On Boussinesq-type models for long longitudinal waves in elastic rods

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations.Comment: 19 pages, 5 figures, submitted to the Special Issue of Wave Motion, "Nonlinear Waves in Solids", in Memory of Professor Alexander M. Samsono

Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties

The paper presents a comprehensive analysis of elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO2 and Al2O3), alumosilicates (montmorillonite, halloysite natural tubules and Mica) and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Composites were fabricated by melt technology. The analysis of composite melts showed that the introduction of Montmorillonite, Multi-walled carbon nanotubes, and Al2O3 particles provided an increase in melt viscosity by an average of 2 to 5 orders of magnitude over the pure polystyrene. Block samples of composites with different filler concentrations were prepared, and their linear and nonlinear elastic properties were studied. The introduction of more rigid particles led to a more profound increase in the elastic modulus of the composite, with the highest rise of about 80% obtained with carbon fillers. Carbon black particles provided also an enhanced strength at break of about 20% higher than that of pure polystyrene. The nonlinear elastic moduli of composites were shown to be more sensitive to addition of filler particles to the polymer matrix than the linear ones. The nonlinearity coefficient $\beta$ comprising the combination of linear and nonlinear elastic moduli of a material demonstrated considerable changes correlating with changes of the Young's modulus. The absolute value of $\beta$ showed rise in 1.5-1.6 times in the CB- and HNT-containing composites as compared to that of pure PS. The changes in nonlinear elasticity of fabricated composites were compared with measurements of the parameters of bulk nonlinear strain waves in them. Variations of wave velocity and decay decrement correlated with observed enhancement of materials nonlinearity

Application of Organic-Inorganic Hybrids in Chemical Analysis, Bio- and Environmental Monitoring

Organic-inorganic hybrids (OIH) are considered to be a powerful platform for applications in many research and industrial fields. This review highlights the application of OIH for chemical analysis, biosensors, and environmental monitoring. A methodology toward metrological traceability measurement and standardization of OIH and demonstration of the role of mathematical modeling in biosensor design are also presented. The importance of the development of novel types of OIH for biosensing applications is highlighted. Finally, current trends in nanometrology and nanobiosensors are presented

Critical analysis and assessment of prospects of development of a tax for digital services

Objective: to critically analyze the international experience and proposals of the Organization for Economic Cooperation and Development (OECD) on the international unification of the digital tax and assess the prospects for the development of this sector of the economy, identify bottlenecks and prospects for the introduction of a similar tax in the Russian Federation.Methods: a dialectical approach to the cognition of economic regularities, which allows analyzing their development and functioning in the context of a set of objective factors, which determined the choice of the following research methods: formal-logical, economic analysis of the main trends in the construction and development of digital taxation, internal and external tax control.Results: the article discusses the current problems, foreign experience and prospects for the transition of states to the introduction of a new indirect tax – a tax on digital services. Forecasts of growth of tax revenues from digital business have been confirmed. The authors identify two trends in the international practice of digital tax development. The main methodological problems of the new tax are outlined, including the preservation of the neutrality principle, the single tax burden, the identification of the users’ location, the determination of income sources. The risks of a significant increase in the tax burden for companies and users, complication of transaction reporting systems, etc. are identified. The allocation of a tax on digital services in the Russian Federation as an independent tax is justified. The positive effect for the state and the Russian market of digital services is indicated.Scientific novelty: the paper summarizes the foreign experience of electronic economy taxation, for the first time justifies the need to adapt the national version of the digital tax, taking into account the peculiarity of the modern political and economic situation; despite the Russian support of the OECD directive, the conclusion is made about the need to segment support for the web economy with an alternative in the form of penalties for abuse in this sphere. This approach can be used as a potential opportunity to protect the national digital services market from international competition and pressure.Practical significance: the main provisions and conclusions of the article can be used in scientific, pedagogical and law enforcement activities when considering issues related to the management of the digital economy, ensuring fairness and neutrality of taxation

Self-exited gas oscillations in Helmholtz resonator type combustor

When the length of the resonance tube is much less and order of the acoustic wavelength is studied. Experimental set-up with a multiport burner is considered. The "energy balance" method is used to calculate the frequency and amplitude of the gas oscillations. The results of measurements and calculations show that increasing the length of the resonance tube causes the excitation oscillation with a first lower frequency. Further, there are no oscillations. When the length of the resonance tube becomes the order of the wavelength, the second resonant frequency is excited. The calculation results are in good agreement with the experimental data