Fractional Distribution of Lead and Cadmium in Sludge and Soil Amended with Sludge Compost

The modified three-step sequential extraction procedure proposed by the BCR was used to predict Pb and Cd fractional distribution in sewage sludge and tomato soil amended with sludge compost. There was no significant increasing of Pb and Cd contents in the soil with sludge application as compared with that in the reference soil. The Pb contents were much lower for the soil samples than for the National Soil Standards of Environmental Quality, but Cd contents in soil were much more than background mean Cd contents. Pb content in soil fractions was followed with residual Pb 〉 reducible Pb 〉 exchangeable and weak acid soluble Pb〉 oxidizable Pb. In all soil samples, the partitioning of Cd had the same extractability in the first two steps of the procedure and the residual fraction. Only a small fraction or almost zero extractability was observed at the oxidation step for Pb and Cd.

Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models

Fractional calculus has been widely used to study the flow of viscoelastic fluids recently,and fractional differential equations have attracted a lot of attention.However,the research has shown that the fractional equation with constant order operators has certain limitations in characterizing some physical phenomena.In this paper,the viscoelastic fluid flow of generalized Maxwell fluids in an infinite straight pipe driven by a periodic pressure gradient is investigated systematically.Consider the complexity of the material structure and multi-scale effects in the viscoelastic fluid flow.The modified time fractional Maxwell models and the corresponding governing equations with distributed/variable order time fractional derivatives are proposed.Based on the L1-approximation formula of Caputo fractional derivatives,the implicit finite difference schemes for the distributed/variable order time fractional governing equations are presented,and the numerical solutions are derived.In order to test the correctness and availability of numerical schemes,two numerical examples are established to give the exact solutions.The comparisons between the numerical solutions and the exact solutions have been made,and their high consistency indicates that the present numerical methods are effective.Then,this paper analyzes the velocity distributions of the distributed/variable order fractional Maxwell governing equations under specific conditions,and discusses the effects of the weight coefficient(α)in distributed order time fractional derivatives,the orderα(r,t)in variable fractional order derivatives,the relaxation timeλ,and the frequencyωof the periodic pressure gradient on the fluid flow velocity.Finally,the flow rates of the distributed/variable order fractional Maxwell governing equations are also studied.

Measurement of oil volume fraction and velocity distributions in vertical oil-in-water flows using ERT and a local probe

This paper presents the use of a high performance dual-plane electrical resistance tomography (ERT) system and a local dual-sensor conductance probe to measure the vertical upward oil-in-water pipe flows in which the mean oil volume fraction is up to 23.1%. A sensitivity coefficient back-projection (SBP) algorithm was adopted to reconstruct the flow distributions and a cross correlation method was applied to obtain the oil velocity distributions. The oil volume fraction and velocity distributions obtained from both measurement techniques were compared and good agreement was found, which indicates that the ERT tech- nique can be used to measure the low fraction oil-water flows. Finally, the factors affecting measurement precision were discussed.

ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented.

Numerical Study of Void Fraction Distribution Propagation in Gas-Liquid Two-Phase Flow

A dynamic propagation model was developed for waves in two-phase flows by assuming that continuity waves and dynamic waves interact nonlinearly for certain flow conditions. The drift-flux model is solved with the one-dimensional continuity equation for gas-liquid two-phase flows as an initial-boundary value problem solved using the characteristic-curve method. The numerical results give the void fraction dis- tribution propagation in a gas-liquid two-phase flow which shows how the flow pattern transition occurs. The numerical simulations of different flow patterns show that the void fraction distribution propagation is deter- mined by the characteristics of the drift-flux between the liquid and gas flows and the void fraction range. Flow pattern transitions begin around a void fraction of 0.27 and end around 0.58. Flow pattern transitions do not occur for very high void concentrations.

Memory dependent anomalous diffusion in comb structure under distributed order time fractional dual-phase-lag model

This paper considers a novel distributed order time fractional dual-phase-lag model to analyze the anomalous diffusion in a comb structure,which has a widespread application in medicine and biology.The newly proposed constitution model is a generalization of the dual-phase-lag model,in which a spectrum of the time fractional derivatives with the memory characteristic governed by the weight coefficient is considered and the formulated governing equation contains both the diffusion and wave characteristics.With the L1-formula to discrete the time Caputo fractional derivatives,the finite difference method is used to discretize the model and the related numerical results are plotted graphically.By adding a source term,an exact solution is defined to verify the correctness of the numerical scheme and the convergence order of the error in spatial direction is presented.Finally,the dynamic characteristics of the particle distributions and the effects of involved parameters on the total number of particles in the x-direction are analyzed in detail.

