The Distribution of the Thermal Field in an Elliptical Electric Conductor Coated with Insulation

The paper determines the stationary thermal field in an elliptical cross-section electric conductor coated with insulation. Heat is generated by the flow of alternating current (AC) through the conducting core, and then dissipated from the insulation surface via convection and radiation. The authors have developed an original method for hybrid (analytical–numerical) modeling of a field. This method has been used to solve the relevant boundary problem of Poisson’s equation. While the eigenfunctions of the Laplace operator were determined analytically, the coefficients of the eigenfunctions were calculated by iteratively solving an appropriate system of algebraic equations. The proposed method enables the analysis of systems with an elliptical geometry and a heterogeneous layered structure (e.g., air, aluminum alloy, PCV), and does not require area discretization (grid). The developed analytical–numerical (AN) method has been positively verified using finite elements (FEs). The determined thermal field is illustrated graphically. The obtained solution has a good physical interpretation.

A Stochastic Multiscale Peridynamic Model for Corrosion-induced Fracture in Reinforced Concrete

Concrete fracture caused by corrosion of reinforcing bars may cause subsequent structure failure. To better predict this process, we introduce a partially-homogenized stochastic peridynamic model with the simplest constitutive relation (linear elastic with brittle failure). The model links microscale information (phase volume fractions of mortar, aggregates, interfaces) to macroscale fracture behavior, while costing the same as a fully homogenized model. We show, and explain why a fully-homogenized peridynamic model fails to capture the correct concrete fracture modes/patterns, while the new model succeeds. The multiscale model predicts the evolution of fracture in reinforced concrete caused by corrosion products expansion in samples with a single or multiple rebars. Non-uniform expansion of corrosion products is enforced here as preset, incremental radial displacements. The computed fracture patterns and the order in which various cracks develop match what is seen in experiments. The model’s robustness is tested under different stochastic realizations and discretization grid types.

HYDROGEOLOGICAL REGIONAL MODEL AS A PERMANENT TOOL IN SOLVING VARIOUS-SCALE TASKS – EXPERIENCE FROM THE LEGNICA-GŁOGÓW COPPER REGION (LGOM)

Regional models, covering several thousand km2, are usually implemented to reflect the functioning of hydrogeological systems, whose internal conditions exert an influence over long distances. These include rivers (a model of a catchment), groundwater basins (models covering recharge areas), large intakes and mines (models covering capture zones). Due to the manner of formulating the hydrogeological task and accuracy dictated by the scale, such models are forgotten immediately after verifying, archiving and introducing the results into planning documents and studies. A numerical model with an area of approx. 3 thousand km2 is presented, which is subject to updates and successfully solves subsequent tasks from 2010. It shows how the solutions can be approached on a local scale, on the order of several tens – several hundred metres, using a 400-metre discretization grid. The construction of the regional model requires a high amount of documentation, field and computer work. Therefore, we should aim to use regional models in the long-term, as permanent, with the involvement of people who participated in their creation.

Affine Tensor Product Model Transformation

This paper introduces the novel concept of Affine Tensor Product (TP) Model and the corresponding model transformation algorithm. Affine TP Model is a unique representation of Linear Parameter Varying systems with advantageous properties that makes it very effective in convex optimization-based controller synthesis. The proposed model form describes the affine geometric structure of the parameter dependencies by a nearly minimum model size and enables a systematic way of geometric complexity reduction. The proposed method is capable of exact analytical model reconstruction and also supports the sampling-based numerical approach with arbitrary discretization grid and interpolation methods. The representation conforms with the latest polytopic model generation and manipulation algorithms. Along these advances, the paper reorganizes and extends the mathematical theory of TP Model Transformation. The practical merit of the proposed concept is demonstrated through a numerical example.

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

A Kusuoka–Lyons–Victoir particle filter

The aim of this paper is to introduce a new numerical algorithm for solving the continuous time nonlinear filtering problem. In particular, we present a particle filter that combines the Kusuoka–Lyons–Victoir (KLV) cubature method on Wiener space to approximate the law of the signal with a minimal variance ‘thinning’ method, called the tree-based branching algorithm (TBBA) to keep the size of the cubature tree constant in time. The novelty of our approach resides in the adaptation of the TBBA algorithm to simultaneously control the computational effort and incorporate the observation data into the system. We provide the rate of convergence of the approximating particle filter in terms of the computational effort (number of particles) and the discretization grid mesh. Finally, we test the performance of the new algorithm on a benchmark problem (the Beneš filter).

Numerical model of the catchments of the oziąbel and wołczyński strumień rivers – Wołczyn municipality

The article presents a numerical model designed for determining groundwater dynamics and water balance of the catchments of the Oziąbel (Czarna Woda) river and the Wołczyński Strumień river in Wołczyn region. Hydrogeological mapping and modelling research covered the area of 238.9 km2. As a result of measurements performed in 2008-2009, flows were determined in major rivers and water table positions were measured at 26 points. In the major part of the area described, the water table, lying at the depth of 1.5-18.7 m, has unconfined character, and the aquifer is built of Neogene (Quaternary) sands and gravels. In the area under study, groundwaters are drawn from 6 wells with total withdrawal of 6133 m3/d. The numerical modelling was performed with the use of Visual Modflow 3.1.0 software. The area was partitioned by a discretization grid with a step size l = 250 m. The conceptual model of the hydrogeological system is based on hydrological data gathered over a period of one year, data from HYDRO bank database, cross-sections and maps. The boundaries of the modelled hydrogeological system were established on the watersheds of the Wołczyński Strumień river and the Oziąbel river, apart from the areas where they run together. The modelled area was extended (271.5 km2) around the Wołczyński Strumień river catchment to achieve a more effective mapping of the anthropogenic impact on its balance and the hydrodynamic system of the catchment area. The structure is characterised by the occurrence of one or rarely two aquifers separated by a pack of Quaternary clays. The investigation produced a detailed water balance and its components.