Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.

Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points.As a result,this problem cannot be solved by the common self-similar-based similarity techniques.This paper proposes a novel,exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils.Considering stress-dependent elastic moduli of soils,new analytical stress and displacement solutions for the nonself-similar problem are developed taking the small strain assumption in the elastic zone.In the plastic zone,the cavity expansion response is formulated into a set of first-order partial differential equations(PDEs)with the combination use of Eulerian and Lagrangian descriptions,and a novel solution algorithm is developed to efficiently solve this complex boundary value problem.The solution is presented in a general form and thus can be useful for a wide range of soils.With the new solution,the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted,which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass.The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

Corrosion and leaching behaviors of Sn-based alloy in simulated soil solutions

The corrosion and leaching behaviors of Sn-0.75Cu solders and joints in NaCl-Na2SO4 and NaCl-Na2SO4-Na2CO3 simulated soil solutions were investigated compared with those in NaCl solution, aiming to assess the potential risk from the electronic-waste disposed in soil. The leaching kinetics of Sn reveals that the leaching amount of Sn increases with increasing the time. The amount of Sn leached from the joint is the largest in NaCl solution.SO4^2- and CO3^2- inhibit the leaching of Sn from the joints, but accelerate that from the solders. Meanwhile, the corrosion layer of the joint in NaCl solution is more porous, and those immersed in NaCl-Na2SO4 and NaCl-Na2SO4-Na2CO3 solutions are compact. The XRD results indicate that the main corrosion products on the solders and joints surfaces are comprised of tin oxide, tin chloride and tin chloride hydroxide. The potentiodynamic polarization measurements for the solders were discussed in the simulated soil solutions.

Improved spatial resolution in soil moisture retrieval at arid mining area using apparent thermal inertia

A surface soil moisture model with improved spatial resolution was developed using remotely sensed apparent thermal inertia（ATI）.The model integrates the surface temperature derived from TM/ETM＋ image and the mean surface temperature from MODIS images to improve the spatial resolution of soil temperature difference based on the heat conduction equation,which is necessary to calculate the ATI.Consequently,the spatial resolution of ATI and SMC can be enhanced from 1 km to 120 m（TM） or 60m（ETM＋）.Moreover,the enhanced ATI has a much stronger correlation coefficient（R^2） with SMC（0.789） than the surface reflectance（0.108） or the ATI derived only from MODIS images（0.264）.Based on the regression statistics of the field SMC measurement and enhanced ATI,a linear regression model with an RMS error of 1.90%was found.

MULTI—ELEMENT DETERMINATION OF SOIL SOLUTION BY INAA

One factor of influencing crop growth is the effective elemental contents, especially trace elements, under the circumstances of the same concentrations of N, P and K in soil. In order to obtain the data of effective elemental contents in soil, a novel method was introduced. In this method, soil solution was extracted by a squeezer. The concentrations of elements in soil solution were determined by INAA. Study on the compositions and the contents of elements in soil solution will provide information on making a suitable soil environment for plant growth and for rational and economical manure.

Effect of Salt Solution on Characteristics of Soil Infiltration

[Objective] The aim was to study the effect of salt solution on characteristics of soil infiltration, and to provide references for the further studies on the effect of water quality on soil infiltration characteristics and its mechanism. [Method] With the NaCl, CaCl2 solutions as the main test materials, the effect of different water quality and salt solution concentration on soil infiltration was studied under one-dimensional vertical ponded water infiltration at laboratory. [Result] The solution concentration could affect the infiltration performance. The trends of the infiltration rates, cumulative infiltrations and wetting front migration distances were all 50 mg/L 100 mg/L 10 mg/L. At the same concentration, the effect of NaCl solution on soil infiltration characteristics was more significant than CaCl2 solution： in the same time, cumulative infiltration and wetting front migration distance of NaCl solution were greater than CaCl2 solution; compared with NaCl solution, CaCl2 solution took longer time to infiltrate the same amount of water. The dynamic changes of infiltration rate, wetting front and cumulative infiltration were well fitted to the Philip model. [Conclusion] This study only conducted indoor experiment to the infiltration of salt solutions, involving in low concentration and small range. Although it provided some references for the study on the effect of water quality on soil infiltration characteristics and its mechanism, studies in larger areas and with bigger concentrations are demanding.

Effect of Different K^+/Mg^(2+) Ration Nutrient Solutions on Soil Salinity

Using simulated soil column experiments, the effects of different dosages and ratios of KCI and MgCI2 mixture on salinization nutrient ions in the secondary salinization soil which had 3 years of planting were studied, with the aim to provide the theory basis for the remediation of secondary salinization soil. Results showed that the content of soil K-, Mg2＋, CI- and the total salinity were increased, with the increasing concentrations of nutrient solution, while Na＋, Ca2＋ and HCO3- contents were reduced. Compared with originals oil, soil K＋, Na＋, Ca2＋, Mg2＋, CI- and total soil salinity were decreased, and HCO3- and SO42 were increased. In terms of the variation of soil total charge, the change ranges in 1：1 treatment varied small, but the residual of soil cationic decreased with increasing application of K＋ in the 2：1 treatment. It could be concluded that balanced and low application fertilizer could alleviate the soil saline, decrease the soil nutrition leaching and improve the balance among ions, while excess fertilization could accelerate the imbalance of zwitterions.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

The semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations （PDFs）, which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pres- sures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are con- ducted on the pore-air and pore-water pressures at different ratios （the air permeability coefficient to the water permeability coefficient） and depths.

