Nonlinear Effects in Rolling Mills Dynamics

This paper intends to describe nonlinear effects occurring in rolling mills dynamics. That is necessarily for vibrations damping and reliable diagnostics of rolling mills equipment under non-stationary working conditions. Three types of nonlinear effects are investigated taking place in drivelines and stands of different design, namely, transient torsional vibrations in hot rolling mills, chatter vibrations in tandem cold rolling mills and parametrical vibrations in high-speed wire and rod rolling mills. The procedure is proposed for natural frequencies identification when short transient torque signals restrict application of the Fourier transform. Some considerations given on using nonlinear effects for wear diagnostics and vibrations control based on natural frequencies and modes analysis of multi-body systems

On calculating the mean values of quantum observables in the optical tomography representation

Given a density operator $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho$. We introduce a dual map from the special class $\mathcal A$ of quantum observables $\hat a$ to a special class of generalized functions $a(X,\phi)$ such that the mean value $_{\hat \rho} =Tr(\hat \rho\hat a)$ is given by the formula $_{\hat \rho}= \int \limits_{0}^{2\pi}\int \limits_{-\infty}^{+\infty}w_{\hat \rho}(X,\phi)a(X,\phi)dXd\phi$. The class $\mathcal A$ includes all the symmetrized polynomials of canonical variables $\hat q$ and $\hat p$.Comment: 8 page

Optical Tomography of Photon-Added Coherent States, Even/Odd Coherent States and Thermal States

Explicit expressions for optical tomograms of the photon-added coherent states, even/odd photon-added coherent states and photon-added thermal states are given in terms of Hermite polynomials. Suggestions for experimental homodyne detection of the considered photon states are presented.Comment: 10 pages, 8 figure

Simulating the Spread of Peste des Petits Ruminants in Kazakhstan Using the North American Animal Disease Spread Model

In this study, we simulated the potential spread of Peste des Petits Ruminants (PPR) between small ruminant (SR) farms in the Republic of Kazakhstan (RK) in case of the disease’s introduction into the country. The simulation was based on actual data on the location and population of SR farms in the RK using the North American Animal Disease Spread Model (NAADSM). The NAADSM employs the stochastic simulations of the between-farm disease spread predicated on the SIR compartmental epidemic model. The most important epidemiological indicators of PPR, demography of SR farms, and livestock management characteristics in the RK were used for model parameterization. This article considers several scenarios for the initial introduction of PPR into the territory of Kazakhstan, based on previously identified high-risk regions and varying sizes of initially infected farms. It is demonstrated that the duration and size of the outbreak do not depend on the size of initially infected farms but rather depend on the livestock concentration and number of farms in the affected area. This implies that the outbreak may affect the largest number of farms in the case of introduction of the disease into farms in southern Kazakhstan. However, even in the most unfavorable scenario, the total number of affected farms does not exceed 2.4% of all SR farms in the RK. The size of the affected area is, in most cases, no larger than an averaged 2-level administrative division’s size, which suggests the scale of a local epidemic. The chosen model provides ample opportunity to study the impact of different control and prevention measures on the spread of PPR as well as to assess the potential economic damage