Estimating the First-year Corrosion Losses of Structural Metals for Continental Regions of the World

The knowledge of the first-year corrosion losses of metals (K1) in various regions of the world is of great importance in engineering applications. The K1 values are used to determine the categories of atmospheric corrosivity, and K1 is also the main parameter in models for the prediction of long-term corrosion losses of metals. In the absence of experimental values of K1, their values can be predicted on the basis of meteorological and aerochemical parameters of the atmosphere using the dose-response functions (DRF). Currently, the DRFs presented in ISO 9223:2012(E) /1/ standard are used for predicting K1 in any region of the world, along with the unified DRFs /2/ and the new DRFs /3/. The predicted values of corrosion losses (K1pr) of carbon steel, zinc, copper and aluminum obtained by various DRFs for various continental regions of the world are presented. In this work we used the atmosphere corrosivity parameters and experimental data on the corrosion losses of metals for the first year of exposure (K1exp) for the locations of the tests performed under the international UN/ECE program, the MICAT project, and the Russian program. For the first time, a comparative assessment of the reliability of various DRFs is given by comparing the values of K1pr and K1ex using graphical and statistical methods. The statistical indicators of reliability of predicting the corrosion losses of metals are calculated for various categories of atmosphere corrosivity. It is shown that the new dose-response functions offer the highest reliability for all categories of atmosphere corrosivity

Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte

Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models

We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-type hyperbolic systems (including the 2D Toda chains), and Euler-Lagrange gauge theories (such as the Yang-Mills theories, gravity, or the Poisson sigma-models). Also, we formulate several open problems.Comment: Proc. 7th International Workshop "Quantum Theory and Symmetries-7" (August 7-13, 2011; CVUT Prague, Czech Republic), 20 page