Search results for "Random model"
showing 4 items of 4 documents
The Multiscale Stochastic Model of Fractional Hereditary Materials (FHM)
2013
Abstract In a recent paper the authors proposed a mechanical model corresponding, exactly, to fractional hereditary materials (FHM). Fractional derivation index 13 E [0,1/2] corresponds to a mechanical model composed by a column of massless newtonian fluid resting on a bed of independent linear springs. Fractional derivation index 13 E [1/2, 1], corresponds, instead, to a mechanical model constituted by massless, shear-type elastic column resting on a bed of linear independent dashpots. The real-order of derivation is related to the exponent of the power-law decay of mechanical characteristics. In this paper the authors aim to introduce a multiscale fractance description of FHM in presence …
Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density functions
2021
[EN] In this work we consider a particular randomized kinetic model for reaction-deactivation of hydrogen peroxide decomposition. We apply the Random Variable Transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the rst probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the Random Variable Transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of comp…
Models of Dynamical Modelling Under Uncertainty
1986
The objective of this work is to modelize the evolution of a Model-System to be adapted to a Random System. This evolution is described by means of the change of a probabilistic function, through deterministic rules and in function of the random responses of the modelized System. This probabilistic function can describe the relative weight of distinct submodels (deterministic or random Systems, with constant or variable stimulus), or the stimulus-response relation in the Model-System (Adaptative Random System). We conclude that the Adaptative Random Model permits a more precise, simple and economical modelling.
First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities
2022
[EN] Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the sake of generality, coefficients and initial condition are assumed to be absolutely continuous complex random variables with an arbitrary joint probability density function. The probability of stability, as well as the density of the equilibrium point, are explicitly determined. The Random Variable Transformation technique is extensively utilized to conduct the overall analysis. Several examples are included to illustrate all the theoretical findings.