The generalized stability indicator of fragment of the network. I. Modeling of the corporate network fragments

In this paper we consider the stability of the enterprise-node that is functioning and has a network of homogeneous companies with regard to their interaction and influence on each other. This means that we come to consider the wider subnet model containing the node structure of homogeneous him nodes and their vendors. Consider also the parameters and factors that have a direct impact on the stability. © 2013 Irina Nizovtseva

Index of the economic interaction effectiveness between the natural monopoly and regions. I. Math Model

In this paper, we proposed option indicator that determines the quality of the interaction regions with natural monopolies. In fact, assessing the effect of the implementation of projects of the program interaction. Evaluation is carried out from the point of view of natural monopoly. © 2013 Irina Nizovtseva

The generalized stability indicator of fragment of the network. II. Critical performance event

The present paper is devoted to a detailed consideration of the criteria of criticality of the performance event. A complete classification of performance events will come to the formation of a probabilistic assessment of the generalized stability of the node-enterprise. This classification reflects the mutual influence of homogeneous nodes in the common corporate network. © 2013 Irina Nizovtseva

Multi-grain evolution under slow, intermediate and fast regimes of solidification in multi-component alloying system

Development of the theory of rapid growth in terms of phase field model was provided for multi-grain case. The growth of polycrystalline multi-component alloying systems, which driving force regarded as the Gibbs free energy change on crystallization, was studied with the help of the model of fast phase transformations. The special attention was given to the specific rapid solidification features, affecting on the need of using both classical slow and fast variables. Finally, the evolution equations for diffusion flux and gradient flow were developed concerning multi-phase interpolation among growing poly-crystallites. In the limit of relaxation time of fast thermodynamic variables the model tends to restore the Moelan's phase field model of anisotropic grain growth. © 2019 Author(s)

Generalization index of the economic interaction effectiveness between the natural monopoly and regions in case of multiple simultaneous projects

In this paper we continue to develop indicator that determines the quality of the interaction regions with natural monopolies. Is considered a generalized example of interaction in which the work is carried out simultaneously on several projects. In an apparent form obtained formalization index interaction to connect the two projects. Indicated by the upper and lower bounds of efficiency for mixed projects © 2014 Irina Nizovtseva

Travelling-wave amplitudes as solutions of the phase-field crystal equation

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E 70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B 75, 064107 (doi:10.1103/PhysRevB.75. 064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen–Cahn type (Galenko & Jou 2005 Phys. Rev. E 71, 046125 (doi:10.1103/ PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the tanh method (Malfliet & Hereman 1996 Phys. Scr. 15, 563–568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput. 154, 713–723 (doi:10.1016/ S0096-3003(03)00745-8)). The general tanh solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general tanh solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D 308, 1–10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 16-11-10095Alexander von Humboldt-Stiftung: 116077950WM1541Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the paper. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (grant no. 16-11-10095), Alexander von Humboldt Foundation (ID 1160779) and the German Space Center Space Management under contract no. 50WM1541

Traveling wave solution of phase field model for multi-grain systems

The system of governing equations was developed in order to descibe the transformation of multiple crystals for the case of rapid solidification. The model represents itself the extention of a phase field model of multi-grain crystallization by Moelans et.al. The traveling wave solution of phase field model were developed and the description of the dynamics of the moving interface is analysed. © 2019 Author(s)

Automated methodology combining assessments and developing solutions about interaction

In this article is solved development of the automated method of integration and processing the received diverse assessments and development the variants of managerial decisions for a large company's interaction with partners, aimed to increase of interaction effectiveness and to allow reduce costs and risks. © 2014 Irina Nizovtseva and Eugeny Sinitsyn

Editorial for the MMAS special issue “Integro-differential models of natural and anthropogenic processes and phenomena”

Open Access funding enabled and organized by Projekt DEAL