Wear of Functionally Graded Coatings under Frictional Heating Conditions

Multilayered and functionally graded coatings are extensively used for protection against wear of the working surfaces of mechanisms and machines subjected to sliding contact. The paper considers the problem of wear of a strip made of a functionally graded material, taking into account the heating of the sliding contact from friction. Wear is modeled by a moving strip along the surface of a hard abrasive in the form of a half-plane. With the help of the integral Laplace transform with respect to time, the solutions are constructed as convolutions from the law of the introduction of an abrasive into the strip and the original in the form of a contour integral of the inverse Laplace transform. The study of the integrands of contour quadratures in the complex plane allowed determination of the regions of stable solutions to the problem. Unstable solutions of the problem lead to the concept of thermoelastic instability of the contact with friction and formed regions of unstable solutions. The solutions obtained made it possible to determine a formula for the coefficient of functionally graded inhomogeneity of the coating material and to study its effect on the occurrence of thermoelastic instability of the contact taking friction into account, as well as on its main characteristics: temperature, displacement, stress and wear of the functionally graded material of the coating. The effects of the abrasive speed, contact stresses and temperature on wear of the coating with the functionally graded inhomogeneity of the material by the depth were investigated.

Control-based continuation: a new approach to prototype synthetic gene networks

Control-Based Continuation (CBC) is a general and systematic method to carry out the bifurcation analysis of physical experiments. CBC does not rely on a mathematical model and thus overcomes the uncertainty introduced when identifying bifurcation curves indirectly through modelling and parameter estimation. We demonstrate, in silico, CBC applicability to biochemical processes by tracking the equilibrium curve of a toggle switch which includes additive process noise and exhibits bistability. We compare results obtained when CBC uses a model-free and model-based control strategy and show that both can track stable and unstable solutions, revealing bistability. We then demonstrate CBC in conditions more representative of a real experiment using an agent-based simulator describing cells growth and division, cell-to-cell variability, spatial distribution, and diffusion of chemicals. We further show how the identified curves can be used for parameter estimation and discuss how CBC can significantly accelerate the prototyping of synthetic gene regulatory networks.

Secondary Faraday waves in microgravity

Recent microgravity experiments have demonstrated that Faraday waves can arise in a secondary instability over the primary columnar patterns that develop after the frozen wave instability. While some numerical studies have investigated this phenomenon, theoretical analyses are only found in the works of Shevtsova et al. (2016) [1] and Lyubimova et al. (2019) [2]. Here, we extend these efforts by analysing the stability of a three-layer system, and derive the critical onset of Faraday waves, which appear via Hopf bifurcation. Numerical simulations — based on a model that reproduces the frozen wave mode with lowest wavenumber — are carried out to test this result and to analyse the character of the bifurcation. The predicted Hopf bifurcation is confirmed, which constitutes the first observation of modulated secondary Faraday waves. The abrupt growth of these modulated waves above onset indicates that the primary bifurcation is subcritical and is accompanied by a saddle-node bifurcation of periodic orbits that stabilises the (branch of) unstable solutions created in the subcritical Hopf bifurcation. Further above onset, these modulated waves are destroyed via a saddle-node heteroclinic bifurcation. Results for an N-layer configuration, which represents a more general frozen wave pattern, are also presented and compared with the three-layer case.

Fractional Skyrmion molecules in a ℂPN−1 model

We study fractional Skyrmions in a ℂP2 baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on ℂP2.

Some issues of solving inverse problems in optical systems with lensless cameras

The inverse problems current state a general characteristic in optics is given, the approaches to their solution, their incorrect and unstable solutions cause are considered, and recommendations for these drawbacks elimination are given. General approaches to solving inverse problems in images reconstruction obtained in lensless cameras based on different masks are also considered, and their advantages and disadvantages in comparison with lensless lenses are pointed out, as well as their further research directions are indicated.

STABILITY ANALYSIS OF RELATIVISTIC POLYTROPES

We study the relativistic self-gravitating, hydrostatic spheres with a polytropic equation of state, considering structures with the polytropic indices n=1(0.5)3 and illustrate the results for the relativistic parameters σ=0−0.75. We determine the critical relativistic parameter at which the mass of the polytrope has a maximum value and represents the first mode of radial instability. For n=1(0.5)2.5, stable relativistic polytropes occur for σ less than the critical values 0.42, 0.20, 0.10, and 0.04, respectively, while unstable relativistic polytropes are obtained when σ is greater than the same values. When n=3.0 and σ>0.5, energetically unstable solutions occur. The results of critical values are in full agreement with those evaluated by several authors. Comparisons between analytical and numerical solutions of the given relativistic functions provide a maximum relative error of order 10−3.

Non-Synchronous Vibration and Lock-in Regimes in Coupled Structures Using Reduced Models

The contribution is aimed at phenomenological modelling and analysis of fundamental properties of non-synchronous vibrations in chosen coupled structures. A van der Pol reduced-order model is employed to simulate the aero-elastic interaction between flexible bodies and fluid. Non-synchronous vibration and frequency lock-in, along with hysteresis, are captured in the main resonance area. Moreover, the model reveals subharmonic resonances accompanied by the existence of unstable solutions and frequency lock-in. The study is further extended to investigate the dynamical behaviour of a coupled cyclic structure, where different modes of vibration due to the aero-elastic interaction are analysed.

Centrifugal Waves in Tornado-like Vortices: Kelvin’s solutions and their Applications to Multiple-Vortex Development and Vortex Breakdown

About 140 years ago, Lord Kelvin derived the equations describing waves that travel along the axis of concentrated vortices such as tornadoes. Although Kelvin’s vortex waves, also known as centrifugal waves, feature prominently in the engineering and uid dynamics literature, they have not attracted as much attention in the field of atmospheric science. To remedy this circumstance, Kelvin’s elegant derivation is retraced, and slightly generalized, to obtain solutions for a hierarchy of vortex ows that model basic features of tornado-like vortices. This treatment seeks to draw attention to the important work that Lord Kelvin did in this field, and reveal the remarkably rich structure and dynamics of these waves. Kelvin’s solutions help explain the vortex breakdown phenomenon routinely observed in modeled tornado-like vortices, and it is shown that his work is compatible with the widely used criticality condition put forth by Benjamin in 1962. Moreover, it is demonstrated that Kelvin’s treatment, with the slight generalization, includes unstable wave solutions that have been invoked to explain some aspects of the formation of multiple-vortex tornadoes. The analysis of the unstable solutions also forms the basis for determining whether e.g., an axisymmetric or a spiral vortex breakdown occurs. Kelvin’s work thus helps understand some of the visible features of tornado-like vortices.