Application of Parallel Difference Tests to Resolve the Axial Activation–Deactivation Profile of Copper–Zinc Oxide Catalyst During Hydrogenation of Methyl Acetate

The deactivation of a copper–zinc oxide catalyst has been studied in a set of parallel tests which covered a range of space-times with equal flow and variable catalyst quantity, from 1/8th bed to full bed. The activation–deactivation trends over time in different segments of the full catalyst bed have been determined by two alternative parallel difference methods. The relative trends in segmental activity over time were followed by (a) using a pre-determined reaction model, and (b) by referencing the axial conversion profile against the initial profile. The trends estimated by both methods were in broad agreement. The results show that the front segment of the catalyst bed experienced a more rapid process of deactivation than the rest of the catalyst bed. This process is consistent with the known susceptibility of this type of catalyst to deactivation by chlorine and sulfur impurities in the feedstock. The main part of the catalyst bed appeared to undergo a process of activation during the first 150 h, followed by a slow process of deactivation which was more rapid during periods at increased temperature. The slow deactivation is most likely associated with sintering of copper particles. The conversion parallel difference method provides a convenient and rapid tool for segmental analysis of parallel life tests, and is well-suited to resolving the impact of a poison front within a catalyst bed.

Bidirectional transfers of the ditransitive construction in Chinese

The Chinese ditransitive construction expresses the ‘bidirectional’ transfers: the movement of the patient either (a) from the subject to indirect object or (b) from the indirect object to subject, a feature that has not been identified in other languages. This construction is thus different from the ditransitive construction in English and other languages whose ditransitive constructions can express only a ‘single-direction’ transfer: the movement of the patient from the subject to indirect object only. This article addresses the reason for the unusual functions of the ditransitive construction in Chinese. A parallel difference between these two languages is found in the semantic structures of those ditransitive verbs: Chinese coins a single verb to express the same type of ‘transfer’ action with opposite directions, but English usually invents two distinct verbs to denote the two antonymous meanings whose directions are opposite; e.g., the Chinese verb jiè subsumes the meanings of both borrow and lend in English. This article argues that the different meanings of the ditransitive constructions of Chinese and English result from the different conceptualizations of their ditransitive verbs. In construction grammar, the following question remains unanswered: where does the meaning of the construction come from? The present analysis provides evidence that the meanings of the verbs within the construction are capable of determining the meaning/function of the whole construction.

A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit-implicit (PASE-I) and pure alternating segment implicit-explicit (PASI-E) are constructed by taking simple classical explicit and implicit schemes, combined with the alternating segment technique. The existence, uniqueness, linear absolute stability, and convergence for the solutions of PASE-I and PASI-E schemes are well illustrated. Both theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are linearly absolute stable, with 2-order time accuracy and 2-order spatial accuracy. Compared with the implicit scheme and the Crank–Nicolson (C-N) scheme, the computational efficiency of the PASE-I (PASI-E) scheme is greatly improved. The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the Burgers–Fisher equation.

A New Kind of Parallel Natural Difference Method for Multi-Term Time Fractional Diffusion Model

Multi-term time fractional diffusion model is not only an important physical subject, but also a practical problem commonly involved in engineering. In this paper, we apply the alternating segment technique to combine the classical explicit and implicit schemes, and propose a parallel nature difference method alternating segment pure explicit–implicit (PASE-I) and alternating segment pure implicit–explicit (PASI-E) difference schemes for multi-term time fractional order diffusion equations. The existence and uniqueness of the solutions are proved, and stability and convergence analysis of the two schemes are also given. Theoretical analyses and numerical experiments show that the PASE-I and PASI-E schemes are unconditionally stable and satisfy second-order accuracy in spatial precision and 2 − α order in time precision. When the computational accuracy is equivalent, the CPU time of the two schemes are reduced by up to 2 / 3 compared with the classical implicit difference method. It indicates that the PASE-I and PASI-E parallel difference methods are efficient and feasible for solving multi-term time fractional diffusion equations.

An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation

The fractional telegraph equation is a kind of important evolution equation, which has an important application in signal analysis such as transmission and propagation of electrical signals. However, it is difficult to obtain the corresponding analytical solution, so it is of great practical value to study the numerical solution. In this paper, the alternating segment pure explicit-implicit (PASE-I) and implicit-explicit (PASI-E) parallel difference schemes are constructed for time fractional telegraph equation. Based on the alternating segment technology, the PASE-I and PASI-E schemes are constructed of the classic explicit scheme and implicit scheme. It can be concluded that the schemes are unconditionally stable and convergent by theoretical analysis. The convergence order of the PASE-I and PASI-E methods is second order in spatial direction and 3-α order in temporal direction. The numerical results are in agreement with the theoretical analysis, which shows that the PASE-I and PASI-E schemes are superior to the classical implicit schemes in both accuracy and efficiency. This implies that the parallel difference schemes are efficient for solving the time fractional telegraph equation.

A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation

The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference schemes. The class of parallel difference schemes constructed in this paper, based on the classical Crank–Nicolson (C–N) scheme and classical explicit and implicit schemes, combines with alternating segment techniques. We illustrate the unique existence, unconditional stability, and convergence of the parallel difference scheme solution theoretically. Numerical experiments verify the theoretical analysis, which shows that the IASC–N scheme has second order spatial accuracy and $2-\alpha $ 2 − α order temporal accuracy, and the computational efficiency is greatly improved compared with the implicit scheme and C–N scheme. The IASC–N scheme has ideal computation accuracy and obvious parallel computing properties, showing that the IASC–N parallel difference method is effective for solving time fractional reaction–diffusion equation.