On the geometry of the pp-Laplacian operator

The $p$-Laplacian operator $\Delta_pu={\rm div }\left(|\nabla u|^{p-2}\nabla u\right)$ is not uniformly elliptic for any $p\in(1,2)\cup(2,\infty)$ and degenerates even more when $p\to \infty$ or $p\to 1$. In those two cases the Dirichlet and eigenvalue problems associated with the $p$-Laplacian lead to intriguing geometric questions, because their limits for $p\to\infty$ or $p\to 1$ can be characterized by the geometry of $\Omega$. In this little survey we recall some well-known results on eigenfunctions of the classical 2-Laplacian and elaborate on their extensions to general $p\in[1,\infty]$. We report also on results concerning the normalized or game-theoretic $p$-Laplacian $$\Delta_p^Nu:=\tfrac{1}{p}|\nabla u|^{2-p}\Delta_pu=\tfrac{1}{p}\Delta_1^Nu+\tfrac{p-1}{p}\Delta_\infty^Nu$$ and its parabolic counterpart $u_t-\Delta_p^N u=0$. These equations are homogeneous of degree 1 and $\Delta_p^N$ is uniformly elliptic for any $p\in (1,\infty)$. In this respect it is more benign than the $p$-Laplacian, but it is not of divergence type.Comment: 15 pages, 5 figures, Survey lecture given at the WIAS conference "Theory and Applications of Partial Differential Equations" in Dec. 201

Evaluation of nonlocal approaches for modelling fracture near nonconvex boundaries

Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the stress-strain equations. However, there is no consensus yet how the influence of boundaries should be taken into account by the averaging procedures. In the present study, nonlocal damage models with different averaging procedures are applied to the modelling of fracture in specimens with various boundary types. Firstly, the nonlocal models are calibrated by fitting load-displacement curves and dissipated energy profiles for direct tension to the results of mesoscale analyses performed using a discrete model. These analyses are set up so that the results are independent of boundaries. Then, the models are applied to two-dimensional simulations of three-point bending tests with a sharp notch, a V-type notch, and a smooth boundary without a notch. The performance of the nonlocal approaches in modelling of fracture near nonconvex boundaries is evaluated by comparison of load-displacement curves and dissipated energy profiles along the beam ligament with the results of meso-scale simulations. As an alternative approach, elastoplasticity combined with nonlocal or over-nonlocal damage is also included in the comparative study

Compact Representation of Value Function in Partially Observable Stochastic Games

Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many practical problems, for example in security, there are exponentially many possible states which causes an insufficient scalability of algorithms for real-world problems. To this end, we propose an abstraction technique that addresses this issue of the curse of dimensionality by projecting high-dimensional beliefs to characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our two main contributions are (1) novel compact representation of the uncertainty in partially observable stochastic games and (2) novel algorithm based on this compact representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm over the compact representation dramatically increases the scalability compared to the state of the art

Modelling public transport accessibility with Monte Carlo stochastic simulations: A case study of Ostrava

Activity-based micro-scale simulation models for transport modelling provide better evaluations of public transport accessibility, enabling researchers to overcome the shortage of reliable real-world data. Current simulation systems face simplifications of personal behaviour, zonal patterns, non-optimisation of public transport trips (choice of the fastest option only), and do not work with real targets and their characteristics. The new TRAMsim system uses a Monte Carlo approach, which evaluates all possible public transport and walking origin-destination (O-D) trips for k-nearest stops within a given time interval, and selects appropriate variants according to the expected scenarios and parameters derived from local surveys. For the city of Ostrava, Czechia, two commuting models were compared based on simulated movements to reach (a) randomly selected large employers and (b) proportionally selected employers using an appropriate distance-decay impedance function derived from various combinations of conditions. The validation of these models confirms the relevance of the proportional gravity-based model. Multidimensional evaluation of the potential accessibility of employers elucidates issues in several localities, including a high number of transfers, high total commuting time, low variety of accessible employers and high pedestrian mode usage. The transport accessibility evaluation based on synthetic trips offers an improved understanding of local situations and helps to assess the impact of planned changes.Web of Science1124art. no. 709

Image Processing on GPUs

Akceleraci zpracování obrazu lze provést více způsoby. Tato práce se zaměří na novou technologii využívající grafické procesory s architekturou, která umožňuje univerzální využití. Architektura nese název NVIDIA CUDATM (Compute unified device architecture). Práce poučí o této technologii a ukáže základní terminologii nutnou pro pochopení následujících kapitol. Pro otestování této technologie je zvoleno zpracování obrazu pomocí konvoluce. Ukážou se některé počáteční a jiné chyby návrhu algoritmu a směr dalšího možného urychlení.Acceleration of image processing can be done by more than one way. This work is oriented to new technology using graphics processing unit with architecture which allows universal usage. The architecture has called as NVIDIA CUDATM (Cumpute unified device architecture). This work instructing about this technology and show basic terminology needed to understand other chapters. Convolution image processing is selected to testing this technology. It describes some first mistakes in algorithm design and show other steps of acceleration.

