A note on the breathing mode of an elastic sphere in Newtonian and complex fluids

Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [M. Pelton et al., "Viscoelastic flows in simple liquids generated by vibrating nanostructures," Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere, also called the breathing mode, in a compressible viscous fluid, and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. The effects of fluid compressibility and viscoelasticity are discussed. Although in the case of longitudinal vibration of bipyramidal nanoparticles, the effects of fluid compressibility were shown to be negligible, we demonstrate that it plays a significant role in the breathing mode of an elastic sphere. On the other hand, despite the different vibration modes, the breathing mode of a sphere triggers a viscoelastic response in water-glycerol mixtures similar to that triggered by the longitudinal vibration of bipyramidal nanoparticles. We also comment on the effect of fluid viscoelasticity on the idea of destroying virus particles by acoustic resonance

Emission spectrum of a dipole in a semi-infinite periodic dielectric structure: effect of the boundary

Journal ArticleThe emission spectrum of a dipole embedded in a semi-infinite photonic crystal is calculated. For simplicity we study the case in which the dielectric function is sinusoidally modulated only along the direction perpendicular to the boundary surface plane. In addition to oscillations of the emission rate with the distance of the dipole from the interface, we also observed that the shape of the emission spectrum srongly depends on the initial phase of the dielectric modulation. When the direction of light propagation inside the periodic structure is not normal to the boundary surface plane, we observed aditional singularities in the emission spectrum, which arise due to different angle dependence of the Bragg stop band for TE and TM polarizations

About the continuity of one operation with convex compacts in finite-dimensional normed spaces

In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case when both compact sets are non-empty convex subsets, such an operation is continuous in the topology generated by the Hausdorff metric. The question of the continuous dependence of the described intersection on the radius of the neighborhood arose as a by-product of the development of the theory of extremal networks. However, it turned out to be interesting in itself, suggesting various generalizations. Therefore, it was decided to publish it separately.Comment: in Russian languag

Transfer ionization and its sensitivity to the ground-state wave function

We present kinematically complete theoretical calculations and experiments for transfer ionization in H$^++$He collisions at 630 keV/u. Experiment and theory are compared on the most detailed level of fully differential cross sections in the momentum space. This allows us to unambiguously identify contributions from the shake-off and two-step-2 mechanisms of the reaction. It is shown that the simultaneous electron transfer and ionization is highly sensitive to the quality of a trial initial-state wave function

Оценка воздействия налогово-бюджетной политики на экономический рост в Республике Армения

Fiscal policy plays a crucial role in ensuring economic growth and development in the country and overcoming economic recessions. The subject of the research is the tax system in the Republic of Armenia. The study aims to identify and assess the impact of the fiscal policy on economic growth in the Republic of Armenia. Since the global financial crisis of 2008, the Armenian economy has been in stagnation, reaching pre-crisis GDP levels only in 2018. Both theory and practice point to the ambiguous nature of the impact of fiscal policy on economic growth. At the same time, the 2020 crisis caused by the pandemic exacerbated the situation by focusing the attention of economists on fiscal policy to stimulate the real sector of the economy, which justifies the relevance of the current study. The paper’s novelty lies in assessing the impact of certain types of taxes on the economic growth rates in Armenia. To achieve the goal of the study, the authors use such methods as a comparative analysis of foreign studies and systemic and statistical analysis. To econometrically assess the impact of taxes on economic growth in the country, a vector autoregression (VAR) model was applied. As a result of the study, the authors found that both tax regulation in general and the individual taxes are restrictive in nature and have a negative impact on economic growth in the country. The authors conclude that such a restrictive policy has led to a slowdown in economic growth in the Republic of Armenia over the past decadesФискальная политика играет ключевую роль как в  обеспечении экономического роста и  развития в  стране, так и  в  преодолении экономических спадов. Предметом исследования является налогово-бюджетная политика Республики Армения (РА). Цель исследования — выявление и оценка влияния налоговой политики на экономический рост в РА. После глобального финансового кризиса 2008 г. экономика Армении находится в стагнации, достигнув предкризисного уровня ВВП только в 2018 г. Как теория, так и практика указывают на неоднозначный характер воздействия фискальной политики на экономический рост в то время, как кризис 2020 г., вызванный пандемией, обострил ситуацию, сфокусировав внимание экономистов на налогово-бюджетной политике для стимулирования реального сектора экономики, что и обосновывает актуальность настоящего исследования. Новизна работы состоит в оценке воздействия отдельных видов налогов на темпы экономического роста в Армении. Для достижения поставленной цели авторы исследования используют такие методы, как сравнительный анализ зарубежных исследований, системный и статистический анализ. В целях эконометрической оценки воздействия налогов на экономический рост в стране применена модель векторной авторегрессии (VAR). В результате исследования авторами было выявлено, что как налоговое регулирование в целом, так и по отдельным налогам носит сдерживающий характер и имеет негативное влияние на темпы экономического роста в стране. Сделан вывод, что такая сдерживающая политика на протяжении последних десятилетий привела к замедлению темпов экономического роста в Республике Армения