Analytical solution to one-dimensional consolidation in unsaturated soils

This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy＇s law and Fick＇s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.

An Analytical Solution for One-Dimensional Water Infiltration and Redistribution in Unsaturated Soil

Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Distribution characteristics of dissolved organic carbon in annular wetland soil-water solutions through soil profiles in the Sanjiang Plain,Northeast China

Overwhelming evidence reveals that concentrations of dissolved organic carbon （DOC） have increased in streams which brings negative environmental impacts. DOC in stream flow is mainly originated from soil-water solutions of watershed. Wetlands prove to be the most sensitive areas as an important DOC reserve between terrestrial and fluvial biogeosystems. This reported study was focused on the distribution characteristics and the controlling factors of DOC in soil-water solutions of annular wetland, i.e., a dishing wetland and a forest wetland together, in the Sanjiang Plain, Northeast China. The results indicate that DOC concentrations in soilwater solutions decreased and then increased with increasing soil depth in the annular wetland. In the upper soil layers of 0-10 cm and 10-20 cm, DOC concentrations in soil-water solutions linearly increased from edge to center of the annular wetland （R^2 = 0.3122 and R^2 = 0.443）. The distribution variations were intimately linked to DOC production and utilization and DOC transport processes in annular wetland soil-water solutions. The concentrations of total organic carbon （TOC）, total carbon （TC） and Fe（II）, DOC mobility and continuous vertical and lateral flow affectext the distribution variations of DOC in soil-water solutions. The correlation coefficients between DOC concentrations and TOC, TC and Fe（II） were 0.974, 0.813 and 0.753 respectively. These distribution characteristics suggested a systematic response of the distribution variations of DOC in annular wetland soil-water solutions to the geometry of closed depressions on a scale of small catchments. However, the DOC in soil pore water of the annular wetland may be the potential source of DOC to stream flow on watershed scale. These observations also implied the fragmentation of wetland landscape could bring the spatial-temporal variations of DOC distribution and exports, which would bring negative environmental impacts in watersheds of the Sanjiang Plain.

Effect of Lanthanum Accumulation on Cation Exchange Capacity and Solution Composition of Red Soil

Pot and adsorpt ion- exchange experiments were carried out by collecting the soil samples from the surfacelayer (0~15 cm) of red soil at the Ecological Experiment Station of Red Soil, the Chinese Academy of Sciences,in Jiangxi Province of China. When concentration of the exogenous La3+ exceeded 400 mg kg-1, therewas less non-exchangeable La3+ than exchangeable La3+ in the soil. Cation exchange capacity of the soilchanged slightly with increasing concentration of the exogenous La3+ in both experiments. However, in theadsorption-exchange experiment, when concentration of the exogenous La3+ was higher than 3Oo mg kg-1 ,exchangeable basic cations decreased significantly, while exchangeable hydrogen and exchangeable aluminumincreased significantly compared with the control treatments. The amounts of base cations (Ca2+ ) Mg2+, K+and Na+) exchanged by La3+ in the supernatant solution increased with the concentration of the exogenousLa3+, especially when concentration of the exogenous La3+ was higher than 50 mg kg-1.

Design of low-alloying and high-performance solid solution-strengthened copper alloys with element substitution for sustainable development

Solid solution-strengthened copper alloys have the advantages of a simple composition and manufacturing process,high mechanical and electrical comprehensive performances,and low cost;thus,they are widely used in high-speed rail contact wires,electronic component connectors,and other devices.Overcoming the contradiction between low alloying and high performance is an important challenge in the development of solid solution-strengthened copper alloys.Taking the typical solid solution-strengthened alloy Cu-4Zn-1Sn as the research object,we proposed using the element In to replace Zn and Sn to achieve low alloying in this work.Two new alloys,Cu-1.5Zn-1Sn-0.4In and Cu-1.5Zn-0.9Sn-0.6In,were designed and prepared.The total weight percentage content of alloying elements decreased by 43%and 41%,respectively,while the product of ultimate tensile strength(UTS)and electrical conductivity(EC)of the annealed state increased by 14%and 15%.After cold rolling with a 90%reduction,the UTS of the two new alloys reached 576 and 627MPa,respectively,the EC was 44.9%IACS and 42.0%IACS,and the product of UTS and EC(UTS×EC)was 97%and 99%higher than that of the annealed state alloy.The dislocations proliferated greatly in cold-rolled alloys,and the strengthening effects of dislocations reached 332 and 356 MPa,respectively,which is the main reason for the considerable improvement in mechanical properties.

