Accounting for Interelement Interferences in Atomic Emission Spectroscopy: A Nonlinear Theory

The article describes a nonlinear theory of how the presence of third elements affects the results of analyzing the elemental composition of substances by means of atomic emission spectroscopy. The theory is based on the assumption that there is an arbitrary relationship between the intensity of the analytical line of the analyte and the concentration of impurities and alloying elements. The theory has been tested on a simulation problem using commercially available equipment (the SPAS-05 spark spectrometer). By comparing the proposed algorithm with the traditional one, which assumes that there is a linear relationship between the intensity of the analytical line of the analyte and the intensities of the spectral lines (or concentrations) in the substance, it was revealed that there is a severalfold decrease in the deviations of nominal impurity concentrations from the measured ones. The results of this study allow for reducing the number of analytical procedures used in analyzing materials that have different compositions and the same matrix element. For instance, it becomes possible to determine the composition of iron-based alloys (low-alloy and carbon steels; high-speed steels; high-alloy, and heat-resistant steels) using one calibration curve within the framework of a universal analytical method.

Superconformal duality-invariant models and $$ \mathcal{N} $$ = 4 SYM effective action

We present $$ \mathcal{N} $$ N = 2 superconformal U(1) duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single $$ \mathcal{N} $$ N = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant $$ \mathcal{N} $$ N = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

Nonlinear Analysis of the Thaw Settlement in Ice-Rich Embankments

In this paper, the law of ice-rich permafrost embankment thaw consolidation is studied based on three-dimensional nonlinear large strain thaw consolidation theory. To avoid problems associated with numerical simulation efficiency and stability when a nonlinear stress-strain relationship is employed, a segment interpolation function is used to implement the nonlinear relationship between the compression modulus and the void ratio, and the corresponding simulation strategy is proposed. Through a comparison of the monitoring and calculated results, it is indicated that the calculation accuracy on ice-rich embankment thaw settlement can be notably improved after nonlinear theory is implemented with the proposed numerical simulation method. A further analysis of the calculated results indicates that the interactive effects between the thermal and mechanical fields can be more reasonably described by nonlinear theory than by linear theory. It is also determined that the postthaw pore water in the shallow embankment dissipates in the early operation period, while in the following long operation period, the development of the permafrost embankment thaw settlement is mainly due to the dissipation of newly postthaw pore water at the thaw depth or the permafrost table. This is one of the main differences in the law of permafrost embankment thaw settlement compared with that of unfrozen embankments.

“Extraordinary” modulation instability in optics and hydrodynamics

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.