Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

A Method Suitable for Extracting Genomic DNA from Animal and Plant——Modified CTAB Method

[Objective] The study aimed to introduce a rapid and effective method that is suitable for extracting genomic DNA from animal and plant. [ Method ] The genomic DNAs were extracted from tender leaves of 24 peanut cuhivars and from the liver, lung and kidney of white mouse through the specifically modified CTAB method. The DNAs were run on agarose gel, next detected by DNA/Protein analyzer. Finally PCR amplification was conducted to detect the quality of DNAs extracted using the modified CTAB method. [ Result] The clear and orderly bands were observed in gel detection, and the values of OD200/OD200 for DNAs extracted via modified CTAB method were between 1.77 - 1.83. The DNAs performed well in PCR amplification. [ Conclusion] The DNAs extracted by modified CTAB method could satisfy the requirement of PCR amplification.

Modified CTAB Method for Extracting Genomic DNA from Wheat Leaf

ObjectiveThe aim was to seek for a rapid DNA minipreparation method from wheat leaf. MethodThe total DNA of wheat leaf was extracted using CTAB, SDS and boiling water, separately, with some modifications. Integrity and purity of nucleic acids were detected through agarose gel electrophoresis, ultraviolet absorption and PCR. ResultThe DNA extracted by the modified CTAB method had high quality and purity, and was not degraded. Two hundreds of DNA samples could be extracted each workday by per capita using this method; and the PCR detection of wheat transgenic plants showed that amplified bands of target gene were clear, without false-positive, and the test results were satisfactory. The DNA purity and concentration extracted by modified SDS method were not as good as that extracted by modified CTAB method, but it also met the DNA requirements of major molecular research. The DNA quantity extracted by modified boiling method was small and there were a lot of impurities in it, PCR detection of this DNA showed no amplified band. ConclusionModified CTAB method is a simple and rapid method for DNA minipreparation from wheat leaf, and was suitable for PCR amplification and other molecular biology researches.

Grouping response method for equivalent static wind loads based on a modified LRC method

Wind loading is one of the most important loads for controlling the design of large-span roof structures. Equivalent static wind loads, which can generally aim at determining a specific response, are widely used by structural designers. A method for equivalent static wind loads applicable to multi-responses is proposed in this paper. A modified load- response-correlation （LRC） method corresponding to a particular peak response is presented, and the similarity algorithm implemented for the group response is described. The main idea of the algorithm is that two responses can be put into one group if the value of one response is close to that of the other response, when the structure is subjected to equivalent static wind loads aiming at the other response. Based on the modified LRC, the grouping response method is put forward to construct equivalent static wind loading. This technique can simultaneously reproduce peak responses for some grouped responses. To verify its computational accuracy, the method is applied to an actual large-span roof structure. Calculation results show that when the similarity of responses in the same group is high, equivalent static wind loads with high accuracy and reasonable magnitude of equivalent static wind distribution can be achieved.

MODIFIED LAYER REMOVAL METHOD FOR MEASUREMENT OF RESIDUAL STRESS DISTRIBUTION IN THICK PRE-STRETCHED ALUMINUM PLATE

The integrated structure parts are widely used in aircraft. The distortion caused by residual stresses in thick pre-stretched aluminum plates during machining integrated parts is a common and serious problem. To predict and control the machining distortion, the residual stress distribution in the thick plate must be measured firstly. The modified removal method for measuring residual stress in thick pre-stretched aluminum plates is proposed and the stress-strain relation matrix is deduced by elasticity theory. The residual stress distribution in specimen of 7050T7451 plate is measured by using the method, and measurement results are analyzed and compared with data obtained by other methods. The method is effective to measure the residual stress.

Calculation of circulation in the South China Sea during summer of 2000 by the modified inverse method

On the basis of hydrographic data obtained in August 2000 cruise, the circulation in the South China Sea (SCS) is computed by the modified inverse method in combination with SSH data from TOPEX/ERS-2 analysis. For study of the dynamical mechanism, which causes the pattern of summer circulation in the SCS, the diagnostic model (Yuan et al. 1982. Acta Oceanologica Sinica,4(1):1-11; Yuan and Su. 1992. Numerical Computation of Physical Oceanography.474-542) is used to simulate numerically the summer circulation in the SCS. The following results have been obtained. (1) The central and southwestern SCSs are dominated mainly by anticy-clonic circulation systems. They are mainly as follows. 1) There is strong anticyclonic eddy southeast of Vietnam (W1). Its horizontal scale is about 300 km, and it extends vertically from the surface to the about 1 000 m level. 2) There are a warm eddy W2 southeast of Zhongsha Islands and the anticyclonic circulation system W3 west off the Luzon Island. 3) There is a stronger cyclonic eddy C1 between the anticyclonic eddies W1 and W2.4) A strong northward coastal jet is present near the coast of Vietnam, and separates from the coast of Vietnam at about 12° N to the northeast.(2)The northern SCS is dominated mainly by a cyclonic circulation system. There is a cyclonic circulation system near and north of Section N2. (3) The southeastern SCS is dominated mainly by the cyclonic circulation system. (4) Comparing the results of circulation in the SCS during the summer of 2000 with those during the summer of 1998, it is found that they agree qualitatively, but there is the some difference between them in quantity.This shows that the circulation in the SCS has obviously seasonal feature. (5) The dynamical mechanism which products the basic pattern of summer circulation is because the following two reasons: 1) the joint effect of the baroclinity and relief (JEBAR) is essential dynamical cause; and 2) it is next important dynamical cause that the interaction between the wind stress and bottom topography under the southerly monsoon. (6) Comparing the hydrographic structure and distribution of stream functions with the SSH data from TOPEX/ERS-2 analysis in the SCS during August of 2000, they agree qualitatively.

