcohol and ether organic compounds about γ∞ in water.The QSPR model established may provide a new powerful method for predicting γ∞ of organic compounds in aqueous systems.

Streaming Potential and Zeta Potential Measurements in Porous Rocks

The measurements of the streaming potential coefficient and the zeta potential of two consolidated samples saturated with four monovalent electrolytes at different electrolyte concentrations have been performed. The experimental results show that the streaming potential coefficient and the zeta potential in magnitude both decrease with increasing electrolyte concentration for all electrolytes. It is also shown that there is a dependence of the streaming potential coefficient on types of electrolyte for a given sample. This is explained by the dependence of the zeta potential and the electrical conductivity on types of electrolyte. Additionally, the variation of the zeta potential with types of electrolyte is also reported and qualitatively explained. From experimental data on the streaming potential coefficient and the zeta potential, the empirical expressions between the streaming potential coefficients, the zeta potential and electrolyte concentration are also obtained. The obtained expressions have the similar forms to those available in literature. However, there is a deviation between them due to dissimilarities of fluid conductivity, fluid pH, mineral composition of porous materials and temperature.

Modified 2CLJDQP model and the second virial coefficients for linear molecules

A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.

ANALYTICAL SOLUTION OF FLOW OF SECOND-ORDER NON-NEWTONIAN FLUIDS THROUGH ANNULAR PIPES

This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

Potential energy curves, transition dipole moments, and radiative lifetimes of KBe molecule

An ab initio calculations on the ground and low-lying excited statesX2∑＋,2^2∑＋,3^2∑＋,1^4∏,2^4∏,1^4∑＋,2^4∑＋,and 3^4∑＋of KBe molecule have been performed using multireference configuration interaction （MRCI） plus Davidsoncorrections （MRCI＋Q） approach with all electron basis set aug-cc-pCV5Z-DK for Be and def2-AQZVPP-JKFI for K.3^2∑＋,1^4∏,2^4∏,1^4∑＋,2^4∑＋and3^4∑＋states are investigated for the first time. Inner shell electron correlations are computed on the potential energy curves （PECs） calculations. The spectroscopic and molecular parameters are also predicted. In addition, The transition properties including transition dipole moment, Franck-Condon factors qv′v″, Einstein coefficients Av′v″, and the radiative lifetimesτ′for the2^2∑＋-X2∑＋,3^2∑＋-X2∑＋,and 2^4∏-1^4∏ transitions are predictedat the same time.

Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media

Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms （Born/ single scattering approximation） are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation （heterogeneous） medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps： firstly, to handle the forward scattering by taking into account the second- order Born approximation, which is related to generalized Radon transform （GRT） about quadratic scattering poten- tial; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation （3c/c0） of background media up to 10 %, andits inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the per- turbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a trans- mission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.