Instytut Podstawowych Problemów Techniki

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The investigation of concrete microstructure and phase composition was performed on concrete specimens produced with and without calcareous fly ash obtained from Bełchatów Power Station. The used calcareous fly ash (designated “W”) was either unprocessed or ground to assumed specific surface and added to concrete mix to substitute 30% of the binder by weight. The following testing methods were used in this research: scanning electron microscopy, differential thermal analysis (DTA) and multiple microindentation. The characteristic features of the investigated microstructures are discussed and the effect of calcareous fly ash on the content of non-evaporable water and portlandite in cement matrix is analysed. The results of microindentation and compressive strength testing were used as the basis for evaluation of the efficiency of calcareous fly ash added to concrete mix.

Słowa kluczowe:

calcareous fly ash, microindentation, microstructure, non-evaporable water, phase composition, portlandite, strength

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Concrete manhole covers of underground cable networks, placed into pavements of roadways and footways, are often subjected to premature damage posing a threat to traffic safety. That is why the investigation was undertaken to increase the durability of precast concrete covers. New concrete mixtures for precast elements as well as the structure of elements (the type of a chassis, the number and arrangement of reinforcement bars) were designed. Experimental research into the load bearing capacity of concrete elements manufactured in multiple precast plants according to the assumed mix design was carried out. The impact of the type of cement, chemical admixtures and fibre reinforcement on the load capacity of precast concrete elements was assessed. The high effectiveness of fibre reinforcement enhancing the load bearing capacity of concrete covers was found.

Słowa kluczowe:

concrete, concrete precast elements, fibre-concrete, load capacity, manhole covers

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A dense packing of the Voronoi polygons (VP) was created by the Centroidal Voronoi (CV) iteration. It includes VPs with 5, 6 or 7 sides. VPs are represented in a dual triangular representation. In this way, a polycrystal containing grains made of hexagons is formed. The grains are separated by lines of 5/7 pairs. To emphasize the orientation of the grains, we colour the edges of triangles according to a saturated colour circle (CC). The colouring depends on the edge direction modulo 60 degrees. Thanks to this, the colour of edges of an equilateral triangle is the same. Since the colours give the direction of the edges, the colours of the edges of the pentagon go in the opposite direction to the colours of the edges of the heptagon. Thus the CV iteration leads to uniform packing and to the famous hexatic phase transition.

Słowa kluczowe:

Voronoi’s polygon, duality, Colour Circle, 5/7 dislocation, film

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Wieże Hanoi są znaną łamigłówką matematyczną, która mimo swej pozornej prostoty jest ważna w różnych dziedzinach nauki. Przypominamy łamigłówkę i dyskutujemy najprostszy algorytm jej rozwiązania, podany przez polskiego matematyka Andrzeja Lissowskiego. Zgodnie z tym algorytmem w każdym kroku korzystamy z dwu pól: pole, z którego bierzemy krążek, i pole, na które krążek kładziemy. Trzecie pole w tym kroku nie pełni żadnej roli. Nazywamy je polem nieruszonym. Na przykład, jeżeli przekładamy krążek z pola A na pole B, to pole C nie jest ruszone. Patrząc na kolejność pól nieruszonych, zauważamy, że pola nieruszone przesuwają się po okręgu. Omawiamy związek algorytmu z innymi zadaniami matematycznymi, takimi jak drzewo Lindenmayera, krzywa smoka i trójkąty Sierpińskiego.

Słowa kluczowe:

okresowość, pole nieruszone, rekurencja, trójkąty Sierpińskiego

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An experimental botanical fact is the spiral growth of leaves and flowers, and in general of plant buds. Each new shoot in the meristem is formed at an angular distance from the previous one equal to the angle of the golden ratio, i.e. 137.5 degrees. What is most astonishing is that the theory of the golden ratio and its connection with Fibonacci numbers also finds its expression in botany. Each bud produces 5, 6 or 7 diagonals. Adding a new point in the middle of the bud system (in the meristem) pushes the existing points apart so that on each dislocation circle there is an exchange of contacts, i.e. the so-called one flip. The article concludes with a proposal to apply the DISCHARGING procedure (used by Heesch to solve the four-color problem) to precisely determine the geometric curvature of the divided tissue. An appendix is also provided, which explains in more detail the lesser-known concepts from mathematics and crystallography used in the article.

Słowa kluczowe:

remodeling of biological tissue, parastichies, Fibonacci-Lucas numbers, leaf buds

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The chapter is discussing meaning of energy and entropy in some equilibrium and non-equilibrium processes of thermodynamics. We pay an attention to the paradox arising between the description of the adiabatic transformation and the result of the Gay-Lusac experiment. According to the known formula for the adiabatic transformation of an ideal gas, the expansion of the gas should be accompanied by a decrease in temperature. Meanwhile, in the Gay-Lusac experiment, the expansion caused by the sudden removal of the plug does not cause a change in the temperature of an ideal gas. Sudden removal does not cause the phenomenon that occurs with slow expansion. Next, we compared the introduction of entropy in phenomenological thermodynamics and in statistical thermodynamics. Further we discuss the entropy change in the diffusion process. It turns out that while the total entropy of the diffusion process increases monotonically with time, the entropy density has local maxima with the value 1/e. We have given the formula for the efficiency of a Brownian engine operating in two phases, at two different temperatures. In the appendices we recall the similarity given by R. Emden for energy and entropy, and we provide a sketch of the history of heat.

Słowa kluczowe:

Gas expansion, ideal gas, van der Waals gas, diffusion, caloric

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