A Numerical Method on Inverse Determination of Heat Transfer Coefficient Based on Thermographic Temperature Measurement

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.

Density of Liquid Ni-Mo Alloys Measured by a Modified Sessile Drop Method

The density of liquid binary Ni-Mo alloys with molybdenum concentration from 0 to 20% (mass fraction) wasmeasured by a modified sessile drop method. It has been found that the density of the liquid Ni-Mo alloys decreaseswith increasing temperature, but increases with the increase of molybdenum concentration in the alloys. The molarvolume of liquid Ni-Mo binary alloys increases with the increase of temperature and molybdenum concentration. Thepartial molar volume of molybdenum in Ni-Mo binary alloy has been approximately calculated as [13.18-2.65×10^(-3)T+(-47.94+3.10×10^(-2)T)×10^(-2)X_(Mo)]×10^(-6)m^3·mol^(-1). The molar volume of Ni-Mo alloy determined inthe present work shows a negative deviation from the ideal linear mixing molar volume.

Density of Ni-Al Alloys in Liquid and Solid-Liquid Coexistence State Measured by a Modified Pycnometric Method

The density of Ni-AI alloys in both liquid state and solid-liquid coexistence state was measured with a modified pycnometric method. It was found that the density of Ni-AI alloys decreases with increasing temperature and Al concentration in the alloys. The molar volume of liquid Ni-AI binary alloys increases with the increase of temperature and Al concentration. The partial molar volume of Al in Ni-AI binary alloy was calculated approximately. The molar volume of liquid Ni-AI alloy determined in the present work shows a negative deviation from the ideal linear molar volume.

Approximate analytical solution in slow-fast system based on modified multi-scale method

A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.

Synthesis of mesoporous carbon as electrode material for supercapacitor by modified template method

The pore structures and electrochemical performances of mesoporous carbons prepared by silica sol template method as electrode material for supercapacitor were investigated. The mean pore size and mass specific capacitance of the mesoporous carbons increase with the increase of mass ratio of silica sol to carbon source （glucose）. A modified template method, combining silica sol template method and ZnCl2 chemical activation method, was proposed to improve the mass specific capacitance of the mesoporous carbon with an improved BET surface area. The correlation of rate capability and pore structure was studied by constant current discharge and electrochemical impedance spectroscopy. A commercially available microporous carbon was used for comparison. The result shows that mesoporous carbon with a larger pore size displays a higher rate capability. Mesoporous carbon synthesized by modified template method has both high mass specific capacitance and good rate capability.

ANALYSIS OF THREE-DIMENSIONAL UPSETTING PROCESS BY THE RIGID-PLASTIC REPRODUCING KERNEL PARTICLE METHOD

A meshless approach, called the rigid-plastic reproducing kernel particle method （RKPM）, is presented for three-dimensional （3D） bulk metal forming simulation. The approach is a combination of RKPM with the flow theory of 3D rigid-plastic mechanics. For the treatments of essential boundary conditions and incompressibility constraint, the boundary singular kernel method and the modified penalty method are utilized, respectively. The arc-tangential friction model is employed to treat the contact conditions. The compression of rectangular blocks, a typical 3D upsetting operation, is analyzed for different friction conditions and the numerical results are compared with those obtained using commercial rigid-plastic FEM （finite element method） software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures which are unavoidable in conventional FEM and can provide results that are in good agreement with finite element predictions.

Seismic passive earth resistance using modified pseudo-dynamic method

In earthquake prone areas, understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures. In this study, the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill. A composite failure surface is considered in the present analysis. Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking. The present method satisfies the boundary conditions. The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion. The acceleration distribution along the depth of the backfill is found to be nonlinear in nature. The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient. The effect of different parameters on the seismic passive earth pressure is studied in detail. A comparison of the present method with other theories is also presented, which shows the merits of the present study.

