The Mössbauer effect and Rudolf enter the Khrushchev thaw

In this article, the earliest works of Soviet scientists on the recoilless resonance scattering of gamma-rays, the first visit of Rudolf Mössbauer to Moscow (1960) and the reciprocal visit of the present author to Los Angeles (1963) are recounted.     

Optical response of Cu clusters in zeolite template

Optical properties of Cu clusters embedded in mordenite are studied experimentally and theoretically. In this work we discuss spectral features of the system at various reduction steps and compare then with the results of spectra obtained within a theoretical model. The model employed consists of Cu clusters embedded in a homogeneous matrix. A second model employed introduced further variation considering a three component system where air or water can be present. The macroscopic dielectric response of the system is obtained within the Maxwell Garnett approximation. In this approach the complex non-local in homogeneous dielectric response of the zeolite+copper system is replaced by an effective homogeneous dielectric function. Metallic clusters can occupy specific available cavities in the zeolite framework. The presence of clusters that are smaller than the cavities in which they reside can lead to an air-Cu or water-Cu interface which allows shifts in surface plasmon resonance energies. As observed experimentally the energy of the main resonance is seen to be insensitive to the filling fraction ratios and highly susceptible to the embedding matrix properties. Reflectance spectra have been obtained which can be explained within this model.     

Oscillations of a statistical scattering in the Rayleigh limit and the Rayleigh law violation

Oscillations of the Rayleigh wave statistical scattering in the Rayleigh limit are theoretically found. These oscillations are violation of the Rayleigh law of scattering. They are caused by the diffraction of a new form - the extraordinary scattering in the Rayleigh limit, which leads to the different frequency dependencies of the scattering coefficient and thus violates the Rayleigh law of scattering. The fundamental physical conception that a wave does not sense the structure of an irregularity in a long-wavelength scattering, when the wavelength is much greater than the character size of the irregularity, i.e. in the Rayleigh limit, is violated as well.     

Energy-Momentum Stability of Icosahedral Configurations of Point Vortices on a Sphere

We investigate the nonlinear stability of the icosahedral relative equilibrium configuration of point vortices on a sphere. The relative equilibrium problem is formulated as a problem of finding the nullspace of the configuration matrix that encodes the geometry of the icosahedron, as in Jamaloodeen and Newton (Proc. Royal Soc. A, Math. Phys. Eng. Sci. 462(2075):3277, 2006). The seven-dimensional nullspace of the configuration matrix, A, associated with the icosahedral geometry gives rise to a basis set of vortex strengths for which the icosahedron stays in relative formation, and we use these values to form the augmented Hamiltonian governing the stability. We choose the basis set made up of (i)?one element with equal strength vortices on every vertex of the icosahedron (the uniform icosahedron); (ii)?six elements made up of equal and opposite antipodal pairs. We start by proving nonlinear stability of the antipodal vortex pair (by direct methods). Following the methods laid out in Simo et al. (Arch. Ration. Mech. Anal. 115(1):15–59, 1991) and Pekarsky and Marsden (J. Math. Phys. 39(11):5894–5907, 1998) and more generally in Marsden and Ratiu (Introduction to Mechanics and Symmetry, 1999), we then combine our knowledge of the nullspace structure of A with the structure of the underlying Hamiltonian, and analyze the stability of the icosahedron using the energy-momentum method. Because the parameter space is large, we focus on the physically motivated and important case obtained by combining the basis elements into (i)?the uniform icosahedron; (ii)?a von Kármán vortex street configuration of equal and opposite staggered, evenly spaced latitudinal rows equidistant from the equator (Chamoun et al. in Phys. Fluids 21:116603, 2009), and (iii)?the North Pole–South Pole equal and opposite vortex pair. Stability boundaries in a three-parameter space are calculated for linear combinations of these grouped basis configurations.     

Entropy as an Objective Function of Optimization Multimodal Transportations

This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks.     

Evolution of structure and physical properties in Al-substituted Ba-hexaferrites

The investigations of the crystal and magnetic structures of the Ba Fe12-xAlx O19(x = 0.1–1.2) solid solutions have been performed with powder neutron diffractometry. Magnetic properties of the Ba Fe12-xAlx O19(x = 0.1–1.2) solid solutions have been measured by vibration sample magnetometry at different temperatures under different magnetic fields.The atomic coordinates and lattice parameters have been Rietveld refined. The invar effect is observed in low temperature range(from 4.2 K to 150 K). It is explained by the thermal oscillation anharmonicity of atoms. The increase of microstress with decreasing temperature is found from Rietveld refinement. The Curie temperature and the change of total magnetic moment per formula unit are found for all compositions of the Ba Fe12-xAlx O19(x = 0.1–1.2) solid solutions. The magnetic structure model is proposed. The most likely reasons and the mechanism of magnetic structure formation are discussed.