Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis

An initial-boundary value problem for a model of stimulated Raman scattering was considered in [Moskovchenko E.A., Kotlyarov V.P., J. Phys. A: Math. Theor. 43 (2010), 055205, 31 pages]. The authors showed that in the long-time range $t\to+\infty$ the $x>0$, $t>0$ quarter plane is divided into 3 regions with qualitatively different asymptotic behavior of the solution: a region of a finite amplitude plane wave, a modulated elliptic wave region and a vanishing dispersive wave region. The asymptotics in the modulated elliptic region was studied under an implicit assumption of the solvability of the corresponding Whitham type equations. Here we establish the existence of these parameters, and thus justify the results by Moskovchenko and Kotlyarov

Democracy and its Deficits: The path towards becoming European-style democracies in Georgia, Moldova and Ukraine. CEPS Working Document No. 2017/12, December 2017

Georgia, Moldova and Ukraine are three participating states of the European Partnership that have chosen to conclude Association Agreements with the European Union, often at the expense of relations with their most powerful neighbour, Russia. They are also rather similar in their levels of democratic development. Within a post-Soviet space, they stand out for their relatively high level of democratic freedoms and political pluralism; none of them, however, can be considered a consolidated democracy, and most analysts describe them as uncertain or hybrid political regimes that combine features of autocracy and democracy. This paper offers a comparative analysis of the three countries’ political systems and aims to interpret both the roots of their relative success, and the nature of the deficits that prevent them from consolidating their democratic institutions. Among these deficits are problems stemming from ethnic, regional and cultural conflicts; strong and weak features in their general constitutional systems; the links between democratic development and government capacity to produce public goods; state capture (including control over the most influential media organisations) by powerful oligarchs and endemic corruption; underdevelopment of political parties and party systems; insufficient trust towards institutions of electoral democracy and a resulting propensity to use extra-constitutional means of political struggle. Civil society organisations have also failed penetrate the wider public and the anti-liberal discourse of traditionally dominant churches and anti-Western media and civil society groups is often supported by Russia. Despite these structural challenges, the commitment to European values and norms demonstrated by societies in these three countries gives hope that they can eventually consolidate their democratic institutions. It is argued that closer ties to the EU are important in explaining their relatively high level of democratic development. For this reason, the consistent and enhanced commitment of the European Union to this region is crucial to their continued success in this area

Micromixers simulation

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.A method for simulating fluid flows in microchannels is proposed. The method is tested using available experimental data obtained in micro-PIV studies of microchannel flows. Flow regimes in Y- and Ttype micromixers are studied. Passive and active mixers are considered. The dependence of the mixing efficiency on the Peclet number is examined, and the possibility of using hydrophobic and ultrahydrophobic coatings is analyzed. An active mixing method using a T-mixer with a harmonically varying flow rate at one of the inlet channels is studied. The dependence of the mixing efficiency on the frequency and amplitude of flow rate variation is determined.This work was supported in part by the Russian Foundation for Basic Researches (grant No. 07-08-00164) and by the grant of the President of the Russian Federation for Support of Leading Scientific Schools (project no. NSh-454.2008.1)