This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of complicated solution patterns. In this paper we show that this chemotaxisdriven instability can be connected to the ill-posed problem defined by the backward in time diffusion process. The method of lines is used to construct robust numerical approximations. At the first step we approximate spatial derivatives in the PDE by applying approximations targeted for special physical processes described by differential equations. The obtained system of ODE is split into a system describing separately fast and slow physical processes and different implicit and explicit numerical solvers are constructed for each subproblem. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.

In this work, the process of roofing projects' execution is considered. The proper analysis of this process is important to optimise the behaviour of a project's participants and to perform risk evaluation. The main result of this work is methodology, which can be used to optimise a project owner's decisions and potentially can be applied for risk control or integrated into expert systems. This methodology includes the application of a decision tree and AHP (analytic hierarchy process) method to perform the modelling for roof installation project selection. In the proposed approach, a decision tree describes the process with nodes representing the states of a project. The tree includes the decision on whether to sell the project results or not, which requires the estimation of the subjective opinion of the project owner. These subjective values are used in the decision tree leaves. We propose to perform this estimation with the AHP method and describe how to do it in this paper. A particular example was considered. The proposed methodology was applied to that case, and all details of the process and results are provided. Using the proposed methodology, the adapted version of a specific, current situation model of project participants' behaviours can be formed, allowing one to make the most efficient decisions in the light of the existing constraints. The application of results can increase the investor protection and contribute to the general sustainability of investments.

Abstract:In this article, the modelling of the judicial conflict-resolution process is considered from a construction investor's point of view. Such modelling is important for improving the risk management for construction investors and supporting sustainable city development by supporting the development of rules regulating the construction process. Thus, this raises the problem of evaluation of different decisions and selection of the optimal one followed by distribution extraction. First, the example of such a process is analysed and schematically represented. Then, it is formalised as a graph, which is described in the form of a decision graph with cycles. We use some natural problem properties and provide the algorithm to convert this graph into a tree. Then, we propose the algorithm to evaluate profits for different scenarios with estimation of time, which is done by integration of an average daily costs function. Afterwards, the optimisation problem is solved and the optimal investor strategy is obtained-this allows one to extract the construction project profit distribution, which can be used for further analysis by standard risk (and other important information)-evaluation techniques. The overall algorithm complexity is analysed, the computational experiment is performed and conclusions are formulated.

In this work, we study the efficiency of developed OpenFOAM-based parallel solver for the simulation of heat transfer in and around the electrical power cables. First benchmark problem considers three cables directly buried in the soil. We study and compare the efficiency of conjugate gradient solver with diagonal incomplete Cholesky (DIC) preconditioner, generalized geometricalgebraic multigrid GAMG solver from OpenFOAM and conjugate gradient solver with GAMG multigrid solver used as preconditioner. The convergence and parallel scalability of the solvers are presented and analyzed on quadrilateral and acute triangle meshes. Second benchmark problem considers a more complicated case, when cables are placed into plastic pipes, which are buried in the soil. Then a coupled multi-physics problem is solved, which describes the heat transfer in cables, air and soil. Non-standard parallelization approach is presented for multi-physics solver. We show the robustness of selected parallel preconditioners. Parallel numerical tests are performed on the cluster of multicore computers.

Abstract. A general methodology for the stability analysis of discrete approximations of nonstationary PDEs is applied to solve the Kuramoto-Tsuzuki equation, including also the Schrödinger problem. Stability regions are constructed for the explicit, backward and symmetrical Euler schemes. The obtained results are applied to solve the Kuramoto-Tsuzuki problem with a non-local integral boundary condition. Results of computational experiments are provided.