Geometrical characteristic investigation of the Baihetan irregular columnar jointed basalt and corresponding numerical reconstruction method

Columnar jointed rock mass with unique geometric and geological properties is one spectacular example of geometrical order in nature.Columnar joints are generally accepted to be formed by spatially uniform volume contraction during cooling.In this paper,substantial field work was performed to study the geological characteristics of irregular columnar jointed basalt on the left bank dam foundation in the Baihetan Hydropower Station,where the columnar jointed rock mass is extensively exposed due to excavation.The quantitative measurements of the sizing of polygonal crack pattern of columnar joints and assessment of their degree of irregularity were summarized.Considering the irregularity of polygonal crack pattern,a modified Voronoi polygon(MVP)method was developed to model the special polygonal crack pattern of columnar joints.The new polygonal pattern obtained by the MVP method consists of a large number of irregular polygons,of which the degree of irregularity is consistent with the field measurement results.This method can reproduce the rapid evolution from an initial ideal regular hexagonal pattern to a final actual irregular polygonal pattern as the degree of irregularity increases.The compression tests of columnar jointed rock mass with different irregularity show that the geometric irregularity has a great influence on its mechanical properties.This numerical construction method provides a reliable way to reconstruct columnar joint structure with specific polygonal crack pattern,which is consistent with onsite columnar jointed basalt.

A Method for Solving Fredholm Integral Equations of the First Kind Based on Chebyshev Wavelets

In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.

Solving mKdV-sinh-Gordon equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ODE method is developed for solving the mKdV-sinh-Gordon equation. As a result, many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV-sinh-Gordon equation by this approach.

A Modified Certainty Coefficient Method(M-CF) for Debris Flow Susceptibility Assessment:A Case Study for the Wenchuan Earthquake Meizoseismal Areas

In the meizoseismal areas hit by the China Wenchuan earthquake on May 12, 2008, the disasterprone environment has changed dramatically, making the susceptibility assessment of debris flow more complex and uncertain. After the earthquake, debris flow hazards occurred frequently and effective susceptibility assessment of debris flow has become extremely important. Shenxi gully in Du Jiangyan city, located in the meizoseismal areas, was selected as the study area. Based on the research of disaster-prone environment and the main factors controlling debris flow, the susceptibility zonations of debris flow were mapped using factor weight method(FW), certainty coefficient method(CF) and geomorphic information entropy method(GI). Through comparative analysis, the study showed that these three methods underestimated susceptible degree of debris flow when used in the meizoseismal areas of Wenchuan earthquake. In order to solve this problem, this paper developed a modified certainty coefficient method(M-CF) to reflect the impact of rich loose materials on the susceptible degree of debris flow. In the modified method, the distribution and area of loose materials were obtained by field investigations and postearthquake remote sensing image, and four data sets, namely, lithology, elevation, slop and aspect, wereused to calculate the CF values. The result of M-CF method is in agreement with field investigations and the accuracy of the method is satisfied. The method has a wide application to the susceptibility assessment of debris flow in the earthquake stricken areas.

Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization

Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.

Modified surgical method of supra-and infratentorial epidural hematoma and the related anatomical study of the squamous part of the occipital bone

BACKGROUND Supra-and infratentorial acute epidural hematoma(SIEDH)is a common posterior cranial fossa epidural hematoma located at the inner surface of the squamous part of the occipital bone(SOB).Traditionally,surgical treatment of the SIEDH requires a combined supra-infratentorial craniotomy.AIM To analyze the morphological characteristics of the SOB and introduce a single supratentorial craniotomy for SIEDH.METHODS Skull computed tomography(CT)scan data from 32 adult patients were collected from January 1,2019 to January 31,2020.On the median sagittal plane of the CT scan,the angle of the SOB(ASOB)was defined by two lines:Line A was defined from the lambdoid suture(LambS)to the external occipital protuberance(EOP),while line B was defined from the EOP to the posterior edge of the foramen magnum(poFM).The operative angle for the SIEDH(OAS)from the supra-to infratentorial epidural space was determined by two lines:The first line passes from the midpoint between the EOP and the LambS to the poFM,while the second line passes from the EOP to the poFM.The ASOB and OAS were measured and analyzed.RESULTS Based on the anatomical study,a single supratentorial craniotomy was performed in 8 patients with SIEDH.The procedure and the results of the modified surgical method were demonstrated in detail.For males,the ASOB was 118.4±4.7 and the OAS was 15.1±1.8;for females,the ASOB was 130.4±5.1 and the OAS was 12.8±2.0.There were significant differences between males and females both in ASOB and OAS.The smaller the ASOB was,the larger the OAS was.The bone flaps in 8 patients were designed above the transverse sinus intraoperatively,and the SIEDH was completely removed without suboccipital craniotomy.The SOB does not present as a single straight plane but bends at an angle around the EOP and the superior nuchal lines.The OAS was negatively correlated with the ASOB.CONCLUSION The single supratentorial craniotomy for SIEDH is reliable and effective.