Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Self-heating and deicing conductive cement. Experimental study and modeling

This research studies the self-heating produced by the application of an electric current to conductive cement pastes with carbonaceous materials. The main parameters studied were: type and percentage of carbonaceous materials, effect of moisture, electrical resistance, power consumption, maximum temperature reached and its evolution and ice melting kinetics are the main parameters studied. A mathematical model is also proposed, which predicts that the degree of heating is adjustable with the applied voltage. Finally, the results have been applied to ensure that cementitious materials studied are feasible to control ice layers in transportation infrastructures.

Multifunctional cement composites strain and damage sensors applied on reinforced concrete (RC) structural elements

In this research, strain-sensing and damage-sensing functional properties of cement composites have been studied on a conventional reinforced concrete (RC) beam. Carbon nanofiber (CNFCC) and fiber (CFCC) cement composites were used as sensors on a 4 m long RC beam. Different casting conditions (in situ or attached), service location (under tension or compression) and electrical contacts (embedded or superficial) were compared. Both CNFCC and CFCC were suitable as strain sensors in reversible (elastic) sensing condition testing. CNFCC showed higher sensitivities (gage factor up to 191.8), while CFCC only reached gage factors values of 178.9 (tension) or 49.5 (compression). Furthermore, damage-sensing tests were run, increasing the applied load progressively up to the RC beam failure. In these conditions, CNFCC sensors were also strain sensitive, but no damage sensing mechanism was detected for the strain levels achieved during the tests. Hence, these cement composites could act as strain sensors, even for severe damaged structures near to their collapse.

Blending of industrial waste from different sources as partial substitution of Portland cement in pastes and mortars

Binary and ternary combinations of sewage sludge ash (SSA) with marble dust (MD), fly ash (FA) and rice husk ash (RHA) as replacement in Portland cement pastes, were assessed. Several tests were carried out at different curing ages: thermogravimetry, density, water absorption, ultrasonic pulse velocity and mechanical strengths. Pozzolanic effects of the mineral admixtures, densities similar to control sample and improved absorptions when combining waste materials were identified. In general, the compressive strength reaches or exceeds the cement strength class, and blending SSA, FA and RHA (30% cement replacement) increase of strength by 9%, compared to the control sample, was achieved.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.