Finite Difference Method for Reaction-Diffusion Nonlocal Boundary Conditions Equation with Nonlocal Boundary Conditions

In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.

Gating System Design for a Magnesium Alloy Casting

The gating system of a cylindrical magnesium casting has been designed by using multiple objective optimiza- tion and Taguchi method.Mold filling and solidification processes were simulated by using MAGMASOFT（？）. The simulation results indicate that the gating system design has a significant effect on the quality of magne- sium castings.In an effort to obtain the optimal design of gating system,the signal-to-noise （S/N） ratio was used to analyze the effect of various gating designs on cavity filling and casting quality by using a weighting method based on the design of an orthogonal array.Four gating system parameters,namely,ingate height, ingate width,runner height,runner width,were optimized with a consideration of multiple objective criteria including filling velocity,shrinkage porosity and product yield.

Analysis and discussion of different methods of artificial ice-high specimen preparation

Because ice-high foundation soil is widely distributed in permafrost regions,the correct preparation of ice-high specimens is of critical interest in engineering design for foundation stability.Past research has shown that the uniaxial compression strength of ice-high frozen soils changes as the ice or total water content increases; the differences of different methods of specimen preparation are analyzed here and the advantages and disadvantages of them are presented.It is confirmed that the role of crushed ice is significantly different from that of naturally frozen ice in frozen soils,and the size and amount of crushed ice will influence the strength and deformation mechanism of frozen soils.Therefore,it is strongly recommended that when a ice-high specimen is artificially prepared,the ice should be frozen through natural means and not be replaced with crushed ice.

Application study of the awning measure to obstruct solar radiation in permafrost regions on the Qinghai-Tibet Plateau

With globe warming, road safety will change dramatically, especially within the Qinghai-Tibet Plateau permafrost regions. Because of higher elevation and better almospheric transparency, the Qinghai-Tibet Plateau has stronger radiation than other regions, which can change the daily variation of ground surface temperature on the Plateau. The awning measure （shading board） is one of the actively protected permafrost measures, which was adopted along the Qinghai-Tibet railway and highway and the Qing-Kang Highway in China. Field test results show that embankment surface month mean net radiation is 60-130 W/m2, but the value is below 20 W/m2 under the shading board, and the reducing level of naRn-al net radiation is 80%-90%. The shading board reduced the heat flow entering into the embankment by 80%,90% or more, with heat entering into the soil on the common embankment, but emitting from the embankment under the shading board. At the same time, ground surface temperature under the shading board is 6-8 ℃ lower than the exposed embankment. Test results show that the shading board measure can rapidly and effectively reduce net radiation and heat flow into the embankment, decrease embankment surface and interior temperature, effectively delay increase rate of soil temperature under globe warming, ensure stability and safety of the embankment, and guarantee unblocked road projects in cold and permafrost regions.

Characteristics of thawed interlayer and its effect on settlement beneath embankment in permafrost regions--A case study for the Qinghai-Tibet Highway

Based on ground temperatures and deformations monitored at the Xieshuihe site along the Qinghai-Tibet Highway(QTH)in permafrost regions from 2004 to 2015,variation of artificial permafrost table(APT),maximum frozen depth(MFD),thawed interlayer thickness(TIT)and ground temperature beneath embankment is analyzed,respectively.The results indicate that under the embankment,the change of APT occurred from October to December of that year and presented a deepening trend.The change of MFD occurred from April to June of that year with no obvious change trend,and TIT had an increasing trend year by year,which mainly resulted from the deepening artificial permafrost table.Mean annual ground temperature at 0.5 m depth was 3.91°C higher beneath the embankment center than that under the natural field.The rising ground temperature at shallow layer of embankment resulted in the development of thawed interlayer beneath the embankment and warming of underlying permafrost.Embankment settlement is closely associated with TIT.Greater settlement easily occurs when permafrost with higher ice content exists under the thawed interlayer,and in turn the settlement is smaller when permafrost with lower ice content exists under the thawed interlayer.

A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.

Experimental study on oxidative decomposition of nitrobenzene in aqueous solution by honeycomb ceramic-catalyzed ozonation

The ozonation of nitrobenzene in aqueous solu-tion was carried out in a semi-batch reactor to investigate the degradation efficiency,the effect factors,and the reaction mechanism,where honeycomb ceramic was used as a cata-lyst.The presence of honeycomb ceramic could improve the degradation rate of nitrobenzene by 15.46%compared to the results of ozonation alone.Under the conditions of this exper-iment,the degradation rate of honeycomb ceramic-catalyzed ozonation increased by 12.94%with the increase of the amount of catalyst from 1 to 5 blocks.The degradation rates all increased greatly with the increase of temperature and pH of the solution in the processes of honeycomb ceramic-catalyzed ozonation and ozonation alone.But,when the pH of the solution increased to 9.50,the advantage of the honey-comb ceramic-catalyzed ozonation process would be lost.The experimental findings indicated that in the processes of ozonation alone and honeycomb ceramic-catalyzed ozona-tion,nitrobenzene was primarily oxidized by•OH free radical in aqueous solution.The adsorption of nitrobenzene was too limited to have an important influence on the degradation rate of nitrobenzene.With the same total dosage of applied ozone,the multiple step addition of ozone showed much higher removal efficiency than that obtained by one step in the two processes.

Analysis of High-Order Absorbing Boundary Conditions for the Schrodinger Equation

The paper is concerned with the numerical solution of Schr¨odinger equations on an unbounded spatial domain.High-order absorbing boundary conditions for one-dimensional domain are derived,and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate.Then a second order finite difference scheme is proposed,and the convergence of the scheme is established as well.Finally,numerical examples are reported to confirm our error estimates of the numerical methods.