Influence of Cooling Scenarios on the Evolution of Microstructures in Nickel-Based Single Crystal Superalloys

The reprecipitation and evolution of γ’ precipitates during various cooling approaches from supersolvus temperature are studied experimentally and via phase field simulation in nickel-based single crystal superalloys. The focus of this paper is to explore the influence of cooling methods on the evolution of the morphology and the distribution of γ’ precipitates. It is demonstrated that small and uniform spherical shape γ’ particles formed with air cooling method. When the average cooling rate decreases, the particle number decreases while the average matrix and precipitate channel widths increase. The shape of γ’ precipitates which changed from spherical to cubic and irregular characteristics due to the elastic interaction and elements diffusion are observed with the decrease of the average cooling rate. The phase field simulation results are in good agreement with the experimental results in this paper. The research is a benefit for the study of the rejuvenation heat treatment in re-service nickel-based superalloys.

Упругое взаимодействие квантовых дисков в гибридных QD/NW-структурах

The elastic interaction of quantum disks (QDs) in a nanowire (NW), i.e., in a hybrid QD/NW structure with sharp heterointerfaces, is considered for the first time. Within the framework of the defect micromechanics approach, the energy of QD pair interaction is established and it is demonstrated that for QDs with a lattice mismatch of the same sign, an attraction zone appears to each other, depending on the ratio of the axial size of the QD to the radius of the NW. The discovered effect should be taken into account when choosing the modes of formation of hybrid QD/NW structures and in models explaining their properties.

Calculation of tectonic stresses in the earth’s crust of SouthWestern Uzbekistan

In this article, based on accounting, the interaction of the Earth’s crust blocks is limited by the deep breaks in the form of three-layer panels. The analysis dependences for tectonic pressure on elasticity parameters and the Earth’s crust layers capacity were obtained using the hypothesis of linear changes of deformations on the height of panels and the elasticity for bottom layers of the Earth’s crust. This paper considers the elastic interaction of crustal blocks bounded by deep faults in the form of three-layer panels. Using the hypothesis of linear measurement of deformations along with the height of the board and the elastic limit for the lower layer of the Earth’s crust, calculated dependences for tectonic stresses on the elasticity and thickness of the layers of the Earth’s crust are obtained.

Integrability and Multisoliton Solutions of the Reverse Space or/and Time Nonlocal Fokas-Lenells (FL) Equation

This paper studies reverse space or/and time nonlocal Fokas-Lenells (FL) equation, which describes the propagation of nonlinear light pulses in monomode optical fibers when certain higher-order nonlinear effects are considered, by Hirota bilinear method. Firstly, variable transformations from reverse space nonlocal FL equation to reverse time and reverse space-time nonlocal FL equations are constructed. Secondly, the one-, two- and three-soliton solutions of the reverse space nonlocal FL equation are derived through Hirota bilinear method, and the soliton solutions of reverse time and reverse space-time nonlocal FL equations are given through variable transformations. Dynamical behaviors of the multisoliton solutions are discussed in detail by analyzing their wave structures. Thirdly, asymptotic analysis of two- and three-soliton solutions of reverse space nonlocal FL equation is used to investigated the elastic interaction and inelastic interaction. At last, the Lax integrability and conservation laws of three types of nonlocal FL equations is studied. The results obtained in this paper possess new properties that different from the ones for FL equation, which are useful in exploring novel physical phenomena of nonlocal systems in nonlinear media.

Lattice dynamics in CePd2Al2 and LaPd2Al2

The interaction between phonons and 4f electrons, which is forming a new quantum state (quasi-bound state) beyond Born-Oppenheimer approximation, is very prominent and lattice dynamics plays here a key role. There is only a small number of compounds in which the experimental observation suggest such a scenario. One of these compounds is CePd2Al2. Here the study of phonon dispersion curves of (Ce,La)Pd2Al2 at 1.5, 7.5, 80 and 300 K is presented. The inelastic X-ray scattering technique was used for mapping the phonon modes at X and Z points as well as in Λ and Δ directions, where the symmetry analysis of phonon modes was performed. The measured spectra are compared with the theoretical calculation, showing very good agreement. The measurements were performed in several Brillouin zones allowing the reconstruction of phonon dispersion curves. The results are discussed with respect to the magneto-elastic interaction and are compared with other cerium compounds. The phonon mode symmetry A1g was found to be unaffected by the interaction, which is in contrast to previous assumptions.

Analytical modeling of the binary dynamic circuit motion

The binary dynamic circuit, which can be a design scheme for a number of technical systems is considered in the paper. The dynamic circuit is characterized by the kinetic energy of the translational motion of two masses, the potential energy of these masses’ elastic interaction and the dissipative function of energy dissipation during their motion. The free motion of a binary dynamic circuit is found according to a given initial phase state. A mathematical model of the binary dynamic circuit motion in the canonical form and the corresponding characteristic equation of the fourth degree are compiled. Analytical modeling of the binary dynamic circuit is carried out on the basis of the proposed particular solution of the complete algebraic equation of the fourth degree. A homogeneous dynamic circuit is considered and the reduced coefficients of elasticity and damping are introduced. The dependence of the reduced coefficients of elasticity and damping is established, which provides the required class of solutions to the characteristic equation. An ordered form of the analytical representation of a dynamic process is proposed in symmetric determinants, which is distinguished by the conservatism of notation with respect to the roots of the characteristic equation and phase coordinates.

Various Soliton Solutions and Asymptotic State Analysis for the Discrete Modified Korteweg-de Vries Equation

Under investigation is the discrete modified Korteweg-de Vries (mKdV) equation, which is an integrable discretization of the continuous mKdV equation that can describe some physical phenomena such as dynamics of anharmonic lattices, solitary waves in dusty plasmas, and fluctuations in nonlinear optics. Through constructing the discrete generalized m , N − m -fold Darboux transformation for this discrete system, the various discrete soliton solutions such as the usual soliton, rational soliton, and their mixed soliton solutions are derived. The elastic interaction phenomena and physical characteristics are discussed and illustrated graphically. The limit states of diverse soliton solutions are analyzed via the asymptotic analysis technique. Numerical simulations are used to display the dynamical behaviors of some soliton solutions. The results given in this paper might be helpful for better understanding the physical phenomena in plasma and nonlinear optics.

Nonlinear Postbuckling of Auxetic-Core Sandwich Toroidal Shell Segments with CNT-Reinforced Face Sheets Under External Pressure

Nonlinear buckling analysis for honeycomb auxetic-core sandwich toroidal shell segments with CNT-reinforced face sheets surrounded by elastic foundations under the radial pressure is presented in this study. The basic equation system of shells is established based on the von Kármán–Donnell nonlinear shell theory, combined with Stein and McElman approximation. Meanwhile, the foundation-shell elastic interaction is simulated by the foundation model based on the Pasternak assumption. The Galerkin procedure is utilized to achieve the pre-buckling and post-buckling responses for the shell, from which the radially critical buckling load is determined. Numerical analysis shows the various influences of auxetic-core layer, CNT-reinforced face sheets, and elastic foundation on the pre-buckling and postbuckling behavior of sandwich shells with CNT reinforced face sheets.