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On Expansivity and Pseudo-Orbit Tracing Property for Cellular Automata

Jalonen Joonatan, Kari Jarkko

Fundamenta Informaticae

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2020

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Vol. 171, nr 1-4

239--259

EN

Ultimate expansivity extends concepts of expansivity and positive expansivity. We consider one-sided variants of ultimate expansivity and pseudo-orbit tracing property (also known as the shadowing property) for surjective one-dimensional cellular automata. We show that ultimately right (or left) expansive surjective cellular automata are chain-transitive; this improves a result by Boyle that expansive reversible cellular automata are chain-transitive. We then use this to show that left-sided pseudo-orbit tracing property and right-sided ultimate expansivity together imply pseudo-orbit tracing property for surjective cellular automata. This reproves some known results, most notably some of Nasu’s. Our result improves Nasu’s result by dropping an assumption of chain-recurrence, however, we remark that this improvement can also be achieved using the Poincaré recurrence theorem. The pseudo-orbit tracing property implies that the trace subshifts of the cellular automaton are sofic shifts. We end by mentioning that among reversible cellular automata over full shifts we have examples of right expansive cellular automata with non-sofic traces, as well as examples of cellular automata with left pseudo-orbit tracing property but non-sofic traces, illustrating that neither assumption can be dropped from the theorem mentioned above. This paper is a generalized and improved version of a conference paper presented in AUTOMATA 2018.

2

Identyfikacja składu mineralnego i pęcznienia gruntów spoistych na podstawie współczynnika swobodnego pęcznienia

Izdebska-Mucha D., Wójcik E.

Biuletyn Państwowego Instytutu Geologicznego

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2016

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nr 466

77--85

EN

The paper presents the results of free swell measurements of Neogene clays and model clay mixtures composed of Wyoming bentonite and Sedlec kaolinite. Modified free swell index (MFSI) as well as free swell ratio (FSR) were determined and analyzed with respect to pore fluid chemistry, mineral composition and clay content. The FSR, defined as the ratio of the equilibrium sediment volume of 10-g oven dried soil in 0.0025% NaCl solution to that in kerosene, has proved to provide only a rough prediction of clay mineralogy in natural soils.

3

Wpływ azotanu litu na ekspansję betonu spowodowaną reakcją alkaliów z kruszywem żwirowym

Owsiak Z., Zapała-Sławeta J.

Cement Wapno Beton

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2015

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R. 20/82, nr 1

25--31

PL

Zapobieganie ekspansji betonu spowodowane reakcją alkaliów z kruszywem żwirowym jest szczególnie trudne ze względu na złożoność jego składu mineralnego. Jedną z metod zmniejszania destrukcyjnej rozszerzalności jest dodatek do betonu azotanu litu. W pracy przedstawiono wyniki badań zapraw wykonanych z reaktywnego kruszywa żwirowego z dodatkiem azotanu litu. Próbki zapraw sporządzono z cementu portlandzkiego o różnej zawartości alkaliów, wynoszących 0,66%; 0,9% oraz 1,1% Na2Oe. Wyniki badań wykazują, że dodatek azotanu litu, w ilości odpowiadającej stosunkowi molowemu Li/Na+K równemu 0,74, powoduje radykalne zmniejszenie ekspansji, utrzymującej się na poziomie znacznie niższym od wyznaczonego w normie ASTM C227.

EN

Preventing of the concrete expansion caused by the alkali-silica reaction in the case of gravel aggregate is a particularly complex issue, due to the complexity of its mineral composition. Addition to the concrete of lithium nitrate is one of the method of decreasing of the destructive expansion. In the paper the results of investigation of the mortars produced from reactive gravel aggregate with the lithium nitrate addition is presented. The mortars samples were produced from Portland cement with different alkalis content of 0.66%, 0.9% and 1.1% of Nape' The results are showing that the lithium nitrate addition, representing the molar ratio Li/Na+K equal to 0.74, drastically decrease the expansion, which is on the significantly lower level to the threshold value given in ASTM C227 standard.