• Computers and Concrete
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• v.11 no.5
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• pp.411-440
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• 2013

Large fluctuations in surface strain at the level of steel are expected in reinforced concrete flexural members at a given stage of loading due to the emergent structure (emergence of new crack patterns). This has been identified in developing deterministic constitutive models for finite element applications in Ibrahimbegovic et al. (2010). The aim of this paper is to identify a suitable probability distribution for describing the large deviations at far from equilibrium points due to emergent structures, based on phenomenological, thermodynamic and statistical considerations. Motivated by the investigations reported by Prigogine (1978) and Rubi (2008), distributions with heavy tails (namely, alpha-stable distributions) are proposed for modeling the variations in strain in reinforced concrete flexural members to account for the large fluctuations. The applicability of alpha-stable distributions at or in the neighborhood of far from equilibrium points is examined based on the results obtained from carefully planned experimental investigations, on seven reinforced concrete flexural members. It is found that alpha-stable distribution performs better than normal distribution for modeling the observed surface strains in reinforced concrete flexural members at these points.

• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1525-1530
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• 2006

A simple oscillating reaction model subject to additive Gaussian white noise is investigated as the model is located in the dynamic region of oscillations. The model is composed of three ordinary differential equations representing the time evolutions of X, Y, and Z, respectively. Initially, a uniform random noise is separately added to the three equations to study the effect of noise on the oscillatory cycle of X, Y, and Z. For a given value of noise intensity, the amplitude of oscillation increases monotonically with time. Furthermore, the noise is added to any one of the three equations to study the impact of noise on one species on the bifurcation behavior of the other.