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.     

Stability of Field Emission from a Single Carbon Nanotube

It has been found experimentally that the field emission current passing through a single multiwall carbon nanotube heats it up and generates a thermionic component. The nanotube is heated by the Joule heat that releases on its series resistance, through which the current passes. From the solution to the heat conduction equation, the overheating temperature of the emitting end has been estimated. Conditions for field emission stability and for the onset of thermal field emission have been found.     

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.     

A New Look at the Spin Glass Problem from a Deep Learning Perspective

Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method.