Design of an effusion cell for the deposition of Sn and Zn ultrathin layers

Tato bakalářská práce se zabývá návrhem a sestavením efuzních cel pro depozici ultra- tenkých vrstev zinku a cínu. V práci jsou úvodem vysvětleny principy funkce efuzních cel, jako je metoda molekulární svazkové epitaxe (MBE) a tvorba efuzního toku. Dále je uve- dené shrnutí obecné konstrukce atomarních zdrojů a rešeršní studie o růstu ultratenkých vrstev a nanostruktur zinku, cínu a jejich sloučenin. V praktické části byly vytvořeny dva návrhy efuzních cel s radiačním ohřevem z karbidu křemíku a ohřevem pomocí dopadu elektronů. Přílohou práce je kompletní výkresová dokumentace navržených efuzních celThis bachelor thesis deals with the design and the construction of effusion cells for the deposition of zinc and tin ultrathin layers. In the introductory part there is an explanation of principles of eusion cells' functions, like a molecular beam epitaxy (MBE) or a construction of the efussion ow. Furthermore, the work describes a general principles of a ccreation of the atom sources. Theoretical part ends with review about the growth of ultrathin layers and nanostructures of zinc, tin and their compounds. Experimental part provides a design of the effusion cells with radiation heating from silicon carbide and heating by electrons impact. The complete drawing documentation of the designed effusion cells is included in the attachment.

Technological tests of pipes

Předložený projekt vypracovaný v rámci bakalářského studia B-STI Strojní inženýrství je zaměřen na problematiku technologických zkoušek trubek. Na základě literární a internetové studie je v práci rozebrán princip jednotlivých technologických zkoušek, postup jejich vyhodnocení a oblasti použití. Pro ucelenou představu o zkouškách trubek jsou v práci uvedeny také základní informace o zkouškách mechanických.The submitted project created in the bachelor studies of B-STI Machinery engineering is focus on problematic of technological tests of pipes. Based on the research of literature and internet mentioned problematic the bachelor thesis describes principle of individual technological tests, the procedure for the evaluation and application. For a complete picture of test tubes in the thesis are also given basic information about the mechanical tests.

Light (Magic of Light)

Předkládaná práce se zabývá v jedné rovině otázkou práce a pracnosti v umění a v druhé rovině vnímáním skutečnosti a její iluze. Zde stručně vysvětluji funkce zrakového systému vedoucí k tvorbě obrazu, vnímání světelných jevů a k tvorbě zrakových klamů (tj. jevů, kdy se náš vjem zcela neshoduje s realitou), které sloužily jako podklad pro řešení formální stránky díla.The present work deals in one level with the issue of work and laboriousness in the arts and in the second plane perception of reality and its illusion. Here, briefly explains the function of the visual system, leading to the formation of the image, perception of light phenomena and to create visual illusions (ie. Phenomena, when our perception completely does not match with reality), which served as the basis for dealing with the formal aspects of the work.

Optimization of Data Storages

V této práci jsou pospány způsoby využití, zapojení a správy diskových polí RAID a jejich optimalizace vzhledem k moderním trendům v oblasti IT.In this work are described methods of using, connecting and managing RAID arrays and their optimization against modern trends in IT section.

Moving Object Detection in Video Using CUDA

Práce se zabývá metodikami detekce pohybu na videozáznamech; výběrem a aplikací vhodných algoritmů za použití technologie CUDA. Tato technologie je dále rozebírána, zkoumána z hlediska její architektury a dalších součástí. Jsou sledovány obecné principy detekce pohybu a navrhovány systémy detekčních algoritmů. Systém je implementován a podroben testům.This thesis deals with methods of moving object detection in video; by selecting and applying proper algorithms and implementing them with CUDA. Technology CUDA is described and wieved it's architecture and other parts. General principles of moving object detection are observed and modification are discussed. Final system is implemented and tested.