Thermodynamic analysis of combined reforming process using Gibbs energy minimization method: In view of solid carbon formation

Thermodynamic analysis was applied to study combined partial oxidation and carbon dioxide reforming of methane in view of carbon formation. The equilibrium calculations employing the Gibbs energy minimization were performed upon wide ranges of pressure （1-25 atm）, temperature （600-1300 K）, carbon dioxide to methane ratio （0-2） and oxygen to methane ratio （0-1）. The thermodynamic results were compared with the results obtained over a Ru supported catalyst. The results revealed that by increasing the reaction pressure methane conversion decreased. Also it was found that the atmospheric pressure is the preferable pressure for both dry reforming and partial oxidation of methane and increasing the temperature caused increases in both activity of carbon and conversion of methane. The results clearly showed that the addition of O2 to the feed mixture could lead to a reduction of carbon deposition.

A Continuous Minimization Method for Solving Optimal Control Problem

In this paper,a kind of continuous minimization method for solving optimal control problem which transforms the problem into solving the initial value problem of ordinary differential equations is presented so that some new algorithms for solving optimal control problem are obtained by constrcting suitable differential equations and choosing some numerical integration formulas, and prove the every accumulation point developed by the methods is a stationary control.We also point out that existing optimization algorithms for computing optimal control,in general,do not gauratee to converge to stationary control.At last,some numerical examples show the method is elective.

Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function

This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).

Comparative study on identification methods of pipe roughness coefficients in water networks

In this paper,we improve object functions and constraint conditions of genetic algorithms (GAs) applied in PRCs identification of water networks.This identification method can increase calculation efficiency,but can not solve an identification problem with infinitely many solutions well.Then we propose PRCs identification based on the minimal norm method,which satisfies observability conditions and has advantages of high computing efficiency and short time consumption.The two identification methods are applied in a water network,and their identification results are compared under the same conditions.From the results,we know that PRCs identification based on the minimal norm method has advantages of higher computing efficiency,shorter time consumption and higher precision.

Improvement of the minimal residual method for solving nonsymmetric linear systems

In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.

Improved modal truncation error in the directly analytical method for damage identification of frame structures

The damage identification is made by the numerical simulation analysis of a five-storey-and-two-span RC frame structure, using improved and unimproved direct analytical method respectively; and the fundamental equations were solved by the minimal least square method （viz. general inverse method）. It demonstrates that the feasibility and the accuracy of the present approach were impoved significantly, compared with the result of unimproved damage identification.

The thermodynamics analysis and experimental validation for complicated systems in CO_2 hydrogenation process

Catalytic conversion of COinto chemicals and fuels is an alternative to alleviate climate change and ocean acidification.The catalytic reduction of COby Hcan lead to the formation of various products:carbon monoxide,carboxylic acids,aldehydes,alcohols and hydrocarbons.In this paper,a comprehensive thermodynamics analysis of COhydrogenation is conducted using the Gibbs free energy minimization method.The results show that COreduction to CO needs a high temperature and H/COratio to achieve a high COconversion.However,synthesis of methanol from COneeds a relatively high pressure and low temperature to minimize the reverse water-gas shift reaction.Direct COhydrogenation to formic acid or formaldehyde is thermodynamically limited.On the contrary,production of CHfrom COhydrogenation is the thermodynamically easiest reaction with nearly 100%CH4 yield at moderate conditions.In addition,complex reactions with more than one product are also calculated in this work.Among the considered carboxylic acids（HCOOH,CHCOOH and CHCOOH）,propionic acid dominates in the product stream（selectivity above 90%）.The same trend can also be found in the hydrogenation of COto aldehydes and alcohols with the major product of propionaldehyde and butanol,respectively.In the process of COhydrogenation to alkenes,low temperature,high pressure,and high Hpartial pressure favor the COconversion.CHis the most thermodynamically favorable among all considered alkynes under different temperatures and pressures.The thermodynamic calculations are validated with experimental results,suggesting that the Gibbs free energy minimization method is effective for thermodynamically understanding the reaction network involved in the COhydrogenation process,which is helpful for the development of high-performance catalysts.

High-precision downward continuation of potential fi elds algorithm utilizing adaptive damping coeffi cient of generalized minimal residuals

The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications.However,the downward continuation of potential fields is a typical linear inverse problem that is ill-posed.Generalized minimal residuals(GMRES)is an eff ective solution to ill-posed inverse problems,but it is unstable under the condition wherein the GMRES is directly applied in the calculation process.Moreover,the long-term behavior of its iterative computation is a disordered,divergent result.Therefore,to obtain stable solutions,GMRES is applied to solve the normal equations of the downward continuation of potential fields;it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient,thus strengthening the stability conditions of the equations of residual minimization.Finally,the stable downward continuation of the potential fields method is proposed.As indicated by the theoretical data and the measured testing data,the method proposed in this paper has the advantages of high-precision and excellent stability.Furthermore,compared with the Tikhonov iteration method,the proposed method avoids the need to choose regularization parameters.

A GLOBALLY DERIVTIVE-FREE DESCENT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.

Local Discontinuous Galerkin Method for Parabolic Interface Problems

In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves. The proposed method is proved to be L2 stable and the order of error estimates in the given norm is O（h｜logh｜^1/2）. Numerical experiments show the efficiency and accuracy of the method.

Clinical efficacy observation of thalamic pain treated with acupuncture under the guidance of evidence-based medicine

Objective To study the feasibility of the crossover trial design and the minimal imbalance index random distribution method in the clinical small-sample-size randomized controlled trial（RCT） research of thalamic pain treated with acupuncture under the guidance of evidence-based medicine（EBM）.Methods The crossover trial design was adopted.Eleven cases with the definite diagnosis were randomized into a program-I group（6 cases,treated with acupuncture before western medicine） and a program-II group（5 cases,treated with western medicine before acupuncture） according to the minimal imbalance index method.In the statistical analysis,the groups were named as an acupuncture group and a western medicine group separately,11 cases in each one.Acupuncture was applied to Xìmén（郄门 PC 4）,Yīnxì（阴郄 HT 6）,Xuèhǎi（血海 SP 10）,etc.In the control treatment,Carbamazepine was prescribed for oral administration.Either the duration of treatment or the wash-out period was 10 days.The visual analogue scale（VAS） was adopted for the efficacy assessment.Results The total effective was 100.0%（11/11） after treatment in either group.The remarkably effective rates were 63.6%（7/11） and 36.4%（4/11） in the acupuncture group and the western medicine group separately,without statistically significant difference in comparison.Conclusion The crossover trial design and the minimal imbalance index distribution method can accomplish RCT of the clinical acupuncture and moxibustion research with the small sample size involved.They can provide the high-quality evidences for clinical acupuncture research.Acupuncture therapy can achieve the same therapeutic effect as Carbamazepine,the common western medicine,and the efficacy of it is potentially superior to that of western medicine.

Sparse approximate solution of fitting surface to scattered points by MLASSO model

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.