Stochastic Processes Occurring during the Transition of Technical State of the Structure

The possibility of applying the theory of stochastic processes for evaluating the dynamic pattern of different states is studied for critical-duty structures. Heterogeneous Markovian processes of technical state transition for metallurgical overhead crane structure, Markovian theorem and Kolmogorov-Chapman equation are analyzed. Markovian chain is reviewed at t →∞, i.e. under marginal steady-state (stabilized) condition. Real values of limit probabilities are obtained for the structure of the metallurgical overhead crane under review. The proposed approach redefines and elaborates the existing methods and procedures for evaluating the technical state of structures and reduces the level of ambiguity associated with such kind of problems.

Problem of Kolmogorov for Markovian chains

The sums of random variables from two-state Markovian chain in the schemes of series are investigated. The sums are approximated by parametrical set of measures, which is constituted by all possible limitmeasures of such sums, after making discrete in continuous cases. The problem of Kolmogorov is under solution: the accuracy of approximation by the most relevant measure from parametrical set is evaluated interms of metrics of variation. The common solution scheme of Kolmogorovæs problem is described and the final results for one particular parametrical measure are presented.

Broad Histogram Simulation: Microcanonical Ising Dynamics

We revisit here a new Monte Carlo approach, namely the Broad Histogram Method. It is based on two quantities, the numbers N up and N dn of potential modifications which could be performed starting from the system's current state, increasing or decreasing its energy E, respectively. Thus, the energy degeneracy g(E) can be directly determined from the microcanonical averages <N up (E)> and <N dn (E)> of these two quantities. This method was first tested by sampling states from a random walk along the energy axis, for which the control of possible correlations between successive averaging states is not an easy task. Neverthless, the resulting microcanonical averages could not depend upon the particular dynamics used to sample the Markovian chain of averaging states. Here, we test the same method within an alternative dynamics for which the quoted control becomes trivial.