Non-metallic catalysts for diamond synthesis under high pressure and high temperature

Recent results on conversion from graphite to diamond by aid of non-metallic catalysts are reviewed. The current status of experimental advances is presented and typical examples from relevant literature are provided for understanding the mechanism of the graphite-diamond conversion by aid of these non-metallic catalysts. Furthermore, a tendency of graphite-diamond transformation assisted by carbonates, sulfates or phosphorus under high pressure and high temperature has been investigated by calculating the activation energy and transformation probability of the carbon atoms over a potential barrier. It was found that the activation energy is highly sensitive to the catalyst chosen. The probability sequence of graphite-diamond transformation with these catalysts was put forward. Project supported by the National Natural Science Foundation of China (Grant No. 19674970).     

Discrete schemes for processes in random media

We present discrete schemes for processes in random media. We prove two results. The first one is the convergence of Sinai's random walks in random environments to the Brox model. The second one is the convergence of random walks in media with random “gates” to a continuous process in a Poisson potential. The proofs are based on the following idea: we consider the discrete media as random potentials for continuous models. Received: 6 May 1999 / Revised version: 18 October 1999 / Published online: 20 October 2000     

Synthesis of C3N4 crystals under high pressure and high temperature

C₃N₄ crystals with the size of several micrometers have been synthesized from C₃N₄H₄ in the presence of nickel-based alloy or cobalt as catalyst under high pressure of 7 GPa and temperature of about 1400°C for 10 min. Scanning electron microscopy, energy-disperse X-ray analysis, and X-ray diffraction were used to examine the grown crystals. The general rule on selecting the starting materials for synthesis of carbon nitride crystals at high pressures and high temperatures is suggested.     

Three-scale convergence for processes in heterogeneous media

In this article, we propose a new notion of multiscale convergence, called ‘three-scale’, which aims to give a topological framework in which to assess complex processes occurring at three different scales or levels within a heterogeneous medium. This generalizes and extends the notion of two-scale convergence, a well-established concept that is now commonly used for obtaining an averaged, asymptotic value (homogenization) of processes that exist on two different spatial scales. The well-posedness of this new concept is justified via a compactness theorem which ensures that all bounded sequences in L ²(Ω) are relative compact with respect to the three-scale convergence. This is taken further by giving a boundedness characterization of three-scale convergent sequences and is then continued with the introduction of the notion of ‘strong three-scale convergence’ whose well-posedness is also discussed. Finally, the three-scale convergence of the gradients is established.     

The dynamics of elastic closed curves under uniform high pressure

We consider the dynamics of an inextensible elastic closed wire in the plane under uniform high pressure. In 1967, Tadjbakhsh and Odeh (J. Math. Anal. Appl. 18:59–74, 1967) posed a variational problem to determine the shape of a buckled elastic ring under uniform pressure. In order to comprehend a dynamics of the wire, we consider the following two mathematical questions: (i) can we construct a gradient flow for the Tadjbakhsh–Odeh functional under the inextensibility condition?; (ii) what is a behavior of the wire governed by the gradient flow near every critical point of the Tadjbakhsh–Odeh variational problem? For (i), first we derive a system of equations which governs the gradient flow, and then, give an affirmative answer to (i) by solving the system involving fourth order parabolic equations. For (ii), we first prove a stability and instability of each critical point by considering the second variation formula of the Tadjbakhsh–Odeh functional. Moreover, we give a lower bound of its Morse index. Finally we prove a dynamical aspects of the wire near each equilibrium state.     

Creep of polymers during tension under conditions of hydrostatic pressure

Hydrostatic pressure results in decrease in the creep rate of a polymer loaded by tensile stress. The decrease in the creep rate is associated with the increase in intermolecular interaction. The correlation found between the creep rate of material loaded by a constant tensile force and with change in the melting temperature of a polymer under pressure appears to be commensurate with change in intermolecular interaction.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 359–362, March–April, 1976.     

