The dynamics of thermal explosion in a fuel droplets/hot air mixture is investigated using the geometrical version of the method of integral manifolds. The results are applied to the modelling of the ignition process in diesel engines. Effects of the thermal radiation, semi-transparency of droplets and oxidizer are taken into account. In contrast to the previous studies, the difference between gas temperature (responsible for convective heating of droplets) and external temperature (responsible for radiative heating of droplets) is taken into account. The dynamics of the explosion is presented in terms of the dynamics of a multi-scale, singularly perturbed system. The relevant parametric regions of this system are analyzed. Explicit analytical formulae for the ignition delay in the presence of thermal radiation are derived. It is shown that the effect of thermal radiation can lead to considerable reduction (up to about 30%) of the total ignition delay time.

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We introduce and study certain distributions generalizing the operation of curvilinear integration for the case where the path of integration is not rectifiable. Then we apply that distributions for solving of boundary value problems of Riemann-Hilbert type in domains with non-rectifiable boundaries.

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We consider interactions of smooth and discontinuous germs as generalized integrations over non‐rectifiable paths with applications in theory of boundary value problems of complex analysis. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we obtain a Cauchy‐type integral representation to solve certain Beltrami equations and apply it for research of the Riemann boundary value problem for that equations on nonrectifiable contours. While more or less studied for piecewise smooth contours, for the case of nonrectifiable curve, this is a pioneer result. There is only one relatively simple type of Beltrami equation that is solved under such condition (see below). Our next goal is to achieve solutions for more types of the Beltrami equations on nonrectifiable curves.

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A framework for a supervisory controller to manage hard and soft exceptions on a shop floor is discussed. Various tasks involved in managing exceptions, the times at which these tasks are to be performed, and their impact on the performance of a supervisory controller are studied. Online simulation methodology is utilized to detect, classify, and handle exceptions.A synchronization procedure, an essential step to perform on-line control using a discreteevent simulation language, is developed. Its main purpose is to resolve discrepancies between the behavior of entities and resources in the simulation model and shop floor. The framework is restricted to manufacturing cells; however, it can easily be extended to manage exceptions in logistics and distribution systems. A simulation model of a flexible manufacturing cell is used to illustrate exception detection and synchronization concepts.