Improvement effect of reversible solid solutions Mg_(2)Ni(Cu)/Mg_(2)Ni(Cu)H_(4)on hydrogen storage performance of MgH_(2)

The hydrogen absorption/desorption kinetic properties of MgH_(2)can be effectively enhanced by doping specific catalysts.In this work,MOFs-derived NiCu@C nanoparticles(~15 nm)with regular core-shell structure were successfully prepared and introduced into MgH_(2)(denoted as MgH_(2)-NiCu@C).The onset and peak temperatures of hydrogen desorption of MgH_(2)-11 wt.%NiCu@C are 175.0℃and282.2℃,respectively.The apparent activation energy of dehydrogenated reaction is 77.2±4.5 kJ/mol for MgH_(2)-11 wt.%NiCu@C,which is lower than half of that of the as-milled MgH_(2).Moreover,MgH_(2)-11 wt.%NiCu@C displays great cyclic stability.The strengthening"hydrogen pumping"effect of reversible solid solutions Mg_(2)Ni(Cu)/Mg_(2)Ni(Cu)H_(4)is proposed to explain the remarkable improvement in hydrogen absorption/desorption kinetic properties of MgH_(2).This work offers a novel perspective for the design of bimetallic nanoparticles and beyond for application in hydrogen storage and other energy related fields.

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

Adsorption behaviors and mechanisms of gold recovery from thiosulfate solution by ion exchange resin

The adsorption behaviors and mechanisms of gold from thiosulfate solution on strong-base anion exchange resin were systematically investigated.The comparison experiment of adsorption ability and selectivity for gold showed that gel Amberlite IRA-400 resin with Type Ⅰ quaternary ammonium functional group had better adsorption performance.The increases of resin dosage,ammonia concentration and solution pH were favorable to gold adsorption,whereas the rises of cupric and thiosulfate concentrations were disadvantageous to gold loading.Microscopic characterization results indicated that gold was adsorbed in the form of [Au(S_(2)O_(3))_(2)]^(3–) complex anion by exchanging with the counter ion Cl^(–) in the functional group of the resin.Density functional theory calculation result manifested that gold adsorption was mainly depended on the hydrogen bond and van der Waals force generated between O atom in [Au(S_(2)O_(3))_(2)]^(3–) and H atom in the quaternary ammonium functional group of the resin.

NH_4^+ Adsorption in a Eum-Orthic Anthrosol at Different Solution/Soil Ratios and Temperatures

Effects of NHj concentiation, solution/soil ratio and temperature on NH_4^+adsorption were studied in a Eum-Orthic Anthrosol. The slopes of the soil NH_4^+ adsorptionisotherms and the fitted n, the coefficient for the adsorption intensity, and kappa, the coefficientrelated to adsorption capacity, of the Freundlich equation increased with increasing solution/soilratio (SSR) and with decreasing temperature (T). For the range of experimental conditions, the valueof delta q/delta c, the rate of change of the amount of NH_4^+ adsorbed in the soil solid phase (q)with respect to the equilibrium concentration of NH_4^+ in soil solution (c), was 0.840, indicatingthat q increased with increasing c. From 2 to 45 deg C, delta q/delta SSR, the rate of change of qwith respect to SSR, decreased from 2.598 to 1.996, showing that q increased with increasing SSR,while its increasing rate decreased with temperature. From SSR 1:1 to 20:1, delta q/delta T, therate of change of q with respect to T, decreased from -- 0.095 to -- 0.361, indicating that qdecreased with increasing temperature, and at the same time the negative effect of temperaturebecame larger as SSR increased. Thus under the experimental conditions the order of importance indetermining the amount of NH_4^+ adsorbed in the soil solid phase was delta q/delta SSR > deltaq/delta c > |delta q/delta T|, indicating that the greatest effect on the amount of NH_4^+ adsorbedwas with the solution/soil ratio; the equilibrium concentration of NH_4^+ had a lesser effect; andtemperature had the least effect.

Solid-solution partitioning of arsenic(As) in the paddy soil profiles in Chengdu Plain,Southwest China

To predict the long-term behavior of arsenic （As） in soil profiles, the solid-solution partitioning of As was studied in four paddy soil profiles obtained from agricultural areas in Chengdu Plain, Southwest China. Paddy soil profile samples were collected and soil solution samples were extracted. Total As contents in soil solution and soil solid were analyzed, along with the soil solid phase properties. The As in soil solu- tion was significantly higher in the upper layer （0--20 cm） and had a definite tendency to decrease towards 40 cm regardless of the sampling locations. When the concentration of arsenic in soil solution decreased, its content in solid phase increased. Field-based partition coefficient （Kd） for As was determined by calculating the ratio of the amount of As in the soil solid phase to the As concentration in the soil solution. Kj values varied widely in vertical samples and correlated well with soil pH, total organic carbon （TOC） and total As. The results of this study would be useful for evaluating the accumulation trends of hrsenic in soil profiles and in improving the management of the agricultural soils.