Numerical calculation and influencing factors of the volume fraction of interfacial transition zone in concrete

The determination of volume fraction of interracial transition zone （ITZ） is very important for investigating the quantitative relationship between the microstructure and macroscopical property of concrete. In this paper, based on Lu and Torquato＇s most nearest surface distribution function, a calculating process of volume fraction of ITZ is given in detail according to the actual sieve curve in concrete. Then, quantitative formulas are put forward to measure the influencing factors on the ｜TZ vol- ume fraction. In order to validate the given model, the volume fractions of ITZ obtained by numerical calculation are compared with those by computer simulation. The results show that the two are in good agreement. The order of the factors influencing the ITZ volume fraction is the ITZ thickness, the volume fraction of aggregate and the maximum aggregate diameter for Fuller gradation in turn. The 1TZ volume fraction obtained from the equal volume fraction （EVF） gradation is always larger than that from the Fuller gradation for a given volume fraction of aggregate.

NUMERICAL ANALYSIS OF THE 3-D FLOW FIELD OF PRESSURE ATOMIZERS WITH V-SHAPED CUT AT ORIFICE

Axisymmetric liquid jets have been studied extensively for more than one century, while non-axisymmetric jets are also very common in engineering applications but attract less concern. Based on Eulerian fluid-fluid model in Fluent software, this article analysizes the 3-D flow fields of pressure atomizers with V-shaped cut at orifice, which will result in a non-axisymmetric liquid jet. Flow rate analysis and jet structure analysis are carried out, the results show that the flow rate can be formulated by adding a correction coefficient to the formula of inviscid axisymmetric jets in atomization regime, when the Weber number is low enough to make the flow fall out of atomization regime, and the jet structure together with the flow rate formula will change. Analysis shows that the evolution of the spray and therefore the structure of the liquid jet are affected much by relative velocity and the local volume fraction of liquid phase.

Two-step calculation method to enable the ecological and human health risk assessment of remediated soil treated through thermal curing

The centralized utilization of heavy-metal-contaminated soil has become the main strategy to remediate brownfield-site pollution.However,few studies have evaluated the ecological and human health risks of reusing these remediated soils.Considering Zn as the target metal,systematic pHdependent leaching and the Community Bureau of Reference(BCR)extraction were conducted at six pH values(pH=2,4,6,8,10,12)for the remediated soil treated through thermal curing.The pHdependent leaching results showed that with the formation of ZnCr2O4 spinel phases,the remediated soil exhibited strong inherent resistance to acidic attack over longer leaching periods.Furthermore,the BCR extraction results showed that the leaching agent pH value mainly affected the acid-soluble fraction content.Moreover,a strong complementary relationship was noted between the leaching and acid-soluble fraction contents,indicating that the sum of these two parameters is representative of the remediated soil risk value.Therefore,we proposed a two-step calculation method to determine the sum of the two heavy metal parameters as the risk value of remediated soil.In contrast to the traditional one-step calculation method,which only uses the leaching content as the risk value,this two-step calculation method can effectively avoid underestimating the risk of remediated soil.

Measurement of J/ψ decays into Λ■ π^+π^-

Based on 58 million J/ψ events collected by the BESⅡ detector at the BEPC, J/ψ→ΛΛ π＋π- is observed for the first time. The branching fraction is measured to be Br（J/ψ→ΛΛ π＋π-）=（4.30±0.13±0.99）×10-3, excluding the decays to intermediate states, namely J/ψ→Ξ-Ξ＋, J/ψ→Σ（1385）-Σ（1385）＋, and J/ψ→Σ（1385）＋Σ（1385）-. The branching fractions for these intermediate resonance channels are measured to be：Br（J/ψ→Ξ-Ξ＋）=（0.90±0.03±0.18）×10-3, Br（J/ψ→Σ（1385）-Σ（1385）＋）=（1.23±0.07±0.30）×10-3,and Br（J/ψ→Σ（1385）＋Σ（1385）-）=（1.50±0.08±0.38）×10-3, respectively. The angular distribution is of the form dN/d（cosθ）α（1＋αcos2θ） with α=（0.35±0.29±0.06） for J/ψ→Ξ-Ξ＋, α=（-0.54±0.22±0.10） for J/ψ→Σ（1385）-Σ（1385）＋, and α=（-0.35±0.29±0.06） for J/ψ→Σ（1385）＋Σ（1385）-.

Joint modeling of longitudinal proportional measurements and survival time with a cure fraction

In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.