Modeling,simulation and adaptive process control of biotechnological processes in decentralized anaerobic treatment of domestic wastewater

Control in anaerobic wastewater treatment plants is difficult to achieve but necessary due to a high sensitivity to disturbances and process complexity. With the help of different mathematical tools, control strategies can be developed. Particularly, a well-defined mathematical model can be highly effective for design, assessment and optimization of treatment plants. However, applications directly in the control system of a treatment plant are hard to achieve due to model complexity and usually require specialized software and the engagement of experts in the subject. The objective of the present study was the development of less empirical methods for assessment and control of a decentralized anaerobic plant for the treatment of domestic wastewater. A lab-scale plant, which consisted of a two-stage anaerobic digestion process followed by an anaerobic ammonium oxidation (ANAMMOX) reactor for nitrogen removal, was used as object of study. Ordinary differential equation models were implemented to simulate the processes that took place in the treatment plant. With the help of the implemented models, control tools were developed. These tools include a standalone application for monitoring of the two-stage anaerobic digestion process and an ammonium estimator for the ANAMMOX reactor by means of artificial neural networks (ANNs). The procedures followed aimed to reduce the amount of experimental work required so they can be easily transferred from laboratory to full-scale conditions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of filtrational gas combustion processes in nonhomogeneous porous media

A one-dimensional two-temperature model of a combustion front moving with filtration of a fuel gaseous mixture in chemically inert porous media with discontinuous thermophysical parameters is investigated from numerical standpoint. From the algorithmic viewpoint, the emphasis is on new applications of two-level explicit and semi-implicit difference schemes with moving adaptive grids. From the angle of physical features of the processes under consideration, the bulk of attention is focused on aspects of combustion front stabilization, which is important in some technical applications.     

Phase transition in layered perovskite-like manganate Ca3Mn2O7 under high pressure

In situ high pressure energy dispersive X-ray diffraction measurements on the layered perovskite-like manganate Ca3Mn2O7 powder under pressures were performed by using the diamond anvil cell with synchrotron radiation. The results show that the structure of layered perovskite-like manganate Ca3Mn2O7 is unstable under pressure due to the easy compression of NaCl-type blocks. The structure of Ca3Mn2O7 underwent two phase transitions under pressures in the range of 0-35 GPa. One was at about 1.3 GPa with the crystal structure changing from tetragonal to orthorhombic. The other was at about 9.5 GPa with the crystal structure changing from orthorhombic back to another tetragonal.     

Prediction of creep of polymeric materials during random processes of change in loading and temperature-humidity conditions of surrounding media

Conclusions 1. On the basis of the exponentialsmoothing method, a method is suggested for estimating the probability characteristics (statistical moments) of nonstationary random processes of change in temperature conditions of the surrounding medium.2. The possibility is shown of the application of the methods of theory of nonstationary random processes to the prediction of creep of polymeric materials which belong to the class of thermal—moisture rheologically simple solids during nonstationary random change in temperature and humidity of the material. The proposed method of prediction has been experimentally confirmed for the example of prolonged (27,000 h) creep of PN-3 polyester resin during simple shear under the climatic conditions of Riga.For Communication 1 see [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 616–621, July–August, 1976.     

Simulation study on the formation and transition properties of cluster structures in liquid metals during rapid cooling processes

For the first time, a molecular dynamics simulation study has been performed for a liquid metal system consisting of 50000 atoms to deeply investigate the transitions of microstructure configurations dudng the rapid cooling processes. Especially, the cluster-type index method has been adopted to analyze the transforming and evolving processes of clusters and cluster configurations from liquid metal atoms. It has been found that the bigger cluster configurations in the system are formed by means of connecting some small clusters (they are combined by several smaller clusters), and not taken on the multi-shells configuration accumulated with an atom as the center and the surrounding atoms arranged according to some fixed pattern. With the decrease in temperature, the probability of repetitive appearance for clusters increases largely, which reveals that clusters are indeed possessing a certain relative stability and continuity (namely hereditary effect). These results will give us an important enlightenment to understand not only the forming mechanisms and microscopic processes of the short-order sections and disorder sparse sections in amorphous structures but also the freezing processes of liquid metals.``     

Kinematic approach to the description of autowave processes in active media

The kinematic approach formulated in the paper is very general. The main results obtained above also remain valid for active media of a more complicated nature than the simple ones described by Eqs. (1). To construct the kinematic theory, it is necessary to know only a few phenomenological parameters such as the propagation velocity of a plane front and the critical curvature. In principle, these parameters can be calculated using the particular equations of the active medium, for example, (1).The value of the phenomenological parameters for an active medium can also be obtained experimentally. For example, for a medium with the Belousov-Zhabotinskii chemical reaction [1] the propagation velocity of a plane front is V₀=2–3 mm/min, D is the diffusion coefficient for the solution and equal to D=1.8·10^–5 cm²/sec, and the rotation frequency is =5 min^–1. Then, as follows from (16), the critical curvature at the free end must be 70 cm^–1, in good agreement with the experimental data.